@prefix wd: <http://www.wikidata.org/entity/> .
@prefix wl: <https://wikilean.jackmccarthy.org/ns#> .
@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .

wd:Q204 wl:formalizedAs "zero_add" .
wd:Q204 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Defs.html#zero_add> .
wd:Q204 wl:formalizedAs "mul_zero" .
wd:Q204 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/GroupWithZero/Defs.html#mul_zero> .
wd:Q204 wl:formalizedAs "Nat.zero_le" .
wd:Q204 wl:formalizedAs "Even.zero" .
wd:Q204 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Even.html#Even.zero> .
wd:Q204 wl:formalizedAs "Ideal.bot_prime" .
wd:Q204 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Ideal/Prime.html#Ideal.bot_prime> .
wd:Q204 wl:formalizedAs "add_zero" .
wd:Q204 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Defs.html#add_zero> .
wd:Q204 wl:formalizedAs "sub_zero" .
wd:Q204 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Basic.html#sub_zero> .
wd:Q204 wl:formalizedAs "inv_zero" .
wd:Q204 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/GroupWithZero/Basic.html#inv_zero> .
wd:Q204 wl:formalizedAs "pow_zero" .
wd:Q204 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Defs.html#pow_zero> .
wd:Q204 wl:formalizedAs "Finset.prod_empty" .
wd:Q204 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/BigOperators/Group/Finset/Defs.html#Finset.prod_empty> .
wd:Q204 wl:formalizedAs "Nat.factorial_zero" .
wd:Q204 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/Factorial/Basic.html#Nat.factorial_zero> .
wd:Q204 wl:formalizedAs "Cardinal.mk_eq_zero" .
wd:Q204 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Basic.html#Cardinal.mk_eq_zero> .
wd:Q204 wl:formalizedAs "Ordinal.bot_eq_zero" .
wd:Q204 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Ordinal/Basic.html#Ordinal.bot_eq_zero> .
wd:Q204 wl:formalizedAs "Zero" .
wd:Q204 wl:formalizedAs "Pi.zero_apply" .
wd:Q204 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Pi/Basic.html#Pi.zero_apply> .
wd:Q204 wl:formalizedAs "CategoryTheory.Limits.IsZero" .
wd:Q204 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Limits/Shapes/ZeroObjects.html#CategoryTheory.Limits.IsZero> .
wd:Q204 wl:formalizedAs "zero_div" .
wd:Q204 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/GroupWithZero/Basic.html#zero_div> .
wd:Q204 wl:formalizedAs "neg_zero" .
wd:Q204 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Defs.html#neg_zero> .
wd:Q199 wl:formalizedAs "Nat.succ" .
wd:Q199 wl:formalizedAs "one_mul" .
wd:Q199 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Defs.html#one_mul> .
wd:Q199 wl:formalizedAs "one_pow" .
wd:Q199 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Defs.html#one_pow> .
wd:Q199 wl:formalizedAs "MulOneClass" .
wd:Q199 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Defs.html#MulOneClass> .
wd:Q199 wl:formalizedAs "IsUnit" .
wd:Q199 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Units/Defs.html#IsUnit> .
wd:Q199 wl:formalizedAs "Nat.factorial_one" .
wd:Q199 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/Factorial/Basic.html#Nat.factorial_one> .
wd:Q199 wl:formalizedAs "Finset.prod_empty" .
wd:Q199 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/BigOperators/Group/Finset/Defs.html#Finset.prod_empty> .
wd:Q199 wl:formalizedAs "unitInterval" .
wd:Q199 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/UnitInterval.html#unitInterval> .
wd:Q199 wl:formalizedAs "IsProbabilityMeasure" .
wd:Q199 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/MeasureTheory/Measure/Typeclasses/Probability.html#IsProbabilityMeasure> .
wd:Q200 wl:formalizedAs "Nat.succ" .
wd:Q200 wl:formalizedAs "Nat.Prime.even_iff" .
wd:Q200 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/Prime/Basic.html#Nat.Prime.even_iff> .
wd:Q200 wl:formalizedAs "even_iff_two_dvd" .
wd:Q200 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Even.html#even_iff_two_dvd> .
wd:Q200 wl:formalizedAs "ZMod.instField" .
wd:Q200 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Field/ZMod.html#ZMod.instField> .
wd:Q200 wl:formalizedAs "ZMod.intCast_zmod_eq_zero_iff_dvd" .
wd:Q200 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/ZMod/Basic.html#ZMod.intCast_zmod_eq_zero_iff_dvd> .
wd:Q200 wl:formalizedAs "CharTwo.add_self_eq_zero" .
wd:Q200 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/CharP/Two.html#CharTwo.add_self_eq_zero> .
wd:Q200 wl:formalizedAs "Function.Involutive" .
wd:Q200 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Logic/Function/Basic.html#Function.Involutive> .
wd:Q202 wl:formalizedAs "Nat.sum_four_squares" .
wd:Q202 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/SumFourSquares.html#Nat.sum_four_squares> .
wd:Q202 wl:formalizedAs "IsKleinFour" .
wd:Q202 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/SpecificGroups/KleinFour.html#IsKleinFour> .
wd:Q181296 wl:formalizedAs "CommGroup" .
wd:Q181296 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Defs.html#CommGroup> .
wd:Q181296 wl:formalizedAs "PUnit.commGroup" .
wd:Q181296 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/PUnit.html#PUnit.commGroup> .
wd:Q181296 wl:formalizedAs "Int.instAddCommGroup" .
wd:Q181296 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Int/Defs.html#Int.instAddCommGroup> .
wd:Q181296 wl:formalizedAs "IsCyclic.commGroup" .
wd:Q181296 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/SpecificGroups/Cyclic/Basic.html#IsCyclic.commGroup> .
wd:Q181296 wl:formalizedAs "NonUnitalNonAssocRing" .
wd:Q181296 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Ring/Defs.html#NonUnitalNonAssocRing> .
wd:Q181296 wl:formalizedAs "instCommGroupUnits" .
wd:Q181296 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Units/Defs.html#instCommGroupUnits> .
wd:Q181296 wl:formalizedAs "Subgroup.normal_of_isMulCommutative" .
wd:Q181296 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Subgroup/Defs.html#Subgroup.normal_of_isMulCommutative> .
wd:Q181296 wl:formalizedAs "Subgroup.toCommGroup" .
wd:Q181296 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Subgroup/Defs.html#Subgroup.toCommGroup> .
wd:Q181296 wl:formalizedAs "CommGroup.is_simple_iff_prime_card" .
wd:Q181296 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/SpecificGroups/Cyclic.html#CommGroup.is_simple_iff_prime_card> .
wd:Q181296 wl:formalizedAs "forget₂AddCommGroupIsEquivalence" .
wd:Q181296 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Category/Grp/ZModuleEquivalence.html#forget₂AddCommGroupIsEquivalence> .
wd:Q181296 wl:formalizedAs "AddCommGroup.toIntModule" .
wd:Q181296 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Module/NatInt.html#AddCommGroup.toIntModule> .
wd:Q181296 wl:formalizedAs "AddCommGroup.equiv_free_prod_directSum_zmod" .
wd:Q181296 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/FiniteAbelian/Basic.html#AddCommGroup.equiv_free_prod_directSum_zmod> .
wd:Q181296 wl:formalizedAs "AddMonoidHom.add" .
wd:Q181296 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Hom/Basic.html#AddMonoidHom.add> .
wd:Q181296 wl:formalizedAs "Module.rank" .
wd:Q181296 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Dimension/Basic.html#Module.rank> .
wd:Q181296 wl:formalizedAs "Module.rank_eq_zero_iff_isTorsion" .
wd:Q181296 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Dimension/Torsion/Finite.html#Module.rank_eq_zero_iff_isTorsion> .
wd:Q181296 wl:formalizedAs "Subgroup.center" .
wd:Q181296 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/Subgroup/Center.html#Subgroup.center> .
wd:Q181296 wl:formalizedAs "Subgroup.center_eq_top_iff" .
wd:Q181296 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/Subgroup/Center.html#Subgroup.center_eq_top_iff> .
wd:Q181296 wl:formalizedAs "commGroupOfCyclicCenterQuotient" .
wd:Q181296 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/SpecificGroups/Cyclic.html#commGroupOfCyclicCenterQuotient> .
wd:Q181296 wl:formalizedAs "AddCommGroup.equiv_directSum_zmod_of_finite" .
wd:Q181296 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/FiniteAbelian/Basic.html#AddCommGroup.equiv_directSum_zmod_of_finite> .
wd:Q181296 wl:formalizedAs "isCyclic_of_prime_card" .
wd:Q181296 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/SpecificGroups/Cyclic/Basic.html#isCyclic_of_prime_card> .
wd:Q181296 wl:formalizedAs "IsPGroup.commutative_of_card_eq_prime_sq" .
wd:Q181296 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/PGroup.html#IsPGroup.commutative_of_card_eq_prime_sq> .
wd:Q181296 wl:formalizedAs "ZMod.chineseRemainder" .
wd:Q181296 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/ZMod/Basic.html#ZMod.chineseRemainder> .
wd:Q181296 wl:formalizedAs "AddGroup.FG" .
wd:Q181296 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/Finiteness.html#AddGroup.FG> .
wd:Q181296 wl:formalizedAs "FreeAbelianGroup.lift" .
wd:Q181296 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/FreeAbelianGroup.html#FreeAbelianGroup.lift> .
wd:Q181296 wl:formalizedAs "Module.Basis.SmithNormalForm" .
wd:Q181296 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/FreeModule/PID.html#Module.Basis.SmithNormalForm> .
wd:Q181296 wl:formalizedAs "Int.instIsAddCyclic" .
wd:Q181296 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/SpecificGroups/Cyclic.html#Int.instIsAddCyclic> .
wd:Q181296 wl:formalizedAs "DivisibleBy" .
wd:Q181296 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/Divisible.html#DivisibleBy> .
wd:Q181296 wl:formalizedAs "Monoid.IsTorsion" .
wd:Q181296 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/Torsion.html#Monoid.IsTorsion> .
wd:Q181296 wl:formalizedAs "Monoid.IsTorsionFree" .
wd:Q181296 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/Torsion.html#Monoid.IsTorsionFree> .
wd:Q181296 wl:formalizedAs "Submodule.instIsTorsionFree" .
wd:Q181296 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Module/Torsion/Basic.html#Submodule.instIsTorsionFree> .
wd:Q181296 wl:formalizedAs "AddCommGrpCat.instAbelian" .
wd:Q181296 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Category/Grp/Abelian.html#AddCommGrpCat.instAbelian> .
wd:Q2553675 wl:formalizedAs "Matrix.transvection" .
wd:Q2553675 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Matrix/Transvection.html#Matrix.transvection> .
wd:Q180969 wl:formalizedAs "MvPolynomial" .
wd:Q180969 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/MvPolynomial/Basic.html#MvPolynomial> .
wd:Q180969 wl:formalizedAs "MvPolynomial.zeroLocus" .
wd:Q180969 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Nullstellensatz.html#MvPolynomial.zeroLocus> .
wd:Q180969 wl:formalizedAs "MvPolynomial.vanishingIdeal" .
wd:Q180969 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Nullstellensatz.html#MvPolynomial.vanishingIdeal> .
wd:Q180969 wl:formalizedAs "PrimeSpectrum.zariskiTopology" .
wd:Q180969 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Spectrum/Prime/Topology.html#PrimeSpectrum.zariskiTopology> .
wd:Q180969 wl:formalizedAs "MvPolynomial.vanishingIdeal_zeroLocus_eq_radical" .
wd:Q180969 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Nullstellensatz.html#MvPolynomial.vanishingIdeal_zeroLocus_eq_radical> .
wd:Q180969 wl:formalizedAs "MvPolynomial.isNoetherianRing" .
wd:Q180969 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Polynomial/Basic.html#MvPolynomial.isNoetherianRing> .
wd:Q180969 wl:formalizedAs "IsIrreducible" .
wd:Q180969 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Irreducible.html#IsIrreducible> .
wd:Q180969 wl:formalizedAs "TopologicalSpace.NoetherianSpace.exists_finset_irreducible" .
wd:Q180969 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/NoetherianSpace.html#TopologicalSpace.NoetherianSpace.exists_finset_irreducible> .
wd:Q180969 wl:formalizedAs "PrimeSpectrum.isIrreducible_iff_vanishingIdeal_isPrime" .
wd:Q180969 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Spectrum/Prime/Topology.html#PrimeSpectrum.isIrreducible_iff_vanishingIdeal_isPrime> .
wd:Q180969 wl:formalizedAs "ContinuousMap.exists_restrict_eq" .
wd:Q180969 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/TietzeExtension.html#ContinuousMap.exists_restrict_eq> .
wd:Q180969 wl:formalizedAs "AlgebraicGeometry.Scheme.functionField" .
wd:Q180969 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/AlgebraicGeometry/FunctionField.html#AlgebraicGeometry.Scheme.functionField> .
wd:Q180969 wl:formalizedAs "AlgebraicGeometry.Scheme.RationalMap" .
wd:Q180969 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/AlgebraicGeometry/Birational/RationalMap.html#AlgebraicGeometry.Scheme.RationalMap> .
wd:Q180969 wl:formalizedAs "Projectivization" .
wd:Q180969 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Projectivization/Basic.html#Projectivization> .
wd:Q180969 wl:formalizedAs "ProjectiveSpectrum.zeroLocus" .
wd:Q180969 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.html#ProjectiveSpectrum.zeroLocus> .
wd:Q180969 wl:formalizedAs "AlgebraicGeometry.Scheme" .
wd:Q180969 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/AlgebraicGeometry/Scheme.html#AlgebraicGeometry.Scheme> .
wd:Q180969 wl:formalizedAs "AlgebraicGeometry.AffineScheme.equivCommRingCat" .
wd:Q180969 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/AlgebraicGeometry/AffineScheme.html#AlgebraicGeometry.AffineScheme.equivCommRingCat> .
wd:Q168817 wl:formalizedAs "IsAlgebraic" .
wd:Q168817 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Algebraic/Defs.html#IsAlgebraic> .
wd:Q168817 wl:formalizedAs "isAlgebraic_int" .
wd:Q168817 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Algebraic/Basic.html#isAlgebraic_int> .
wd:Q168817 wl:formalizedAs "algebraicClosure" .
wd:Q168817 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/FieldTheory/AlgebraicClosure.html#algebraicClosure> .
wd:Q168817 wl:formalizedAs "Transcendental" .
wd:Q168817 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Algebraic/Defs.html#Transcendental> .
wd:Q168817 wl:formalizedAs "isAlgebraic_rat" .
wd:Q168817 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Algebraic/Basic.html#isAlgebraic_rat> .
wd:Q168817 wl:formalizedAs "GaussianInt" .
wd:Q168817 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/Zsqrtd/GaussianInt.html#GaussianInt> .
wd:Q168817 wl:formalizedAs "Real.isAlgebraic_cos_rat_mul_pi" .
wd:Q168817 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/Niven.html#Real.isAlgebraic_cos_rat_mul_pi> .
wd:Q168817 wl:formalizedAs "IsFractionRing.isAlgebraic_iff" .
wd:Q168817 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Localization/Integral.html#IsFractionRing.isAlgebraic_iff> .
wd:Q168817 wl:formalizedAs "minpoly" .
wd:Q168817 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/FieldTheory/Minpoly/Basic.html#minpoly> .
wd:Q168817 wl:formalizedAs "Algebraic.countable" .
wd:Q168817 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/AlgebraicCard.html#Algebraic.countable> .
wd:Q168817 wl:formalizedAs "IntermediateField.adjoin.finiteDimensional" .
wd:Q168817 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/FieldTheory/IntermediateField/Adjoin/Basic.html#IntermediateField.adjoin.finiteDimensional> .
wd:Q168817 wl:formalizedAs "IntermediateField.finiteDimensional_adjoin" .
wd:Q168817 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/FieldTheory/IntermediateField/Adjoin/Basic.html#IntermediateField.finiteDimensional_adjoin> .
wd:Q168817 wl:formalizedAs "Subalgebra.algebraicClosure" .
wd:Q168817 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Algebraic/Integral.html#Subalgebra.algebraicClosure> .
wd:Q168817 wl:formalizedAs "algebraicClosure.isAlgClosure" .
wd:Q168817 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/FieldTheory/AlgebraicClosure.html#algebraicClosure.isAlgClosure> .
wd:Q168817 wl:formalizedAs "IsIntegral" .
wd:Q168817 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/IntegralClosure/IsIntegral/Defs.html#IsIntegral> .
wd:Q168817 wl:formalizedAs "integralClosure" .
wd:Q168817 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/IntegralClosure/Algebra/Basic.html#integralClosure> .
wd:Q168817 wl:formalizedAs "NumberField.RingOfIntegers" .
wd:Q168817 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/NumberField/Basic.html#NumberField.RingOfIntegers> .
wd:Q613048 wl:formalizedAs "PythagoreanTriple" .
wd:Q613048 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/PythagoreanTriples.html#PythagoreanTriple> .
wd:Q613048 wl:formalizedAs "NumberField.Units.exist_unique_eq_mul_prod" .
wd:Q613048 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/NumberField/Units/DirichletTheorem.html#NumberField.Units.exist_unique_eq_mul_prod> .
wd:Q613048 wl:formalizedAs "Real.exists_int_int_abs_mul_sub_le" .
wd:Q613048 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/DiophantineApproximation/Basic.html#Real.exists_int_int_abs_mul_sub_le> .
wd:Q613048 wl:formalizedAs "Ideal" .
wd:Q613048 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Ideal/Defs.html#Ideal> .
wd:Q613048 wl:formalizedAs "Prime" .
wd:Q613048 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Prime/Defs.html#Prime> .
wd:Q613048 wl:formalizedAs "Associated" .
wd:Q613048 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/GroupWithZero/Associated.html#Associated> .
wd:Q613048 wl:formalizedAs "UniqueFactorizationMonoid" .
wd:Q613048 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/UniqueFactorizationDomain/Defs.html#UniqueFactorizationMonoid> .
wd:Q613048 wl:formalizedAs "Irreducible" .
wd:Q613048 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Irreducible/Defs.html#Irreducible> .
wd:Q613048 wl:formalizedAs "Ideal.uniqueFactorizationMonoid" .
wd:Q613048 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/DedekindDomain/Ideal/Basic.html#Ideal.uniqueFactorizationMonoid> .
wd:Q613048 wl:formalizedAs "Nat.Prime.sq_add_sq" .
wd:Q613048 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/SumTwoSquares.html#Nat.Prime.sq_add_sq> .
wd:Q613048 wl:formalizedAs "FractionalIdeal" .
wd:Q613048 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/FractionalIdeal/Basic.html#FractionalIdeal> .
wd:Q613048 wl:formalizedAs "ClassGroup" .
wd:Q613048 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/ClassGroup.html#ClassGroup> .
wd:Q613048 wl:formalizedAs "NumberField.classNumber" .
wd:Q613048 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/NumberField/ClassNumber.html#NumberField.classNumber> .
wd:Q613048 wl:formalizedAs "NumberField.InfinitePlace.IsReal" .
wd:Q613048 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/NumberField/InfinitePlace/Basic.html#NumberField.InfinitePlace.IsReal> .
wd:Q613048 wl:formalizedAs "NumberField.InfinitePlace.card_add_two_mul_card_eq_rank" .
wd:Q613048 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/NumberField/InfinitePlace/Basic.html#NumberField.InfinitePlace.card_add_two_mul_card_eq_rank> .
wd:Q613048 wl:formalizedAs "NumberField.mixedEmbedding" .
wd:Q613048 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/NumberField/CanonicalEmbedding/Basic.html#NumberField.mixedEmbedding> .
wd:Q613048 wl:formalizedAs "NumberField.mixedEmbedding.mixedSpace" .
wd:Q613048 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/NumberField/CanonicalEmbedding/Basic.html#NumberField.mixedEmbedding.mixedSpace> .
wd:Q613048 wl:formalizedAs "NumberField.discr" .
wd:Q613048 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/NumberField/Discriminant/Defs.html#NumberField.discr> .
wd:Q613048 wl:formalizedAs "padicNorm" .
wd:Q613048 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/Padics/PadicNorm.html#padicNorm> .
wd:Q613048 wl:formalizedAs "Rat.AbsoluteValue.equiv_real_or_padic" .
wd:Q613048 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/Ostrowski.html#Rat.AbsoluteValue.equiv_real_or_padic> .
wd:Q613048 wl:formalizedAs "NumberField.FinitePlace" .
wd:Q613048 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/NumberField/Completion/FinitePlace.html#NumberField.FinitePlace> .
wd:Q613048 wl:formalizedAs "NumberField.AdeleRing" .
wd:Q613048 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/NumberField/AdeleRing.html#NumberField.AdeleRing> .
wd:Q613048 wl:formalizedAs "Int.isUnit_iff" .
wd:Q613048 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Int/Units.html#Int.isUnit_iff> .
wd:Q613048 wl:formalizedAs "NumberField.Units.regulator" .
wd:Q613048 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/NumberField/Units/Regulator.html#NumberField.Units.regulator> .
wd:Q613048 wl:formalizedAs "NumberField.dedekindZeta" .
wd:Q613048 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/NumberField/DedekindZeta.html#NumberField.dedekindZeta> .
wd:Q613048 wl:formalizedAs "IsDedekindDomain.HeightOneSpectrum.adicCompletion" .
wd:Q613048 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/DedekindDomain/AdicValuation.html#IsDedekindDomain.HeightOneSpectrum.adicCompletion> .
wd:Q613048 wl:formalizedAs "NumberField.RingOfIntegers.instFintypeClassGroup" .
wd:Q613048 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/NumberField/ClassNumber.html#NumberField.RingOfIntegers.instFintypeClassGroup> .
wd:Q613048 wl:formalizedAs "legendreSym.quadratic_reciprocity" .
wd:Q613048 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/LegendreSymbol/QuadraticReciprocity.html#legendreSym.quadratic_reciprocity> .
wd:Q613048 wl:formalizedAs "NumberField.tendsto_sub_one_mul_dedekindZeta_nhdsGT" .
wd:Q613048 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/NumberField/DedekindZeta.html#NumberField.tendsto_sub_one_mul_dedekindZeta_nhdsGT> .
wd:Q212803 wl:formalizedAs "subgroupIsFreeOfIsFree" .
wd:Q212803 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/FreeGroup/NielsenSchreier.html#subgroupIsFreeOfIsFree> .
wd:Q212803 wl:formalizedAs "HomotopyGroup" .
wd:Q212803 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Homotopy/HomotopyGroup.html#HomotopyGroup> .
wd:Q212803 wl:formalizedAs "FundamentalGroup" .
wd:Q212803 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/AlgebraicTopology/FundamentalGroupoid/FundamentalGroup.html#FundamentalGroup> .
wd:Q212803 wl:formalizedAs "singularHomologyFunctor" .
wd:Q212803 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/AlgebraicTopology/SingularHomology/Basic.html#singularHomologyFunctor> .
wd:Q212803 wl:formalizedAs "HomologicalComplex.homology" .
wd:Q212803 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Homology/ShortComplex/HomologicalComplex.html#HomologicalComplex.homology> .
wd:Q212803 wl:formalizedAs "IsManifold" .
wd:Q212803 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Manifold/IsManifold/Basic.html#IsManifold> .
wd:Q212803 wl:formalizedAs "Geometry.SimplicialComplex" .
wd:Q212803 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Convex/SimplicialComplex/Basic.html#Geometry.SimplicialComplex> .
wd:Q212803 wl:formalizedAs "CWComplex" .
wd:Q212803 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/CWComplex/Classical/Basic.html#CWComplex> .
wd:Q212803 wl:formalizedAs "AddCommGroup.equiv_free_prod_directSum_zmod" .
wd:Q212803 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/FiniteAbelian/Basic.html#AddCommGroup.equiv_free_prod_directSum_zmod> .
wd:Q212803 wl:formalizedAs "Complex.isAlgClosed" .
wd:Q212803 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Complex/Polynomial/Basic.html#Complex.isAlgClosed> .
wd:Q648995 wl:formalizedAs "MvPolynomial.vanishingIdeal_zeroLocus_eq_radical" .
wd:Q648995 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Nullstellensatz.html#MvPolynomial.vanishingIdeal_zeroLocus_eq_radical> .
wd:Q648995 wl:formalizedAs "MvPolynomial.zeroLocus" .
wd:Q648995 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Nullstellensatz.html#MvPolynomial.zeroLocus> .
wd:Q648995 wl:formalizedAs "MvPolynomial.vanishingIdeal" .
wd:Q648995 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Nullstellensatz.html#MvPolynomial.vanishingIdeal> .
wd:Q648995 wl:formalizedAs "ProjectiveSpectrum.zeroLocus" .
wd:Q648995 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.html#ProjectiveSpectrum.zeroLocus> .
wd:Q648995 wl:formalizedAs "WeierstrassCurve.IsElliptic" .
wd:Q648995 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/AlgebraicGeometry/EllipticCurve/Weierstrass.html#WeierstrassCurve.IsElliptic> .
wd:Q648995 wl:formalizedAs "AlgebraicGeometry.Scheme" .
wd:Q648995 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/AlgebraicGeometry/Scheme.html#AlgebraicGeometry.Scheme> .
wd:Q8366 wl:formalizedAs "List.mergeSort" .
wd:Q8366 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/List/Sort.html#List.mergeSort> .
wd:Q333464 wl:formalizedAs "Asymptotics.IsBigO" .
wd:Q333464 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Asymptotics/Defs.html#Asymptotics.IsBigO> .
wd:Q58413 wl:formalizedAs "EuclideanGeometry.Sphere.thales_theorem" .
wd:Q58413 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Euclidean/Angle/Sphere.html#EuclideanGeometry.Sphere.thales_theorem> .
wd:Q58413 wl:formalizedAs "EuclideanGeometry.dist_sq_eq_dist_sq_add_dist_sq_iff_angle_eq_pi_div_two" .
wd:Q58413 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Euclidean/Angle/Unoriented/RightAngle.html#EuclideanGeometry.dist_sq_eq_dist_sq_add_dist_sq_iff_angle_eq_pi_div_two> .
wd:Q58413 wl:formalizedAs "EuclideanGeometry.Sphere.IsTangentAt.mem_and_mem_iff_eq" .
wd:Q58413 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Euclidean/Sphere/Tangent.html#EuclideanGeometry.Sphere.IsTangentAt.mem_and_mem_iff_eq> .
wd:Q58413 wl:formalizedAs "irrational_sqrt_natCast_iff" .
wd:Q58413 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/Real/Irrational.html#irrational_sqrt_natCast_iff> .
wd:Q58413 wl:formalizedAs "Nat.gcd" .
wd:Q58413 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/GCD/Basic.html#Nat.gcd> .
wd:Q58413 wl:formalizedAs "Nat.exists_infinite_primes" .
wd:Q58413 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/Prime/Infinite.html#Nat.exists_infinite_primes> .
wd:Q58413 wl:formalizedAs "Even.mul_right" .
wd:Q58413 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Ring/Parity.html#Even.mul_right> .
wd:Q58413 wl:formalizedAs "Int.ModEq" .
wd:Q58413 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Int/ModEq.html#Int.ModEq> .
wd:Q58413 wl:formalizedAs "DedekindCut" .
wd:Q58413 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/Completion.html#DedekindCut> .
wd:Q11352 wl:formalizedAs "EuclideanGeometry.angle" .
wd:Q11352 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Euclidean/Angle/Unoriented/Affine.html#EuclideanGeometry.angle> .
wd:Q11352 wl:formalizedAs "Orientation.oangle" .
wd:Q11352 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Euclidean/Angle/Oriented/Basic.html#Orientation.oangle> .
wd:Q11352 wl:formalizedAs "EuclideanGeometry.angle_add_of_ne_of_ne" .
wd:Q11352 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Euclidean/Triangle.html#EuclideanGeometry.angle_add_of_ne_of_ne> .
wd:Q11352 wl:formalizedAs "Sbtw.oangle_eq_left_right" .
wd:Q11352 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.html#Sbtw.oangle_eq_left_right> .
wd:Q11352 wl:formalizedAs "EuclideanGeometry.angle_add_angle_add_angle_eq_pi" .
wd:Q11352 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Euclidean/Triangle.html#EuclideanGeometry.angle_add_angle_add_angle_eq_pi> .
wd:Q11352 wl:formalizedAs "Real.Angle.angle_eq_iff_two_pi_dvd_sub" .
wd:Q11352 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.html#Real.Angle.angle_eq_iff_two_pi_dvd_sub> .
wd:Q11352 wl:formalizedAs "InnerProductGeometry.cos_angle" .
wd:Q11352 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Euclidean/Angle/Unoriented/Basic.html#InnerProductGeometry.cos_angle> .
wd:Q11352 wl:formalizedAs "InnerProductGeometry.angle" .
wd:Q11352 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Euclidean/Angle/Unoriented/Basic.html#InnerProductGeometry.angle> .
wd:Q11205 wl:formalizedAs "Nat" .
wd:Q11205 wl:formalizedAs "Int" .
wd:Q11205 wl:formalizedAs "Cardinal" .
wd:Q11205 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Defs.html#Cardinal> .
wd:Q11205 wl:formalizedAs "Ordinal" .
wd:Q11205 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Ordinal/Basic.html#Ordinal> .
wd:Q11205 wl:formalizedAs "Rat" .
wd:Q11205 wl:formalizedAs "Irrational" .
wd:Q11205 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/Real/Irrational.html#Irrational> .
wd:Q11205 wl:formalizedAs "Real" .
wd:Q11205 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Real/Basic.html#Real> .
wd:Q11205 wl:formalizedAs "MulOneClass" .
wd:Q11205 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Defs.html#MulOneClass> .
wd:Q11205 wl:formalizedAs "mul_inv_cancel" .
wd:Q11205 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Defs.html#mul_inv_cancel> .
wd:Q11205 wl:formalizedAs "CommMagma" .
wd:Q11205 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Defs.html#CommMagma> .
wd:Q11205 wl:formalizedAs "Semigroup" .
wd:Q11205 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Defs.html#Semigroup> .
wd:Q11205 wl:formalizedAs "Add" .
wd:Q11205 wl:formalizedAs "Finset.sum" .
wd:Q11205 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/BigOperators/Group/Finset/Defs.html#Finset.sum> .
wd:Q11205 wl:formalizedAs "sub_eq_add_neg" .
wd:Q11205 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Basic.html#sub_eq_add_neg> .
wd:Q11205 wl:formalizedAs "add_zero" .
wd:Q11205 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Defs.html#add_zero> .
wd:Q11205 wl:formalizedAs "add_comm" .
wd:Q11205 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Defs.html#add_comm> .
wd:Q11205 wl:formalizedAs "Mul" .
wd:Q11205 wl:formalizedAs "div_eq_mul_inv" .
wd:Q11205 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Defs.html#div_eq_mul_inv> .
wd:Q11205 wl:formalizedAs "mul_one" .
wd:Q11205 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Defs.html#mul_one> .
wd:Q11205 wl:formalizedAs "mul_comm" .
wd:Q11205 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Defs.html#mul_comm> .
wd:Q11205 wl:formalizedAs "Monoid.npow" .
wd:Q11205 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Defs.html#Monoid.npow> .
wd:Q11205 wl:formalizedAs "Real.rpow" .
wd:Q11205 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Pow/Real.html#Real.rpow> .
wd:Q11205 wl:formalizedAs "Real.log" .
wd:Q11205 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Log/Basic.html#Real.log> .
wd:Q11205 wl:formalizedAs "nsmul_eq_mul" .
wd:Q11205 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Ring/Defs.html#nsmul_eq_mul> .
wd:Q11205 wl:formalizedAs "npowBinRec" .
wd:Q11205 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Defs.html#npowBinRec> .
wd:Q11205 wl:formalizedAs "Nat.primeFactorsList_unique" .
wd:Q11205 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/Factors.html#Nat.primeFactorsList_unique> .
wd:Q11205 wl:formalizedAs "Nat.exists_infinite_primes" .
wd:Q11205 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/Prime/Infinite.html#Nat.exists_infinite_primes> .
wd:Q11205 wl:formalizedAs "FermatLastTheorem" .
wd:Q11205 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/FLT/Basic.html#FermatLastTheorem> .
wd:Q11205 wl:formalizedAs "div_add_div_same" .
wd:Q11205 wl:formalizedAs "div_mul_div_comm" .
wd:Q11205 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Basic.html#div_mul_div_comm> .
wd:Q11205 wl:formalizedAs "Real.rpow_pos_of_pos" .
wd:Q11205 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Pow/Real.html#Real.rpow_pos_of_pos> .
wd:Q11205 wl:formalizedAs "round" .
wd:Q11205 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Order/Round.html#round> .
wd:Q11205 wl:formalizedAs "ZMod" .
wd:Q11205 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/ZMod/Defs.html#ZMod> .
wd:Q11205 wl:formalizedAs "Matrix" .
wd:Q11205 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Matrix/Defs.html#Matrix> .
wd:Q11205 wl:formalizedAs "Nat.zero" .
wd:Q11205 wl:formalizedAs "Nat.succ" .
wd:Q11205 wl:formalizedAs "Nat.succ_injective" .
wd:Q11205 wl:formalizedAs "Nat.succ_ne_zero" .
wd:Q11205 wl:formalizedAs "Nat.rec" .
wd:Q755991 wl:formalizedAs "IsManifold" .
wd:Q755991 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Manifold/IsManifold/Basic.html#IsManifold> .
wd:Q755991 wl:formalizedAs "ContMDiffVectorBundle" .
wd:Q755991 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Manifold/VectorBundle/Basic.html#ContMDiffVectorBundle> .
wd:Q17736 wl:formalizedAs "FirstOrder.Language.Theory" .
wd:Q17736 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Syntax.html#FirstOrder.Language.Theory> .
wd:Q17736 wl:formalizedAs "ConditionallyCompleteLinearOrderedField.uniqueOrderRingIso" .
wd:Q17736 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Order/CompleteField.html#ConditionallyCompleteLinearOrderedField.uniqueOrderRingIso> .
wd:Q17736 wl:formalizedAs "FirstOrder.Language.Theory.exists_elementaryEmbedding_card_eq" .
wd:Q17736 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Satisfiability.html#FirstOrder.Language.Theory.exists_elementaryEmbedding_card_eq> .
wd:Q220680 wl:formalizedAs "ContractingWith" .
wd:Q220680 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/MetricSpace/Contracting.html#ContractingWith> .
wd:Q220680 wl:formalizedAs "ContractingWith.exists_fixedPoint" .
wd:Q220680 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/MetricSpace/Contracting.html#ContractingWith.exists_fixedPoint> .
wd:Q220680 wl:formalizedAs "ContractingWith.apriori_dist_iterate_fixedPoint_le" .
wd:Q220680 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/MetricSpace/Contracting.html#ContractingWith.apriori_dist_iterate_fixedPoint_le> .
wd:Q220680 wl:formalizedAs "LipschitzWith" .
wd:Q220680 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/EMetricSpace/Lipschitz.html#LipschitzWith> .
wd:Q220680 wl:formalizedAs "IsPicardLindelof.exists_eq_forall_mem_Icc_hasDerivWithinAt" .
wd:Q220680 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/ODE/PicardLindelof.html#IsPicardLindelof.exists_eq_forall_mem_Icc_hasDerivWithinAt> .
wd:Q220680 wl:formalizedAs "HasStrictFDerivAt.toOpenPartialHomeomorph" .
wd:Q220680 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/InverseFunctionTheorem/FDeriv.html#HasStrictFDerivAt.toOpenPartialHomeomorph> .
wd:Q220680 wl:formalizedAs "ContractingWith.isFixedPt_fixedPoint_iterate" .
wd:Q220680 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/MetricSpace/Contracting.html#ContractingWith.isFixedPt_fixedPoint_iterate> .
wd:Q182505 wl:formalizedAs "ProbabilityTheory.cond_eq_inv_mul_cond_mul" .
wd:Q182505 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Probability/ConditionalProbability.html#ProbabilityTheory.cond_eq_inv_mul_cond_mul> .
wd:Q182505 wl:formalizedAs "ProbabilityTheory.cond" .
wd:Q182505 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Probability/ConditionalProbability.html#ProbabilityTheory.cond> .
wd:Q182505 wl:formalizedAs "ProbabilityTheory.cond_mul_eq_inter" .
wd:Q182505 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Probability/ConditionalProbability.html#ProbabilityTheory.cond_mul_eq_inter> .
wd:Q182505 wl:formalizedAs "ProbabilityTheory.posterior_eq_withDensity" .
wd:Q182505 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Probability/Kernel/Posterior.html#ProbabilityTheory.posterior_eq_withDensity> .
wd:Q182505 wl:formalizedAs "MeasureTheory.Measure.withDensity_rnDeriv_eq" .
wd:Q182505 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/MeasureTheory/Measure/Decomposition/RadonNikodym.html#MeasureTheory.Measure.withDensity_rnDeriv_eq> .
wd:Q214728 wl:formalizedAs "AffineMap.lineMap" .
wd:Q214728 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/AffineSpace/AffineMap.html#AffineMap.lineMap> .
wd:Q214728 wl:formalizedAs "AffineMap.lineMap_apply_module" .
wd:Q214728 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/AffineSpace/AffineMap.html#AffineMap.lineMap_apply_module> .
wd:Q214728 wl:formalizedAs "bernsteinPolynomial" .
wd:Q214728 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Polynomial/Bernstein.html#bernsteinPolynomial> .
wd:Q4907197 wl:formalizedAs "Function.Injective" .
wd:Q4907197 wl:formalizedAs "Function.Surjective" .
wd:Q4907197 wl:formalizedAs "Function.Bijective" .
wd:Q4907197 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Logic/Function/Defs.html#Function.Bijective> .
wd:Q4907197 wl:formalizedAs "Function.injective_iff_hasLeftInverse" .
wd:Q4907197 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Logic/Function/Basic.html#Function.injective_iff_hasLeftInverse> .
wd:Q4907197 wl:formalizedAs "Equiv.ofInjective" .
wd:Q4907197 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Logic/Equiv/Set.html#Equiv.ofInjective> .
wd:Q4907197 wl:formalizedAs "Function.Injective.comp" .
wd:Q4907197 wl:formalizedAs "Function.Embedding.injective" .
wd:Q4907197 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Logic/Embedding/Basic.html#Function.Embedding.injective> .
wd:Q4907197 wl:formalizedAs "Function.surjective_iff_hasRightInverse" .
wd:Q4907197 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Logic/Function/Basic.html#Function.surjective_iff_hasRightInverse> .
wd:Q4907197 wl:formalizedAs "Setoid.quotientKerEquivOfSurjective" .
wd:Q4907197 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Setoid/Basic.html#Setoid.quotientKerEquivOfSurjective> .
wd:Q4907197 wl:formalizedAs "Function.Surjective.comp" .
wd:Q4907197 wl:formalizedAs "Function.bijective_iff_has_inverse" .
wd:Q4907197 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Logic/Function/Basic.html#Function.bijective_iff_has_inverse> .
wd:Q4907197 wl:formalizedAs "Function.Bijective.comp" .
wd:Q4907197 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Logic/Function/Defs.html#Function.Bijective.comp> .
wd:Q4907197 wl:formalizedAs "Equiv.Perm.permGroup" .
wd:Q4907197 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/End.html#Equiv.Perm.permGroup> .
wd:Q4907197 wl:formalizedAs "Cardinal.eq" .
wd:Q4907197 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Defs.html#Cardinal.eq> .
wd:Q4907197 wl:formalizedAs "Cardinal.le_def" .
wd:Q4907197 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Order.html#Cardinal.le_def> .
wd:Q4907197 wl:formalizedAs "Function.bijective_id" .
wd:Q4907197 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Logic/Function/Defs.html#Function.bijective_id> .
wd:Q4907197 wl:formalizedAs "Real.expOrderIso" .
wd:Q4907197 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Exp.html#Real.expOrderIso> .
wd:Q4907197 wl:formalizedAs "Set.image_preimage_subset" .
wd:Q4907197 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Set/Image.html#Set.image_preimage_subset> .
wd:Q4907197 wl:formalizedAs "CategoryTheory.Types.mono_iff_injective" .
wd:Q4907197 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Types/Basic.html#CategoryTheory.Types.mono_iff_injective> .
wd:Q185547 wl:formalizedAs "ProbabilityTheory.binomial" .
wd:Q185547 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Probability/Distributions/Binomial.html#ProbabilityTheory.binomial> .
wd:Q185547 wl:formalizedAs "PMF.bernoulli" .
wd:Q185547 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Probability/ProbabilityMassFunction/Constructions.html#PMF.bernoulli> .
wd:Q185547 wl:formalizedAs "PMF.binomial_one_eq_bernoulli" .
wd:Q185547 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Probability/ProbabilityMassFunction/Binomial.html#PMF.binomial_one_eq_bernoulli> .
wd:Q185547 wl:formalizedAs "PMF.binomial_apply" .
wd:Q185547 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Probability/ProbabilityMassFunction/Binomial.html#PMF.binomial_apply> .
wd:Q185547 wl:formalizedAs "ProbabilityTheory.tendsto_choose_mul_pow_of_tendsto_mul_atTop" .
wd:Q185547 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Probability/Distributions/Poisson/PoissonLimitThm.html#ProbabilityTheory.tendsto_choose_mul_pow_of_tendsto_mul_atTop> .
wd:Q4973304 wl:formalizedAs "DistribLattice.booleanAlgebraOfComplemented" .
wd:Q4973304 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/BooleanAlgebra/Defs.html#DistribLattice.booleanAlgebraOfComplemented> .
wd:Q4973304 wl:formalizedAs "BooleanAlgebra.toBooleanRing" .
wd:Q4973304 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Ring/BooleanRing.html#BooleanAlgebra.toBooleanRing> .
wd:Q4973304 wl:formalizedAs "BooleanAlgebra" .
wd:Q4973304 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/BooleanAlgebra/Defs.html#BooleanAlgebra> .
wd:Q4973304 wl:formalizedAs "PUnit.instBooleanAlgebra" .
wd:Q4973304 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/BooleanAlgebra/Defs.html#PUnit.instBooleanAlgebra> .
wd:Q4973304 wl:formalizedAs "inf_eq_left" .
wd:Q4973304 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/Lattice.html#inf_eq_left> .
wd:Q4973304 wl:formalizedAs "BooleanAlgebra.toBoundedOrder" .
wd:Q4973304 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/BooleanAlgebra/Defs.html#BooleanAlgebra.toBoundedOrder> .
wd:Q4973304 wl:formalizedAs "compl_unique" .
wd:Q4973304 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/Heyting/Basic.html#compl_unique> .
wd:Q4973304 wl:formalizedAs "OrderDual.instBooleanAlgebra" .
wd:Q4973304 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/BooleanAlgebra/Basic.html#OrderDual.instBooleanAlgebra> .
wd:Q4973304 wl:formalizedAs "Bool.instBooleanAlgebra" .
wd:Q4973304 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/BooleanAlgebra/Defs.html#Bool.instBooleanAlgebra> .
wd:Q4973304 wl:formalizedAs "Set.instBooleanAlgebra" .
wd:Q4973304 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/BooleanAlgebra/Set.html#Set.instBooleanAlgebra> .
wd:Q4973304 wl:formalizedAs "TopologicalSpace.Clopens.instBooleanAlgebra" .
wd:Q4973304 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Sets/Closeds.html#TopologicalSpace.Clopens.instBooleanAlgebra> .
wd:Q4973304 wl:formalizedAs "instBooleanAlgebraSubtypeIsIdempotentElem" .
wd:Q4973304 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Order/Ring/Idempotent.html#instBooleanAlgebraSubtypeIsIdempotentElem> .
wd:Q4973304 wl:formalizedAs "BoundedLatticeHom" .
wd:Q4973304 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/Hom/BoundedLattice.html#BoundedLatticeHom> .
wd:Q4973304 wl:formalizedAs "map_compl&#x27;" .
wd:Q4973304 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/Hom/BoundedLattice.html#map_compl'> .
wd:Q4973304 wl:formalizedAs "OrderIso" .
wd:Q4973304 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/Hom/Basic.html#OrderIso> .
wd:Q4973304 wl:formalizedAs "BooleanRing.toBooleanAlgebra" .
wd:Q4973304 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Ring/BooleanRing.html#BooleanRing.toBooleanAlgebra> .
wd:Q4973304 wl:formalizedAs "boolRingCatEquivBoolAlg" .
wd:Q4973304 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Category/BoolRing.html#boolRingCatEquivBoolAlg> .
wd:Q4973304 wl:formalizedAs "Order.Ideal" .
wd:Q4973304 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/Ideal.html#Order.Ideal> .
wd:Q4973304 wl:formalizedAs "Order.Ideal.IsPrime" .
wd:Q4973304 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/PrimeIdeal.html#Order.Ideal.IsPrime> .
wd:Q4973304 wl:formalizedAs "Order.Ideal.IsMaximal" .
wd:Q4973304 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/Ideal.html#Order.Ideal.IsMaximal> .
wd:Q4973304 wl:formalizedAs "Order.Ideal.IsPrime.isMaximal" .
wd:Q4973304 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/PrimeIdeal.html#Order.Ideal.IsPrime.isMaximal> .
wd:Q4973304 wl:formalizedAs "Order.PFilter" .
wd:Q4973304 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/PFilter.html#Order.PFilter> .
wd:Q4973304 wl:formalizedAs "Ultrafilter.exists_le" .
wd:Q4973304 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/Filter/Ultrafilter/Defs.html#Ultrafilter.exists_le> .
wd:Q4973304 wl:formalizedAs "GeneralizedBooleanAlgebra" .
wd:Q4973304 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/BooleanAlgebra/Defs.html#GeneralizedBooleanAlgebra> .
wd:Q1144897 wl:formalizedAs "exists_mem_Icc_isFixedPt_of_mapsTo" .
wd:Q1144897 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Order/IntermediateValue.html#exists_mem_Icc_isFixedPt_of_mapsTo> .
wd:Q263809 wl:formalizedAs "CStarAlgebra" .
wd:Q263809 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/CStarAlgebra/Classes.html#CStarAlgebra> .
wd:Q263809 wl:formalizedAs "ZeroAtInftyContinuousMap.instNonUnitalCommCStarAlgebra" .
wd:Q263809 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/CStarAlgebra/ContinuousMap.html#ZeroAtInftyContinuousMap.instNonUnitalCommCStarAlgebra> .
wd:Q263809 wl:formalizedAs "CStarRing.norm_star_mul_self" .
wd:Q263809 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/CStarAlgebra/Basic.html#CStarRing.norm_star_mul_self> .
wd:Q263809 wl:formalizedAs "StarAlgHom" .
wd:Q263809 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Star/StarAlgHom.html#StarAlgHom> .
wd:Q263809 wl:formalizedAs "NonUnitalStarAlgHom.norm_apply_le" .
wd:Q263809 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/CStarAlgebra/Spectrum.html#NonUnitalStarAlgHom.norm_apply_le> .
wd:Q263809 wl:formalizedAs "StarAlgEquiv" .
wd:Q263809 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Star/StarAlgHom.html#StarAlgEquiv> .
wd:Q263809 wl:formalizedAs "StarSubalgebra.cstarAlgebra" .
wd:Q263809 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/CStarAlgebra/Classes.html#StarSubalgebra.cstarAlgebra> .
wd:Q263809 wl:formalizedAs "IsSelfAdjoint" .
wd:Q263809 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Star/SelfAdjoint.html#IsSelfAdjoint> .
wd:Q263809 wl:formalizedAs "nonneg_iff_isSelfAdjoint_and_quasispectrumRestricts" .
wd:Q263809 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/CStarAlgebra/ContinuousFunctionalCalculus/Instances.html#nonneg_iff_isSelfAdjoint_and_quasispectrumRestricts> .
wd:Q263809 wl:formalizedAs "CStarAlgebra.increasingApproximateUnit" .
wd:Q263809 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/CStarAlgebra/ApproximateUnit.html#CStarAlgebra.increasingApproximateUnit> .
wd:Q263809 wl:formalizedAs "Matrix.instCStarRing" .
wd:Q263809 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/CStarAlgebra/Matrix.html#Matrix.instCStarRing> .
wd:Q263809 wl:formalizedAs "ContinuousLinearMap.instCStarAlgebra" .
wd:Q263809 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/CStarAlgebra/ContinuousLinearMap.html#ContinuousLinearMap.instCStarAlgebra> .
wd:Q263809 wl:formalizedAs "gelfandStarTransform" .
wd:Q263809 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/CStarAlgebra/GelfandDuality.html#gelfandStarTransform> .
wd:Q263809 wl:formalizedAs "VonNeumannAlgebra" .
wd:Q263809 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/VonNeumannAlgebra/Basic.html#VonNeumannAlgebra> .
wd:Q729471 wl:formalizedAs "Uncountable" .
wd:Q729471 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Countable/Defs.html#Uncountable> .
wd:Q729471 wl:formalizedAs "Function.cantor_surjective" .
wd:Q729471 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Logic/Function/Basic.html#Function.cantor_surjective> .
wd:Q729471 wl:formalizedAs "Cardinal.not_countable_real" .
wd:Q729471 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Real/Cardinality.html#Cardinal.not_countable_real> .
wd:Q729471 wl:formalizedAs "Cardinal.cantorFunction_injective" .
wd:Q729471 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Real/Cardinality.html#Cardinal.cantorFunction_injective> .
wd:Q729471 wl:formalizedAs "Cardinal.cantor" .
wd:Q729471 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Order.html#Cardinal.cantor> .
wd:Q729471 wl:formalizedAs "Cardinal.le_def" .
wd:Q729471 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Order.html#Cardinal.le_def> .
wd:Q729471 wl:formalizedAs "Function.Embedding.schroeder_bernstein" .
wd:Q729471 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/SchroederBernstein.html#Function.Embedding.schroeder_bernstein> .
wd:Q729471 wl:formalizedAs "ComputablePred.halting_problem" .
wd:Q729471 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Computability/Halting.html#ComputablePred.halting_problem> .
wd:Q4049983 wl:formalizedAs "Cardinal.mk" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Defs.html#Cardinal.mk> .
wd:Q4049983 wl:formalizedAs "Cardinal.eq" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Defs.html#Cardinal.eq> .
wd:Q4049983 wl:formalizedAs "Set" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Set/Defs.html#Set> .
wd:Q4049983 wl:formalizedAs "Cardinal.aleph0" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Defs.html#Cardinal.aleph0> .
wd:Q4049983 wl:formalizedAs "Function.Injective" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Logic/Function/Defs.html#Function.Injective> .
wd:Q4049983 wl:formalizedAs "Function.Surjective" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Logic/Function/Defs.html#Function.Surjective> .
wd:Q4049983 wl:formalizedAs "Function.Bijective" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Logic/Function/Defs.html#Function.Bijective> .
wd:Q4049983 wl:formalizedAs "Cardinal.le_def" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Order.html#Cardinal.le_def> .
wd:Q4049983 wl:formalizedAs "schroeder_bernstein" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/SchroederBernstein.html#schroeder_bernstein> .
wd:Q4049983 wl:formalizedAs "Ordinal.type" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Ordinal/Basic.html#Ordinal.type> .
wd:Q4049983 wl:formalizedAs "WellOrderingRel" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Order.html#WellOrderingRel> .
wd:Q4049983 wl:formalizedAs "Countable" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Countable/Defs.html#Countable> .
wd:Q4049983 wl:formalizedAs "Set.Countable" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Set/Countable.html#Set.Countable> .
wd:Q4049983 wl:formalizedAs "Rat" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Rat/Defs.html#Rat> .
wd:Q4049983 wl:formalizedAs "Cardinal.mkRat" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Rat/Cardinal.html#Cardinal.mkRat> .
wd:Q4049983 wl:formalizedAs "IsAlgebraic" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Algebraic/Defs.html#IsAlgebraic> .
wd:Q4049983 wl:formalizedAs "Transcendental" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Algebraic/Defs.html#Transcendental> .
wd:Q4049983 wl:formalizedAs "Algebraic.countable" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/AlgebraicCard.html#Algebraic.countable> .
wd:Q4049983 wl:formalizedAs "Uncountable" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Countable/Defs.html#Uncountable> .
wd:Q4049983 wl:formalizedAs "Cardinal.not_countable_real" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Real/Cardinality.html#Cardinal.not_countable_real> .
wd:Q4049983 wl:formalizedAs "Cardinal.mk_set_nat" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Continuum.html#Cardinal.mk_set_nat> .
wd:Q4049983 wl:formalizedAs "Cardinal.mk_real" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Real/Cardinality.html#Cardinal.mk_real> .
wd:Q4049983 wl:formalizedAs "Cardinal.cantor" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Order.html#Cardinal.cantor> .
wd:Q4049983 wl:formalizedAs "Cardinal" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Defs.html#Cardinal> .
wd:Q4049983 wl:formalizedAs "Nat.card" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Finite.html#Nat.card> .
wd:Q4049983 wl:formalizedAs "Finite.injective_iff_surjective" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Fintype/Card.html#Finite.injective_iff_surjective> .
wd:Q4049983 wl:formalizedAs "Cardinal.add_def" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Defs.html#Cardinal.add_def> .
wd:Q4049983 wl:formalizedAs "Cardinal.mk_prod" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Defs.html#Cardinal.mk_prod> .
wd:Q4049983 wl:formalizedAs "Finset.inclusion_exclusion_card_biUnion" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Combinatorics/Enumerative/InclusionExclusion.html#Finset.inclusion_exclusion_card_biUnion> .
wd:Q4049983 wl:formalizedAs "Finite" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Finite/Defs.html#Finite> .
wd:Q4049983 wl:formalizedAs "Cardinal.aleph" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Aleph.html#Cardinal.aleph> .
wd:Q4049983 wl:formalizedAs "Ordinal" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Ordinal/Basic.html#Ordinal> .
wd:Q4049983 wl:formalizedAs "Ordinal.omega0" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Ordinal/Basic.html#Ordinal.omega0> .
wd:Q4049983 wl:formalizedAs "Ordinal.omega" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Aleph.html#Ordinal.omega> .
wd:Q4049983 wl:formalizedAs "Cardinal.aleph_succ" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Aleph.html#Cardinal.aleph_succ> .
wd:Q4049983 wl:formalizedAs "Cardinal.mem_range_aleph_iff" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Aleph.html#Cardinal.mem_range_aleph_iff> .
wd:Q4049983 wl:formalizedAs "Cardinal.mul_def" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Defs.html#Cardinal.mul_def> .
wd:Q4049983 wl:formalizedAs "Cardinal.sum_lt_prod" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Order.html#Cardinal.sum_lt_prod> .
wd:Q4049983 wl:formalizedAs "Cardinal.add_eq_self" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Arithmetic.html#Cardinal.add_eq_self> .
wd:Q4049983 wl:formalizedAs "Cardinal.mk_arrow" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Defs.html#Cardinal.mk_arrow> .
wd:Q4049983 wl:formalizedAs "Cardinal.power_zero" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Defs.html#Cardinal.power_zero> .
wd:Q4049983 wl:formalizedAs "Cardinal.mk_set" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Order.html#Cardinal.mk_set> .
wd:Q4049983 wl:formalizedAs "not_small_cardinal" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Basic.html#not_small_cardinal> .
wd:Q4049983 wl:formalizedAs "Real" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Real/Basic.html#Real> .
wd:Q4049983 wl:formalizedAs "Cardinal.continuum" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Continuum.html#Cardinal.continuum> .
wd:Q4049983 wl:formalizedAs "Cardinal.mk_Ioo_real" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Real/Cardinality.html#Cardinal.mk_Ioo_real> .
wd:Q4049983 wl:formalizedAs "Real.tanOrderIso" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Trigonometric/Arctan.html#Real.tanOrderIso> .
wd:Q4049983 wl:formalizedAs "cantorSet" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Instances/CantorSet.html#cantorSet> .
wd:Q4049983 wl:formalizedAs "Cardinal.continuum_power_aleph0" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Continuum.html#Cardinal.continuum_power_aleph0> .
wd:Q4049983 wl:formalizedAs "Cardinal.aleph0_lt_continuum" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Continuum.html#Cardinal.aleph0_lt_continuum> .
wd:Q4049983 wl:formalizedAs "Cardinal.beth" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Aleph.html#Cardinal.beth> .
wd:Q4049983 wl:formalizedAs "ZFSet.omega" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/ZFC/Basic.html#ZFSet.omega> .
wd:Q4049983 wl:formalizedAs "ZFSet.powerset" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/ZFC/Basic.html#ZFSet.powerset> .
wd:Q4049983 wl:formalizedAs "ZFSet.choice" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/ZFC/Class.html#ZFSet.choice> .
wd:Q4049983 wl:formalizedAs "Cardinal.IsInaccessible" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Regular.html#Cardinal.IsInaccessible> .
wd:Q4049983 wl:formalizedAs "ZFSet.vonNeumann" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/ZFC/VonNeumann.html#ZFSet.vonNeumann> .
wd:Q4049983 wl:formalizedAs "Finset.card_lt_card" .
wd:Q4049983 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Finset/Card.html#Finset.card_lt_card> .
wd:Q22952648 wl:formalizedAs "Cardinal.continuum" .
wd:Q22952648 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Continuum.html#Cardinal.continuum> .
wd:Q22952648 wl:formalizedAs "Cardinal.mk_set_nat" .
wd:Q22952648 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Continuum.html#Cardinal.mk_set_nat> .
wd:Q22952648 wl:formalizedAs "Cardinal.eq" .
wd:Q22952648 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Defs.html#Cardinal.eq> .
wd:Q22952648 wl:formalizedAs "Cardinal.mk_Ioo_real" .
wd:Q22952648 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Real/Cardinality.html#Cardinal.mk_Ioo_real> .
wd:Q22952648 wl:formalizedAs "Cardinal.not_countable_real" .
wd:Q22952648 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Real/Cardinality.html#Cardinal.not_countable_real> .
wd:Q22952648 wl:formalizedAs "Cardinal.cantor" .
wd:Q22952648 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Order.html#Cardinal.cantor> .
wd:Q22952648 wl:formalizedAs "Function.Embedding.schroeder_bernstein" .
wd:Q22952648 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/SchroederBernstein.html#Function.Embedding.schroeder_bernstein> .
wd:Q22952648 wl:formalizedAs "Cardinal.mk_real" .
wd:Q22952648 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Real/Cardinality.html#Cardinal.mk_real> .
wd:Q22952648 wl:formalizedAs "Cardinal.continuum_power_aleph0" .
wd:Q22952648 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Continuum.html#Cardinal.continuum_power_aleph0> .
wd:Q22952648 wl:formalizedAs "Cardinal.beth" .
wd:Q22952648 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Aleph.html#Cardinal.beth> .
wd:Q22952648 wl:formalizedAs "Cardinal.sum_lt_prod" .
wd:Q22952648 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Order.html#Cardinal.sum_lt_prod> .
wd:Q22952648 wl:formalizedAs "Algebraic.cardinalMk_of_countable_of_charZero" .
wd:Q22952648 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/AlgebraicCard.html#Algebraic.cardinalMk_of_countable_of_charZero> .
wd:Q719395 wl:formalizedAs "CategoryTheory.Category" .
wd:Q719395 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Category/Basic.html#CategoryTheory.Category> .
wd:Q719395 wl:formalizedAs "CategoryTheory.Functor" .
wd:Q719395 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Functor/Basic.html#CategoryTheory.Functor> .
wd:Q719395 wl:formalizedAs "Quiver.Hom" .
wd:Q719395 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Combinatorics/Quiver/Basic.html#Quiver.Hom> .
wd:Q719395 wl:formalizedAs "CategoryTheory.SmallCategory" .
wd:Q719395 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Category/Basic.html#CategoryTheory.SmallCategory> .
wd:Q719395 wl:formalizedAs "CategoryTheory.LocallySmall" .
wd:Q719395 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/EssentiallySmall.html#CategoryTheory.LocallySmall> .
wd:Q719395 wl:formalizedAs "CategoryTheory.types" .
wd:Q719395 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Types/Basic.html#CategoryTheory.types> .
wd:Q719395 wl:formalizedAs "CategoryTheory.RelCat" .
wd:Q719395 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Category/RelCat.html#CategoryTheory.RelCat> .
wd:Q719395 wl:formalizedAs "CategoryTheory.Discrete" .
wd:Q719395 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Discrete/Basic.html#CategoryTheory.Discrete> .
wd:Q719395 wl:formalizedAs "Preorder.smallCategory" .
wd:Q719395 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Category/Preorder.html#Preorder.smallCategory> .
wd:Q719395 wl:formalizedAs "Quiver.IsThin" .
wd:Q719395 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Combinatorics/Quiver/Basic.html#Quiver.IsThin> .
wd:Q719395 wl:formalizedAs "CategoryTheory.SingleObj" .
wd:Q719395 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/SingleObj.html#CategoryTheory.SingleObj> .
wd:Q719395 wl:formalizedAs "CategoryTheory.Iso" .
wd:Q719395 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Iso.html#CategoryTheory.Iso> .
wd:Q719395 wl:formalizedAs "CategoryTheory.Groupoid" .
wd:Q719395 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Groupoid.html#CategoryTheory.Groupoid> .
wd:Q719395 wl:formalizedAs "FundamentalGroupoid" .
wd:Q719395 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/AlgebraicTopology/FundamentalGroupoid/Basic.html#FundamentalGroupoid> .
wd:Q719395 wl:formalizedAs "CategoryTheory.Paths" .
wd:Q719395 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/PathCategory/Basic.html#CategoryTheory.Paths> .
wd:Q719395 wl:formalizedAs "Preord" .
wd:Q719395 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/Category/Preord.html#Preord> .
wd:Q719395 wl:formalizedAs "CategoryTheory.ConcreteCategory" .
wd:Q719395 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/ConcreteCategory/Basic.html#CategoryTheory.ConcreteCategory> .
wd:Q719395 wl:formalizedAs "GrpCat" .
wd:Q719395 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Category/Grp/Basic.html#GrpCat> .
wd:Q719395 wl:formalizedAs "Ab" .
wd:Q719395 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Category/Grp/Basic.html#Ab> .
wd:Q719395 wl:formalizedAs "CategoryTheory.Cat" .
wd:Q719395 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Category/Cat.html#CategoryTheory.Cat> .
wd:Q719395 wl:formalizedAs "CategoryTheory.Functor.category" .
wd:Q719395 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Functor/Category.html#CategoryTheory.Functor.category> .
wd:Q719395 wl:formalizedAs "CategoryTheory.Category.opposite" .
wd:Q719395 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Opposites.html#CategoryTheory.Category.opposite> .
wd:Q719395 wl:formalizedAs "CategoryTheory.prod" .
wd:Q719395 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Products/Basic.html#CategoryTheory.prod> .
wd:Q719395 wl:formalizedAs "CategoryTheory.Quotient" .
wd:Q719395 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Quotient.html#CategoryTheory.Quotient> .
wd:Q719395 wl:formalizedAs "CategoryTheory.Over" .
wd:Q719395 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Comma/Over/Basic.html#CategoryTheory.Over> .
wd:Q719395 wl:formalizedAs "CategoryTheory.Under" .
wd:Q719395 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Comma/Over/Basic.html#CategoryTheory.Under> .
wd:Q719395 wl:formalizedAs "CategoryTheory.Localization" .
wd:Q719395 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Localization/Construction.html#CategoryTheory.Localization> .
wd:Q719395 wl:formalizedAs "CategoryTheory.Mono" .
wd:Q719395 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Category/Basic.html#CategoryTheory.Mono> .
wd:Q719395 wl:formalizedAs "CategoryTheory.Epi" .
wd:Q719395 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Category/Basic.html#CategoryTheory.Epi> .
wd:Q719395 wl:formalizedAs "CategoryTheory.IsSplitEpi" .
wd:Q719395 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/EpiMono.html#CategoryTheory.IsSplitEpi> .
wd:Q719395 wl:formalizedAs "CategoryTheory.IsSplitMono" .
wd:Q719395 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/EpiMono.html#CategoryTheory.IsSplitMono> .
wd:Q719395 wl:formalizedAs "CategoryTheory.IsIso" .
wd:Q719395 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Iso.html#CategoryTheory.IsIso> .
wd:Q719395 wl:formalizedAs "CategoryTheory.End" .
wd:Q719395 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Endomorphism.html#CategoryTheory.End> .
wd:Q719395 wl:formalizedAs "CategoryTheory.End.monoid" .
wd:Q719395 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Endomorphism.html#CategoryTheory.End.monoid> .
wd:Q719395 wl:formalizedAs "CategoryTheory.Aut" .
wd:Q719395 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Endomorphism.html#CategoryTheory.Aut> .
wd:Q719395 wl:formalizedAs "CategoryTheory.IsSplitEpi.epi" .
wd:Q719395 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/EpiMono.html#CategoryTheory.IsSplitEpi.epi> .
wd:Q719395 wl:formalizedAs "CategoryTheory.Preadditive" .
wd:Q719395 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Preadditive/Basic.html#CategoryTheory.Preadditive> .
wd:Q719395 wl:formalizedAs "CategoryTheory.Abelian" .
wd:Q719395 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Abelian/Basic.html#CategoryTheory.Abelian> .
wd:Q719395 wl:formalizedAs "AddCommGrpCat" .
wd:Q719395 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Category/Grp/Abelian.html#AddCommGrpCat> .
wd:Q719395 wl:formalizedAs "CategoryTheory.EnrichedCategory" .
wd:Q719395 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Enriched/Basic.html#CategoryTheory.EnrichedCategory> .
wd:Q719395 wl:formalizedAs "CategoryTheory.Limits.HasLimits" .
wd:Q719395 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Limits/HasLimits.html#CategoryTheory.Limits.HasLimits> .
wd:Q719395 wl:formalizedAs "CategoryTheory.Limits.Types.hasLimitsOfSize" .
wd:Q719395 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Limits/Types/Limits.html#CategoryTheory.Limits.Types.hasLimitsOfSize> .
wd:Q719395 wl:formalizedAs "CategoryTheory.CartesianClosed" .
wd:Q719395 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Monoidal/Closed/Cartesian.html#CategoryTheory.CartesianClosed> .
wd:Q656772 wl:formalizedAs "Matrix.aeval_self_charpoly" .
wd:Q656772 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Matrix/Charpoly/Basic.html#Matrix.aeval_self_charpoly> .
wd:Q656772 wl:formalizedAs "Matrix.charpoly" .
wd:Q656772 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Matrix/Charpoly/Basic.html#Matrix.charpoly> .
wd:Q656772 wl:formalizedAs "Matrix.pow_eq_aeval_mod_charpoly" .
wd:Q656772 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Matrix/Charpoly/Coeff.html#Matrix.pow_eq_aeval_mod_charpoly> .
wd:Q656772 wl:formalizedAs "Matrix.minpoly_dvd_charpoly" .
wd:Q656772 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Matrix/Charpoly/Minpoly.html#Matrix.minpoly_dvd_charpoly> .
wd:Q656772 wl:formalizedAs "Matrix.charpoly_fin_two" .
wd:Q656772 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Matrix/Charpoly/Coeff.html#Matrix.charpoly_fin_two> .
wd:Q656772 wl:formalizedAs "Matrix.adjugate" .
wd:Q656772 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Matrix/Adjugate.html#Matrix.adjugate> .
wd:Q656772 wl:formalizedAs "Polynomial.div_modByMonic_unique" .
wd:Q656772 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Polynomial/Div.html#Polynomial.div_modByMonic_unique> .
wd:Q656772 wl:formalizedAs "Submodule.eq_bot_of_le_smul_of_le_jacobson_bot" .
wd:Q656772 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Nakayama.html#Submodule.eq_bot_of_le_smul_of_le_jacobson_bot> .
wd:Q166314 wl:formalizedAs "MulAction.IsTopologicallyTransitive" .
wd:Q166314 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Dynamics/Transitive.html#MulAction.IsTopologicallyTransitive> .
wd:Q193878 wl:formalizedAs "Nat.chineseRemainderOfFinset" .
wd:Q193878 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/ChineseRemainder.html#Nat.chineseRemainderOfFinset> .
wd:Q193878 wl:formalizedAs "ZMod.chineseRemainder" .
wd:Q193878 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/ZMod/Basic.html#ZMod.chineseRemainder> .
wd:Q193878 wl:formalizedAs "Nat.chineseRemainder_modEq_unique" .
wd:Q193878 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/ModEq.html#Nat.chineseRemainder_modEq_unique> .
wd:Q193878 wl:formalizedAs "Ideal.quotientInfToPiQuotient_surj" .
wd:Q193878 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Ideal/Quotient/Operations.html#Ideal.quotientInfToPiQuotient_surj> .
wd:Q193878 wl:formalizedAs "Nat.chineseRemainder" .
wd:Q193878 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/ModEq.html#Nat.chineseRemainder> .
wd:Q193878 wl:formalizedAs "Nat.chineseRemainderOfList" .
wd:Q193878 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/ChineseRemainder.html#Nat.chineseRemainderOfList> .
wd:Q193878 wl:formalizedAs "Ideal.quotientInfRingEquivPiQuotient" .
wd:Q193878 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Ideal/Quotient/Operations.html#Ideal.quotientInfRingEquivPiQuotient> .
wd:Q193878 wl:formalizedAs "Lagrange.interpolate" .
wd:Q193878 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Lagrange.html#Lagrange.interpolate> .
wd:Q193878 wl:formalizedAs "Nat.chineseRemainder&#x27;" .
wd:Q193878 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/ModEq.html#Nat.chineseRemainder'> .
wd:Q193878 wl:formalizedAs "Ideal.isCoprime_iff_exists" .
wd:Q193878 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Ideal/Operations.html#Ideal.isCoprime_iff_exists> .
wd:Q193878 wl:formalizedAs "Ideal.prod_eq_iInf_of_pairwise_isCoprime" .
wd:Q193878 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Ideal/Operations.html#Ideal.prod_eq_iInf_of_pairwise_isCoprime> .
wd:Q193878 wl:formalizedAs "CompleteOrthogonalIdempotents" .
wd:Q193878 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Idempotents.html#CompleteOrthogonalIdempotents> .
wd:Q193878 wl:formalizedAs "linearIndependent_monoidHom" .
wd:Q193878 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/LinearIndependent/Basic.html#linearIndependent_monoidHom> .
wd:Q5150824 wl:formalizedAs "Configuration.ProjectivePlane" .
wd:Q5150824 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Combinatorics/Configuration.html#Configuration.ProjectivePlane> .
wd:Q5150824 wl:formalizedAs "Configuration.HasLines.card_le" .
wd:Q5150824 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Combinatorics/Configuration.html#Configuration.HasLines.card_le> .
wd:Q848569 wl:formalizedAs "CompleteSpace" .
wd:Q848569 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/UniformSpace/Cauchy.html#CompleteSpace> .
wd:Q848569 wl:formalizedAs "CauchySeq" .
wd:Q848569 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/UniformSpace/Cauchy.html#CauchySeq> .
wd:Q848569 wl:formalizedAs "IsCompact.nonempty_iInter_of_sequence_nonempty_isCompact_isClosed" .
wd:Q848569 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Compactness/Compact.html#IsCompact.nonempty_iInter_of_sequence_nonempty_isCompact_isClosed> .
wd:Q848569 wl:formalizedAs "IsClosed.isComplete" .
wd:Q848569 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/UniformSpace/Cauchy.html#IsClosed.isComplete> .
wd:Q848569 wl:formalizedAs "Real.instCompleteSpace" .
wd:Q848569 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/UniformSpace/Real.html#Real.instCompleteSpace> .
wd:Q848569 wl:formalizedAs "Pi.complete" .
wd:Q848569 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/UniformSpace/Pi.html#Pi.complete> .
wd:Q848569 wl:formalizedAs "BoundedContinuousFunction.instCompleteSpace" .
wd:Q848569 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/ContinuousMap/Bounded/Basic.html#BoundedContinuousFunction.instCompleteSpace> .
wd:Q848569 wl:formalizedAs "Padic.instCompleteSpace" .
wd:Q848569 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/Padics/PadicNumbers.html#Padic.instCompleteSpace> .
wd:Q848569 wl:formalizedAs "IsCompact.isComplete" .
wd:Q848569 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/UniformSpace/Cauchy.html#IsCompact.isComplete> .
wd:Q848569 wl:formalizedAs "isCompact_iff_totallyBounded_isComplete" .
wd:Q848569 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/UniformSpace/Cauchy.html#isCompact_iff_totallyBounded_isComplete> .
wd:Q848569 wl:formalizedAs "ProperSpace.isCompact_closedBall" .
wd:Q848569 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/MetricSpace/ProperSpace.html#ProperSpace.isCompact_closedBall> .
wd:Q848569 wl:formalizedAs "IsComplete.isClosed" .
wd:Q848569 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/UniformSpace/CompleteSeparated.html#IsComplete.isClosed> .
wd:Q848569 wl:formalizedAs "BaireSpace.of_completelyPseudoMetrizable" .
wd:Q848569 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Baire/CompleteMetrizable.html#BaireSpace.of_completelyPseudoMetrizable> .
wd:Q848569 wl:formalizedAs "ContractingWith.fixedPoint" .
wd:Q848569 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/MetricSpace/Contracting.html#ContractingWith.fixedPoint> .
wd:Q848569 wl:formalizedAs "HasStrictFDerivAt.toOpenPartialHomeomorph" .
wd:Q848569 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/InverseFunctionTheorem/FDeriv.html#HasStrictFDerivAt.toOpenPartialHomeomorph> .
wd:Q848569 wl:formalizedAs "UniformSpace.Completion" .
wd:Q848569 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/UniformSpace/Completion.html#UniformSpace.Completion> .
wd:Q848569 wl:formalizedAs "Completion.extension_unique" .
wd:Q848569 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/UniformSpace/Completion.html#Completion.extension_unique> .
wd:Q848569 wl:formalizedAs "AbstractCompletion.compareEquiv" .
wd:Q848569 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/UniformSpace/AbstractCompletion.html#AbstractCompletion.compareEquiv> .
wd:Q848569 wl:formalizedAs "Completion.instPseudoMetricSpace" .
wd:Q848569 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/MetricSpace/Completion.html#Completion.instPseudoMetricSpace> .
wd:Q848569 wl:formalizedAs "Completion.coe_isometry" .
wd:Q848569 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/MetricSpace/Completion.html#Completion.coe_isometry> .
wd:Q848569 wl:formalizedAs "Real.equivCauchy" .
wd:Q848569 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Real/Basic.html#Real.equivCauchy> .
wd:Q848569 wl:formalizedAs "Padic" .
wd:Q848569 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/Padics/PadicNumbers.html#Padic> .
wd:Q848569 wl:formalizedAs "UniformSpace.Completion.instNormedSpace" .
wd:Q848569 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Normed/Module/Completion.html#UniformSpace.Completion.instNormedSpace> .
wd:Q848569 wl:formalizedAs "UniformSpace.Completion.innerProductSpace" .
wd:Q848569 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/InnerProductSpace/Completion.html#UniformSpace.Completion.innerProductSpace> .
wd:Q848569 wl:formalizedAs "IsCompletelyMetrizableSpace" .
wd:Q848569 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Metrizable/CompletelyMetrizable.html#IsCompletelyMetrizableSpace> .
wd:Q848569 wl:formalizedAs "PolishSpace" .
wd:Q848569 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/MetricSpace/Polish.html#PolishSpace> .
wd:Q848569 wl:formalizedAs "IsTopologicalGroup.completeSpace_rightUniformSpace_iff_leftUniformSpace" .
wd:Q848569 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Algebra/IsUniformGroup/Basic.html#IsTopologicalGroup.completeSpace_rightUniformSpace_iff_leftUniformSpace> .
wd:Q848569 wl:formalizedAs "Cauchy" .
wd:Q848569 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/UniformSpace/Cauchy.html#Cauchy> .
wd:Q1148456 wl:formalizedAs "Computable" .
wd:Q1148456 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Computability/Partrec.html#Computable> .
wd:Q1148456 wl:formalizedAs "Nat.Partrec" .
wd:Q1148456 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Computability/Partrec.html#Nat.Partrec> .
wd:Q1148456 wl:formalizedAs "ComputablePred" .
wd:Q1148456 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Computability/RE.html#ComputablePred> .
wd:Q1148456 wl:formalizedAs "REPred" .
wd:Q1148456 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Computability/RE.html#REPred> .
wd:Q1148456 wl:formalizedAs "Language" .
wd:Q1148456 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Computability/Language.html#Language> .
wd:Q1148456 wl:formalizedAs "Nat.Primrec.add" .
wd:Q1148456 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Computability/Primrec/Basic.html#Nat.Primrec.add> .
wd:Q1148456 wl:formalizedAs "Computable.comp" .
wd:Q1148456 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Computability/Partrec.html#Computable.comp> .
wd:Q1148456 wl:formalizedAs "ack" .
wd:Q1148456 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Computability/Ackermann.html#ack> .
wd:Q1148456 wl:formalizedAs "ComputableIn" .
wd:Q1148456 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Computability/RecursiveIn.html#ComputableIn> .
wd:Q205084 wl:formalizedAs "Turing.TM2ComputableInPolyTime" .
wd:Q205084 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Computability/TuringMachine/Computable.html#Turing.TM2ComputableInPolyTime> .
wd:Q205084 wl:formalizedAs "Turing.TM0.Machine" .
wd:Q205084 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Computability/TuringMachine/PostTuringMachine.html#Turing.TM0.Machine> .
wd:Q319141 wl:formalizedAs "FermatLastTheorem" .
wd:Q319141 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/FLT/Basic.html#FermatLastTheorem> .
wd:Q319141 wl:formalizedAs "SimplyConnectedSpace.nonempty_homeomorph_sphere_three" .
wd:Q319141 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Manifold/PoincareConjecture.html#SimplyConnectedSpace.nonempty_homeomorph_sphere_three> .
wd:Q319141 wl:formalizedAs "ContinuousMap.HomotopyEquiv.nonempty_homeomorph_sphere" .
wd:Q319141 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Manifold/PoincareConjecture.html#ContinuousMap.HomotopyEquiv.nonempty_homeomorph_sphere> .
wd:Q319141 wl:formalizedAs "RiemannHypothesis" .
wd:Q319141 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/LSeries/RiemannZeta.html#RiemannHypothesis> .
wd:Q208416 wl:formalizedAs "Cardinal.sum_lt_prod" .
wd:Q208416 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Order.html#Cardinal.sum_lt_prod> .
wd:Q208416 wl:formalizedAs "Cardinal.eq" .
wd:Q208416 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Defs.html#Cardinal.eq> .
wd:Q208416 wl:formalizedAs "Cardinal.mkRat" .
wd:Q208416 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Rat/Cardinal.html#Cardinal.mkRat> .
wd:Q208416 wl:formalizedAs "Cardinal.aleph0_lt_continuum" .
wd:Q208416 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Continuum.html#Cardinal.aleph0_lt_continuum> .
wd:Q208416 wl:formalizedAs "Cardinal.aleph_one_le_iff" .
wd:Q208416 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Aleph.html#Cardinal.aleph_one_le_iff> .
wd:Q208416 wl:formalizedAs "Cardinal.power_le_power_left" .
wd:Q208416 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Order.html#Cardinal.power_le_power_left> .
wd:Q193657 wl:formalizedAs "Convex" .
wd:Q193657 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Convex/Basic.html#Convex> .
wd:Q193657 wl:formalizedAs "convexHull" .
wd:Q193657 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Convex/Hull.html#convexHull> .
wd:Q193657 wl:formalizedAs "ConvexOn" .
wd:Q193657 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Convex/Function.html#ConvexOn> .
wd:Q193657 wl:formalizedAs "convex_iff_add_mem" .
wd:Q193657 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Convex/Basic.html#convex_iff_add_mem> .
wd:Q193657 wl:formalizedAs "Convex.affine_image" .
wd:Q193657 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Convex/Basic.html#Convex.affine_image> .
wd:Q193657 wl:formalizedAs "Convex.isPathConnected" .
wd:Q193657 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Convex/PathConnected.html#Convex.isPathConnected> .
wd:Q193657 wl:formalizedAs "StrictConvex" .
wd:Q193657 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Convex/Strict.html#StrictConvex> .
wd:Q193657 wl:formalizedAs "AbsConvex" .
wd:Q193657 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/LocallyConvex/AbsConvex.html#AbsConvex> .
wd:Q193657 wl:formalizedAs "convex_iff_ordConnected" .
wd:Q193657 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Convex/Basic.html#convex_iff_ordConnected> .
wd:Q193657 wl:formalizedAs "Convex.sum_mem" .
wd:Q193657 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Convex/Combination.html#Convex.sum_mem> .
wd:Q193657 wl:formalizedAs "Finset.centerMass" .
wd:Q193657 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Convex/Combination.html#Finset.centerMass> .
wd:Q193657 wl:formalizedAs "convex_empty" .
wd:Q193657 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Convex/Basic.html#convex_empty> .
wd:Q193657 wl:formalizedAs "convex_sInter" .
wd:Q193657 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Convex/Basic.html#convex_sInter> .
wd:Q193657 wl:formalizedAs "DirectedOn.convex_sUnion" .
wd:Q193657 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Convex/Basic.html#DirectedOn.convex_sUnion> .
wd:Q193657 wl:formalizedAs "IsExtreme" .
wd:Q193657 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Convex/Extreme.html#IsExtreme> .
wd:Q193657 wl:formalizedAs "Set.extremePoints" .
wd:Q193657 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Convex/Extreme.html#Set.extremePoints> .
wd:Q193657 wl:formalizedAs "closure_convexHull_extremePoints" .
wd:Q193657 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Convex/KreinMilman.html#closure_convexHull_extremePoints> .
wd:Q193657 wl:formalizedAs "StrictConvexSpace.extremePoints_closedBall_eq_sphere" .
wd:Q193657 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Convex/Strict/Extreme.html#StrictConvexSpace.extremePoints_closedBall_eq_sphere> .
wd:Q193657 wl:formalizedAs "Convex.closure" .
wd:Q193657 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Convex/Topology.html#Convex.closure> .
wd:Q193657 wl:formalizedAs "Convex.add_smul" .
wd:Q193657 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Convex/Basic.html#Convex.add_smul> .
wd:Q193657 wl:formalizedAs "convexHull_min" .
wd:Q193657 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Convex/Hull.html#convexHull_min> .
wd:Q193657 wl:formalizedAs "Set.add" .
wd:Q193657 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Pointwise/Set/Basic.html#Set.add> .
wd:Q193657 wl:formalizedAs "Set.addMonoid" .
wd:Q193657 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Pointwise/Set/Basic.html#Set.addMonoid> .
wd:Q193657 wl:formalizedAs "convexHull_add" .
wd:Q193657 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Convex/Combination.html#convexHull_add> .
wd:Q193657 wl:formalizedAs "convexHull_sum" .
wd:Q193657 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Convex/Combination.html#convexHull_sum> .
wd:Q193657 wl:formalizedAs "convexHullAddMonoidHom" .
wd:Q193657 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Convex/Combination.html#convexHullAddMonoidHom> .
wd:Q193657 wl:formalizedAs "IsCompact.add" .
wd:Q193657 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Algebra/Monoid.html#IsCompact.add> .
wd:Q193657 wl:formalizedAs "IsClosed.add_left_of_isCompact" .
wd:Q193657 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Algebra/Group/Pointwise.html#IsClosed.add_left_of_isCompact> .
wd:Q193657 wl:formalizedAs "StarConvex" .
wd:Q193657 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Convex/Star.html#StarConvex> .
wd:Q193657 wl:formalizedAs "Convex.starConvex" .
wd:Q193657 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Convex/Basic.html#Convex.starConvex> .
wd:Q193657 wl:formalizedAs "Set.OrdConnected" .
wd:Q193657 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/Interval/Set/Defs.html#Set.OrdConnected> .
wd:Q193657 wl:formalizedAs "Convexity.ConvexSpace" .
wd:Q193657 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Convex/ConvexSpace/Defs.html#Convexity.ConvexSpace> .
wd:Q66707394 wl:formalizedAs "Set.Countable" .
wd:Q66707394 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Set/Countable.html#Set.Countable> .
wd:Q66707394 wl:formalizedAs "Denumerable" .
wd:Q66707394 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Logic/Denumerable.html#Denumerable> .
wd:Q66707394 wl:formalizedAs "Function.cantor_surjective" .
wd:Q66707394 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Logic/Function/Basic.html#Function.cantor_surjective> .
wd:Q66707394 wl:formalizedAs "countable_iff_exists_injective" .
wd:Q66707394 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Countable/Defs.html#countable_iff_exists_injective> .
wd:Q66707394 wl:formalizedAs "countable_iff_exists_surjective" .
wd:Q66707394 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Countable/Defs.html#countable_iff_exists_surjective> .
wd:Q66707394 wl:formalizedAs "Uncountable" .
wd:Q66707394 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Countable/Defs.html#Uncountable> .
wd:Q66707394 wl:formalizedAs "Infinite" .
wd:Q66707394 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Finite/Defs.html#Infinite> .
wd:Q66707394 wl:formalizedAs "Equiv" .
wd:Q66707394 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Logic/Equiv/Defs.html#Equiv> .
wd:Q66707394 wl:formalizedAs "Cardinal.eq" .
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wd:Q66707394 wl:formalizedAs "Cardinal.not_countable_real" .
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wd:Q66707394 wl:formalizedAs "Cardinal.mk_real" .
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wd:Q66707394 wl:formalizedAs "Set.Finite.countable" .
wd:Q66707394 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Set/Countable.html#Set.Finite.countable> .
wd:Q66707394 wl:formalizedAs "Set.countable_infinite_iff_nonempty_denumerable" .
wd:Q66707394 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Basic.html#Set.countable_infinite_iff_nonempty_denumerable> .
wd:Q66707394 wl:formalizedAs "Denumerable.prod" .
wd:Q66707394 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Logic/Denumerable.html#Denumerable.prod> .
wd:Q66707394 wl:formalizedAs "Algebraic.countable" .
wd:Q66707394 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/AlgebraicCard.html#Algebraic.countable> .
wd:Q66707394 wl:formalizedAs "Subtype.countable" .
wd:Q66707394 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Countable/Defs.html#Subtype.countable> .
wd:Q66707394 wl:formalizedAs "Set.Countable.mono" .
wd:Q66707394 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Set/Countable.html#Set.Countable.mono> .
wd:Q66707394 wl:formalizedAs "Set.Countable.prod" .
wd:Q66707394 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Set/Countable.html#Set.Countable.prod> .
wd:Q66707394 wl:formalizedAs "Denumerable.int" .
wd:Q66707394 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Logic/Denumerable.html#Denumerable.int> .
wd:Q66707394 wl:formalizedAs "Set.Countable.union" .
wd:Q66707394 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Set/Countable.html#Set.Countable.union> .
wd:Q66707394 wl:formalizedAs "Set.countable_iUnion" .
wd:Q66707394 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Set/Countable.html#Set.countable_iUnion> .
wd:Q66707394 wl:formalizedAs "denumerableList" .
wd:Q66707394 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Logic/Equiv/List.html#denumerableList> .
wd:Q66707394 wl:formalizedAs "Set.countable_setOf_finite_subset" .
wd:Q66707394 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Set/Countable.html#Set.countable_setOf_finite_subset> .
wd:Q66707394 wl:formalizedAs "Function.Injective.countable" .
wd:Q66707394 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Countable/Defs.html#Function.Injective.countable> .
wd:Q66707394 wl:formalizedAs "Cardinal.cantor" .
wd:Q66707394 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Order.html#Cardinal.cantor> .
wd:Q66707394 wl:formalizedAs "IsWellOrder" .
wd:Q66707394 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/RelClasses.html#IsWellOrder> .
wd:Q7874246 wl:formalizedAs "CoxeterMatrix.Group" .
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wd:Q7874246 wl:formalizedAs "CoxeterSystem" .
wd:Q7874246 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/Coxeter/Basic.html#CoxeterSystem> .
wd:Q7874246 wl:formalizedAs "CoxeterSystem.simple_mul_simple_self" .
wd:Q7874246 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/Coxeter/Basic.html#CoxeterSystem.simple_mul_simple_self> .
wd:Q7874246 wl:formalizedAs "CoxeterMatrix" .
wd:Q7874246 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/Coxeter/Matrix.html#CoxeterMatrix> .
wd:Q7874246 wl:formalizedAs "CoxeterSystem.length" .
wd:Q7874246 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/Coxeter/Length.html#CoxeterSystem.length> .
wd:Q7874246 wl:formalizedAs "CoxeterSystem.IsReduced" .
wd:Q7874246 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/Coxeter/Length.html#CoxeterSystem.IsReduced> .
wd:Q7874246 wl:formalizedAs "CoxeterSystem.lengthParity" .
wd:Q7874246 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/Coxeter/Length.html#CoxeterSystem.lengthParity> .
wd:Q190556 wl:formalizedAs "Complex.cos_add_sin_mul_I_pow" .
wd:Q190556 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Complex/Trigonometric.html#Complex.cos_add_sin_mul_I_pow> .
wd:Q190556 wl:formalizedAs "Complex.exp_mul_I" .
wd:Q190556 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Complex/Trigonometric.html#Complex.exp_mul_I> .
wd:Q190556 wl:formalizedAs "Complex.cos_three_mul" .
wd:Q190556 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Complex/Trigonometric.html#Complex.cos_three_mul> .
wd:Q190556 wl:formalizedAs "Polynomial.Chebyshev.T_complex_cos" .
wd:Q190556 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Trigonometric/Chebyshev/Basic.html#Polynomial.Chebyshev.T_complex_cos> .
wd:Q1058314 wl:formalizedAs "Diffeomorph" .
wd:Q1058314 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Manifold/Diffeomorph.html#Diffeomorph> .
wd:Q1058314 wl:formalizedAs "Diffeomorph.toHomeomorph" .
wd:Q1058314 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Manifold/Diffeomorph.html#Diffeomorph.toHomeomorph> .
wd:Q1058314 wl:formalizedAs "IsLocalDiffeomorph" .
wd:Q1058314 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Manifold/LocalDiffeomorph.html#IsLocalDiffeomorph> .
wd:Q1058314 wl:formalizedAs "IsImmersion" .
wd:Q1058314 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Manifold/Immersion.html#IsImmersion> .
wd:Q628007 wl:formalizedAs "shift_eq_sum_fwdDiff_iter" .
wd:Q628007 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/ForwardDiff.html#shift_eq_sum_fwdDiff_iter> .
wd:Q628007 wl:formalizedAs "Polynomial.fwdDiff_iter_degree_eq_factorial" .
wd:Q628007 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/ForwardDiff.html#Polynomial.fwdDiff_iter_degree_eq_factorial> .
wd:Q628007 wl:formalizedAs "AnalyticAt" .
wd:Q628007 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Analytic/Basic.html#AnalyticAt> .
wd:Q628007 wl:formalizedAs "taylorWithin" .
wd:Q628007 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/Taylor.html#taylorWithin> .
wd:Q628007 wl:formalizedAs "Lagrange.interpolate" .
wd:Q628007 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Lagrange.html#Lagrange.interpolate> .
wd:Q149999 wl:formalizedAs "deriv" .
wd:Q149999 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/Deriv/Basic.html#deriv> .
wd:Q149999 wl:formalizedAs "HasDerivAt" .
wd:Q149999 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/Deriv/Basic.html#HasDerivAt> .
wd:Q149999 wl:formalizedAs "deriv_pow" .
wd:Q149999 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/Deriv/Pow.html#deriv_pow> .
wd:Q149999 wl:formalizedAs "hasFDerivAt_iff_isLittleO" .
wd:Q149999 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/FDeriv/Defs.html#hasFDerivAt_iff_isLittleO> .
wd:Q149999 wl:formalizedAs "IsLocalExtr.deriv_eq_zero" .
wd:Q149999 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/LocalExtr/Basic.html#IsLocalExtr.deriv_eq_zero> .
wd:Q149999 wl:formalizedAs "exists_deriv_eq_zero" .
wd:Q149999 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/LocalExtr/Rolle.html#exists_deriv_eq_zero> .
wd:Q149999 wl:formalizedAs "exists_deriv_eq_slope" .
wd:Q149999 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/Deriv/MeanValue.html#exists_deriv_eq_slope> .
wd:Q149999 wl:formalizedAs "is_const_of_deriv_eq_zero" .
wd:Q149999 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/MeanValue.html#is_const_of_deriv_eq_zero> .
wd:Q149999 wl:formalizedAs "taylor_mean_remainder_lagrange" .
wd:Q149999 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/Taylor.html#taylor_mean_remainder_lagrange> .
wd:Q149999 wl:formalizedAs "isLocalMax_of_deriv" .
wd:Q149999 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/DerivativeTest.html#isLocalMax_of_deriv> .
wd:Q149999 wl:formalizedAs "isLocalMin_of_deriv_deriv_pos" .
wd:Q149999 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/DerivativeTest.html#isLocalMin_of_deriv_deriv_pos> .
wd:Q149999 wl:formalizedAs "IsLocalExtr.fderiv_eq_zero" .
wd:Q149999 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/LocalExtr/Basic.html#IsLocalExtr.fderiv_eq_zero> .
wd:Q149999 wl:formalizedAs "ImplicitFunctionData.implicitFunction" .
wd:Q149999 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/Implicit.html#ImplicitFunctionData.implicitFunction> .
wd:Q149999 wl:formalizedAs "HasStrictFDerivAt.to_localInverse" .
wd:Q149999 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/InverseFunctionTheorem/FDeriv.html#HasStrictFDerivAt.to_localInverse> .
wd:Q11214 wl:formalizedAs "HarmonicAt" .
wd:Q11214 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/InnerProductSpace/Harmonic/Basic.html#HarmonicAt> .
wd:Q188444 wl:formalizedAs "IsRiemannianManifold" .
wd:Q188444 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Manifold/Riemannian/Basic.html#IsRiemannianManifold> .
wd:Q188444 wl:formalizedAs "LieGroup" .
wd:Q188444 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Manifold/Algebra/LieGroup.html#LieGroup> .
wd:Q188444 wl:formalizedAs "GroupLieAlgebra" .
wd:Q188444 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Manifold/GroupLieAlgebra.html#GroupLieAlgebra> .
wd:Q2502381 wl:formalizedAs "ContDiffOn" .
wd:Q2502381 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/ContDiff/Defs.html#ContDiffOn> .
wd:Q2502381 wl:formalizedAs "EuclideanSpace.instIsManifoldSphere" .
wd:Q2502381 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Manifold/Instances/Sphere.html#EuclideanSpace.instIsManifoldSphere> .
wd:Q2502381 wl:formalizedAs "VectorField.mlieBracket" .
wd:Q2502381 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Manifold/VectorField/LieBracket.html#VectorField.mlieBracket> .
wd:Q2502381 wl:formalizedAs "RiemannianMetric" .
wd:Q2502381 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/VectorBundle/Riemannian.html#RiemannianMetric> .
wd:Q2502381 wl:formalizedAs "pathELength_comp_of_monotoneOn" .
wd:Q2502381 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Manifold/Riemannian/PathELength.html#pathELength_comp_of_monotoneOn> .
wd:Q2502381 wl:formalizedAs "EuclideanGeometry.law_cos" .
wd:Q2502381 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Euclidean/Triangle.html#EuclideanGeometry.law_cos> .
wd:Q272621 wl:formalizedAs "Representation" .
wd:Q272621 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RepresentationTheory/Basic.html#Representation> .
wd:Q1195339 wl:formalizedAs "SimpleGraph.hasse" .
wd:Q1195339 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Combinatorics/SimpleGraph/Hasse.html#SimpleGraph.hasse> .
wd:Q1195339 wl:formalizedAs "Quiver.Arborescence" .
wd:Q1195339 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Combinatorics/Quiver/Arborescence.html#Quiver.Arborescence> .
wd:Q20968946 wl:formalizedAs "slope" .
wd:Q20968946 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/AffineSpace/Slope.html#slope> .
wd:Q20968946 wl:formalizedAs "BoxIntegral.integralSum" .
wd:Q20968946 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/BoxIntegral/Basic.html#BoxIntegral.integralSum> .
wd:Q20968946 wl:formalizedAs "intervalIntegral.integral_eq_sub_of_hasDerivAt" .
wd:Q20968946 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/MeasureTheory/Integral/IntervalIntegral/FundThmCalculus.html#intervalIntegral.integral_eq_sub_of_hasDerivAt> .
wd:Q20968946 wl:formalizedAs "Finset.sum_range_sub" .
wd:Q20968946 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/BigOperators/Group/Finset/Basic.html#Finset.sum_range_sub> .
wd:Q20968946 wl:formalizedAs "fwdDiff" .
wd:Q20968946 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/ForwardDiff.html#fwdDiff> .
wd:Q20968946 wl:formalizedAs "fwdDiff_const" .
wd:Q20968946 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/ForwardDiff.html#fwdDiff_const> .
wd:Q20968946 wl:formalizedAs "fwdDiff_add" .
wd:Q20968946 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/ForwardDiff.html#fwdDiff_add> .
wd:Q20968946 wl:formalizedAs "fwdDiff_smul" .
wd:Q20968946 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/ForwardDiff.html#fwdDiff_smul> .
wd:Q20968946 wl:formalizedAs "Geometry.SimplicialComplex" .
wd:Q20968946 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Convex/SimplicialComplex/Basic.html#Geometry.SimplicialComplex> .
wd:Q20968946 wl:formalizedAs "AlgebraicTopology.AlternatingFaceMapComplex.objD" .
wd:Q20968946 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/AlgebraicTopology/AlternatingFaceMapComplex.html#AlgebraicTopology.AlternatingFaceMapComplex.objD> .
wd:Q20968946 wl:formalizedAs "HomologicalComplex.cycles" .
wd:Q20968946 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Homology/HomologicalComplex.html#HomologicalComplex.cycles> .
wd:Q20968946 wl:formalizedAs "HomologicalComplex.d_comp_d" .
wd:Q20968946 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Homology/HomologicalComplex.html#HomologicalComplex.d_comp_d> .
wd:Q20968946 wl:formalizedAs "ChainComplex" .
wd:Q20968946 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Homology/HomologicalComplex.html#ChainComplex> .
wd:Q20968946 wl:formalizedAs "HomologicalComplex.Hom" .
wd:Q20968946 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Homology/HomologicalComplex.html#HomologicalComplex.Hom> .
wd:Q20968946 wl:formalizedAs "CochainComplex" .
wd:Q20968946 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Homology/HomologicalComplex.html#CochainComplex> .
wd:Q20968946 wl:formalizedAs "groupCohomology.cocycles" .
wd:Q20968946 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RepresentationTheory/Homological/GroupCohomology/Basic.html#groupCohomology.cocycles> .
wd:Q121416 wl:formalizedAs "peirce" .
wd:Q121416 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Logic/Basic.html#peirce> .
wd:Q865811 wl:formalizedAs "Distribution" .
wd:Q865811 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Distribution/Distribution.html#Distribution> .
wd:Q865811 wl:formalizedAs "TestFunction" .
wd:Q865811 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Distribution/TestFunction.html#TestFunction> .
wd:Q865811 wl:formalizedAs "Distribution.delta" .
wd:Q865811 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Distribution/Distribution.html#Distribution.delta> .
wd:Q865811 wl:formalizedAs "TemperedDistribution.toTemperedDistribution_dirac_eq_delta" .
wd:Q865811 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Distribution/TemperedDistribution.html#TemperedDistribution.toTemperedDistribution_dirac_eq_delta> .
wd:Q865811 wl:formalizedAs "Distribution.lineDerivCLM" .
wd:Q865811 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Distribution/Distribution.html#Distribution.lineDerivCLM> .
wd:Q865811 wl:formalizedAs "HasCompactSupport" .
wd:Q865811 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Support.html#HasCompactSupport> .
wd:Q865811 wl:formalizedAs "MeasureTheory.LocallyIntegrable" .
wd:Q865811 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/MeasureTheory/Function/LocallyIntegrable.html#MeasureTheory.LocallyIntegrable> .
wd:Q865811 wl:formalizedAs "ae_eq_of_integral_contDiff_smul_eq" .
wd:Q865811 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Distribution/AEEqOfIntegralContDiff.html#ae_eq_of_integral_contDiff_smul_eq> .
wd:Q865811 wl:formalizedAs "LineDeriv.iteratedLineDerivOp" .
wd:Q865811 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Distribution/DerivNotation.html#LineDeriv.iteratedLineDerivOp> .
wd:Q865811 wl:formalizedAs "Distribution.IsVanishingOn" .
wd:Q865811 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Distribution/Support.html#Distribution.IsVanishingOn> .
wd:Q865811 wl:formalizedAs "Distribution.dsupport" .
wd:Q865811 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Distribution/Support.html#Distribution.dsupport> .
wd:Q865811 wl:formalizedAs "TemperedDistribution" .
wd:Q865811 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Distribution/TemperedDistribution.html#TemperedDistribution> .
wd:Q865811 wl:formalizedAs "SchwartzMap" .
wd:Q865811 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Distribution/SchwartzSpace/Basic.html#SchwartzMap> .
wd:Q865811 wl:formalizedAs "SchwartzMap.seminorm" .
wd:Q865811 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Distribution/SchwartzSpace/Basic.html#SchwartzMap.seminorm> .
wd:Q865811 wl:formalizedAs "SchwartzMap.fourierTransformCLM" .
wd:Q865811 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Distribution/SchwartzSpace/Fourier.html#SchwartzMap.fourierTransformCLM> .
wd:Q865811 wl:formalizedAs "TemperedDistribution.derivCLM" .
wd:Q865811 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Distribution/TemperedDistribution.html#TemperedDistribution.derivCLM> .
wd:Q865811 wl:formalizedAs "Function.HasTemperateGrowth.toTemperedDistribution" .
wd:Q865811 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Distribution/TemperedDistribution.html#Function.HasTemperateGrowth.toTemperedDistribution> .
wd:Q865811 wl:formalizedAs "TemperedDistribution.instFourierTransform" .
wd:Q865811 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Distribution/TemperedDistribution.html#TemperedDistribution.instFourierTransform> .
wd:Q865811 wl:formalizedAs "FourierTransform.fourierCLE" .
wd:Q865811 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Fourier/Notation.html#FourierTransform.fourierCLE> .
wd:Q752487 wl:formalizedAs "Module.Dual" .
wd:Q752487 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Dual/Defs.html#Module.Dual> .
wd:Q752487 wl:formalizedAs "StrongDual" .
wd:Q752487 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Algebra/Module/LinearMap.html#StrongDual> .
wd:Q752487 wl:formalizedAs "Module.Dual.eval" .
wd:Q752487 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Dual/Defs.html#Module.Dual.eval> .
wd:Q752487 wl:formalizedAs "Basis.dualBasis" .
wd:Q752487 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Dual/Basis.html#Basis.dualBasis> .
wd:Q752487 wl:formalizedAs "Basis.dualBasis_apply_self" .
wd:Q752487 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Dual/Basis.html#Basis.dualBasis_apply_self> .
wd:Q752487 wl:formalizedAs "Module.lift_rank_lt_rank_dual" .
wd:Q752487 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Dimension/ErdosKaplansky.html#Module.lift_rank_lt_rank_dual> .
wd:Q752487 wl:formalizedAs "Module.rank_dual_eq_card_dual_of_aleph0_le_rank" .
wd:Q752487 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Dimension/ErdosKaplansky.html#Module.rank_dual_eq_card_dual_of_aleph0_le_rank> .
wd:Q752487 wl:formalizedAs "LinearMap.BilinForm.toDual" .
wd:Q752487 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/BilinearForm/Properties.html#LinearMap.BilinForm.toDual> .
wd:Q752487 wl:formalizedAs "Module.evalEquiv" .
wd:Q752487 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Dual/Defs.html#Module.evalEquiv> .
wd:Q752487 wl:formalizedAs "LinearMap.dualMap" .
wd:Q752487 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Dual/Defs.html#LinearMap.dualMap> .
wd:Q752487 wl:formalizedAs "Module.Dual.transpose_apply" .
wd:Q752487 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Dual/Defs.html#Module.Dual.transpose_apply> .
wd:Q752487 wl:formalizedAs "LinearMap.toMatrix_transpose" .
wd:Q752487 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Matrix/Dual.html#LinearMap.toMatrix_transpose> .
wd:Q752487 wl:formalizedAs "Submodule.dualAnnihilator" .
wd:Q752487 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Dual/Defs.html#Submodule.dualAnnihilator> .
wd:Q752487 wl:formalizedAs "Submodule.dualAnnihilator_sup_eq" .
wd:Q752487 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Dual/Defs.html#Submodule.dualAnnihilator_sup_eq> .
wd:Q752487 wl:formalizedAs "Module.dualAnnihilator_gc" .
wd:Q752487 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Dual/Defs.html#Module.dualAnnihilator_gc> .
wd:Q752487 wl:formalizedAs "Submodule.dualQuotEquivDualAnnihilator" .
wd:Q752487 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Dual/Lemmas.html#Submodule.dualQuotEquivDualAnnihilator> .
wd:Q752487 wl:formalizedAs "Module.dualProdDualEquivDual" .
wd:Q752487 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Dual/Lemmas.html#Module.dualProdDualEquivDual> .
wd:Q752487 wl:formalizedAs "LinearMap.toContinuousLinearMap" .
wd:Q752487 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Algebra/Module/FiniteDimension.html#LinearMap.toContinuousLinearMap> .
wd:Q752487 wl:formalizedAs "ContinuousLinearMap.toNormedAddCommGroup" .
wd:Q752487 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Normed/Operator/NormedSpace.html#ContinuousLinearMap.toNormedAddCommGroup> .
wd:Q752487 wl:formalizedAs "WeakDual" .
wd:Q752487 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Algebra/Module/Spaces/WeakDual.html#WeakDual> .
wd:Q752487 wl:formalizedAs "InnerProductSpace.toDual" .
wd:Q752487 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/InnerProductSpace/Dual.html#InnerProductSpace.toDual> .
wd:Q752487 wl:formalizedAs "RealRMK.integral_rieszMeasure" .
wd:Q752487 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/MeasureTheory/Integral/RieszMarkovKakutani/Real.html#RealRMK.integral_rieszMeasure> .
wd:Q752487 wl:formalizedAs "NormedSpace.inclusionInDoubleDual" .
wd:Q752487 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Normed/Module/DoubleDual.html#NormedSpace.inclusionInDoubleDual> .
wd:Q752487 wl:formalizedAs "NormedSpace.inclusionInDoubleDualLi" .
wd:Q752487 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Normed/Module/DoubleDual.html#NormedSpace.inclusionInDoubleDualLi> .
wd:Q211294 wl:formalizedAs "pow_zero" .
wd:Q211294 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Defs.html#pow_zero> .
wd:Q211294 wl:formalizedAs "add_comm" .
wd:Q211294 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Defs.html#add_comm> .
wd:Q211294 wl:formalizedAs "left_distrib" .
wd:Q211294 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Ring/Defs.html#left_distrib> .
wd:Q211294 wl:formalizedAs "EuclideanGeometry.dist_sq_eq_dist_sq_add_dist_sq_iff_angle_eq_pi_div_two" .
wd:Q211294 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Euclidean/Angle/Unoriented/RightAngle.html#EuclideanGeometry.dist_sq_eq_dist_sq_add_dist_sq_iff_angle_eq_pi_div_two> .
wd:Q211294 wl:formalizedAs "mul_lt_mul_of_neg_left" .
wd:Q211294 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Order/Ring/Unbundled/Basic.html#mul_lt_mul_of_neg_left> .
wd:Q211294 wl:formalizedAs "eq_equivalence" .
wd:Q211294 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Logic/Basic.html#eq_equivalence> .
wd:Q211294 wl:formalizedAs "Eq.subst" .
wd:Q211294 wl:formalizedAs "lt_trans" .
wd:Q211294 wl:formalizedAs "ge_iff_le" .
wd:Q211294 wl:formalizedAs "mul_eq_zero" .
wd:Q211294 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/GroupWithZero/Defs.html#mul_eq_zero> .
wd:Q211294 wl:formalizedAs "quadratic_eq_zero_iff" .
wd:Q211294 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/QuadraticDiscriminant.html#quadratic_eq_zero_iff> .
wd:Q211294 wl:formalizedAs "Real.rpow_inv_natCast_pow" .
wd:Q211294 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Pow/Real.html#Real.rpow_inv_natCast_pow> .
wd:Q268493 wl:formalizedAs "WeierstrassCurve.Affine.Nonsingular" .
wd:Q268493 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/AlgebraicGeometry/EllipticCurve/Affine/Basic.html#WeierstrassCurve.Affine.Nonsingular> .
wd:Q268493 wl:formalizedAs "WeierstrassCurve.IsShortNF" .
wd:Q268493 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/AlgebraicGeometry/EllipticCurve/NormalForms.html#WeierstrassCurve.IsShortNF> .
wd:Q268493 wl:formalizedAs "WeierstrassCurve.Affine.Point.instAddCommGroup" .
wd:Q268493 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/AlgebraicGeometry/EllipticCurve/Affine/Point.html#WeierstrassCurve.Affine.Point.instAddCommGroup> .
wd:Q268493 wl:formalizedAs "WeierstrassCurve.Affine.Point.neg" .
wd:Q268493 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/AlgebraicGeometry/EllipticCurve/Affine/Point.html#WeierstrassCurve.Affine.Point.neg> .
wd:Q268493 wl:formalizedAs "WeierstrassCurve.Affine.Point.add" .
wd:Q268493 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/AlgebraicGeometry/EllipticCurve/Affine/Point.html#WeierstrassCurve.Affine.Point.add> .
wd:Q268493 wl:formalizedAs "WeierstrassCurve.Affine.Point" .
wd:Q268493 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/AlgebraicGeometry/EllipticCurve/Affine/Point.html#WeierstrassCurve.Affine.Point> .
wd:Q268493 wl:formalizedAs "WeierstrassCurve.Affine.Point.map" .
wd:Q268493 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/AlgebraicGeometry/EllipticCurve/Affine/Point.html#WeierstrassCurve.Affine.Point.map> .
wd:Q268493 wl:formalizedAs "WeierstrassCurve.Affine.slope_of_X_ne" .
wd:Q268493 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/AlgebraicGeometry/EllipticCurve/Affine/Formula.html#WeierstrassCurve.Affine.slope_of_X_ne> .
wd:Q268493 wl:formalizedAs "WeierstrassCurve.Affine.negY" .
wd:Q268493 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/AlgebraicGeometry/EllipticCurve/Affine/Formula.html#WeierstrassCurve.Affine.negY> .
wd:Q268493 wl:formalizedAs "WeierstrassCurve.Affine.slope_of_Y_ne" .
wd:Q268493 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/AlgebraicGeometry/EllipticCurve/Affine/Formula.html#WeierstrassCurve.Affine.slope_of_Y_ne> .
wd:Q268493 wl:formalizedAs "WeierstrassCurve.Affine.slope" .
wd:Q268493 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/AlgebraicGeometry/EllipticCurve/Affine/Formula.html#WeierstrassCurve.Affine.slope> .
wd:Q268493 wl:formalizedAs "WeierstrassCurve.LFunction" .
wd:Q268493 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/AlgebraicGeometry/EllipticCurve/LFunction.html#WeierstrassCurve.LFunction> .
wd:Q268493 wl:formalizedAs "WeierstrassCurve.exists_variableChange_isShortNF" .
wd:Q268493 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/AlgebraicGeometry/EllipticCurve/NormalForms.html#WeierstrassCurve.exists_variableChange_isShortNF> .
wd:Q268493 wl:formalizedAs "WeierstrassCurve.exists_variableChange_isCharThreeNF" .
wd:Q268493 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/AlgebraicGeometry/EllipticCurve/NormalForms.html#WeierstrassCurve.exists_variableChange_isCharThreeNF> .
wd:Q268493 wl:formalizedAs "WeierstrassCurve.exists_variableChange_isCharTwoNF" .
wd:Q268493 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/AlgebraicGeometry/EllipticCurve/NormalForms.html#WeierstrassCurve.exists_variableChange_isCharTwoNF> .
wd:Q268493 wl:formalizedAs "PeriodPair.derivWeierstrassP_sq" .
wd:Q268493 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Elliptic/Weierstrass.html#PeriodPair.derivWeierstrassP_sq> .
wd:Q268493 wl:formalizedAs "PeriodPair.weierstrassP_add_coe" .
wd:Q268493 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Elliptic/Weierstrass.html#PeriodPair.weierstrassP_add_coe> .
wd:Q268493 wl:formalizedAs "WeierstrassCurve.exists_variableChange_of_j_eq" .
wd:Q268493 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/AlgebraicGeometry/EllipticCurve/IsomOfJ.html#WeierstrassCurve.exists_variableChange_of_j_eq> .
wd:Q268493 wl:formalizedAs "PeriodPair.g₂" .
wd:Q268493 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Elliptic/Weierstrass.html#PeriodPair.g₂> .
wd:Q1332450 wl:formalizedAs "Projectivization.equivSubmodule" .
wd:Q1332450 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Projectivization/Basic.html#Projectivization.equivSubmodule> .
wd:Q842346 wl:formalizedAs "Eq" .
wd:Q842346 wl:formalizedAs "Ne" .
wd:Q842346 wl:formalizedAs "Eq.refl" .
wd:Q842346 wl:formalizedAs "Eq.symm" .
wd:Q842346 wl:formalizedAs "Eq.trans" .
wd:Q842346 wl:formalizedAs "Eq.subst" .
wd:Q842346 wl:formalizedAs "congrArg" .
wd:Q842346 wl:formalizedAs "BEq" .
wd:Q842346 wl:formalizedAs "funext" .
wd:Q842346 wl:formalizedAs "rfl" .
wd:Q842346 wl:formalizedAs "Set.ext" .
wd:Q842346 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Set/Defs.html#Set.ext> .
wd:Q842346 wl:formalizedAs "setOf" .
wd:Q842346 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Set/Defs.html#setOf> .
wd:Q842346 wl:formalizedAs "Set.ext_iff" .
wd:Q842346 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Set/Defs.html#Set.ext_iff> .
wd:Q842346 wl:formalizedAs "Prod.ext_iff" .
wd:Q842346 wl:formalizedAs "FP.Float" .
wd:Q842346 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/FP/Basic.html#FP.Float> .
wd:Q842346 wl:formalizedAs "Equivalence" .
wd:Q842346 wl:formalizedAs "Setoid.isPartition_classes" .
wd:Q842346 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Setoid/Partition.html#Setoid.isPartition_classes> .
wd:Q842346 wl:formalizedAs "Setoid.bot_def" .
wd:Q842346 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Setoid/Basic.html#Setoid.bot_def> .
wd:Q842346 wl:formalizedAs "Con" .
wd:Q842346 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/Congruence/Defs.html#Con> .
wd:Q842346 wl:formalizedAs "CategoryTheory.Iso" .
wd:Q842346 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Iso.html#CategoryTheory.Iso> .
wd:Q842346 wl:formalizedAs "Equiv" .
wd:Q842346 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Logic/Equiv/Defs.html#Equiv> .
wd:Q842346 wl:formalizedAs "MulEquiv" .
wd:Q842346 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Equiv/Defs.html#MulEquiv> .
wd:Q842346 wl:formalizedAs "zmodMulEquivOfGenerator" .
wd:Q842346 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/SpecificGroups/Cyclic.html#zmodMulEquivOfGenerator> .
wd:Q842346 wl:formalizedAs "LinearEquiv.nonempty_equiv_iff_rank_eq" .
wd:Q842346 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Dimension/Free.html#LinearEquiv.nonempty_equiv_iff_rank_eq> .
wd:Q842346 wl:formalizedAs "EuclideanGeometry.dist_sq_eq_dist_sq_add_dist_sq_iff_angle_eq_pi_div_two" .
wd:Q842346 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Euclidean/Angle/Unoriented/RightAngle.html#EuclideanGeometry.dist_sq_eq_dist_sq_add_dist_sq_iff_angle_eq_pi_div_two> .
wd:Q842346 wl:formalizedAs "EuclideanSpace.volume_ball" .
wd:Q842346 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/MeasureTheory/Measure/Lebesgue/VolumeOfBalls.html#EuclideanSpace.volume_ball> .
wd:Q842346 wl:formalizedAs "Similar" .
wd:Q842346 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/MetricSpace/Similarity.html#Similar> .
wd:Q230848 wl:formalizedAs "EuclideanDomain.gcd" .
wd:Q230848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/EuclideanDomain/Defs.html#EuclideanDomain.gcd> .
wd:Q230848 wl:formalizedAs "Nat.gcd_sub_self_left" .
wd:Q230848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/GCD/Basic.html#Nat.gcd_sub_self_left> .
wd:Q230848 wl:formalizedAs "Int.gcd_eq_gcd_ab" .
wd:Q230848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Int/GCD.html#Int.gcd_eq_gcd_ab> .
wd:Q230848 wl:formalizedAs "Nat.gcd" .
wd:Q230848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/GCD/Basic.html#Nat.gcd> .
wd:Q230848 wl:formalizedAs "Nat.Coprime" .
wd:Q230848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/GCD/Basic.html#Nat.Coprime> .
wd:Q230848 wl:formalizedAs "Nat.dvd_gcd" .
wd:Q230848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/GCD/Basic.html#Nat.dvd_gcd> .
wd:Q230848 wl:formalizedAs "Nat.factorization_gcd" .
wd:Q230848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/Factorization/Basic.html#Nat.factorization_gcd> .
wd:Q230848 wl:formalizedAs "Int.gcd_least_linear" .
wd:Q230848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Int/GCD.html#Int.gcd_least_linear> .
wd:Q230848 wl:formalizedAs "Nat.gcd_rec" .
wd:Q230848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/GCD/Basic.html#Nat.gcd_rec> .
wd:Q230848 wl:formalizedAs "Nat.gcd_comm" .
wd:Q230848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/GCD/Basic.html#Nat.gcd_comm> .
wd:Q230848 wl:formalizedAs "EuclideanDomain.div_add_mod" .
wd:Q230848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/EuclideanDomain/Defs.html#EuclideanDomain.div_add_mod> .
wd:Q230848 wl:formalizedAs "Int.ediv_emod_unique" .
wd:Q230848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Int/Lemmas.html#Int.ediv_emod_unique> .
wd:Q230848 wl:formalizedAs "Nat.xgcd" .
wd:Q230848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Int/GCD.html#Nat.xgcd> .
wd:Q230848 wl:formalizedAs "EuclideanDomain.gcd_eq_gcd_ab" .
wd:Q230848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/EuclideanDomain/Basic.html#EuclideanDomain.gcd_eq_gcd_ab> .
wd:Q230848 wl:formalizedAs "span_gcd" .
wd:Q230848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/PrincipalIdealDomain.html#span_gcd> .
wd:Q230848 wl:formalizedAs "IsPrincipalIdealRing" .
wd:Q230848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Ideal/Span.html#IsPrincipalIdealRing> .
wd:Q230848 wl:formalizedAs "Nat.gcd_eq_gcd_ab" .
wd:Q230848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Int/GCD.html#Nat.gcd_eq_gcd_ab> .
wd:Q230848 wl:formalizedAs "Nat.Prime.dvd_mul" .
wd:Q230848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/Prime/Defs.html#Nat.Prime.dvd_mul> .
wd:Q230848 wl:formalizedAs "Nat.Coprime.mul_right" .
wd:Q230848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/GCD/Basic.html#Nat.Coprime.mul_right> .
wd:Q230848 wl:formalizedAs "Nat.factorization_inj" .
wd:Q230848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/Factorization/Defs.html#Nat.factorization_inj> .
wd:Q230848 wl:formalizedAs "Int.gcd_dvd_iff" .
wd:Q230848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Int/GCD.html#Int.gcd_dvd_iff> .
wd:Q230848 wl:formalizedAs "ZMod.instField" .
wd:Q230848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Field/ZMod.html#ZMod.instField> .
wd:Q230848 wl:formalizedAs "ZMod.unitOfCoprime" .
wd:Q230848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/ZMod/Basic.html#ZMod.unitOfCoprime> .
wd:Q230848 wl:formalizedAs "ZMod.chineseRemainder" .
wd:Q230848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/ZMod/Basic.html#ZMod.chineseRemainder> .
wd:Q230848 wl:formalizedAs "EuclideanDomain" .
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wd:Q230848 wl:formalizedAs "GenContFract.terminates_iff_rat" .
wd:Q230848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/ContinuedFractions/Computation/TerminatesIffRat.html#GenContFract.terminates_iff_rat> .
wd:Q230848 wl:formalizedAs "Polynomial.instEuclideanDomain" .
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wd:Q230848 wl:formalizedAs "EuclideanDomain.gcd_dvd_left" .
wd:Q230848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/EuclideanDomain/Basic.html#EuclideanDomain.gcd_dvd_left> .
wd:Q230848 wl:formalizedAs "GaussianInt" .
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wd:Q230848 wl:formalizedAs "PrincipalIdealRing.to_uniqueFactorizationMonoid" .
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wd:Q230848 wl:formalizedAs "Zsqrtd.norm" .
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wd:Q230848 wl:formalizedAs "EuclideanDomain.to_principal_ideal_domain" .
wd:Q230848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/PrincipalIdealDomain.html#EuclideanDomain.to_principal_ideal_domain> .
wd:Q230848 wl:formalizedAs "Zsqrtd" .
wd:Q230848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/Zsqrtd/Basic.html#Zsqrtd> .
wd:Q230848 wl:formalizedAs "Nat.sum_four_squares" .
wd:Q230848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/SumFourSquares.html#Nat.sum_four_squares> .
wd:Q162886 wl:formalizedAs "EuclideanGeometry.dist_sq_eq_dist_sq_add_dist_sq_iff_angle_eq_pi_div_two" .
wd:Q162886 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Euclidean/Angle/Unoriented/RightAngle.html#EuclideanGeometry.dist_sq_eq_dist_sq_add_dist_sq_iff_angle_eq_pi_div_two> .
wd:Q162886 wl:formalizedAs "Nat.exists_infinite_primes" .
wd:Q162886 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/Prime/Infinite.html#Nat.exists_infinite_primes> .
wd:Q162886 wl:formalizedAs "EuclideanGeometry.angle_eq_angle_of_dist_eq" .
wd:Q162886 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Euclidean/Triangle.html#EuclideanGeometry.angle_eq_angle_of_dist_eq> .
wd:Q162886 wl:formalizedAs "EuclideanGeometry.angle_add_angle_add_angle_eq_pi" .
wd:Q162886 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Euclidean/Triangle.html#EuclideanGeometry.angle_add_angle_add_angle_eq_pi> .
wd:Q162886 wl:formalizedAs "EuclideanGeometry.angle_eq_pi_div_two_iff_mem_sphere_of_isDiameter" .
wd:Q162886 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Euclidean/Angle/Sphere.html#EuclideanGeometry.angle_eq_pi_div_two_iff_mem_sphere_of_isDiameter> .
wd:Q162886 wl:formalizedAs "EuclideanGeometry.side_side_side" .
wd:Q162886 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Euclidean/Congruence.html#EuclideanGeometry.side_side_side> .
wd:Q162886 wl:formalizedAs "EuclideanGeometry.similar_of_angle_angle" .
wd:Q162886 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Euclidean/Similarity.html#EuclideanGeometry.similar_of_angle_angle> .
wd:Q162886 wl:formalizedAs "MeasureTheory.Measure.addHaar_smul" .
wd:Q162886 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/MeasureTheory/Measure/Lebesgue/EqHaar.html#MeasureTheory.Measure.addHaar_smul> .
wd:Q162886 wl:formalizedAs "Congruent" .
wd:Q162886 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/MetricSpace/Congruence.html#Congruent> .
wd:Q162886 wl:formalizedAs "Similar" .
wd:Q162886 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/MetricSpace/Similarity.html#Similar> .
wd:Q162886 wl:formalizedAs "EuclideanSpace.dist_eq" .
wd:Q162886 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/InnerProductSpace/PiL2.html#EuclideanSpace.dist_eq> .
wd:Q162886 wl:formalizedAs "and_not_self_iff" .
wd:Q162886 wl:formalizedAs "em" .
wd:Q162886 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Logic/Basic.html#em> .
wd:Q168698 wl:formalizedAs "Real.exp" .
wd:Q168698 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Complex/Exponential.html#Real.exp> .
wd:Q168698 wl:formalizedAs "Real.exp_add" .
wd:Q168698 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Complex/Exponential.html#Real.exp_add> .
wd:Q168698 wl:formalizedAs "Real.tendsto_exp_div_pow_atTop" .
wd:Q168698 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Exp.html#Real.tendsto_exp_div_pow_atTop> .
wd:Q168698 wl:formalizedAs "Real.exp_pos" .
wd:Q168698 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Complex/Exponential.html#Real.exp_pos> .
wd:Q168698 wl:formalizedAs "Real.hasDerivAt_exp" .
wd:Q168698 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/ExpDeriv.html#Real.hasDerivAt_exp> .
wd:Q168698 wl:formalizedAs "Real.exp_log" .
wd:Q168698 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Log/Basic.html#Real.exp_log> .
wd:Q168698 wl:formalizedAs "Complex.exp" .
wd:Q168698 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Complex/Exponential.html#Complex.exp> .
wd:Q168698 wl:formalizedAs "Complex.isCauSeq_norm_exp" .
wd:Q168698 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Complex/Exponential.html#Complex.isCauSeq_norm_exp> .
wd:Q168698 wl:formalizedAs "Real.tendsto_one_add_div_pow_exp" .
wd:Q168698 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Complex/LogBounds.html#Real.tendsto_one_add_div_pow_exp> .
wd:Q168698 wl:formalizedAs "Real.exp_neg" .
wd:Q168698 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Complex/Exponential.html#Real.exp_neg> .
wd:Q168698 wl:formalizedAs "Real.exp_strictMono" .
wd:Q168698 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Complex/Exponential.html#Real.exp_strictMono> .
wd:Q168698 wl:formalizedAs "Real.rpow" .
wd:Q168698 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Pow/Real.html#Real.rpow> .
wd:Q168698 wl:formalizedAs "Complex.analyticOnNhd_cexp" .
wd:Q168698 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/ExpDeriv.html#Complex.analyticOnNhd_cexp> .
wd:Q168698 wl:formalizedAs "Complex.tendsto_one_add_div_pow_exp" .
wd:Q168698 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Complex/LogBounds.html#Complex.tendsto_one_add_div_pow_exp> .
wd:Q168698 wl:formalizedAs "Complex.exp_add" .
wd:Q168698 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Complex/Exponential.html#Complex.exp_add> .
wd:Q168698 wl:formalizedAs "Complex.exp_log" .
wd:Q168698 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Complex/Log.html#Complex.exp_log> .
wd:Q168698 wl:formalizedAs "Complex.exp_periodic" .
wd:Q168698 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.html#Complex.exp_periodic> .
wd:Q168698 wl:formalizedAs "Complex.exp_conj" .
wd:Q168698 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Complex/Exponential.html#Complex.exp_conj> .
wd:Q168698 wl:formalizedAs "Complex.norm_exp" .
wd:Q168698 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Complex/Trigonometric.html#Complex.norm_exp> .
wd:Q168698 wl:formalizedAs "Complex.exp_mul_I" .
wd:Q168698 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Complex/Trigonometric.html#Complex.exp_mul_I> .
wd:Q168698 wl:formalizedAs "Complex.exp_eq_exp_re_mul_sin_add_cos" .
wd:Q168698 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Complex/Trigonometric.html#Complex.exp_eq_exp_re_mul_sin_add_cos> .
wd:Q168698 wl:formalizedAs "Complex.two_cos" .
wd:Q168698 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Complex/Trigonometric.html#Complex.two_cos> .
wd:Q168698 wl:formalizedAs "NormedSpace.exp" .
wd:Q168698 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Normed/Algebra/Exponential.html#NormedSpace.exp> .
wd:Q168698 wl:formalizedAs "NormedSpace.isUnit_exp" .
wd:Q168698 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Normed/Algebra/Exponential.html#NormedSpace.isUnit_exp> .
wd:Q5446431 wl:formalizedAs "CategoryTheory.Functor.Fiber" .
wd:Q5446431 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/FiberedCategory/Fiber.html#CategoryTheory.Functor.Fiber> .
wd:Q5446431 wl:formalizedAs "CategoryTheory.Functor.IsStronglyCartesian" .
wd:Q5446431 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/FiberedCategory/Cartesian.html#CategoryTheory.Functor.IsStronglyCartesian> .
wd:Q5446431 wl:formalizedAs "CategoryTheory.Functor.IsPreFibered.pullbackObj" .
wd:Q5446431 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/FiberedCategory/Fibered.html#CategoryTheory.Functor.IsPreFibered.pullbackObj> .
wd:Q5446431 wl:formalizedAs "CategoryTheory.Functor.IsStronglyCartesian.isIso_of_base_isIso" .
wd:Q5446431 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/FiberedCategory/Cartesian.html#CategoryTheory.Functor.IsStronglyCartesian.isIso_of_base_isIso> .
wd:Q5446431 wl:formalizedAs "CategoryTheory.Functor.IsCartesian.domainUniqueUpToIso" .
wd:Q5446431 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/FiberedCategory/Cartesian.html#CategoryTheory.Functor.IsCartesian.domainUniqueUpToIso> .
wd:Q5446431 wl:formalizedAs "CategoryTheory.BasedCategory" .
wd:Q5446431 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/FiberedCategory/BasedCategory.html#CategoryTheory.BasedCategory> .
wd:Q5446431 wl:formalizedAs "CategoryTheory.BasedCategory.bicategory" .
wd:Q5446431 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/FiberedCategory/BasedCategory.html#CategoryTheory.BasedCategory.bicategory> .
wd:Q5446431 wl:formalizedAs "CategoryTheory.Functor.IsFibered" .
wd:Q5446431 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/FiberedCategory/Fibered.html#CategoryTheory.Functor.IsFibered> .
wd:Q5446431 wl:formalizedAs "CategoryTheory.Pseudofunctor.CoGrothendieck.forget" .
wd:Q5446431 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/FiberedCategory/Grothendieck.html#CategoryTheory.Pseudofunctor.CoGrothendieck.forget> .
wd:Q5446431 wl:formalizedAs "CategoryTheory.Functor.IsStronglyCocartesian" .
wd:Q5446431 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/FiberedCategory/Cocartesian.html#CategoryTheory.Functor.IsStronglyCocartesian> .
wd:Q4055684 wl:formalizedAs "FirstOrder.Language" .
wd:Q4055684 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Basic.html#FirstOrder.Language> .
wd:Q4055684 wl:formalizedAs "FirstOrder.Language.Theory" .
wd:Q4055684 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Syntax.html#FirstOrder.Language.Theory> .
wd:Q4055684 wl:formalizedAs "FirstOrder.Language.Structure" .
wd:Q4055684 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Basic.html#FirstOrder.Language.Structure> .
wd:Q4055684 wl:formalizedAs "FirstOrder.Language.Term" .
wd:Q4055684 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Syntax.html#FirstOrder.Language.Term> .
wd:Q4055684 wl:formalizedAs "FirstOrder.Language.Relations" .
wd:Q4055684 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Basic.html#FirstOrder.Language.Relations> .
wd:Q4055684 wl:formalizedAs "FirstOrder.Language.Functions" .
wd:Q4055684 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Basic.html#FirstOrder.Language.Functions> .
wd:Q4055684 wl:formalizedAs "FirstOrder.Language.Constants" .
wd:Q4055684 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Basic.html#FirstOrder.Language.Constants> .
wd:Q4055684 wl:formalizedAs "FirstOrder.Language.BoundedFormula" .
wd:Q4055684 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Syntax.html#FirstOrder.Language.BoundedFormula> .
wd:Q4055684 wl:formalizedAs "FirstOrder.Language.BoundedFormula.IsAtomic" .
wd:Q4055684 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Complexity.html#FirstOrder.Language.BoundedFormula.IsAtomic> .
wd:Q4055684 wl:formalizedAs "FirstOrder.Language.BoundedFormula.freeVarFinset" .
wd:Q4055684 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Syntax.html#FirstOrder.Language.BoundedFormula.freeVarFinset> .
wd:Q4055684 wl:formalizedAs "FirstOrder.Language.Sentence" .
wd:Q4055684 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Syntax.html#FirstOrder.Language.Sentence> .
wd:Q4055684 wl:formalizedAs "FirstOrder.Language.BoundedFormula.Realize" .
wd:Q4055684 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Semantics.html#FirstOrder.Language.BoundedFormula.Realize> .
wd:Q4055684 wl:formalizedAs "FirstOrder.Language.Theory.IsSatisfiable" .
wd:Q4055684 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Satisfiability.html#FirstOrder.Language.Theory.IsSatisfiable> .
wd:Q4055684 wl:formalizedAs "FirstOrder.Language.Theory.ModelsBoundedFormula" .
wd:Q4055684 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Satisfiability.html#FirstOrder.Language.Theory.ModelsBoundedFormula> .
wd:Q4055684 wl:formalizedAs "FirstOrder.Language.Theory.Model" .
wd:Q4055684 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Semantics.html#FirstOrder.Language.Theory.Model> .
wd:Q4055684 wl:formalizedAs "FirstOrder.Language.Term.bdEqual" .
wd:Q4055684 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Syntax.html#FirstOrder.Language.Term.bdEqual> .
wd:Q4055684 wl:formalizedAs "FirstOrder.Language.exists_elementarySubstructure_card_eq" .
wd:Q4055684 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Skolem.html#FirstOrder.Language.exists_elementarySubstructure_card_eq> .
wd:Q4055684 wl:formalizedAs "FirstOrder.Language.Theory.isSatisfiable_iff_isFinitelySatisfiable" .
wd:Q4055684 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Satisfiability.html#FirstOrder.Language.Theory.isSatisfiable_iff_isFinitelySatisfiable> .
wd:Q4055684 wl:formalizedAs "FirstOrder.Language.Theory.exists_model_card_eq" .
wd:Q4055684 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Satisfiability.html#FirstOrder.Language.Theory.exists_model_card_eq> .
wd:Q4055684 wl:formalizedAs "ExistsUnique" .
wd:Q4055684 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Logic/ExistsUnique.html#ExistsUnique> .
wd:Q976981 wl:formalizedAs "EuclideanSpace.volume_ball" .
wd:Q976981 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/MeasureTheory/Measure/Lebesgue/VolumeOfBalls.html#EuclideanSpace.volume_ball> .
wd:Q976981 wl:formalizedAs "FirstOrder.Language.BoundedFormula" .
wd:Q976981 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Syntax.html#FirstOrder.Language.BoundedFormula> .
wd:Q184410 wl:formalizedAs "SimpleGraph.degree" .
wd:Q184410 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Combinatorics/SimpleGraph/Finite.html#SimpleGraph.degree> .
wd:Q184410 wl:formalizedAs "SimpleGraph.nonempty_hom_of_forall_finite_subgraph_hom" .
wd:Q184410 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Combinatorics/SimpleGraph/Finsubgraph.html#SimpleGraph.nonempty_hom_of_forall_finite_subgraph_hom> .
wd:Q1365258 wl:formalizedAs "MeasureTheory.Integrable.fourier_inversion" .
wd:Q1365258 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Fourier/Inversion.html#MeasureTheory.Integrable.fourier_inversion> .
wd:Q1365258 wl:formalizedAs "VectorFourier.fourierIntegral" .
wd:Q1365258 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Fourier/FourierTransform.html#VectorFourier.fourierIntegral> .
wd:Q1365258 wl:formalizedAs "MeasureTheory.Lp.fourierTransformₗᵢ" .
wd:Q1365258 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Fourier/LpSpace.html#MeasureTheory.Lp.fourierTransformₗᵢ> .
wd:Q1365258 wl:formalizedAs "hasDerivAt_exp" .
wd:Q1365258 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Exponential.html#hasDerivAt_exp> .
wd:Q1365258 wl:formalizedAs "Real.fourier_mul_convolution_eq" .
wd:Q1365258 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Fourier/Convolution.html#Real.fourier_mul_convolution_eq> .
wd:Q1365258 wl:formalizedAs "Real.fourierIntegral" .
wd:Q1365258 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Fourier/FourierTransform.html#Real.fourierIntegral> .
wd:Q1365258 wl:formalizedAs "Real.fourierIntegralInv" .
wd:Q1365258 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Fourier/FourierTransform.html#Real.fourierIntegralInv> .
wd:Q1365258 wl:formalizedAs "AddCircle.hasSum_fourier_series_of_summable" .
wd:Q1365258 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Fourier/AddCircle.html#AddCircle.hasSum_fourier_series_of_summable> .
wd:Q1365258 wl:formalizedAs "Real.tsum_eq_tsum_fourier_of_rpow_decay" .
wd:Q1365258 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Fourier/PoissonSummation.html#Real.tsum_eq_tsum_fourier_of_rpow_decay> .
wd:Q1365258 wl:formalizedAs "ZMod.dft" .
wd:Q1365258 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Fourier/ZMod.html#ZMod.dft> .
wd:Q1365258 wl:formalizedAs "ZMod.invDFT_def" .
wd:Q1365258 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Fourier/ZMod.html#ZMod.invDFT_def> .
wd:Q81392 wl:formalizedAs "MeasureTheory.dimH" .
wd:Q81392 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/MetricSpace/HausdorffDimension.html#MeasureTheory.dimH> .
wd:Q81392 wl:formalizedAs "NowhereDifferentiable.exists_uniformContinuous_and_not_differentiableAt" .
wd:Q81392 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Counterexamples/NowhereDifferentiable.html#NowhereDifferentiable.exists_uniformContinuous_and_not_differentiableAt> .
wd:Q81392 wl:formalizedAs "cantorSet" .
wd:Q81392 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Instances/CantorSet.html#cantorSet> .
wd:Q864475 wl:formalizedAs "CategoryTheory.Functor" .
wd:Q864475 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Functor/Basic.html#CategoryTheory.Functor> .
wd:Q864475 wl:formalizedAs "CategoryTheory.Functor.op" .
wd:Q864475 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Opposites.html#CategoryTheory.Functor.op> .
wd:Q864475 wl:formalizedAs "CategoryTheory.prod" .
wd:Q864475 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Products/Basic.html#CategoryTheory.prod> .
wd:Q864475 wl:formalizedAs "CategoryTheory.Functor.map_isIso" .
wd:Q864475 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Iso.html#CategoryTheory.Functor.map_isIso> .
wd:Q864475 wl:formalizedAs "CategoryTheory.Functor.comp" .
wd:Q864475 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Functor/Basic.html#CategoryTheory.Functor.comp> .
wd:Q864475 wl:formalizedAs "CategoryTheory.SingleObj" .
wd:Q864475 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/SingleObj.html#CategoryTheory.SingleObj> .
wd:Q864475 wl:formalizedAs "TopCat.Presheaf" .
wd:Q864475 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Sheaves/Presheaf.html#TopCat.Presheaf> .
wd:Q864475 wl:formalizedAs "CategoryTheory.Functor.const" .
wd:Q864475 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Functor/Const.html#CategoryTheory.Functor.const> .
wd:Q864475 wl:formalizedAs "CategoryTheory.Functor.id" .
wd:Q864475 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Functor/Basic.html#CategoryTheory.Functor.id> .
wd:Q864475 wl:formalizedAs "CategoryTheory.Functor.diag" .
wd:Q864475 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Products/Basic.html#CategoryTheory.Functor.diag> .
wd:Q864475 wl:formalizedAs "CategoryTheory.Limits.lim" .
wd:Q864475 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Limits/HasLimits.html#CategoryTheory.Limits.lim> .
wd:Q864475 wl:formalizedAs "CategoryTheory.MonoidalCategory.tensor" .
wd:Q864475 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Monoidal/Category.html#CategoryTheory.MonoidalCategory.tensor> .
wd:Q864475 wl:formalizedAs "CategoryTheory.forget" .
wd:Q864475 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/ConcreteCategory/Forget.html#CategoryTheory.forget> .
wd:Q864475 wl:formalizedAs "MonCat.free" .
wd:Q864475 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Category/MonCat/Adjunctions.html#MonCat.free> .
wd:Q864475 wl:formalizedAs "CategoryTheory.Functor.hom" .
wd:Q864475 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Functor/Hom.html#CategoryTheory.Functor.hom> .
wd:Q864475 wl:formalizedAs "CategoryTheory.Functor.IsRepresentable" .
wd:Q864475 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Yoneda.html#CategoryTheory.Functor.IsRepresentable> .
wd:Q864475 wl:formalizedAs "CategoryTheory.Functor.category" .
wd:Q864475 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Functor/Category.html#CategoryTheory.Functor.category> .
wd:Q44455 wl:formalizedAs "Sion.exists_isSaddlePointOn" .
wd:Q44455 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Sion.html#Sion.exists_isSaddlePointOn> .
wd:Q621550 wl:formalizedAs "TopologicalSpace" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Defs/Basic.html#TopologicalSpace> .
wd:Q621550 wl:formalizedAs "IsOpen" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Defs/Basic.html#IsOpen> .
wd:Q621550 wl:formalizedAs "TopologicalSpace.IsTopologicalBasis" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Bases.html#TopologicalSpace.IsTopologicalBasis> .
wd:Q621550 wl:formalizedAs "instTopologicalSpaceSubtype" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Constructions.html#instTopologicalSpaceSubtype> .
wd:Q621550 wl:formalizedAs "instTopologicalSpaceProd" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Constructions.html#instTopologicalSpaceProd> .
wd:Q621550 wl:formalizedAs "TopologicalSpace.coinduced" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Defs/Induced.html#TopologicalSpace.coinduced> .
wd:Q621550 wl:formalizedAs "DiscreteTopology" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Order.html#DiscreteTopology> .
wd:Q621550 wl:formalizedAs "IndiscreteTopology" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Order.html#IndiscreteTopology> .
wd:Q621550 wl:formalizedAs "CofiniteTopology" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Constructions.html#CofiniteTopology> .
wd:Q621550 wl:formalizedAs "Real.pseudoMetricSpace" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/MetricSpace/Pseudo/Defs.html#Real.pseudoMetricSpace> .
wd:Q621550 wl:formalizedAs "PseudoMetricSpace" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/MetricSpace/Pseudo/Defs.html#PseudoMetricSpace> .
wd:Q621550 wl:formalizedAs "PrimeSpectrum.zariskiTopology" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Spectrum/Prime/Topology.html#PrimeSpectrum.zariskiTopology> .
wd:Q621550 wl:formalizedAs "sierpinskiSpace" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Order.html#sierpinskiSpace> .
wd:Q621550 wl:formalizedAs "OrderTopology" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Order/Basic.html#OrderTopology> .
wd:Q621550 wl:formalizedAs "ContinuousAt" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Defs/Filter.html#ContinuousAt> .
wd:Q621550 wl:formalizedAs "continuous_of_discreteTopology" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Order.html#continuous_of_discreteTopology> .
wd:Q621550 wl:formalizedAs "continuousAt_def" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Continuous.html#continuousAt_def> .
wd:Q621550 wl:formalizedAs "Continuous.tendsto" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Continuous.html#Continuous.tendsto> .
wd:Q621550 wl:formalizedAs "SeqContinuous" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Defs/Sequences.html#SeqContinuous> .
wd:Q621550 wl:formalizedAs "Continuous.seqContinuous" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Sequences.html#Continuous.seqContinuous> .
wd:Q621550 wl:formalizedAs "continuous_iff_seqContinuous" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Sequences.html#continuous_iff_seqContinuous> .
wd:Q621550 wl:formalizedAs "continuous_iff_continuousAt" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Continuous.html#continuous_iff_continuousAt> .
wd:Q621550 wl:formalizedAs "closure" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Defs/Basic.html#closure> .
wd:Q621550 wl:formalizedAs "continuous_iff_image_closure_subset_closure_image" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Continuous.html#continuous_iff_image_closure_subset_closure_image> .
wd:Q621550 wl:formalizedAs "Continuous.comp" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Continuous.html#Continuous.comp> .
wd:Q621550 wl:formalizedAs "IsCompact.image" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Compactness/Compact.html#IsCompact.image> .
wd:Q621550 wl:formalizedAs "IsConnected.image" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Connected/Basic.html#IsConnected.image> .
wd:Q621550 wl:formalizedAs "IsPathConnected.image" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Connected/PathConnected.html#IsPathConnected.image> .
wd:Q621550 wl:formalizedAs "IsLindelof.image" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Compactness/Lindelof.html#IsLindelof.image> .
wd:Q621550 wl:formalizedAs "ContinuousOn.isSeparable_image" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/MetricSpace/Pseudo/Basic.html#ContinuousOn.isSeparable_image> .
wd:Q621550 wl:formalizedAs "TopologicalSpace.le_def" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Order.html#TopologicalSpace.le_def> .
wd:Q621550 wl:formalizedAs "continuous_id_iff_le" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Order.html#continuous_id_iff_le> .
wd:Q621550 wl:formalizedAs "IsOpenMap" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Maps/Basic.html#IsOpenMap> .
wd:Q621550 wl:formalizedAs "Homeomorph" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Homeomorph/Defs.html#Homeomorph> .
wd:Q621550 wl:formalizedAs "Continuous.homeoOfEquivCompactToT2" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Homeomorph/Lemmas.html#Continuous.homeoOfEquivCompactToT2> .
wd:Q621550 wl:formalizedAs "TopologicalSpace.induced" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Defs/Induced.html#TopologicalSpace.induced> .
wd:Q621550 wl:formalizedAs "CompactSpace" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Defs/Filter.html#CompactSpace> .
wd:Q621550 wl:formalizedAs "IsCompact" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Defs/Filter.html#IsCompact> .
wd:Q621550 wl:formalizedAs "isCompact_Icc" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Order/IsLUB.html#isCompact_Icc> .
wd:Q621550 wl:formalizedAs "isCompact_iff_isClosed_bounded" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/MetricSpace/Bounded.html#isCompact_iff_isClosed_bounded> .
wd:Q621550 wl:formalizedAs "IsCompact.isClosed" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Separation/Hausdorff.html#IsCompact.isClosed> .
wd:Q621550 wl:formalizedAs "IsCompact.tendsto_subseq" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Sequences.html#IsCompact.tendsto_subseq> .
wd:Q621550 wl:formalizedAs "exists_embedding_euclidean_of_compact" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Manifold/WhitneyEmbedding.html#exists_embedding_euclidean_of_compact> .
wd:Q621550 wl:formalizedAs "ConnectedSpace" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Connected/Basic.html#ConnectedSpace> .
wd:Q621550 wl:formalizedAs "isPreconnected_iff_subset_of_disjoint" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Connected/Clopen.html#isPreconnected_iff_subset_of_disjoint> .
wd:Q621550 wl:formalizedAs "isPreconnected_Icc" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Order/IntermediateValue.html#isPreconnected_Icc> .
wd:Q621550 wl:formalizedAs "IsPreconnected.image" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Connected/Basic.html#IsPreconnected.image> .
wd:Q621550 wl:formalizedAs "connectedComponent" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Connected/Basic.html#connectedComponent> .
wd:Q621550 wl:formalizedAs "connectedComponentSetoid" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Connected/Clopen.html#connectedComponentSetoid> .
wd:Q621550 wl:formalizedAs "TotallyDisconnectedSpace" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Connected/TotallyDisconnected.html#TotallyDisconnectedSpace> .
wd:Q621550 wl:formalizedAs "TotallySeparatedSpace" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Connected/TotallyDisconnected.html#TotallySeparatedSpace> .
wd:Q621550 wl:formalizedAs "TotallySeparatedSpace.totallyDisconnectedSpace" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Connected/TotallyDisconnected.html#TotallySeparatedSpace.totallyDisconnectedSpace> .
wd:Q621550 wl:formalizedAs "Path" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Path.html#Path> .
wd:Q621550 wl:formalizedAs "pathComponent" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Connected/PathConnected.html#pathComponent> .
wd:Q621550 wl:formalizedAs "PathConnectedSpace" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Connected/PathConnected.html#PathConnectedSpace> .
wd:Q621550 wl:formalizedAs "PathConnectedSpace.connectedSpace" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Connected/PathConnected.html#PathConnectedSpace.connectedSpace> .
wd:Q621550 wl:formalizedAs "Pi.topologicalSpace" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Constructions.html#Pi.topologicalSpace> .
wd:Q621550 wl:formalizedAs "IsTopologicalBasis.prod" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Bases.html#IsTopologicalBasis.prod> .
wd:Q621550 wl:formalizedAs "isCompact_pi_infinite" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Compactness/Compact.html#isCompact_pi_infinite> .
wd:Q621550 wl:formalizedAs "T0Space" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Separation/Basic.html#T0Space> .
wd:Q621550 wl:formalizedAs "T1Space" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Separation/Basic.html#T1Space> .
wd:Q621550 wl:formalizedAs "T2Space" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Separation/Hausdorff.html#T2Space> .
wd:Q621550 wl:formalizedAs "T25Space" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Separation/Hausdorff.html#T25Space> .
wd:Q621550 wl:formalizedAs "RegularSpace" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Separation/Regular.html#RegularSpace> .
wd:Q621550 wl:formalizedAs "CompletelyRegularSpace" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Separation/CompletelyRegular.html#CompletelyRegularSpace> .
wd:Q621550 wl:formalizedAs "NormalSpace" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Separation/Regular.html#NormalSpace> .
wd:Q621550 wl:formalizedAs "exists_continuous_zero_one_of_isClosed" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/UrysohnsLemma.html#exists_continuous_zero_one_of_isClosed> .
wd:Q621550 wl:formalizedAs "CompletelyNormalSpace" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Separation/Regular.html#CompletelyNormalSpace> .
wd:Q621550 wl:formalizedAs "PerfectlyNormalSpace" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Separation/GDelta.html#PerfectlyNormalSpace> .
wd:Q621550 wl:formalizedAs "ContinuousMap.exists_restrict_eq" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/TietzeExtension.html#ContinuousMap.exists_restrict_eq> .
wd:Q621550 wl:formalizedAs "SequentialSpace" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Defs/Sequences.html#SequentialSpace> .
wd:Q621550 wl:formalizedAs "FirstCountableTopology" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Bases.html#FirstCountableTopology> .
wd:Q621550 wl:formalizedAs "SecondCountableTopology" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Bases.html#SecondCountableTopology> .
wd:Q621550 wl:formalizedAs "SeparableSpace" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Bases.html#SeparableSpace> .
wd:Q621550 wl:formalizedAs "LindelofSpace" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Compactness/Lindelof.html#LindelofSpace> .
wd:Q621550 wl:formalizedAs "SigmaCompactSpace" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Compactness/SigmaCompact.html#SigmaCompactSpace> .
wd:Q621550 wl:formalizedAs "FirstCountableTopology.frechetUrysohnSpace" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Sequences.html#FirstCountableTopology.frechetUrysohnSpace> .
wd:Q621550 wl:formalizedAs "SecondCountableTopology.to_firstCountableTopology" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Bases.html#SecondCountableTopology.to_firstCountableTopology> .
wd:Q621550 wl:formalizedAs "IsSigmaCompact.isLindelof" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Compactness/Lindelof.html#IsSigmaCompact.isLindelof> .
wd:Q621550 wl:formalizedAs "UniformSpace.firstCountableTopology" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/UniformSpace/Cauchy.html#UniformSpace.firstCountableTopology> .
wd:Q621550 wl:formalizedAs "MetricSpace" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/MetricSpace/Defs.html#MetricSpace> .
wd:Q621550 wl:formalizedAs "EMetric.instParacompactSpace" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/EMetricSpace/Paracompact.html#EMetric.instParacompactSpace> .
wd:Q621550 wl:formalizedAs "metrizableSpace_of_t3_secondCountable" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Metrizable/Urysohn.html#metrizableSpace_of_t3_secondCountable> .
wd:Q621550 wl:formalizedAs "dense_sInter_of_isOpen" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Baire/Lemmas.html#dense_sInter_of_isOpen> .
wd:Q621550 wl:formalizedAs "IsOpen.baireSpace" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Baire/Lemmas.html#IsOpen.baireSpace> .
wd:Q621550 wl:formalizedAs "TopologicalSpace.MetrizableSpace" .
wd:Q621550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Metrizable/Basic.html#TopologicalSpace.MetrizableSpace> .
wd:Q213488 wl:formalizedAs "Manifold.pathELength" .
wd:Q213488 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Manifold/Riemannian/PathELength.html#Manifold.pathELength> .
wd:Q213488 wl:formalizedAs "Manifold.riemannianEDist" .
wd:Q213488 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Manifold/Riemannian/PathELength.html#Manifold.riemannianEDist> .
wd:Q2662474 wl:formalizedAs "SimpleGraph.mulCayley" .
wd:Q2662474 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Combinatorics/SimpleGraph/Cayley.html#SimpleGraph.mulCayley> .
wd:Q2662474 wl:formalizedAs "Int.instAddCommGroup" .
wd:Q2662474 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Int/Defs.html#Int.instAddCommGroup> .
wd:Q2662474 wl:formalizedAs "FreeGroup" .
wd:Q2662474 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/FreeGroup/Basic.html#FreeGroup> .
wd:Q2662474 wl:formalizedAs "Monoid.CoprodI" .
wd:Q2662474 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/CoprodI.html#Monoid.CoprodI> .
wd:Q2662474 wl:formalizedAs "Equiv.Perm" .
wd:Q2662474 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Logic/Equiv/Defs.html#Equiv.Perm> .
wd:Q2662474 wl:formalizedAs "CoxeterSystem" .
wd:Q2662474 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/Coxeter/Basic.html#CoxeterSystem> .
wd:Q8087 wl:formalizedAs "ChartedSpace" .
wd:Q8087 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Manifold/ChartedSpace.html#ChartedSpace> .
wd:Q8087 wl:formalizedAs "IsManifold" .
wd:Q8087 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Manifold/IsManifold/Basic.html#IsManifold> .
wd:Q8087 wl:formalizedAs "InnerProductGeometry.angle" .
wd:Q8087 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Euclidean/Angle/Unoriented/Basic.html#InnerProductGeometry.angle> .
wd:Q8087 wl:formalizedAs "EuclideanGeometry.angle" .
wd:Q8087 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Euclidean/Angle/Unoriented/Affine.html#EuclideanGeometry.angle> .
wd:Q8087 wl:formalizedAs "EuclideanSpace.dist_eq" .
wd:Q8087 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/InnerProductSpace/PiL2.html#EuclideanSpace.dist_eq> .
wd:Q8087 wl:formalizedAs "MetricSpace" .
wd:Q8087 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/MetricSpace/Defs.html#MetricSpace> .
wd:Q8087 wl:formalizedAs "MeasureTheory.Measure" .
wd:Q8087 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/MeasureTheory/Measure/MeasureSpaceDef.html#MeasureTheory.Measure> .
wd:Q8087 wl:formalizedAs "Similar" .
wd:Q8087 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/MetricSpace/Similarity.html#Similar> .
wd:Q8087 wl:formalizedAs "MvPolynomial.vanishingIdeal_zeroLocus_eq_radical" .
wd:Q8087 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Nullstellensatz.html#MvPolynomial.vanishingIdeal_zeroLocus_eq_radical> .
wd:Q8087 wl:formalizedAs "Convex" .
wd:Q8087 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Convex/Basic.html#Convex> .
wd:Q200787 wl:formalizedAs "FirstOrder.Language.Theory.IsComplete" .
wd:Q200787 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Satisfiability.html#FirstOrder.Language.Theory.IsComplete> .
wd:Q200787 wl:formalizedAs "FirstOrder.Field.ACF_isComplete" .
wd:Q200787 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Algebra/Field/IsAlgClosed.html#FirstOrder.Field.ACF_isComplete> .
wd:Q200787 wl:formalizedAs "Nat.Partrec.Code.halting_problem" .
wd:Q200787 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Computability/Halting.html#Nat.Partrec.Code.halting_problem> .
wd:Q504843 wl:formalizedAs "SimpleGraph.Coloring" .
wd:Q504843 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Combinatorics/SimpleGraph/Coloring/VertexColoring.html#SimpleGraph.Coloring> .
wd:Q504843 wl:formalizedAs "SimpleGraph.Colorable" .
wd:Q504843 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Combinatorics/SimpleGraph/Coloring/VertexColoring.html#SimpleGraph.Colorable> .
wd:Q504843 wl:formalizedAs "SimpleGraph.chromaticNumber" .
wd:Q504843 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Combinatorics/SimpleGraph/Coloring/VertexColoring.html#SimpleGraph.chromaticNumber> .
wd:Q504843 wl:formalizedAs "SimpleGraph.chromaticNumber_eq_iff_colorable_not_colorable" .
wd:Q504843 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Combinatorics/SimpleGraph/Coloring/VertexColoring.html#SimpleGraph.chromaticNumber_eq_iff_colorable_not_colorable> .
wd:Q504843 wl:formalizedAs "SimpleGraph.Coloring.colorClass" .
wd:Q504843 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Combinatorics/SimpleGraph/Coloring/VertexColoring.html#SimpleGraph.Coloring.colorClass> .
wd:Q504843 wl:formalizedAs "SimpleGraph.partitionable_iff_colorable" .
wd:Q504843 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Combinatorics/SimpleGraph/Partition.html#SimpleGraph.partitionable_iff_colorable> .
wd:Q504843 wl:formalizedAs "SimpleGraph.chromaticNumber_le_card" .
wd:Q504843 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Combinatorics/SimpleGraph/Coloring/VertexColoring.html#SimpleGraph.chromaticNumber_le_card> .
wd:Q504843 wl:formalizedAs "SimpleGraph.chromaticNumber_eq_one_iff" .
wd:Q504843 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Combinatorics/SimpleGraph/Coloring/VertexColoring.html#SimpleGraph.chromaticNumber_eq_one_iff> .
wd:Q504843 wl:formalizedAs "SimpleGraph.chromaticNumber_top" .
wd:Q504843 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Combinatorics/SimpleGraph/Coloring/VertexColoring.html#SimpleGraph.chromaticNumber_top> .
wd:Q504843 wl:formalizedAs "SimpleGraph.isBipartite_iff_exists_isBipartiteWith" .
wd:Q504843 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Combinatorics/SimpleGraph/Bipartite.html#SimpleGraph.isBipartite_iff_exists_isBipartiteWith> .
wd:Q504843 wl:formalizedAs "SimpleGraph.IsClique.card_le_chromaticNumber" .
wd:Q504843 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Combinatorics/SimpleGraph/Coloring/VertexColoring.html#SimpleGraph.IsClique.card_le_chromaticNumber> .
wd:Q504843 wl:formalizedAs "SimpleGraph.nonempty_hom_of_forall_finite_subgraph_hom" .
wd:Q504843 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Combinatorics/SimpleGraph/Finsubgraph.html#SimpleGraph.nonempty_hom_of_forall_finite_subgraph_hom> .
wd:Q131476 wl:formalizedAs "SimpleGraph" .
wd:Q131476 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Combinatorics/SimpleGraph/Basic.html#SimpleGraph> .
wd:Q131476 wl:formalizedAs "Quiver" .
wd:Q131476 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Combinatorics/Quiver/Basic.html#Quiver> .
wd:Q131476 wl:formalizedAs "Graph" .
wd:Q131476 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Combinatorics/Graph/Basic.html#Graph> .
wd:Q131476 wl:formalizedAs "SimpleGraph.Coloring" .
wd:Q131476 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Combinatorics/SimpleGraph/Coloring/VertexColoring.html#SimpleGraph.Coloring> .
wd:Q131476 wl:formalizedAs "SimpleGraph.isTuranMaximal_iff_nonempty_iso_turanGraph" .
wd:Q131476 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Combinatorics/SimpleGraph/Extremal/Turan.html#SimpleGraph.isTuranMaximal_iff_nonempty_iso_turanGraph> .
wd:Q131476 wl:formalizedAs "SimpleGraph.szemeredi_regularity" .
wd:Q131476 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Combinatorics/SimpleGraph/Regularity/Lemma.html#SimpleGraph.szemeredi_regularity> .
wd:Q131476 wl:formalizedAs "SimpleGraph.IsTree" .
wd:Q131476 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Combinatorics/SimpleGraph/Acyclic.html#SimpleGraph.IsTree> .
wd:Q131476 wl:formalizedAs "SimpleGraph.incMatrix" .
wd:Q131476 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Combinatorics/SimpleGraph/IncMatrix.html#SimpleGraph.incMatrix> .
wd:Q131476 wl:formalizedAs "SimpleGraph.adjMatrix" .
wd:Q131476 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Combinatorics/SimpleGraph/AdjMatrix.html#SimpleGraph.adjMatrix> .
wd:Q131476 wl:formalizedAs "SimpleGraph.degMatrix" .
wd:Q131476 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Combinatorics/SimpleGraph/LapMatrix.html#SimpleGraph.degMatrix> .
wd:Q131476 wl:formalizedAs "SimpleGraph.lapMatrix" .
wd:Q131476 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Combinatorics/SimpleGraph/LapMatrix.html#SimpleGraph.lapMatrix> .
wd:Q131752 wl:formalizedAs "GCDMonoid.gcd" .
wd:Q131752 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/GCDMonoid/Basic.html#GCDMonoid.gcd> .
wd:Q131752 wl:formalizedAs "Nat.gcd" .
wd:Q131752 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Tactic/NormNum/GCD.html#Nat.gcd> .
wd:Q131752 wl:formalizedAs "Int.gcd" .
wd:Q131752 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Int/GCD.html#Int.gcd> .
wd:Q131752 wl:formalizedAs "EuclideanDomain.gcd_zero_right" .
wd:Q131752 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/EuclideanDomain/Basic.html#EuclideanDomain.gcd_zero_right> .
wd:Q131752 wl:formalizedAs "gcd_eq_zero_iff" .
wd:Q131752 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/GCDMonoid/Basic.html#gcd_eq_zero_iff> .
wd:Q131752 wl:formalizedAs "dvd_gcd_iff" .
wd:Q131752 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/GCDMonoid/Basic.html#dvd_gcd_iff> .
wd:Q131752 wl:formalizedAs "Nat.Coprime" .
wd:Q131752 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/GCD/Basic.html#Nat.Coprime> .
wd:Q131752 wl:formalizedAs "Nat.gcd_mul_lcm" .
wd:Q131752 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/GCDMonoid/Nat.html#Nat.gcd_mul_lcm> .
wd:Q131752 wl:formalizedAs "Nat.factorization_gcd" .
wd:Q131752 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/Factorization/Basic.html#Nat.factorization_gcd> .
wd:Q131752 wl:formalizedAs "Nat.gcd_sub_self_left" .
wd:Q131752 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/GCD/Basic.html#Nat.gcd_sub_self_left> .
wd:Q131752 wl:formalizedAs "EuclideanDomain.gcd_val" .
wd:Q131752 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/EuclideanDomain/Basic.html#EuclideanDomain.gcd_val> .
wd:Q131752 wl:formalizedAs "EuclideanDomain.gcd_self" .
wd:Q131752 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/EuclideanDomain/Basic.html#EuclideanDomain.gcd_self> .
wd:Q131752 wl:formalizedAs "Int.gcd_eq_gcd_ab" .
wd:Q131752 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Int/GCD.html#Int.gcd_eq_gcd_ab> .
wd:Q131752 wl:formalizedAs "IsCoprime.dvd_of_dvd_mul_right" .
wd:Q131752 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Coprime/Basic.html#IsCoprime.dvd_of_dvd_mul_right> .
wd:Q131752 wl:formalizedAs "Nat.gcd_mul_left" .
wd:Q131752 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/GCD/Basic.html#Nat.gcd_mul_left> .
wd:Q131752 wl:formalizedAs "Nat.gcd_add_mul_right_left" .
wd:Q131752 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/GCD/Basic.html#Nat.gcd_add_mul_right_left> .
wd:Q131752 wl:formalizedAs "Nat.gcd_div" .
wd:Q131752 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/GCD/Basic.html#Nat.gcd_div> .
wd:Q131752 wl:formalizedAs "Nat.coprime_div_gcd_div_gcd" .
wd:Q131752 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/GCD/Basic.html#Nat.coprime_div_gcd_div_gcd> .
wd:Q131752 wl:formalizedAs "gcd_comm" .
wd:Q131752 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/GCDMonoid/Basic.html#gcd_comm> .
wd:Q131752 wl:formalizedAs "gcd_assoc" .
wd:Q131752 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/GCDMonoid/Basic.html#gcd_assoc> .
wd:Q131752 wl:formalizedAs "Nat.Coprime.gcd_mul" .
wd:Q131752 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/GCD/Basic.html#Nat.Coprime.gcd_mul> .
wd:Q131752 wl:formalizedAs "gcd_mul_lcm" .
wd:Q131752 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/GCDMonoid/Basic.html#gcd_mul_lcm> .
wd:Q131752 wl:formalizedAs "Nat.totient_gcd_mul_totient_mul" .
wd:Q131752 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/Totient.html#Nat.totient_gcd_mul_totient_mul> .
wd:Q131752 wl:formalizedAs "GCDMonoid" .
wd:Q131752 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/GCDMonoid/Basic.html#GCDMonoid> .
wd:Q131752 wl:formalizedAs "UniqueFactorizationMonoid.toGCDMonoid" .
wd:Q131752 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/UniqueFactorizationDomain/GCDMonoid.html#UniqueFactorizationMonoid.toGCDMonoid> .
wd:Q131752 wl:formalizedAs "EuclideanDomain.gcd" .
wd:Q131752 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/EuclideanDomain/Defs.html#EuclideanDomain.gcd> .
wd:Q131752 wl:formalizedAs "span_gcd" .
wd:Q131752 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/PrincipalIdealDomain.html#span_gcd> .
wd:Q288465 wl:formalizedAs "MulAction" .
wd:Q288465 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Action/Defs.html#MulAction> .
wd:Q288465 wl:formalizedAs "Representation" .
wd:Q288465 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RepresentationTheory/Basic.html#Representation> .
wd:Q288465 wl:formalizedAs "Equiv.Perm.applyMulAction" .
wd:Q288465 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Action/End.html#Equiv.Perm.applyMulAction> .
wd:Q288465 wl:formalizedAs "FaithfulSMul" .
wd:Q288465 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Action/Faithful.html#FaithfulSMul> .
wd:Q288465 wl:formalizedAs "MulAction.IsPretransitive" .
wd:Q288465 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Action/Pretransitive.html#MulAction.IsPretransitive> .
wd:Q288465 wl:formalizedAs "MulAction.IsMultiplyPretransitive" .
wd:Q288465 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/GroupAction/MultipleTransitivity.html#MulAction.IsMultiplyPretransitive> .
wd:Q288465 wl:formalizedAs "Equiv.Perm.isMultiplyPretransitive" .
wd:Q288465 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/GroupAction/MultipleTransitivity.html#Equiv.Perm.isMultiplyPretransitive> .
wd:Q288465 wl:formalizedAs "MulAction.IsPreprimitive" .
wd:Q288465 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/GroupAction/Primitive.html#MulAction.IsPreprimitive> .
wd:Q288465 wl:formalizedAs "ProperlyDiscontinuousSMul" .
wd:Q288465 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Algebra/ConstMulAction.html#ProperlyDiscontinuousSMul> .
wd:Q288465 wl:formalizedAs "ContinuousSMul" .
wd:Q288465 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Algebra/MulAction.html#ContinuousSMul> .
wd:Q288465 wl:formalizedAs "ProperSMul" .
wd:Q288465 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Algebra/ProperAction/Basic.html#ProperSMul> .
wd:Q288465 wl:formalizedAs "IsSemisimpleRepresentation" .
wd:Q288465 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RepresentationTheory/Semisimple.html#IsSemisimpleRepresentation> .
wd:Q288465 wl:formalizedAs "MulAction.orbit" .
wd:Q288465 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/GroupAction/Defs.html#MulAction.orbit> .
wd:Q288465 wl:formalizedAs "MulAction.orbitRel" .
wd:Q288465 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/GroupAction/Defs.html#MulAction.orbitRel> .
wd:Q288465 wl:formalizedAs "MulAction.pretransitive_iff_subsingleton_quotient" .
wd:Q288465 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/GroupAction/Basic.html#MulAction.pretransitive_iff_subsingleton_quotient> .
wd:Q288465 wl:formalizedAs "MulAction.orbitRel.Quotient" .
wd:Q288465 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/GroupAction/Defs.html#MulAction.orbitRel.Quotient> .
wd:Q288465 wl:formalizedAs "MulAction.IsInvariantBlock" .
wd:Q288465 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/GroupAction/Blocks.html#MulAction.IsInvariantBlock> .
wd:Q288465 wl:formalizedAs "MulAction.IsFixedBlock.orbit" .
wd:Q288465 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/GroupAction/Blocks.html#MulAction.IsFixedBlock.orbit> .
wd:Q288465 wl:formalizedAs "MulAction.fixedPoints" .
wd:Q288465 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/GroupAction/Defs.html#MulAction.fixedPoints> .
wd:Q288465 wl:formalizedAs "MulAction.fixedBy" .
wd:Q288465 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/GroupAction/Defs.html#MulAction.fixedBy> .
wd:Q288465 wl:formalizedAs "MulAction.stabilizer" .
wd:Q288465 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/GroupAction/Defs.html#MulAction.stabilizer> .
wd:Q288465 wl:formalizedAs "MulAction.stabilizer_smul_eq_stabilizer_map_conj" .
wd:Q288465 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/GroupAction/Basic.html#MulAction.stabilizer_smul_eq_stabilizer_map_conj> .
wd:Q288465 wl:formalizedAs "MulAction.orbitEquivQuotientStabilizer" .
wd:Q288465 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/GroupAction/Quotient.html#MulAction.orbitEquivQuotientStabilizer> .
wd:Q288465 wl:formalizedAs "MulAction.sum_card_fixedBy_eq_card_orbits_mul_card_group" .
wd:Q288465 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/GroupAction/Quotient.html#MulAction.sum_card_fixedBy_eq_card_orbits_mul_card_group> .
wd:Q288465 wl:formalizedAs "Monoid.toMulAction" .
wd:Q288465 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Action/Defs.html#Monoid.toMulAction> .
wd:Q288465 wl:formalizedAs "MulAction.quotient" .
wd:Q288465 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/GroupAction/Quotient.html#MulAction.quotient> .
wd:Q288465 wl:formalizedAs "ConjAct" .
wd:Q288465 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/GroupAction/ConjAct.html#ConjAct> .
wd:Q288465 wl:formalizedAs "Units.instMulAction" .
wd:Q288465 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Action/Units.html#Units.instMulAction> .
wd:Q288465 wl:formalizedAs "LinearEquiv.applyDistribMulAction" .
wd:Q288465 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Module/Equiv/Basic.html#LinearEquiv.applyDistribMulAction> .
wd:Q288465 wl:formalizedAs "CategoryTheory.Action" .
wd:Q288465 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Action/Basic.html#CategoryTheory.Action> .
wd:Q288465 wl:formalizedAs "AlgEquiv.applyMulSemiringAction" .
wd:Q288465 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Algebra/Equiv.html#AlgEquiv.applyMulSemiringAction> .
wd:Q288465 wl:formalizedAs "Flow" .
wd:Q288465 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Dynamics/Flow.html#Flow> .
wd:Q288465 wl:formalizedAs "Set.mulAction" .
wd:Q288465 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Action/Pointwise/Set/Basic.html#Set.mulAction> .
wd:Q288465 wl:formalizedAs "CategoryTheory.ActionCategory" .
wd:Q288465 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Action.html#CategoryTheory.ActionCategory> .
wd:Q288465 wl:formalizedAs "MulActionHom" .
wd:Q288465 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/GroupAction/Hom.html#MulActionHom> .
wd:Q288465 wl:formalizedAs "CategoryTheory.actionAsFunctor" .
wd:Q288465 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Action.html#CategoryTheory.actionAsFunctor> .
wd:Q1055807 wl:formalizedAs "Action.ρAut" .
wd:Q1055807 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Action/Basic.html#Action.ρAut> .
wd:Q1055807 wl:formalizedAs "Representation" .
wd:Q1055807 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RepresentationTheory/Basic.html#Representation> .
wd:Q1055807 wl:formalizedAs "Action.IsContinuous" .
wd:Q1055807 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Action/Continuous.html#Action.IsContinuous> .
wd:Q1055807 wl:formalizedAs "MonoidHom.ker" .
wd:Q1055807 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Subgroup/Ker.html#MonoidHom.ker> .
wd:Q1055807 wl:formalizedAs "Representation.IntertwiningMap" .
wd:Q1055807 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RepresentationTheory/Intertwining.html#Representation.IntertwiningMap> .
wd:Q1055807 wl:formalizedAs "Representation.Equiv" .
wd:Q1055807 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RepresentationTheory/Intertwining.html#Representation.Equiv> .
wd:Q1055807 wl:formalizedAs "Subrepresentation" .
wd:Q1055807 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RepresentationTheory/Subrepresentation.html#Subrepresentation> .
wd:Q1055807 wl:formalizedAs "Representation.IsIrreducible" .
wd:Q1055807 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RepresentationTheory/Irreducible.html#Representation.IsIrreducible> .
wd:Q1055807 wl:formalizedAs "Representation.IsSemisimpleRepresentation" .
wd:Q1055807 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RepresentationTheory/Semisimple.html#Representation.IsSemisimpleRepresentation> .
wd:Q1055807 wl:formalizedAs "MulAction" .
wd:Q1055807 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Action/Defs.html#MulAction> .
wd:Q1055807 wl:formalizedAs "MulAction.bijective" .
wd:Q1055807 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Action/Basic.html#MulAction.bijective> .
wd:Q1055807 wl:formalizedAs "Action.functorCategoryEquivalence" .
wd:Q1055807 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Action/Basic.html#Action.functorCategoryEquivalence> .
wd:Q1055807 wl:formalizedAs "Rep" .
wd:Q1055807 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RepresentationTheory/Rep/Basic.html#Rep> .
wd:Q326908 wl:formalizedAs "SeparatedNhds" .
wd:Q326908 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Separation/SeparatedNhds.html#SeparatedNhds> .
wd:Q326908 wl:formalizedAs "T2Space" .
wd:Q326908 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Separation/Hausdorff.html#T2Space> .
wd:Q326908 wl:formalizedAs "R1Space" .
wd:Q326908 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Separation/Basic.html#R1Space> .
wd:Q326908 wl:formalizedAs "R1Space.t2Space_iff_t0Space" .
wd:Q326908 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Separation/Hausdorff.html#R1Space.t2Space_iff_t0Space> .
wd:Q326908 wl:formalizedAs "SeparationQuotient.t2Space_iff" .
wd:Q326908 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Separation/Hausdorff.html#SeparationQuotient.t2Space_iff> .
wd:Q326908 wl:formalizedAs "t2_iff_isClosed_diagonal" .
wd:Q326908 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Separation/Hausdorff.html#t2_iff_isClosed_diagonal> .
wd:Q326908 wl:formalizedAs "t2Space_of_metrizableSpace" .
wd:Q326908 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Metrizable/Basic.html#t2Space_of_metrizableSpace> .
wd:Q326908 wl:formalizedAs "CofiniteTopology.instT1Space" .
wd:Q326908 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Separation/Basic.html#CofiniteTopology.instT1Space> .
wd:Q326908 wl:formalizedAs "PseudoMetrizableSpace.regularSpace" .
wd:Q326908 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Metrizable/Basic.html#PseudoMetrizableSpace.regularSpace> .
wd:Q326908 wl:formalizedAs "Prod.t2Space" .
wd:Q326908 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Separation/Hausdorff.html#Prod.t2Space> .
wd:Q326908 wl:formalizedAs "T2Space.t1Space" .
wd:Q326908 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Separation/Hausdorff.html#T2Space.t1Space> .
wd:Q326908 wl:formalizedAs "R1Space.instR0Space" .
wd:Q326908 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Separation/Basic.html#R1Space.instR0Space> .
wd:Q326908 wl:formalizedAs "R1Space.quasiSober" .
wd:Q326908 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Sober.html#R1Space.quasiSober> .
wd:Q326908 wl:formalizedAs "IsCompact.isClosed" .
wd:Q326908 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Separation/Hausdorff.html#IsCompact.isClosed> .
wd:Q326908 wl:formalizedAs "SeparatedNhds.of_isCompact_isCompact" .
wd:Q326908 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Separation/Hausdorff.html#SeparatedNhds.of_isCompact_isCompact> .
wd:Q326908 wl:formalizedAs "NormalSpace.of_compactSpace_r1Space" .
wd:Q326908 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Separation/Regular.html#NormalSpace.of_compactSpace_r1Space> .
wd:Q326908 wl:formalizedAs "t2Space_iff_of_isOpenQuotientMap" .
wd:Q326908 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Separation/Hausdorff.html#t2Space_iff_of_isOpenQuotientMap> .
wd:Q326908 wl:formalizedAs "isClosed_eq" .
wd:Q326908 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Separation/Hausdorff.html#isClosed_eq> .
wd:Q326908 wl:formalizedAs "Continuous.ext_on" .
wd:Q326908 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Separation/Hausdorff.html#Continuous.ext_on> .
wd:Q326908 wl:formalizedAs "T2Space.r1Space" .
wd:Q326908 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Separation/Hausdorff.html#T2Space.r1Space> .
wd:Q326908 wl:formalizedAs "instRegularSpaceOfWeaklyLocallyCompactSpaceOfR1Space" .
wd:Q326908 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Separation/Regular.html#instRegularSpaceOfWeaklyLocallyCompactSpaceOfR1Space> .
wd:Q326908 wl:formalizedAs "CompleteSpace" .
wd:Q326908 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/UniformSpace/Cauchy.html#CompleteSpace> .
wd:Q326908 wl:formalizedAs "ContinuousMap.instCommCStarAlgebra" .
wd:Q326908 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/CStarAlgebra/ContinuousMap.html#ContinuousMap.instCommCStarAlgebra> .
wd:Q273167 wl:formalizedAs "MeasureTheory.IsProbabilityMeasure" .
wd:Q273167 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/MeasureTheory/Measure/Typeclasses/Probability.html#MeasureTheory.IsProbabilityMeasure> .
wd:Q273167 wl:formalizedAs "RiemannHypothesis" .
wd:Q273167 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/LSeries/RiemannZeta.html#RiemannHypothesis> .
wd:Q5018842 wl:formalizedAs "left_distrib" .
wd:Q5018842 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Ring/Defs.html#left_distrib> .
wd:Q5018842 wl:formalizedAs "mul_comm" .
wd:Q5018842 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Defs.html#mul_comm> .
wd:Q5018842 wl:formalizedAs "mul_self_sub_mul_self" .
wd:Q5018842 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Ring/Commute.html#mul_self_sub_mul_self> .
wd:Q5018842 wl:formalizedAs "add_sq" .
wd:Q5018842 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Ring/Defs.html#add_sq> .
wd:Q5018842 wl:formalizedAs "Nat.chineseRemainder" .
wd:Q5018842 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/ChineseRemainder.html#Nat.chineseRemainder> .
wd:Q5018842 wl:formalizedAs "Polynomial" .
wd:Q5018842 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Polynomial/Basic.html#Polynomial> .
wd:Q5018842 wl:formalizedAs "sq_add_sq_mul" .
wd:Q5018842 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/SumTwoSquares.html#sq_add_sq_mul> .
wd:Q5018842 wl:formalizedAs "quadratic_eq_zero_iff" .
wd:Q5018842 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/QuadraticDiscriminant.html#quadratic_eq_zero_iff> .
wd:Q5018842 wl:formalizedAs "PythagoreanTriple" .
wd:Q5018842 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/PythagoreanTriples.html#PythagoreanTriple> .
wd:Q5018842 wl:formalizedAs "Pell.IsFundamental.eq_zpow_or_neg_zpow" .
wd:Q5018842 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/Pell.html#Pell.IsFundamental.eq_zpow_or_neg_zpow> .
wd:Q5018842 wl:formalizedAs "quadratic_ne_zero_of_discrim_ne_sq" .
wd:Q5018842 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/QuadraticDiscriminant.html#quadratic_ne_zero_of_discrim_ne_sq> .
wd:Q5018842 wl:formalizedAs "Matrix.det" .
wd:Q5018842 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Matrix/Determinant/Basic.html#Matrix.det> .
wd:Q5018842 wl:formalizedAs "Complex.exists_root" .
wd:Q5018842 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Complex/Polynomial/Basic.html#Complex.exists_root> .
wd:Q5018842 wl:formalizedAs "isSolvable_gal_of_irreducible" .
wd:Q5018842 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/FieldTheory/AbelRuffini.html#isSolvable_gal_of_irreducible> .
wd:Q5018842 wl:formalizedAs "intermediateFieldEquivSubgroup" .
wd:Q5018842 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/FieldTheory/Galois/Basic.html#intermediateFieldEquivSubgroup> .
wd:Q2393733 wl:formalizedAs "EuclideanGeometry.dist_sq_eq_dist_sq_add_dist_sq_iff_angle_eq_pi_div_two" .
wd:Q2393733 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Euclidean/Angle/Unoriented/RightAngle.html#EuclideanGeometry.dist_sq_eq_dist_sq_add_dist_sq_iff_angle_eq_pi_div_two> .
wd:Q3893386 wl:formalizedAs "InnerProductGeometry.norm_add_sq_eq_norm_sq_add_norm_sq&#x27;" .
wd:Q3893386 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Euclidean/Angle/Unoriented/RightAngle.html#InnerProductGeometry.norm_add_sq_eq_norm_sq_add_norm_sq'> .
wd:Q3893386 wl:formalizedAs "Nat.Prime.dvd_mul" .
wd:Q3893386 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/Prime/Defs.html#Nat.Prime.dvd_mul> .
wd:Q3893386 wl:formalizedAs "Nat.fib" .
wd:Q3893386 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/Fib/Basic.html#Nat.fib> .
wd:Q3893386 wl:formalizedAs "Matrix.cramer" .
wd:Q3893386 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Matrix/Adjugate.html#Matrix.cramer> .
wd:Q3893386 wl:formalizedAs "Field" .
wd:Q3893386 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Field/Defs.html#Field> .
wd:Q3893386 wl:formalizedAs "Cardinal.aleph" .
wd:Q3893386 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Aleph.html#Cardinal.aleph> .
wd:Q185264 wl:formalizedAs "norm_add_sq_eq_norm_sq_add_norm_sq_iff_angle_eq_pi_div_two" .
wd:Q185264 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Euclidean/Angle/Unoriented/RightAngle.html#norm_add_sq_eq_norm_sq_add_norm_sq_iff_angle_eq_pi_div_two> .
wd:Q185264 wl:formalizedAs "Nat.Perfect" .
wd:Q185264 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/Divisors.html#Nat.Perfect> .
wd:Q185264 wl:formalizedAs "quadratic_eq_zero_iff" .
wd:Q185264 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/QuadraticDiscriminant.html#quadratic_eq_zero_iff> .
wd:Q185264 wl:formalizedAs "EuclideanGeometry.thales_theorem" .
wd:Q185264 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Euclidean/Angle/Sphere.html#EuclideanGeometry.thales_theorem> .
wd:Q185264 wl:formalizedAs "irrational_sqrt_two" .
wd:Q185264 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/Real/Irrational.html#irrational_sqrt_two> .
wd:Q185264 wl:formalizedAs "Nat.exists_infinite_primes" .
wd:Q185264 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/Prime/Infinite.html#Nat.exists_infinite_primes> .
wd:Q185264 wl:formalizedAs "EuclideanGeometry.mul_dist_add_mul_dist_eq_mul_dist_of_cospherical" .
wd:Q185264 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Euclidean/Sphere/Ptolemy.html#EuclideanGeometry.mul_dist_add_mul_dist_eq_mul_dist_of_cospherical> .
wd:Q185264 wl:formalizedAs "Nat.choose_succ_succ" .
wd:Q185264 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/Choose/Basic.html#Nat.choose_succ_succ> .
wd:Q185264 wl:formalizedAs "add_pow" .
wd:Q185264 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/Choose/Sum.html#add_pow> .
wd:Q185264 wl:formalizedAs "Nat.fib" .
wd:Q185264 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/Fib/Basic.html#Nat.fib> .
wd:Q185264 wl:formalizedAs "Real.sin" .
wd:Q185264 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.html#Real.sin> .
wd:Q185264 wl:formalizedAs "Zsqrtd.norm_mul" .
wd:Q185264 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/Zsqrtd/Basic.html#Zsqrtd.norm_mul> .
wd:Q185264 wl:formalizedAs "exists_hasDerivAt_eq_slope" .
wd:Q185264 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/Deriv/MeanValue.html#exists_hasDerivAt_eq_slope> .
wd:Q185264 wl:formalizedAs "Pell.exists_of_not_isSquare" .
wd:Q185264 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/Pell.html#Pell.exists_of_not_isSquare> .
wd:Q185264 wl:formalizedAs "Real.tendsto_sum_pi_div_four" .
wd:Q185264 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Real/Pi/Leibniz.html#Real.tendsto_sum_pi_div_four> .
wd:Q185264 wl:formalizedAs "Real.hasSum_arctan" .
wd:Q185264 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Complex/Arctan.html#Real.hasSum_arctan> .
wd:Q185264 wl:formalizedAs "Real.hasSum_cos" .
wd:Q185264 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Trigonometric/Series.html#Real.hasSum_cos> .
wd:Q185264 wl:formalizedAs "Real.cos_eq_tsum" .
wd:Q185264 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Trigonometric/Series.html#Real.cos_eq_tsum> .
wd:Q185264 wl:formalizedAs "Complex" .
wd:Q185264 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Complex/Basic.html#Complex> .
wd:Q185264 wl:formalizedAs "Complex.I" .
wd:Q185264 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Complex/Basic.html#Complex.I> .
wd:Q185264 wl:formalizedAs "Complex.exists_root" .
wd:Q185264 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Complex/Polynomial/Basic.html#Complex.exists_root> .
wd:Q185264 wl:formalizedAs "legendreSym.quadratic_reciprocity" .
wd:Q185264 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/LegendreSymbol/QuadraticReciprocity.html#legendreSym.quadratic_reciprocity> .
wd:Q185264 wl:formalizedAs "ChartedSpace" .
wd:Q185264 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Manifold/ChartedSpace.html#ChartedSpace> .
wd:Q185264 wl:formalizedAs "Module" .
wd:Q185264 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Module/Defs.html#Module> .
wd:Q185264 wl:formalizedAs "Quaternion" .
wd:Q185264 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Quaternion.html#Quaternion> .
wd:Q185264 wl:formalizedAs "BooleanAlgebra" .
wd:Q185264 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/BooleanAlgebra/Defs.html#BooleanAlgebra> .
wd:Q185264 wl:formalizedAs "isSolvable_gal_of_irreducible" .
wd:Q185264 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/FieldTheory/AbelRuffini.html#isSolvable_gal_of_irreducible> .
wd:Q185264 wl:formalizedAs "ZFSet" .
wd:Q185264 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/ZFC/Basic.html#ZFSet> .
wd:Q185264 wl:formalizedAs "Padic" .
wd:Q185264 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/Padics/PadicNumbers.html#Padic> .
wd:Q185264 wl:formalizedAs "MeasureTheory.IsProbabilityMeasure" .
wd:Q185264 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/MeasureTheory/Measure/Typeclasses/Probability.html#MeasureTheory.IsProbabilityMeasure> .
wd:Q185264 wl:formalizedAs "MeasureTheory.lintegral" .
wd:Q185264 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/MeasureTheory/Integral/Lebesgue/Basic.html#MeasureTheory.lintegral> .
wd:Q185264 wl:formalizedAs "Hyperreal" .
wd:Q185264 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Real/Hyperreal.html#Hyperreal> .
wd:Q185264 wl:formalizedAs "LucasLehmer.lucas_lehmer_sufficiency" .
wd:Q185264 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/LucasLehmer.html#LucasLehmer.lucas_lehmer_sufficiency> .
wd:Q5870804 wl:formalizedAs "Differentiable" .
wd:Q5870804 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/FDeriv/Defs.html#Differentiable> .
wd:Q5870804 wl:formalizedAs "Continuous" .
wd:Q5870804 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Defs/Basic.html#Continuous> .
wd:Q5870804 wl:formalizedAs "BooleanRing" .
wd:Q5870804 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Ring/BooleanRing.html#BooleanRing> .
wd:Q5870804 wl:formalizedAs "Classical.epsilon" .
wd:Q5870804 wl:formalizedAs "Partrec" .
wd:Q5870804 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Computability/Partrec.html#Partrec> .
wd:Q5870804 wl:formalizedAs "halting_problem" .
wd:Q5870804 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Computability/Halting.html#halting_problem> .
wd:Q5870804 wl:formalizedAs "ZFSet.sep" .
wd:Q5870804 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/ZFC/Basic.html#ZFSet.sep> .
wd:Q5870804 wl:formalizedAs "ZFSet.pair" .
wd:Q5870804 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/ZFC/Basic.html#ZFSet.pair> .
wd:Q5887297 wl:formalizedAs "CategoryTheory.LocallySmall" .
wd:Q5887297 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/EssentiallySmall.html#CategoryTheory.LocallySmall> .
wd:Q5887297 wl:formalizedAs "CategoryTheory.coyoneda" .
wd:Q5887297 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Yoneda.html#CategoryTheory.coyoneda> .
wd:Q5887297 wl:formalizedAs "CategoryTheory.yoneda" .
wd:Q5887297 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Yoneda.html#CategoryTheory.yoneda> .
wd:Q5887297 wl:formalizedAs "CategoryTheory.Functor.hom" .
wd:Q5887297 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Functor/Hom.html#CategoryTheory.Functor.hom> .
wd:Q5887297 wl:formalizedAs "CategoryTheory.yonedaEquiv" .
wd:Q5887297 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Yoneda.html#CategoryTheory.yonedaEquiv> .
wd:Q5887297 wl:formalizedAs "CategoryTheory.MonoidalClosed.internalHom" .
wd:Q5887297 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Monoidal/Closed/Basic.html#CategoryTheory.MonoidalClosed.internalHom> .
wd:Q5887297 wl:formalizedAs "CategoryTheory.MonoidalClosed" .
wd:Q5887297 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Monoidal/Closed/Basic.html#CategoryTheory.MonoidalClosed> .
wd:Q5887297 wl:formalizedAs "CategoryTheory.ihom.adjunction" .
wd:Q5887297 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Monoidal/Closed/Basic.html#CategoryTheory.ihom.adjunction> .
wd:Q5887297 wl:formalizedAs "CategoryTheory.ihom" .
wd:Q5887297 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Monoidal/Closed/Basic.html#CategoryTheory.ihom> .
wd:Q5887297 wl:formalizedAs "CategoryTheory.Functor.IsRepresentable" .
wd:Q5887297 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Yoneda.html#CategoryTheory.Functor.IsRepresentable> .
wd:Q5887297 wl:formalizedAs "CategoryTheory.Profunctor.id" .
wd:Q5887297 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Profunctor/Basic.html#CategoryTheory.Profunctor.id> .
wd:Q5887297 wl:formalizedAs "CategoryTheory.Adjunction.rightAdjoint_preservesLimits" .
wd:Q5887297 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Adjunction/Limits.html#CategoryTheory.Adjunction.rightAdjoint_preservesLimits> .
wd:Q5887297 wl:formalizedAs "CategoryTheory.projective_iff_preservesEpimorphisms_coyoneda_obj" .
wd:Q5887297 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Preadditive/Projective/Basic.html#CategoryTheory.projective_iff_preservesEpimorphisms_coyoneda_obj> .
wd:Q5887297 wl:formalizedAs "TensorProduct.lift.equiv" .
wd:Q5887297 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/TensorProduct/Basic.html#TensorProduct.lift.equiv> .
wd:Q579978 wl:formalizedAs "ChainComplex" .
wd:Q579978 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Homology/HomologicalComplex.html#ChainComplex> .
wd:Q579978 wl:formalizedAs "HomologicalComplex.d" .
wd:Q579978 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Homology/HomologicalComplex.html#HomologicalComplex.d> .
wd:Q579978 wl:formalizedAs "HomologicalComplex.homology" .
wd:Q579978 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Homology/ShortComplex/HomologicalComplex.html#HomologicalComplex.homology> .
wd:Q579978 wl:formalizedAs "HomologicalComplex.Acyclic" .
wd:Q579978 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Homology/ShortComplex/HomologicalComplex.html#HomologicalComplex.Acyclic> .
wd:Q579978 wl:formalizedAs "singularChainComplexFunctor" .
wd:Q579978 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/AlgebraicTopology/SingularHomology/Basic.html#singularChainComplexFunctor> .
wd:Q579978 wl:formalizedAs "CategoryTheory.ShortComplex.Exact" .
wd:Q579978 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Homology/ShortComplex/Exact.html#CategoryTheory.ShortComplex.Exact> .
wd:Q579978 wl:formalizedAs "CategoryTheory.ShortComplex.ShortExact" .
wd:Q579978 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Homology/ShortComplex/ShortExact.html#CategoryTheory.ShortComplex.ShortExact> .
wd:Q579978 wl:formalizedAs "CategoryTheory.Abelian.isIso_of_epi_of_isIso_of_isIso_of_mono" .
wd:Q579978 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Abelian/DiagramLemmas/Four.html#CategoryTheory.Abelian.isIso_of_epi_of_isIso_of_isIso_of_mono> .
wd:Q579978 wl:formalizedAs "CategoryTheory.ShortComplex.SnakeInput.snake_lemma" .
wd:Q579978 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Homology/ShortComplex/SnakeLemma.html#CategoryTheory.ShortComplex.SnakeInput.snake_lemma> .
wd:Q579978 wl:formalizedAs "CategoryTheory.Abelian" .
wd:Q579978 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Abelian/Basic.html#CategoryTheory.Abelian> .
wd:Q579978 wl:formalizedAs "CategoryTheory.Functor.rightDerived" .
wd:Q579978 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Abelian/RightDerived.html#CategoryTheory.Functor.rightDerived> .
wd:Q579978 wl:formalizedAs "Ext" .
wd:Q579978 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Abelian/Ext.html#Ext> .
wd:Q579978 wl:formalizedAs "CategoryTheory.Tor" .
wd:Q579978 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Monoidal/Tor.html#CategoryTheory.Tor> .
wd:Q579978 wl:formalizedAs "CategoryTheory.SpectralSequence" .
wd:Q579978 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Homology/SpectralSequence/Basic.html#CategoryTheory.SpectralSequence> .
wd:Q579978 wl:formalizedAs "singularHomologyFunctor" .
wd:Q579978 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/AlgebraicTopology/SingularHomology/Basic.html#singularHomologyFunctor> .
wd:Q579978 wl:formalizedAs "HomologicalComplex.Hom" .
wd:Q579978 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Homology/HomologicalComplex.html#HomologicalComplex.Hom> .
wd:Q579978 wl:formalizedAs "HomologicalComplex.QuasiIso" .
wd:Q579978 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Homology/QuasiIso.html#HomologicalComplex.QuasiIso> .
wd:Q579978 wl:formalizedAs "HomologicalComplex.homologyFunctor" .
wd:Q579978 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Homology/ShortComplex/HomologicalComplex.html#HomologicalComplex.homologyFunctor> .
wd:Q579978 wl:formalizedAs "CategoryTheory.ShortComplex.ShortExact.δ" .
wd:Q579978 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Homology/HomologySequence.html#CategoryTheory.ShortComplex.ShortExact.δ> .
wd:Q215111 wl:formalizedAs "map_one" .
wd:Q215111 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Hom/Defs.html#map_one> .
wd:Q215111 wl:formalizedAs "MulHom" .
wd:Q215111 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Hom/Defs.html#MulHom> .
wd:Q215111 wl:formalizedAs "MonoidHom" .
wd:Q215111 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Hom/Defs.html#MonoidHom> .
wd:Q215111 wl:formalizedAs "RingHom" .
wd:Q215111 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Ring/Hom/Defs.html#RingHom> .
wd:Q215111 wl:formalizedAs "NonUnitalRingHom" .
wd:Q215111 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Ring/Hom/Defs.html#NonUnitalRingHom> .
wd:Q215111 wl:formalizedAs "LinearMap" .
wd:Q215111 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Module/LinearMap/Defs.html#LinearMap> .
wd:Q215111 wl:formalizedAs "AlgHom" .
wd:Q215111 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Algebra/Hom.html#AlgHom> .
wd:Q215111 wl:formalizedAs "Matrix.scalar" .
wd:Q215111 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Matrix/Basic.html#Matrix.scalar> .
wd:Q215111 wl:formalizedAs "MulEquiv" .
wd:Q215111 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Equiv/Defs.html#MulEquiv> .
wd:Q215111 wl:formalizedAs "CategoryTheory.Iso" .
wd:Q215111 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Iso.html#CategoryTheory.Iso> .
wd:Q215111 wl:formalizedAs "EquivLike.bijective" .
wd:Q215111 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/FunLike/Equiv.html#EquivLike.bijective> .
wd:Q215111 wl:formalizedAs "MulEquiv.ofBijective" .
wd:Q215111 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Equiv/Defs.html#MulEquiv.ofBijective> .
wd:Q215111 wl:formalizedAs "Homeomorph" .
wd:Q215111 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Homeomorph/Defs.html#Homeomorph> .
wd:Q215111 wl:formalizedAs "Monoid.End" .
wd:Q215111 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Hom/Defs.html#Monoid.End> .
wd:Q215111 wl:formalizedAs "Monoid.End.instMonoid" .
wd:Q215111 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Hom/Defs.html#Monoid.End.instMonoid> .
wd:Q215111 wl:formalizedAs "Module.End.instRing" .
wd:Q215111 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Module/LinearMap/End.html#Module.End.instRing> .
wd:Q215111 wl:formalizedAs "MulAut" .
wd:Q215111 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/End.html#MulAut> .
wd:Q215111 wl:formalizedAs "LinearMap.GeneralLinearGroup" .
wd:Q215111 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/GeneralLinearGroup/Basic.html#LinearMap.GeneralLinearGroup> .
wd:Q215111 wl:formalizedAs "CategoryTheory.mono_iff_injective" .
wd:Q215111 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Types/Basic.html#CategoryTheory.mono_iff_injective> .
wd:Q215111 wl:formalizedAs "CategoryTheory.Mono" .
wd:Q215111 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Category/Basic.html#CategoryTheory.Mono> .
wd:Q215111 wl:formalizedAs "CategoryTheory.SplitMono" .
wd:Q215111 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/EpiMono.html#CategoryTheory.SplitMono> .
wd:Q215111 wl:formalizedAs "CategoryTheory.IsSplitMono.mono" .
wd:Q215111 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/EpiMono.html#CategoryTheory.IsSplitMono.mono> .
wd:Q215111 wl:formalizedAs "CategoryTheory.ConcreteCategory.mono_of_injective" .
wd:Q215111 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/ConcreteCategory/EpiMono.html#CategoryTheory.ConcreteCategory.mono_of_injective> .
wd:Q215111 wl:formalizedAs "CategoryTheory.epi_iff_surjective" .
wd:Q215111 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Types/Basic.html#CategoryTheory.epi_iff_surjective> .
wd:Q215111 wl:formalizedAs "CategoryTheory.Epi" .
wd:Q215111 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Category/Basic.html#CategoryTheory.Epi> .
wd:Q215111 wl:formalizedAs "IsLocalization.epi" .
wd:Q215111 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Category/Ring/Instances.html#IsLocalization.epi> .
wd:Q215111 wl:formalizedAs "CategoryTheory.SplitEpi" .
wd:Q215111 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/EpiMono.html#CategoryTheory.SplitEpi> .
wd:Q215111 wl:formalizedAs "CategoryTheory.SplitEpi.epi" .
wd:Q215111 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/EpiMono.html#CategoryTheory.SplitEpi.epi> .
wd:Q215111 wl:formalizedAs "Con.ker" .
wd:Q215111 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/Congruence/Hom.html#Con.ker> .
wd:Q215111 wl:formalizedAs "Con.quotientKerEquivRange" .
wd:Q215111 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/Congruence/Basic.html#Con.quotientKerEquivRange> .
wd:Q215111 wl:formalizedAs "QuotientGroup.con_ker_eq_conKer" .
wd:Q215111 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/QuotientGroup/Defs.html#QuotientGroup.con_ker_eq_conKer> .
wd:Q215111 wl:formalizedAs "FirstOrder.Language.Hom" .
wd:Q215111 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Basic.html#FirstOrder.Language.Hom> .
wd:Q215111 wl:formalizedAs "SimpleGraph.Hom" .
wd:Q215111 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Combinatorics/SimpleGraph/Maps.html#SimpleGraph.Hom> .
wd:Q1279571 wl:formalizedAs "EuclideanGeometry.dist_sq_eq_dist_sq_add_dist_sq_iff_angle_eq_pi_div_two" .
wd:Q1279571 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Euclidean/Angle/Unoriented/RightAngle.html#EuclideanGeometry.dist_sq_eq_dist_sq_add_dist_sq_iff_angle_eq_pi_div_two> .
wd:Q1279571 wl:formalizedAs "PythagoreanTriple" .
wd:Q1279571 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/PythagoreanTriples.html#PythagoreanTriple> .
wd:Q1279571 wl:formalizedAs "Nat.choose_succ_succ" .
wd:Q1279571 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/Choose/Basic.html#Nat.choose_succ_succ> .
wd:Q1279571 wl:formalizedAs "Nat.sum_range_choose" .
wd:Q1279571 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/Choose/Sum.html#Nat.sum_range_choose> .
wd:Q1279571 wl:formalizedAs "Nat.factorial" .
wd:Q1279571 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/Factorial/Basic.html#Nat.factorial> .
wd:Q1279571 wl:formalizedAs "Real.sin" .
wd:Q1279571 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.html#Real.sin> .
wd:Q1279571 wl:formalizedAs "Real.pi_gt_d4" .
wd:Q1279571 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Real/Pi/Bounds.html#Real.pi_gt_d4> .
wd:Q1279571 wl:formalizedAs "Real.sin_sq_add_cos_sq" .
wd:Q1279571 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.html#Real.sin_sq_add_cos_sq> .
wd:Q1279571 wl:formalizedAs "mul_zero" .
wd:Q1279571 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/GroupWithZero/Basic.html#mul_zero> .
wd:Q1279571 wl:formalizedAs "quadratic_eq_zero_iff" .
wd:Q1279571 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/QuadraticDiscriminant.html#quadratic_eq_zero_iff> .
wd:Q1279571 wl:formalizedAs "sq_add_mul_sq_mul_sq_add_mul_sq" .
wd:Q1279571 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Ring/Identities.html#sq_add_mul_sq_mul_sq_add_mul_sq> .
wd:Q1279571 wl:formalizedAs "Real.deriv_sin" .
wd:Q1279571 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.html#Real.deriv_sin> .
wd:Q1279571 wl:formalizedAs "exists_deriv_eq_zero" .
wd:Q1279571 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/LocalExtr/Rolle.html#exists_deriv_eq_zero> .
wd:Q1279571 wl:formalizedAs "Real.pi_gt_d6" .
wd:Q1279571 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Real/Pi/Bounds.html#Real.pi_gt_d6> .
wd:Q1279571 wl:formalizedAs "mul_self_eq_mul_self_iff" .
wd:Q1279571 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Ring/Commute.html#mul_self_eq_mul_self_iff> .
wd:Q1279571 wl:formalizedAs "Real.sin_add" .
wd:Q1279571 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Complex/Trigonometric.html#Real.sin_add> .
wd:Q1279571 wl:formalizedAs "Real.hasSum_sin" .
wd:Q1279571 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Trigonometric/Series.html#Real.hasSum_sin> .
wd:Q1279571 wl:formalizedAs "tsum_geometric_of_lt_one" .
wd:Q1279571 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecificLimits/Basic.html#tsum_geometric_of_lt_one> .
wd:Q1279571 wl:formalizedAs "Real.hasSum_arctan" .
wd:Q1279571 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Complex/Arctan.html#Real.hasSum_arctan> .
wd:Q1279571 wl:formalizedAs "Real.tendsto_sum_pi_div_four" .
wd:Q1279571 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Real/Pi/Leibniz.html#Real.tendsto_sum_pi_div_four> .
wd:Q1279571 wl:formalizedAs "exists_hasDerivAt_eq_slope" .
wd:Q1279571 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/Deriv/MeanValue.html#exists_hasDerivAt_eq_slope> .
wd:Q131222 wl:formalizedAs "Real.negMulLog_zero" .
wd:Q131222 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Log/NegMulLog.html#Real.negMulLog_zero> .
wd:Q131222 wl:formalizedAs "Real.binEntropy" .
wd:Q131222 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/BinaryEntropy.html#Real.binEntropy> .
wd:Q131222 wl:formalizedAs "Real.binEntropy_le_log_two" .
wd:Q131222 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/BinaryEntropy.html#Real.binEntropy_le_log_two> .
wd:Q131222 wl:formalizedAs "InformationTheory.klDiv" .
wd:Q131222 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/InformationTheory/KullbackLeibler/Basic.html#InformationTheory.klDiv> .
wd:Q12503 wl:formalizedAs "Int" .
wd:Q12503 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Int/Notation.html#Int> .
wd:Q12503 wl:formalizedAs "Denumerable.int" .
wd:Q12503 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Logic/Denumerable.html#Denumerable.int> .
wd:Q12503 wl:formalizedAs "Int.instCommRing" .
wd:Q12503 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Ring/Int/Defs.html#Int.instCommRing> .
wd:Q12503 wl:formalizedAs "Int.instAddCommGroup" .
wd:Q12503 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Int/Defs.html#Int.instAddCommGroup> .
wd:Q12503 wl:formalizedAs "CommRingCat.zIsInitial" .
wd:Q12503 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Category/Ring/Constructions.html#CommRingCat.zIsInitial> .
wd:Q12503 wl:formalizedAs "RingHom.injective_int" .
wd:Q12503 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Int/CharZero.html#RingHom.injective_int> .
wd:Q12503 wl:formalizedAs "instIsAddCyclicInt" .
wd:Q12503 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/SpecificGroups/Cyclic.html#instIsAddCyclicInt> .
wd:Q12503 wl:formalizedAs "intCyclicAddEquiv" .
wd:Q12503 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/SpecificGroups/Cyclic.html#intCyclicAddEquiv> .
wd:Q12503 wl:formalizedAs "Int.instCommMonoid" .
wd:Q12503 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Int/Defs.html#Int.instCommMonoid> .
wd:Q12503 wl:formalizedAs "Int.instIsDomain" .
wd:Q12503 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Ring/Int/Defs.html#Int.instIsDomain> .
wd:Q12503 wl:formalizedAs "Int.not_isField" .
wd:Q12503 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Ring/Int/Field.html#Int.not_isField> .
wd:Q12503 wl:formalizedAs "Rat.isFractionRing" .
wd:Q12503 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Localization/FractionRing.html#Rat.isFractionRing> .
wd:Q12503 wl:formalizedAs "Int.ediv_emod_unique&#x27;&#x27;" .
wd:Q12503 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Int/Lemmas.html#Int.ediv_emod_unique''> .
wd:Q12503 wl:formalizedAs "Int.euclideanDomain" .
wd:Q12503 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/EuclideanDomain/Int.html#Int.euclideanDomain> .
wd:Q12503 wl:formalizedAs "Nat.primeFactorsList_unique" .
wd:Q12503 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/Factors.html#Nat.primeFactorsList_unique> .
wd:Q12503 wl:formalizedAs "Int.instLinearOrder" .
wd:Q12503 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Int/Order/Basic.html#Int.instLinearOrder> .
wd:Q12503 wl:formalizedAs "Int.instIsStrictOrderedRing" .
wd:Q12503 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Order/Ring/Int.html#Int.instIsStrictOrderedRing> .
wd:Q12503 wl:formalizedAs "sub_eq_add_neg" .
wd:Q12503 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Defs.html#sub_eq_add_neg> .
wd:Q12503 wl:formalizedAs "Equiv.intEquivNat" .
wd:Q12503 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Logic/Equiv/Nat.html#Equiv.intEquivNat> .
wd:Q12503 wl:formalizedAs "Cardinal.mk_int" .
wd:Q12503 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Basic.html#Cardinal.mk_int> .
wd:Q12503 wl:formalizedAs "Function.Bijective" .
wd:Q12503 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Logic/Function/Defs.html#Function.Bijective> .
wd:Q187631 wl:formalizedAs "AffineMap.lineMap" .
wd:Q187631 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/AffineSpace/AffineMap.html#AffineMap.lineMap> .
wd:Q187631 wl:formalizedAs "AffineMap.lineMap_apply_ring" .
wd:Q187631 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/AffineSpace/AffineMap.html#AffineMap.lineMap_apply_ring> .
wd:Q187631 wl:formalizedAs "Lagrange.interpolate" .
wd:Q187631 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Lagrange.html#Lagrange.interpolate> .
wd:Q187631 wl:formalizedAs "Lagrange.eq_interpolate_iff" .
wd:Q187631 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Lagrange.html#Lagrange.eq_interpolate_iff> .
wd:Q16743426 wl:formalizedAs "Circle.instCommGroup" .
wd:Q16743426 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Complex/Circle.html#Circle.instCommGroup> .
wd:Q16743426 wl:formalizedAs "CommGroup" .
wd:Q16743426 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Defs.html#CommGroup> .
wd:Q16743426 wl:formalizedAs "Group" .
wd:Q16743426 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Defs.html#Group> .
wd:Q16743426 wl:formalizedAs "Int.instAddCommGroup" .
wd:Q16743426 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Int/Defs.html#Int.instAddCommGroup> .
wd:Q838495 wl:formalizedAs "Module.End.genEigenspace" .
wd:Q838495 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Eigenspace/Basic.html#Module.End.genEigenspace> .
wd:Q838495 wl:formalizedAs "Module.End.maxGenEigenspaceIndex" .
wd:Q838495 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Eigenspace/Basic.html#Module.End.maxGenEigenspaceIndex> .
wd:Q838495 wl:formalizedAs "Module.End.exists_isNilpotent_isSemisimple" .
wd:Q838495 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/JordanChevalley.html#Module.End.exists_isNilpotent_isSemisimple> .
wd:Q838495 wl:formalizedAs "spectrum.map_polynomial_aeval_of_degree_pos" .
wd:Q838495 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/FieldTheory/IsAlgClosed/Spectrum.html#spectrum.map_polynomial_aeval_of_degree_pos> .
wd:Q838495 wl:formalizedAs "Matrix.charpoly_units_conj" .
wd:Q838495 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Matrix/Charpoly/Basic.html#Matrix.charpoly_units_conj> .
wd:Q838495 wl:formalizedAs "LinearMap.aeval_self_charpoly" .
wd:Q838495 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Charpoly/Basic.html#LinearMap.aeval_self_charpoly> .
wd:Q838495 wl:formalizedAs "minpoly" .
wd:Q838495 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/FieldTheory/Minpoly/Basic.html#minpoly> .
wd:Q838495 wl:formalizedAs "IsCompactOperator.hasEigenvalue_iff_mem_spectrum" .
wd:Q838495 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Normed/Operator/Compact/FredholmAlternative.html#IsCompactOperator.hasEigenvalue_iff_mem_spectrum> .
wd:Q1765138 wl:formalizedAs "tsum_geometric_of_lt_one" .
wd:Q1765138 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecificLimits/Basic.html#tsum_geometric_of_lt_one> .
wd:Q1765138 wl:formalizedAs "Real.hasSum_sin" .
wd:Q1765138 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Trigonometric/Series.html#Real.hasSum_sin> .
wd:Q1765138 wl:formalizedAs "Real.hasSum_cos" .
wd:Q1765138 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Trigonometric/Series.html#Real.hasSum_cos> .
wd:Q1765138 wl:formalizedAs "Real.tendsto_sum_pi_div_four" .
wd:Q1765138 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Real/Pi/Leibniz.html#Real.tendsto_sum_pi_div_four> .
wd:Q1765138 wl:formalizedAs "Real.deriv_sin" .
wd:Q1765138 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.html#Real.deriv_sin> .
wd:Q11476 wl:formalizedAs "Isometry" .
wd:Q11476 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/MetricSpace/Isometry.html#Isometry> .
wd:Q11476 wl:formalizedAs "Matrix.mem_orthogonalGroup_iff&#x27;" .
wd:Q11476 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/UnitaryGroup.html#Matrix.mem_orthogonalGroup_iff'> .
wd:Q1225713 wl:formalizedAs "ringKrullDim" .
wd:Q1225713 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/KrullDimension/Basic.html#ringKrullDim> .
wd:Q1225713 wl:formalizedAs "ringKrullDim_eq_zero_of_field" .
wd:Q1225713 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/KrullDimension/Field.html#ringKrullDim_eq_zero_of_field> .
wd:Q1225713 wl:formalizedAs "Ring.krullDimLE_zero_and_isLocalRing_tfae" .
wd:Q1225713 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/KrullDimension/Zero.html#Ring.krullDimLE_zero_and_isLocalRing_tfae> .
wd:Q1225713 wl:formalizedAs "RelSeries.length" .
wd:Q1225713 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/RelSeries.html#RelSeries.length> .
wd:Q1225713 wl:formalizedAs "Ideal.primeHeight" .
wd:Q1225713 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Ideal/Height.html#Ideal.primeHeight> .
wd:Q1225713 wl:formalizedAs "Ideal.primeHeight_eq_zero_iff" .
wd:Q1225713 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Ideal/Height.html#Ideal.primeHeight_eq_zero_iff> .
wd:Q1225713 wl:formalizedAs "Ideal.sup_primeHeight_of_maximal_eq_ringKrullDim" .
wd:Q1225713 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Ideal/Height.html#Ideal.sup_primeHeight_of_maximal_eq_ringKrullDim> .
wd:Q1225713 wl:formalizedAs "Ideal.finiteHeight_of_isNoetherianRing" .
wd:Q1225713 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Ideal/KrullsHeightTheorem.html#Ideal.finiteHeight_of_isNoetherianRing> .
wd:Q1225713 wl:formalizedAs "Ideal.height_le_iff_exists_minimalPrimes" .
wd:Q1225713 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Ideal/KrullsHeightTheorem.html#Ideal.height_le_iff_exists_minimalPrimes> .
wd:Q1225713 wl:formalizedAs "Ideal.height" .
wd:Q1225713 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Ideal/Height.html#Ideal.height> .
wd:Q1225713 wl:formalizedAs "PrimeSpectrum.topologicalKrullDim_eq_ringKrullDim" .
wd:Q1225713 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Spectrum/Prime/Topology.html#PrimeSpectrum.topologicalKrullDim_eq_ringKrullDim> .
wd:Q1225713 wl:formalizedAs "MvPolynomial.ringKrullDim_of_isNoetherianRing" .
wd:Q1225713 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/KrullDimension/Polynomial.html#MvPolynomial.ringKrullDim_of_isNoetherianRing> .
wd:Q1225713 wl:formalizedAs "Polynomial.ringKrullDim_of_isNoetherianRing" .
wd:Q1225713 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/KrullDimension/Polynomial.html#Polynomial.ringKrullDim_of_isNoetherianRing> .
wd:Q1225713 wl:formalizedAs "IsPrincipalIdealRing.ringKrullDim_eq_one" .
wd:Q1225713 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/KrullDimension/PID.html#IsPrincipalIdealRing.ringKrullDim_eq_one> .
wd:Q1225713 wl:formalizedAs "Ring.KrullDimLE.isField_of_isDomain" .
wd:Q1225713 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/KrullDimension/Zero.html#Ring.KrullDimLE.isField_of_isDomain> .
wd:Q1225713 wl:formalizedAs "ringKrullDim_eq_bot_of_subsingleton" .
wd:Q1225713 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/KrullDimension/Basic.html#ringKrullDim_eq_bot_of_subsingleton> .
wd:Q1225713 wl:formalizedAs "ringKrullDim_nonneg_of_nontrivial" .
wd:Q1225713 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/KrullDimension/Basic.html#ringKrullDim_nonneg_of_nontrivial> .
wd:Q1225713 wl:formalizedAs "isArtinianRing_iff_isNoetherianRing_krullDimLE_zero" .
wd:Q1225713 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/HopkinsLevitzki.html#isArtinianRing_iff_isNoetherianRing_krullDimLE_zero> .
wd:Q1225713 wl:formalizedAs "Module.supportDim" .
wd:Q1225713 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/KrullDimension/Module.html#Module.supportDim> .
wd:Q199691 wl:formalizedAs "ProbabilityTheory.mgf" .
wd:Q199691 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Probability/Moments/Basic.html#ProbabilityTheory.mgf> .
wd:Q484637 wl:formalizedAs "AffineMap" .
wd:Q484637 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/AffineSpace/AffineMap.html#AffineMap> .
wd:Q202843 wl:formalizedAs "IsMinOn.of_isLocalMin_of_convex_univ" .
wd:Q202843 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Convex/Extrema.html#IsMinOn.of_isLocalMin_of_convex_univ> .
wd:Q8078 wl:formalizedAs "em" .
wd:Q8078 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Logic/Basic.html#em> .
wd:Q8078 wl:formalizedAs "inf_sup_left" .
wd:Q8078 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/Lattice.html#inf_sup_left> .
wd:Q1166618 wl:formalizedAs "Metric.continuousAt_iff" .
wd:Q1166618 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/MetricSpace/Pseudo/Defs.html#Metric.continuousAt_iff> .
wd:Q1166618 wl:formalizedAs "Cardinal.not_countable_real" .
wd:Q1166618 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Real/Cardinality.html#Cardinal.not_countable_real> .
wd:Q1166618 wl:formalizedAs "Function.cantor_surjective" .
wd:Q1166618 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Logic/Function/Basic.html#Function.cantor_surjective> .
wd:Q1166618 wl:formalizedAs "exists_wellFoundedLT" .
wd:Q1166618 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Order.html#exists_wellFoundedLT> .
wd:Q1166618 wl:formalizedAs "ZFSet.isOrdinal_notMem_univ" .
wd:Q1166618 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/ZFC/Class.html#ZFSet.isOrdinal_notMem_univ> .
wd:Q1166618 wl:formalizedAs "FirstOrder.Language.exists_elementarySubstructure_card_eq" .
wd:Q1166618 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Skolem.html#FirstOrder.Language.exists_elementarySubstructure_card_eq> .
wd:Q1166618 wl:formalizedAs "FirstOrder.Language.Theory.isSatisfiable_iff_isFinitelySatisfiable" .
wd:Q1166618 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Satisfiability.html#FirstOrder.Language.Theory.isSatisfiable_iff_isFinitelySatisfiable> .
wd:Q1166618 wl:formalizedAs "FirstOrder.Language" .
wd:Q1166618 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Basic.html#FirstOrder.Language> .
wd:Q1166618 wl:formalizedAs "ZFSet" .
wd:Q1166618 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/ZFC/Basic.html#ZFSet> .
wd:Q1166618 wl:formalizedAs "Classical.axiomOfChoice" .
wd:Q1166618 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Logic/Basic.html#Classical.axiomOfChoice> .
wd:Q1166618 wl:formalizedAs "FirstOrder.Language.Theory" .
wd:Q1166618 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Syntax.html#FirstOrder.Language.Theory> .
wd:Q1166618 wl:formalizedAs "ComputablePred.halting_problem" .
wd:Q1166618 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Computability/Halting.html#ComputablePred.halting_problem> .
wd:Q141495 wl:formalizedAs "IsMinOn" .
wd:Q141495 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/Filter/Extr.html#IsMinOn> .
wd:Q141495 wl:formalizedAs "IsLocalMin" .
wd:Q141495 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Order/LocalExtr.html#IsLocalMin> .
wd:Q141495 wl:formalizedAs "IsMinOn.of_isLocalMin_of_convex_univ" .
wd:Q141495 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Convex/Extrema.html#IsMinOn.of_isLocalMin_of_convex_univ> .
wd:Q141495 wl:formalizedAs "IsCompact.exists_isMinOn" .
wd:Q141495 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Order/Compact.html#IsCompact.exists_isMinOn> .
wd:Q141495 wl:formalizedAs "LowerSemicontinuousOn.exists_isMinOn" .
wd:Q141495 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Semicontinuity/Basic.html#LowerSemicontinuousOn.exists_isMinOn> .
wd:Q141495 wl:formalizedAs "IsLocalExtr.hasDerivAt_eq_zero" .
wd:Q141495 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/LocalExtr/Basic.html#IsLocalExtr.hasDerivAt_eq_zero> .
wd:Q141495 wl:formalizedAs "IsLocalExtrOn.exists_multipliers_of_hasStrictFDerivAt_1d" .
wd:Q141495 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/LagrangeMultipliers.html#IsLocalExtrOn.exists_multipliers_of_hasStrictFDerivAt_1d> .
wd:Q156495 wl:formalizedAs "intervalIntegral.integral_eq_sub_of_hasDerivAt" .
wd:Q156495 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/MeasureTheory/Integral/IntervalIntegral/FundThmCalculus.html#intervalIntegral.integral_eq_sub_of_hasDerivAt> .
wd:Q156495 wl:formalizedAs "IsLocalExtr.deriv_eq_zero" .
wd:Q156495 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/LocalExtr/Basic.html#IsLocalExtr.deriv_eq_zero> .
wd:Q156495 wl:formalizedAs "fourierCoeff" .
wd:Q156495 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Fourier/AddCircle.html#fourierCoeff> .
wd:Q156495 wl:formalizedAs "IsRiemannianManifold" .
wd:Q156495 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Manifold/Riemannian/Basic.html#IsRiemannianManifold> .
wd:Q156495 wl:formalizedAs "HilbertSpace" .
wd:Q156495 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/InnerProductSpace/Defs.html#HilbertSpace> .
wd:Q156495 wl:formalizedAs "spectrum" .
wd:Q156495 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Algebra/Spectrum/Basic.html#spectrum> .
wd:Q395 wl:formalizedAs "FermatLastTheorem" .
wd:Q395 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/FLT/Basic.html#FermatLastTheorem> .
wd:Q395 wl:formalizedAs "Module" .
wd:Q395 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Module/Defs.html#Module> .
wd:Q395 wl:formalizedAs "BooleanAlgebra" .
wd:Q395 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/BooleanAlgebra/Defs.html#BooleanAlgebra> .
wd:Q395 wl:formalizedAs "Function.cantor_surjective" .
wd:Q395 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Logic/Function/Basic.html#Function.cantor_surjective> .
wd:Q395 wl:formalizedAs "Module.Flat.of_free" .
wd:Q395 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Flat/Basic.html#Module.Flat.of_free> .
wd:Q395 wl:formalizedAs "Nat.exists_infinite_primes" .
wd:Q395 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/Prime/Infinite.html#Nat.exists_infinite_primes> .
wd:Q1045555 wl:formalizedAs "ProbabilityTheory.multivariateGaussian" .
wd:Q1045555 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Probability/Distributions/Gaussian/Multivariate.html#ProbabilityTheory.multivariateGaussian> .
wd:Q51501 wl:formalizedAs "gradient" .
wd:Q51501 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/Gradient/Basic.html#gradient> .
wd:Q51501 wl:formalizedAs "hasDerivAt_integral_of_dominated_loc_of_lip" .
wd:Q51501 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/ParametricIntegral.html#hasDerivAt_integral_of_dominated_loc_of_lip> .
wd:Q2796622 wl:formalizedAs "Finset.centroid" .
wd:Q2796622 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/AffineSpace/Centroid.html#Finset.centroid> .
wd:Q2796622 wl:formalizedAs "Real.geom_mean_le_arith_mean" .
wd:Q2796622 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/MeanInequalities.html#Real.geom_mean_le_arith_mean> .
wd:Q2796622 wl:formalizedAs "Finset.affineCombination" .
wd:Q2796622 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/AffineSpace/Combination.html#Finset.affineCombination> .
wd:Q2796622 wl:formalizedAs "MeasureTheory.average" .
wd:Q2796622 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/MeasureTheory/Integral/Average.html#MeasureTheory.average> .
wd:Q226995 wl:formalizedAs "ConvexOn.map_integral_le" .
wd:Q226995 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Convex/Integral.html#ConvexOn.map_integral_le> .
wd:Q464794 wl:formalizedAs "LinearMap.BilinForm.IsOrtho" .
wd:Q464794 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/BilinearForm/Orthogonal.html#LinearMap.BilinForm.IsOrtho> .
wd:Q464794 wl:formalizedAs "LinearMap.BilinForm.toDual" .
wd:Q464794 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/BilinearForm/Properties.html#LinearMap.BilinForm.toDual> .
wd:Q464794 wl:formalizedAs "LinearMap.BilinForm.nondegenerate_iff_ker_eq_bot" .
wd:Q464794 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/BilinearForm/Properties.html#LinearMap.BilinForm.nondegenerate_iff_ker_eq_bot> .
wd:Q467606 wl:formalizedAs "FirstOrder.Language.BoundedFormula" .
wd:Q467606 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Syntax.html#FirstOrder.Language.BoundedFormula> .
wd:Q467606 wl:formalizedAs "FirstOrder.Language.Sentence" .
wd:Q467606 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Syntax.html#FirstOrder.Language.Sentence> .
wd:Q467606 wl:formalizedAs "FirstOrder.Language.Theory" .
wd:Q467606 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Syntax.html#FirstOrder.Language.Theory> .
wd:Q467606 wl:formalizedAs "FirstOrder.Language.Theory.IsSatisfiable" .
wd:Q467606 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Satisfiability.html#FirstOrder.Language.Theory.IsSatisfiable> .
wd:Q467606 wl:formalizedAs "FirstOrder.Language.Theory.IsComplete" .
wd:Q467606 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Satisfiability.html#FirstOrder.Language.Theory.IsComplete> .
wd:Q467606 wl:formalizedAs "FirstOrder.Language.completeTheory" .
wd:Q467606 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Semantics.html#FirstOrder.Language.completeTheory> .
wd:Q467606 wl:formalizedAs "FirstOrder.Language" .
wd:Q467606 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Basic.html#FirstOrder.Language> .
wd:Q467606 wl:formalizedAs "FirstOrder.Language.Structure" .
wd:Q467606 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Basic.html#FirstOrder.Language.Structure> .
wd:Q467606 wl:formalizedAs "FirstOrder.Language.Theory.Model" .
wd:Q467606 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Semantics.html#FirstOrder.Language.Theory.Model> .
wd:Q467606 wl:formalizedAs "FirstOrder.Language.Substructure" .
wd:Q467606 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Substructures.html#FirstOrder.Language.Substructure> .
wd:Q467606 wl:formalizedAs "FirstOrder.Language.ElementarySubstructure" .
wd:Q467606 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/ElementarySubstructures.html#FirstOrder.Language.ElementarySubstructure> .
wd:Q467606 wl:formalizedAs "FirstOrder.Language.ElementarySubstructure.theory_model_iff" .
wd:Q467606 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/ElementarySubstructures.html#FirstOrder.Language.ElementarySubstructure.theory_model_iff> .
wd:Q467606 wl:formalizedAs "FirstOrder.Language.ElementaryEmbedding" .
wd:Q467606 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/ElementaryMaps.html#FirstOrder.Language.ElementaryEmbedding> .
wd:Q467606 wl:formalizedAs "FirstOrder.Language.Embedding.toHom" .
wd:Q467606 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Basic.html#FirstOrder.Language.Embedding.toHom> .
wd:Q467606 wl:formalizedAs "FirstOrder.Language.LHom.reduct" .
wd:Q467606 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/LanguageMap.html#FirstOrder.Language.LHom.reduct> .
wd:Q467606 wl:formalizedAs "FirstOrder.Language.Theory.isSatisfiable_iff_isFinitelySatisfiable" .
wd:Q467606 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Satisfiability.html#FirstOrder.Language.Theory.isSatisfiable_iff_isFinitelySatisfiable> .
wd:Q467606 wl:formalizedAs "FirstOrder.Language.exists_elementarySubstructure_card_eq" .
wd:Q467606 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Skolem.html#FirstOrder.Language.exists_elementarySubstructure_card_eq> .
wd:Q467606 wl:formalizedAs "FirstOrder.Language.Theory.exists_large_model_of_infinite_model" .
wd:Q467606 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Satisfiability.html#FirstOrder.Language.Theory.exists_large_model_of_infinite_model> .
wd:Q467606 wl:formalizedAs "Set.Definable" .
wd:Q467606 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Definability.html#Set.Definable> .
wd:Q467606 wl:formalizedAs "FirstOrder.Language.Substructure.isElementary_of_exists" .
wd:Q467606 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/ElementarySubstructures.html#FirstOrder.Language.Substructure.isElementary_of_exists> .
wd:Q467606 wl:formalizedAs "Set.DefinableFun" .
wd:Q467606 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Definability.html#Set.DefinableFun> .
wd:Q467606 wl:formalizedAs "FirstOrder.Language.Theory.typeOf" .
wd:Q467606 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Types.html#FirstOrder.Language.Theory.typeOf> .
wd:Q467606 wl:formalizedAs "FirstOrder.Language.Theory.CompleteType" .
wd:Q467606 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Types.html#FirstOrder.Language.Theory.CompleteType> .
wd:Q467606 wl:formalizedAs "FirstOrder.Language.DefinableSet.instBooleanAlgebra" .
wd:Q467606 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Definability.html#FirstOrder.Language.DefinableSet.instBooleanAlgebra> .
wd:Q467606 wl:formalizedAs "FirstOrder.Language.Theory.CompleteType.instCompactSpace" .
wd:Q467606 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Topology/Types.html#FirstOrder.Language.Theory.CompleteType.instCompactSpace> .
wd:Q467606 wl:formalizedAs "FirstOrder.Language.Ultraproduct.structure" .
wd:Q467606 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Ultraproducts.html#FirstOrder.Language.Ultraproduct.structure> .
wd:Q467606 wl:formalizedAs "FirstOrder.Language.Ultraproduct.sentence_realize" .
wd:Q467606 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Ultraproducts.html#FirstOrder.Language.Ultraproduct.sentence_realize> .
wd:Q467606 wl:formalizedAs "Cardinal.Categorical" .
wd:Q467606 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Satisfiability.html#Cardinal.Categorical> .
wd:Q467606 wl:formalizedAs "Order.iso_of_countable_dense" .
wd:Q467606 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/CountableDenseLinearOrder.html#Order.iso_of_countable_dense> .
wd:Q467606 wl:formalizedAs "FirstOrder.Language.IsFraisseLimit" .
wd:Q467606 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Fraisse.html#FirstOrder.Language.IsFraisseLimit> .
wd:Q18848 wl:formalizedAs "Module" .
wd:Q18848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Module/Defs.html#Module> .
wd:Q18848 wl:formalizedAs "Module.AEval" .
wd:Q18848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Polynomial/Module/AEval.html#Module.AEval> .
wd:Q18848 wl:formalizedAs "AddCommGroup.uniqueIntModule" .
wd:Q18848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Module/NatInt.html#AddCommGroup.uniqueIntModule> .
wd:Q18848 wl:formalizedAs "Module.Free" .
wd:Q18848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/FreeModule/Basic.html#Module.Free> .
wd:Q18848 wl:formalizedAs "Pi.module" .
wd:Q18848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Module/Pi.html#Pi.module> .
wd:Q18848 wl:formalizedAs "Submodule" .
wd:Q18848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Module/Submodule/Defs.html#Submodule> .
wd:Q18848 wl:formalizedAs "MulOpposite" .
wd:Q18848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Opposites.html#MulOpposite> .
wd:Q18848 wl:formalizedAs "Module.compHom" .
wd:Q18848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Algebra/RestrictScalars.html#Module.compHom> .
wd:Q18848 wl:formalizedAs "Submodule.span" .
wd:Q18848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Span/Defs.html#Submodule.span> .
wd:Q18848 wl:formalizedAs "Submodule.instIsModularLattice" .
wd:Q18848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Span/Basic.html#Submodule.instIsModularLattice> .
wd:Q18848 wl:formalizedAs "LinearMap" .
wd:Q18848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Module/LinearMap/Defs.html#LinearMap> .
wd:Q18848 wl:formalizedAs "LinearEquiv" .
wd:Q18848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Module/Equiv/Defs.html#LinearEquiv> .
wd:Q18848 wl:formalizedAs "LinearMap.ker" .
wd:Q18848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Module/Submodule/Ker.html#LinearMap.ker> .
wd:Q18848 wl:formalizedAs "LinearMap.quotKerEquivRange" .
wd:Q18848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Isomorphisms.html#LinearMap.quotKerEquivRange> .
wd:Q18848 wl:formalizedAs "ModuleCat.abelian" .
wd:Q18848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Category/ModuleCat/Abelian.html#ModuleCat.abelian> .
wd:Q18848 wl:formalizedAs "Module.Finite" .
wd:Q18848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Finiteness/Defs.html#Module.Finite> .
wd:Q18848 wl:formalizedAs "Module.Projective" .
wd:Q18848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Module/Projective.html#Module.Projective> .
wd:Q18848 wl:formalizedAs "Module.Injective" .
wd:Q18848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Module/Injective.html#Module.Injective> .
wd:Q18848 wl:formalizedAs "Module.Flat" .
wd:Q18848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Flat/Basic.html#Module.Flat> .
wd:Q18848 wl:formalizedAs "IsSimpleModule" .
wd:Q18848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/SimpleModule/Basic.html#IsSimpleModule> .
wd:Q18848 wl:formalizedAs "IsSemisimpleModule" .
wd:Q18848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/SimpleModule/Basic.html#IsSemisimpleModule> .
wd:Q18848 wl:formalizedAs "FaithfulSMul" .
wd:Q18848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Action/Faithful.html#FaithfulSMul> .
wd:Q18848 wl:formalizedAs "Module.IsTorsionFree" .
wd:Q18848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Module/Torsion/Free.html#Module.IsTorsionFree> .
wd:Q18848 wl:formalizedAs "IsNoetherian" .
wd:Q18848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Noetherian/Defs.html#IsNoetherian> .
wd:Q18848 wl:formalizedAs "IsArtinian" .
wd:Q18848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Artinian/Defs.html#IsArtinian> .
wd:Q18848 wl:formalizedAs "SetLike.GradedSMul" .
wd:Q18848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Module/GradedModule.html#SetLike.GradedSMul> .
wd:Q18848 wl:formalizedAs "Representation" .
wd:Q18848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RepresentationTheory/Basic.html#Representation> .
wd:Q18848 wl:formalizedAs "Module.toAddMonoidEnd" .
wd:Q18848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Module/End.html#Module.toAddMonoidEnd> .
wd:Q18848 wl:formalizedAs "SheafOfModules" .
wd:Q18848 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Category/ModuleCat/Sheaf.html#SheafOfModules> .
wd:Q232207 wl:formalizedAs "ProbabilityTheory.strong_law_ae" .
wd:Q232207 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Probability/StrongLaw.html#ProbabilityTheory.strong_law_ae> .
wd:Q190529 wl:formalizedAs "one_add_one_eq_two" .
wd:Q190529 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/Cast/Defs.html#one_add_one_eq_two> .
wd:Q190529 wl:formalizedAs "Set.empty_def" .
wd:Q190529 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Set/Basic.html#Set.empty_def> .
wd:Q190529 wl:formalizedAs "Function.Bijective" .
wd:Q190529 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Logic/Function/Defs.html#Function.Bijective> .
wd:Q190529 wl:formalizedAs "Metric.ball" .
wd:Q190529 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/MetricSpace/Pseudo/Defs.html#Metric.ball> .
wd:Q233858 wl:formalizedAs "Circle" .
wd:Q233858 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Complex/Circle.html#Circle> .
wd:Q233858 wl:formalizedAs "DualNumber" .
wd:Q233858 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/DualNumber.html#DualNumber> .
wd:Q617295 wl:formalizedAs "DFA" .
wd:Q617295 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Computability/DFA.html#DFA> .
wd:Q617295 wl:formalizedAs "NFA" .
wd:Q617295 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Computability/NFA.html#NFA> .
wd:Q617295 wl:formalizedAs "DFA.toNFA_correct" .
wd:Q617295 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Computability/NFA.html#DFA.toNFA_correct> .
wd:Q617295 wl:formalizedAs "NFA.toDFA_correct" .
wd:Q617295 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Computability/NFA.html#NFA.toDFA_correct> .
wd:Q617295 wl:formalizedAs "NFA.accepts" .
wd:Q617295 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Computability/NFA.html#NFA.accepts> .
wd:Q617295 wl:formalizedAs "NFA.accepts_iff_exists_path" .
wd:Q617295 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Computability/NFA.html#NFA.accepts_iff_exists_path> .
wd:Q617295 wl:formalizedAs "NFA.evalFrom" .
wd:Q617295 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Computability/NFA.html#NFA.evalFrom> .
wd:Q617295 wl:formalizedAs "DFA.toNFA" .
wd:Q617295 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Computability/NFA.html#DFA.toNFA> .
wd:Q617295 wl:formalizedAs "εNFA" .
wd:Q617295 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Computability/EpsilonNFA.html#εNFA> .
wd:Q617295 wl:formalizedAs "εNFA.εClosure" .
wd:Q617295 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Computability/EpsilonNFA.html#εNFA.εClosure> .
wd:Q617295 wl:formalizedAs "εNFA.evalFrom" .
wd:Q617295 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Computability/EpsilonNFA.html#εNFA.evalFrom> .
wd:Q617295 wl:formalizedAs "εNFA.accepts" .
wd:Q617295 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Computability/EpsilonNFA.html#εNFA.accepts> .
wd:Q617295 wl:formalizedAs "εNFA.toNFA_correct" .
wd:Q617295 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Computability/EpsilonNFA.html#εNFA.toNFA_correct> .
wd:Q617295 wl:formalizedAs "εNFA.toNFA_evalFrom_match" .
wd:Q617295 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Computability/EpsilonNFA.html#εNFA.toNFA_evalFrom_match> .
wd:Q617295 wl:formalizedAs "Language.IsRegular.add" .
wd:Q617295 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Computability/DFA.html#Language.IsRegular.add> .
wd:Q617295 wl:formalizedAs "Language.IsRegular.inf" .
wd:Q617295 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Computability/DFA.html#Language.IsRegular.inf> .
wd:Q617295 wl:formalizedAs "Language.IsRegular.compl" .
wd:Q617295 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Computability/DFA.html#Language.IsRegular.compl> .
wd:Q12479 wl:formalizedAs "Int" .
wd:Q12479 wl:formalizedAs "PythagoreanTriple" .
wd:Q12479 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/PythagoreanTriples.html#PythagoreanTriple> .
wd:Q12479 wl:formalizedAs "Mul" .
wd:Q12479 wl:formalizedAs "Dvd.dvd" .
wd:Q12479 wl:formalizedAs "Nat.div_add_mod" .
wd:Q12479 wl:formalizedAs "Nat.three_dvd_iff" .
wd:Q12479 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/Digits/Div.html#Nat.three_dvd_iff> .
wd:Q12479 wl:formalizedAs "Nat.gcd" .
wd:Q12479 wl:formalizedAs "Nat.Coprime" .
wd:Q12479 wl:formalizedAs "EuclideanDomain.gcd" .
wd:Q12479 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/EuclideanDomain/Defs.html#EuclideanDomain.gcd> .
wd:Q12479 wl:formalizedAs "GenContFract" .
wd:Q12479 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/ContinuedFractions/Basic.html#GenContFract> .
wd:Q12479 wl:formalizedAs "Nat.Prime" .
wd:Q12479 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/Prime/Defs.html#Nat.Prime> .
wd:Q12479 wl:formalizedAs "Nat.exists_infinite_primes" .
wd:Q12479 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/Prime/Infinite.html#Nat.exists_infinite_primes> .
wd:Q12479 wl:formalizedAs "Nat.factorization" .
wd:Q12479 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/Factorization/Defs.html#Nat.factorization> .
wd:Q12479 wl:formalizedAs "Nat.primeFactorsList" .
wd:Q12479 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/Factors.html#Nat.primeFactorsList> .
wd:Q12479 wl:formalizedAs "Nat.Prime.dvd_mul" .
wd:Q12479 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/Prime/Defs.html#Nat.Prime.dvd_mul> .
wd:Q12479 wl:formalizedAs "Nat.primeFactorsList_unique" .
wd:Q12479 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/Factors.html#Nat.primeFactorsList_unique> .
wd:Q12479 wl:formalizedAs "ZMod" .
wd:Q12479 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/ZMod/Defs.html#ZMod> .
wd:Q12479 wl:formalizedAs "Int.ModEq" .
wd:Q12479 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Int/ModEq.html#Int.ModEq> .
wd:Q12479 wl:formalizedAs "ZMod.pow_card" .
wd:Q12479 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/FieldTheory/Finite/Basic.html#ZMod.pow_card> .
wd:Q12479 wl:formalizedAs "Nat.ModEq.pow_totient" .
wd:Q12479 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/FieldTheory/Finite/Basic.html#Nat.ModEq.pow_totient> .
wd:Q12479 wl:formalizedAs "Filter.Tendsto" .
wd:Q12479 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/Filter/Basic.html#Filter.Tendsto> .
wd:Q12479 wl:formalizedAs "Complex.I" .
wd:Q12479 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Complex/Basic.html#Complex.I> .
wd:Q12479 wl:formalizedAs "Complex.re" .
wd:Q12479 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Complex/Basic.html#Complex.re> .
wd:Q12479 wl:formalizedAs "Nat.primeCounting" .
wd:Q12479 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/PrimeCounting.html#Nat.primeCounting> .
wd:Q12479 wl:formalizedAs "riemannZeta" .
wd:Q12479 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/LSeries/RiemannZeta.html#riemannZeta> .
wd:Q12479 wl:formalizedAs "riemannZeta_eulerProduct" .
wd:Q12479 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/EulerProduct/DirichletLSeries.html#riemannZeta_eulerProduct> .
wd:Q12479 wl:formalizedAs "RiemannHypothesis" .
wd:Q12479 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/LSeries/RiemannZeta.html#RiemannHypothesis> .
wd:Q12479 wl:formalizedAs "Ideal.IsPrime" .
wd:Q12479 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Ideal/Prime.html#Ideal.IsPrime> .
wd:Q12479 wl:formalizedAs "dedekindZeta" .
wd:Q12479 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/NumberField/DedekindZeta.html#dedekindZeta> .
wd:Q12479 wl:formalizedAs "IsAlgebraic" .
wd:Q12479 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Algebraic/Defs.html#IsAlgebraic> .
wd:Q12479 wl:formalizedAs "NumberField" .
wd:Q12479 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/NumberField/Basic.html#NumberField> .
wd:Q12479 wl:formalizedAs "IsAbelianGalois" .
wd:Q12479 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/FieldTheory/Galois/Abelian.html#IsAbelianGalois> .
wd:Q12479 wl:formalizedAs "Real.infinite_rat_abs_sub_lt_one_div_den_sq_of_irrational" .
wd:Q12479 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/DiophantineApproximation/Basic.html#Real.infinite_rat_abs_sub_lt_one_div_den_sq_of_irrational> .
wd:Q12479 wl:formalizedAs "Transcendental" .
wd:Q12479 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Algebraic/Defs.html#Transcendental> .
wd:Q11216 wl:formalizedAs "Lagrange.interpolate" .
wd:Q11216 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Lagrange.html#Lagrange.interpolate> .
wd:Q11216 wl:formalizedAs "IsLocalExtrOn.exists_multipliers_of_hasStrictFDerivAt" .
wd:Q11216 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/LagrangeMultipliers.html#IsLocalExtrOn.exists_multipliers_of_hasStrictFDerivAt> .
wd:Q82990 wl:formalizedAs "Nat.ofDigits" .
wd:Q82990 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/Digits/Defs.html#Nat.ofDigits> .
wd:Q82990 wl:formalizedAs "Nat.ofDigits_eq_sum_mapIdx" .
wd:Q82990 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/Digits/Lemmas.html#Nat.ofDigits_eq_sum_mapIdx> .
wd:Q753445 wl:formalizedAs "trapezoidal_integral" .
wd:Q753445 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/MeasureTheory/Integral/IntervalIntegral/TrapezoidalRule.html#trapezoidal_integral> .
wd:Q753445 wl:formalizedAs "MeasureTheory.integral_prod" .
wd:Q753445 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/MeasureTheory/Integral/Prod.html#MeasureTheory.integral_prod> .
wd:Q541182 wl:formalizedAs "IsPicardLindelof.exists_eq_forall_mem_Icc_hasDerivWithinAt" .
wd:Q541182 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/ODE/PicardLindelof.html#IsPicardLindelof.exists_eq_forall_mem_Icc_hasDerivWithinAt> .
wd:Q131030 wl:formalizedAs "Module.End" .
wd:Q131030 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Module/LinearMap/End.html#Module.End> .
wd:Q131030 wl:formalizedAs "LinearMap" .
wd:Q131030 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Module/LinearMap/Defs.html#LinearMap> .
wd:Q131030 wl:formalizedAs "LinearMap.toMatrix" .
wd:Q131030 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Matrix/ToLin.html#LinearMap.toMatrix> .
wd:Q131030 wl:formalizedAs "lp" .
wd:Q131030 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Normed/Lp/lpSpace.html#lp> .
wd:Q131030 wl:formalizedAs "ContinuousLinearMap.toNormedRing" .
wd:Q131030 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Normed/Operator/NormedSpace.html#ContinuousLinearMap.toNormedRing> .
wd:Q131030 wl:formalizedAs "ContinuousLinearMap" .
wd:Q131030 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Algebra/Module/LinearMap.html#ContinuousLinearMap> .
wd:Q131030 wl:formalizedAs "ContinuousLinearMap.addCommGroup" .
wd:Q131030 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Algebra/Module/LinearMap.html#ContinuousLinearMap.addCommGroup> .
wd:Q131030 wl:formalizedAs "gradient" .
wd:Q131030 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/Gradient/Basic.html#gradient> .
wd:Q131030 wl:formalizedAs "LinearMap.GeneralLinearGroup" .
wd:Q131030 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/GeneralLinearGroup/Basic.html#LinearMap.GeneralLinearGroup> .
wd:Q131030 wl:formalizedAs "Matrix.orthogonalGroup" .
wd:Q131030 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/UnitaryGroup.html#Matrix.orthogonalGroup> .
wd:Q131030 wl:formalizedAs "Matrix.specialOrthogonalGroup" .
wd:Q131030 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/UnitaryGroup.html#Matrix.specialOrthogonalGroup> .
wd:Q131030 wl:formalizedAs "VectorFourier.fourierIntegral" .
wd:Q131030 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Fourier/FourierTransform.html#VectorFourier.fourierIntegral> .
wd:Q191780 wl:formalizedAs "Ordinal" .
wd:Q191780 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Ordinal/Basic.html#Ordinal> .
wd:Q191780 wl:formalizedAs "InitialSeg.total" .
wd:Q191780 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/InitialSeg.html#InitialSeg.total> .
wd:Q191780 wl:formalizedAs "IsWellOrder" .
wd:Q191780 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/RelClasses.html#IsWellOrder> .
wd:Q191780 wl:formalizedAs "Ordinal.type" .
wd:Q191780 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Ordinal/Basic.html#Ordinal.type> .
wd:Q191780 wl:formalizedAs "Ordinal.omega0" .
wd:Q191780 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Ordinal/Basic.html#Ordinal.omega0> .
wd:Q191780 wl:formalizedAs "Ordinal.lt_wf" .
wd:Q191780 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Ordinal/Basic.html#Ordinal.lt_wf> .
wd:Q191780 wl:formalizedAs "OrderIso" .
wd:Q191780 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/Hom/Basic.html#OrderIso> .
wd:Q191780 wl:formalizedAs "Ordinal.isEquivalent" .
wd:Q191780 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Ordinal/Basic.html#Ordinal.isEquivalent> .
wd:Q191780 wl:formalizedAs "ZFSet.omega" .
wd:Q191780 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/ZFC/Basic.html#ZFSet.omega> .
wd:Q191780 wl:formalizedAs "ZFSet.IsOrdinal" .
wd:Q191780 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/ZFC/Ordinal.html#ZFSet.IsOrdinal> .
wd:Q191780 wl:formalizedAs "ZFSet.IsOrdinal.mem" .
wd:Q191780 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/ZFC/Ordinal.html#ZFSet.IsOrdinal.mem> .
wd:Q191780 wl:formalizedAs "ZFSet.IsOrdinal.subset_iff_eq_or_mem" .
wd:Q191780 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/ZFC/Ordinal.html#ZFSet.IsOrdinal.subset_iff_eq_or_mem> .
wd:Q191780 wl:formalizedAs "Ordinal.bddAbove_of_small" .
wd:Q191780 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Ordinal/Family.html#Ordinal.bddAbove_of_small> .
wd:Q191780 wl:formalizedAs "Order.lt_succ" .
wd:Q191780 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/SuccPred/Basic.html#Order.lt_succ> .
wd:Q191780 wl:formalizedAs "not_small_ordinal" .
wd:Q191780 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Ordinal/Family.html#not_small_ordinal> .
wd:Q191780 wl:formalizedAs "Ordinal.type_eq" .
wd:Q191780 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Ordinal/Basic.html#Ordinal.type_eq> .
wd:Q191780 wl:formalizedAs "Ordinal.zero_or_succ_or_isSuccLimit" .
wd:Q191780 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Ordinal/Arithmetic.html#Ordinal.zero_or_succ_or_isSuccLimit> .
wd:Q191780 wl:formalizedAs "Ordinal.zero_le" .
wd:Q191780 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Ordinal/Basic.html#Ordinal.zero_le> .
wd:Q191780 wl:formalizedAs "Order.succ" .
wd:Q191780 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/SuccPred/Basic.html#Order.succ> .
wd:Q191780 wl:formalizedAs "Order.IsSuccLimit" .
wd:Q191780 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/SuccPred/Limit.html#Order.IsSuccLimit> .
wd:Q191780 wl:formalizedAs "Ordinal.isSuccLimit_iff" .
wd:Q191780 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Ordinal/Arithmetic.html#Ordinal.isSuccLimit_iff> .
wd:Q191780 wl:formalizedAs "IsSuccPrelimit.sSup_Iio" .
wd:Q191780 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Ordinal/Family.html#IsSuccPrelimit.sSup_Iio> .
wd:Q191780 wl:formalizedAs "Ordinal.omega0_le_of_isSuccLimit" .
wd:Q191780 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Ordinal/Arithmetic.html#Ordinal.omega0_le_of_isSuccLimit> .
wd:Q191780 wl:formalizedAs "Ordinal.le_iSup" .
wd:Q191780 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Ordinal/Family.html#Ordinal.le_iSup> .
wd:Q191780 wl:formalizedAs "Order.IsNormal" .
wd:Q191780 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/IsNormal.html#Order.IsNormal> .
wd:Q191780 wl:formalizedAs "Ordinal.induction" .
wd:Q191780 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Ordinal/Basic.html#Ordinal.induction> .
wd:Q191780 wl:formalizedAs "Ordinal.limitRecOn" .
wd:Q191780 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Ordinal/Arithmetic.html#Ordinal.limitRecOn> .
wd:Q191780 wl:formalizedAs "Ordinal.instPow" .
wd:Q191780 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Ordinal/Exponential.html#Ordinal.instPow> .
wd:Q191780 wl:formalizedAs "Ordinal.not_bddAbove_fp" .
wd:Q191780 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Ordinal/FixedPoint.html#Ordinal.not_bddAbove_fp> .
wd:Q191780 wl:formalizedAs "Ordinal.enumOrd" .
wd:Q191780 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Ordinal/Enum.html#Ordinal.enumOrd> .
wd:Q191780 wl:formalizedAs "Ordinal.isPrincipal_add_iff_add_lt_ne_self" .
wd:Q191780 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Ordinal/Principal.html#Ordinal.isPrincipal_add_iff_add_lt_ne_self> .
wd:Q191780 wl:formalizedAs "Ordinal.epsilon" .
wd:Q191780 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Ordinal/Veblen.html#Ordinal.epsilon> .
wd:Q191780 wl:formalizedAs "Ordinal.CNF" .
wd:Q191780 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Ordinal/CantorNormalForm.html#Ordinal.CNF> .
wd:Q191780 wl:formalizedAs "Cardinal.ord" .
wd:Q191780 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Ordinal/Basic.html#Cardinal.ord> .
wd:Q191780 wl:formalizedAs "Ordinal.isSuccLimit_ord" .
wd:Q191780 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Ordinal/Arithmetic.html#Ordinal.isSuccLimit_ord> .
wd:Q191780 wl:formalizedAs "Ordinal.omega" .
wd:Q191780 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Aleph.html#Ordinal.omega> .
wd:Q191780 wl:formalizedAs "Ordinal.cof" .
wd:Q191780 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Cofinality/Ordinal.html#Ordinal.cof> .
wd:Q191780 wl:formalizedAs "Ordinal.cof_eq_aleph0_of_isSuccLimit" .
wd:Q191780 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Cofinality/Ordinal.html#Ordinal.cof_eq_aleph0_of_isSuccLimit> .
wd:Q191780 wl:formalizedAs "Ordinal.cof_succ" .
wd:Q191780 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Cofinality/Ordinal.html#Ordinal.cof_succ> .
wd:Q191780 wl:formalizedAs "Ordinal.cof_ord_cof" .
wd:Q191780 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Cofinality/Ordinal.html#Ordinal.cof_ord_cof> .
wd:Q191780 wl:formalizedAs "IsCofinal" .
wd:Q191780 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/Bounds/Defs.html#IsCofinal> .
wd:Q191780 wl:formalizedAs "Ordinal.IsAcc" .
wd:Q191780 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Ordinal/Topology.html#Ordinal.IsAcc> .
wd:Q191780 wl:formalizedAs "Ordinal.isClosed_iff_iSup" .
wd:Q191780 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Ordinal/Topology.html#Ordinal.isClosed_iff_iSup> .
wd:Q191780 wl:formalizedAs "Ordinal.epsilon_zero_eq_nfp" .
wd:Q191780 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Ordinal/Veblen.html#Ordinal.epsilon_zero_eq_nfp> .
wd:Q191780 wl:formalizedAs "derivedSet" .
wd:Q191780 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/DerivedSet.html#derivedSet> .
wd:Q1783179 wl:formalizedAs "Matrix.orthogonalGroup" .
wd:Q1783179 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/UnitaryGroup.html#Matrix.orthogonalGroup> .
wd:Q1783179 wl:formalizedAs "Matrix.specialOrthogonalGroup" .
wd:Q1783179 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/UnitaryGroup.html#Matrix.specialOrthogonalGroup> .
wd:Q1783179 wl:formalizedAs "Matrix.mem_orthogonalGroup_iff" .
wd:Q1783179 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/UnitaryGroup.html#Matrix.mem_orthogonalGroup_iff> .
wd:Q1783179 wl:formalizedAs "LinearIsometryEquiv.instGroup" .
wd:Q1783179 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Normed/Operator/LinearIsometry.html#LinearIsometryEquiv.instGroup> .
wd:Q1783179 wl:formalizedAs "AffineIsometryEquiv.instGroup" .
wd:Q1783179 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Normed/Affine/Isometry.html#AffineIsometryEquiv.instGroup> .
wd:Q1783179 wl:formalizedAs "Matrix.det_of_mem_unitary" .
wd:Q1783179 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/UnitaryGroup.html#Matrix.det_of_mem_unitary> .
wd:Q1783179 wl:formalizedAs "Matrix.mem_specialOrthogonalGroup_iff" .
wd:Q1783179 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/UnitaryGroup.html#Matrix.mem_specialOrthogonalGroup_iff> .
wd:Q1783179 wl:formalizedAs "Submodule.reflection" .
wd:Q1783179 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/InnerProductSpace/Projection/Reflection.html#Submodule.reflection> .
wd:Q1783179 wl:formalizedAs "QuadraticForm.equivalent_one_zero_neg_one_weighted_sum_squared" .
wd:Q1783179 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/QuadraticForm/Real.html#QuadraticForm.equivalent_one_zero_neg_one_weighted_sum_squared> .
wd:Q1783179 wl:formalizedAs "QuadraticForm.equivalent_of_isAlgClosed" .
wd:Q1783179 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/QuadraticForm/AlgClosed.html#QuadraticForm.equivalent_of_isAlgClosed> .
wd:Q1783179 wl:formalizedAs "char_dvd_card_solutions_of_sum_lt" .
wd:Q1783179 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/FieldTheory/ChevalleyWarning.html#char_dvd_card_solutions_of_sum_lt> .
wd:Q1783179 wl:formalizedAs "LieAlgebra.Orthogonal.so" .
wd:Q1783179 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Lie/Classical.html#LieAlgebra.Orthogonal.so> .
wd:Q1783179 wl:formalizedAs "LinearIsometry.isConformalMap" .
wd:Q1783179 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Normed/Operator/Conformal.html#LinearIsometry.isConformalMap> .
wd:Q1783179 wl:formalizedAs "pinGroup" .
wd:Q1783179 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/CliffordAlgebra/SpinGroup.html#pinGroup> .
wd:Q1783179 wl:formalizedAs "spinGroup" .
wd:Q1783179 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/CliffordAlgebra/SpinGroup.html#spinGroup> .
wd:Q333871 wl:formalizedAs "Matrix.orthogonalGroup" .
wd:Q333871 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/UnitaryGroup.html#Matrix.orthogonalGroup> .
wd:Q333871 wl:formalizedAs "Matrix.mem_orthogonalGroup_iff" .
wd:Q333871 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/UnitaryGroup.html#Matrix.mem_orthogonalGroup_iff> .
wd:Q333871 wl:formalizedAs "Matrix.specialOrthogonalGroup" .
wd:Q333871 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/UnitaryGroup.html#Matrix.specialOrthogonalGroup> .
wd:Q333871 wl:formalizedAs "Matrix.permMatrix_one" .
wd:Q333871 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Matrix/Permutation.html#Matrix.permMatrix_one> .
wd:Q333871 wl:formalizedAs "Equiv.swap" .
wd:Q333871 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Logic/Equiv/Basic.html#Equiv.swap> .
wd:Q333871 wl:formalizedAs "Matrix.det_of_mem_unitary" .
wd:Q333871 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/UnitaryGroup.html#Matrix.det_of_mem_unitary> .
wd:Q333871 wl:formalizedAs "Matrix.det_permutation" .
wd:Q333871 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Matrix/Permutation.html#Matrix.det_permutation> .
wd:Q333871 wl:formalizedAs "LieAlgebra.Orthogonal.so" .
wd:Q333871 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Lie/Classical.html#LieAlgebra.Orthogonal.so> .
wd:Q333871 wl:formalizedAs "exp_mem_unitary_of_mem_skewAdjoint" .
wd:Q333871 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Normed/Algebra/Exponential.html#exp_mem_unitary_of_mem_skewAdjoint> .
wd:Q333871 wl:formalizedAs "Matrix.IsHermitian.spectral_theorem" .
wd:Q333871 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Matrix/Spectrum.html#Matrix.IsHermitian.spectral_theorem> .
wd:Q746242 wl:formalizedAs "ComputablePred.halting_problem" .
wd:Q746242 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Computability/Halting.html#ComputablePred.halting_problem> .
wd:Q48297 wl:formalizedAs "AffineMap" .
wd:Q48297 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/AffineSpace/AffineMap.html#AffineMap> .
wd:Q1413083 wl:formalizedAs "Real.logb" .
wd:Q1413083 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Log/Base.html#Real.logb> .
wd:Q1413083 wl:formalizedAs "Nat.descFactorial" .
wd:Q1413083 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/Factorial/Basic.html#Nat.descFactorial> .
wd:Q1413083 wl:formalizedAs "circleMap" .
wd:Q1413083 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Complex/CircleMap.html#circleMap> .
wd:Q1413083 wl:formalizedAs "ProbabilityTheory.poissonPMF" .
wd:Q1413083 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Probability/Distributions/Poisson/Basic.html#ProbabilityTheory.poissonPMF> .
wd:Q1413083 wl:formalizedAs "ProbabilityTheory.gaussianReal" .
wd:Q1413083 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Probability/Distributions/Gaussian/Real.html#ProbabilityTheory.gaussianReal> .
wd:Q1187620 wl:formalizedAs "SimpleGraph.IsClique" .
wd:Q1187620 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Combinatorics/SimpleGraph/Clique.html#SimpleGraph.IsClique> .
wd:Q1187620 wl:formalizedAs "SimpleGraph.cliqueNum" .
wd:Q1187620 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Combinatorics/SimpleGraph/Clique.html#SimpleGraph.cliqueNum> .
wd:Q1187620 wl:formalizedAs "SimpleGraph.Coloring" .
wd:Q1187620 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Combinatorics/SimpleGraph/Coloring/VertexColoring.html#SimpleGraph.Coloring> .
wd:Q1187620 wl:formalizedAs "SimpleGraph.chromaticNumber" .
wd:Q1187620 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Combinatorics/SimpleGraph/Coloring/VertexColoring.html#SimpleGraph.chromaticNumber> .
wd:Q1187620 wl:formalizedAs "SimpleGraph.cliqueNum_le_chromaticNumber" .
wd:Q1187620 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Combinatorics/SimpleGraph/Coloring/VertexColoring.html#SimpleGraph.cliqueNum_le_chromaticNumber> .
wd:Q1187620 wl:formalizedAs "PartialOrder" .
wd:Q1187620 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/Defs/PartialOrder.html#PartialOrder> .
wd:Q1187620 wl:formalizedAs "IncompRel" .
wd:Q1187620 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/Comparable.html#IncompRel> .
wd:Q1187620 wl:formalizedAs "IsChain" .
wd:Q1187620 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/Preorder/Chain.html#IsChain> .
wd:Q1187620 wl:formalizedAs "IsAntichain" .
wd:Q1187620 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/Antichain.html#IsAntichain> .
wd:Q161519 wl:formalizedAs "Fintype.card_perm" .
wd:Q161519 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Fintype/Perm.html#Fintype.card_perm> .
wd:Q161519 wl:formalizedAs "Equiv.Perm" .
wd:Q161519 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Logic/Equiv/Defs.html#Equiv.Perm> .
wd:Q161519 wl:formalizedAs "Equiv.permGroup" .
wd:Q161519 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/End.html#Equiv.permGroup> .
wd:Q161519 wl:formalizedAs "Equiv.Perm.one_def" .
wd:Q161519 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/Perm/Basic.html#Equiv.Perm.one_def> .
wd:Q161519 wl:formalizedAs "Equiv.Perm.cycleFactorsFinset_noncommProd" .
wd:Q161519 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/Perm/Cycle/Factors.html#Equiv.Perm.cycleFactorsFinset_noncommProd> .
wd:Q161519 wl:formalizedAs "Equiv.Perm.IsCycle" .
wd:Q161519 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/Perm/Cycle/Basic.html#Equiv.Perm.IsCycle> .
wd:Q161519 wl:formalizedAs "Function.IsFixedPt" .
wd:Q161519 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Logic/Function/Defs.html#Function.IsFixedPt> .
wd:Q161519 wl:formalizedAs "derangements" .
wd:Q161519 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Combinatorics/Derangements/Basic.html#derangements> .
wd:Q161519 wl:formalizedAs "Equiv.swap" .
wd:Q161519 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Logic/Equiv/Basic.html#Equiv.swap> .
wd:Q161519 wl:formalizedAs "Equiv.Perm.Disjoint.commute" .
wd:Q161519 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/Perm/Support.html#Equiv.Perm.Disjoint.commute> .
wd:Q161519 wl:formalizedAs "Equiv.Perm.formPerm_reverse" .
wd:Q161519 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/Perm/Cycle/Concrete.html#Equiv.Perm.formPerm_reverse> .
wd:Q161519 wl:formalizedAs "Equiv.Perm.mul_apply" .
wd:Q161519 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/Perm/Basic.html#Equiv.Perm.mul_apply> .
wd:Q161519 wl:formalizedAs "Equiv.trans" .
wd:Q161519 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Logic/Equiv/Defs.html#Equiv.trans> .
wd:Q161519 wl:formalizedAs "Fintype.card_embedding_eq" .
wd:Q161519 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Fintype/CardEmbedding.html#Fintype.card_embedding_eq> .
wd:Q161519 wl:formalizedAs "descPochhammer" .
wd:Q161519 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Polynomial/Pochhammer.html#descPochhammer> .
wd:Q161519 wl:formalizedAs "Finset.powersetCard" .
wd:Q161519 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Finset/Powerset.html#Finset.powersetCard> .
wd:Q161519 wl:formalizedAs "Finset.card_powersetCard" .
wd:Q161519 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Finset/Powerset.html#Finset.card_powersetCard> .
wd:Q161519 wl:formalizedAs "Nat.choose" .
wd:Q161519 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/Choose/Basic.html#Nat.choose> .
wd:Q161519 wl:formalizedAs "Fintype.card_pi_const" .
wd:Q161519 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Fintype/BigOperators.html#Fintype.card_pi_const> .
wd:Q161519 wl:formalizedAs "Equiv.Perm.cycleType" .
wd:Q161519 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/Perm/Cycle/Type.html#Equiv.Perm.cycleType> .
wd:Q161519 wl:formalizedAs "Equiv.Perm.card_of_cycleType" .
wd:Q161519 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/Perm/Centralizer.html#Equiv.Perm.card_of_cycleType> .
wd:Q161519 wl:formalizedAs "IsConj" .
wd:Q161519 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Conj.html#IsConj> .
wd:Q161519 wl:formalizedAs "Equiv.Perm.isConj_iff_cycleType_eq" .
wd:Q161519 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/Perm/Cycle/Type.html#Equiv.Perm.isConj_iff_cycleType_eq> .
wd:Q161519 wl:formalizedAs "orderOf" .
wd:Q161519 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/OrderOfElement.html#orderOf> .
wd:Q161519 wl:formalizedAs "Equiv.Perm.lcm_cycleType" .
wd:Q161519 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/Perm/Cycle/Type.html#Equiv.Perm.lcm_cycleType> .
wd:Q161519 wl:formalizedAs "Equiv.Perm.truncSwapFactors" .
wd:Q161519 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/Perm/Sign.html#Equiv.Perm.truncSwapFactors> .
wd:Q161519 wl:formalizedAs "Equiv.Perm.sign" .
wd:Q161519 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/Perm/Sign.html#Equiv.Perm.sign> .
wd:Q161519 wl:formalizedAs "Matrix.det_permutation" .
wd:Q161519 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Matrix/Permutation.html#Matrix.det_permutation> .
wd:Q161519 wl:formalizedAs "Equiv.Perm.permMatrix" .
wd:Q161519 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Matrix/Permutation.html#Equiv.Perm.permMatrix> .
wd:Q161519 wl:formalizedAs "Matrix.permMatrixHom" .
wd:Q161519 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Matrix/Permutation.html#Matrix.permMatrixHom> .
wd:Q530152 wl:formalizedAs "IsPicardLindelof.exists_eq_forall_mem_Icc_hasDerivWithinAt" .
wd:Q530152 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/ODE/PicardLindelof.html#IsPicardLindelof.exists_eq_forall_mem_Icc_hasDerivWithinAt> .
wd:Q530152 wl:formalizedAs "IsPicardLindelof.picard_eq_of_hasDerivAt" .
wd:Q530152 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/ODE/PicardLindelof.html#IsPicardLindelof.picard_eq_of_hasDerivAt> .
wd:Q530152 wl:formalizedAs "ODE.picard" .
wd:Q530152 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/ODE/PicardLindelof.html#ODE.picard> .
wd:Q530152 wl:formalizedAs "ContractingWith.tendsto_iterate_fixedPoint" .
wd:Q530152 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/MetricSpace/Contracting.html#ContractingWith.tendsto_iterate_fixedPoint> .
wd:Q530152 wl:formalizedAs "ContractingWith.exists_fixedPoint" .
wd:Q530152 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/MetricSpace/Contracting.html#ContractingWith.exists_fixedPoint> .
wd:Q530152 wl:formalizedAs "IsPicardLindelof.FunSpace.exists_contractingWith_iterate_next" .
wd:Q530152 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/ODE/PicardLindelof.html#IsPicardLindelof.FunSpace.exists_contractingWith_iterate_next> .
wd:Q530152 wl:formalizedAs "IsPicardLindelof.FunSpace.dist_iterate_next_apply_le" .
wd:Q530152 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/ODE/PicardLindelof.html#IsPicardLindelof.FunSpace.dist_iterate_next_apply_le> .
wd:Q530152 wl:formalizedAs "ContractingWith.isFixedPt_fixedPoint_iterate" .
wd:Q530152 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/MetricSpace/Contracting.html#ContractingWith.isFixedPt_fixedPoint_iterate> .
wd:Q530152 wl:formalizedAs "ContDiffAt.exists_forall_mem_closedBall_exists_eq_forall_mem_Ioo_hasDerivAt" .
wd:Q530152 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/ODE/PicardLindelof.html#ContDiffAt.exists_forall_mem_closedBall_exists_eq_forall_mem_Ioo_hasDerivAt> .
wd:Q188276 wl:formalizedAs "Fintype.exists_ne_map_eq_of_card_lt" .
wd:Q188276 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Fintype/Pigeonhole.html#Fintype.exists_ne_map_eq_of_card_lt> .
wd:Q188276 wl:formalizedAs "Fintype.exists_lt_card_fiber_of_mul_lt_card" .
wd:Q188276 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Combinatorics/Pigeonhole.html#Fintype.exists_lt_card_fiber_of_mul_lt_card> .
wd:Q188276 wl:formalizedAs "Function.Embedding.isEmpty_of_card_lt" .
wd:Q188276 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Fintype/Pigeonhole.html#Function.Embedding.isEmpty_of_card_lt> .
wd:Q188276 wl:formalizedAs "AddCircle.denseRange_zsmul_coe_iff" .
wd:Q188276 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Instances/AddCircle/DenseSubgroup.html#AddCircle.denseRange_zsmul_coe_iff> .
wd:Q188276 wl:formalizedAs "Finite.exists_ne_map_eq_of_infinite" .
wd:Q188276 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Fintype/Pigeonhole.html#Finite.exists_ne_map_eq_of_infinite> .
wd:Q188276 wl:formalizedAs "Fintype.exists_card_fiber_le_of_card_le_mul" .
wd:Q188276 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Combinatorics/Pigeonhole.html#Fintype.exists_card_fiber_le_of_card_le_mul> .
wd:Q188276 wl:formalizedAs "Finset.exists_ne_map_eq_of_card_lt_of_maps_to" .
wd:Q188276 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Finset/Card.html#Finset.exists_ne_map_eq_of_card_lt_of_maps_to> .
wd:Q188276 wl:formalizedAs "Fintype.card_le_of_injective" .
wd:Q188276 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Fintype/Card.html#Fintype.card_le_of_injective> .
wd:Q188276 wl:formalizedAs "Fintype.card_le_of_surjective" .
wd:Q188276 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Fintype/Card.html#Fintype.card_le_of_surjective> .
wd:Q188276 wl:formalizedAs "Fintype.exists_le_card_fiber_of_mul_le_card" .
wd:Q188276 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Combinatorics/Pigeonhole.html#Fintype.exists_le_card_fiber_of_mul_le_card> .
wd:Q188276 wl:formalizedAs "Fintype.exists_card_fiber_lt_of_card_lt_mul" .
wd:Q188276 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Combinatorics/Pigeonhole.html#Fintype.exists_card_fiber_lt_of_card_lt_mul> .
wd:Q188276 wl:formalizedAs "Cardinal.le_def" .
wd:Q188276 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Order.html#Cardinal.le_def> .
wd:Q188276 wl:formalizedAs "Cardinal.exists_uncountable_fiber" .
wd:Q188276 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Pigeonhole.html#Cardinal.exists_uncountable_fiber> .
wd:Q188276 wl:formalizedAs "Cardinal.infinite_pigeonhole" .
wd:Q188276 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Pigeonhole.html#Cardinal.infinite_pigeonhole> .
wd:Q205692 wl:formalizedAs "poissonMeasure" .
wd:Q205692 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Probability/Distributions/Poisson/Basic.html#poissonMeasure> .
wd:Q205692 wl:formalizedAs "poissonMeasure_singleton" .
wd:Q205692 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Probability/Distributions/Poisson/Basic.html#poissonMeasure_singleton> .
wd:Q205692 wl:formalizedAs "tendsto_choose_mul_pow_of_tendsto_mul_atTop" .
wd:Q205692 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Probability/Distributions/Poisson/PoissonLimitThm.html#tendsto_choose_mul_pow_of_tendsto_mul_atTop> .
wd:Q206925 wl:formalizedAs "FormalMultilinearSeries" .
wd:Q206925 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/FormalMultilinearSeries.html#FormalMultilinearSeries> .
wd:Q206925 wl:formalizedAs "Polynomial.taylor" .
wd:Q206925 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Polynomial/Taylor.html#Polynomial.taylor> .
wd:Q206925 wl:formalizedAs "tsum_geometric_of_norm_lt_one" .
wd:Q206925 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecificLimits/Normed.html#tsum_geometric_of_norm_lt_one> .
wd:Q206925 wl:formalizedAs "NormedSpace.exp_eq_tsum" .
wd:Q206925 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Normed/Algebra/Exponential.html#NormedSpace.exp_eq_tsum> .
wd:Q206925 wl:formalizedAs "Real.sin_eq_tsum" .
wd:Q206925 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Trigonometric/Series.html#Real.sin_eq_tsum> .
wd:Q206925 wl:formalizedAs "FormalMultilinearSeries.radius" .
wd:Q206925 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Analytic/ConvergenceRadius.html#FormalMultilinearSeries.radius> .
wd:Q206925 wl:formalizedAs "FormalMultilinearSeries.radius_inv_eq_limsup" .
wd:Q206925 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Analytic/RadiusLiminf.html#FormalMultilinearSeries.radius_inv_eq_limsup> .
wd:Q206925 wl:formalizedAs "FormalMultilinearSeries.ofScalars_radius_eq_inv_of_tendsto" .
wd:Q206925 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Analytic/OfScalars.html#FormalMultilinearSeries.ofScalars_radius_eq_inv_of_tendsto> .
wd:Q206925 wl:formalizedAs "FormalMultilinearSeries.summable_norm_apply" .
wd:Q206925 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Analytic/ConvergenceRadius.html#FormalMultilinearSeries.summable_norm_apply> .
wd:Q206925 wl:formalizedAs "Real.tendsto_tsum_powerSeries_nhdsWithin_lt" .
wd:Q206925 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Complex/AbelLimit.html#Real.tendsto_tsum_powerSeries_nhdsWithin_lt> .
wd:Q206925 wl:formalizedAs "HasFPowerSeriesOnBall.add" .
wd:Q206925 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Analytic/Constructions.html#HasFPowerSeriesOnBall.add> .
wd:Q206925 wl:formalizedAs "FormalMultilinearSeries.min_radius_le_radius_add" .
wd:Q206925 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Analytic/ConvergenceRadius.html#FormalMultilinearSeries.min_radius_le_radius_add> .
wd:Q206925 wl:formalizedAs "AnalyticAt.mul" .
wd:Q206925 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Analytic/Constructions.html#AnalyticAt.mul> .
wd:Q206925 wl:formalizedAs "tsum_mul_tsum_eq_tsum_sum_antidiagonal" .
wd:Q206925 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Algebra/InfiniteSum/Ring.html#tsum_mul_tsum_eq_tsum_sum_antidiagonal> .
wd:Q206925 wl:formalizedAs "PowerSeries.inv" .
wd:Q206925 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/PowerSeries/Inverse.html#PowerSeries.inv> .
wd:Q206925 wl:formalizedAs "HasFPowerSeriesOnBall.fderiv" .
wd:Q206925 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/FDeriv/Analytic.html#HasFPowerSeriesOnBall.fderiv> .
wd:Q206925 wl:formalizedAs "AnalyticAt" .
wd:Q206925 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Analytic/Basic.html#AnalyticAt> .
wd:Q206925 wl:formalizedAs "FormalMultilinearSeries.analyticOnNhd" .
wd:Q206925 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Analytic/ChangeOrigin.html#FormalMultilinearSeries.analyticOnNhd> .
wd:Q206925 wl:formalizedAs "DifferentiableOn.analyticAt" .
wd:Q206925 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Complex/CauchyIntegral.html#DifferentiableOn.analyticAt> .
wd:Q206925 wl:formalizedAs "AnalyticAt.contDiffAt" .
wd:Q206925 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/ContDiff/Defs.html#AnalyticAt.contDiffAt> .
wd:Q206925 wl:formalizedAs "HasFPowerSeriesOnBall.factorial_smul" .
wd:Q206925 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/FDeriv/Analytic.html#HasFPowerSeriesOnBall.factorial_smul> .
wd:Q206925 wl:formalizedAs "HasFPowerSeriesOnBall.hasSum_iteratedFDeriv" .
wd:Q206925 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/FDeriv/Analytic.html#HasFPowerSeriesOnBall.hasSum_iteratedFDeriv> .
wd:Q206925 wl:formalizedAs "AnalyticOnNhd.eqOn_of_preconnected_of_eventuallyEq" .
wd:Q206925 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Analytic/Uniqueness.html#AnalyticOnNhd.eqOn_of_preconnected_of_eventuallyEq> .
wd:Q206925 wl:formalizedAs "PowerSeries.mk" .
wd:Q206925 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/PowerSeries/Basic.html#PowerSeries.mk> .
wd:Q206925 wl:formalizedAs "FormalMultilinearSeries.hasFPowerSeriesOnBall" .
wd:Q206925 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Analytic/Basic.html#FormalMultilinearSeries.hasFPowerSeriesOnBall> .
wd:Q206925 wl:formalizedAs "PowerSeries" .
wd:Q206925 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/PowerSeries/Basic.html#PowerSeries> .
wd:Q206925 wl:formalizedAs "MvPowerSeries" .
wd:Q206925 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/MvPowerSeries/Basic.html#MvPowerSeries> .
wd:Q206925 wl:formalizedAs "PowerSeries.order" .
wd:Q206925 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/PowerSeries/Order.html#PowerSeries.order> .
wd:Q915906 wl:formalizedAs "PresentedGroup" .
wd:Q915906 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/PresentedGroup.html#PresentedGroup> .
wd:Q915906 wl:formalizedAs "FreeGroup" .
wd:Q915906 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/FreeGroup/Basic.html#FreeGroup> .
wd:Q915906 wl:formalizedAs "Group.IsFinitelyPresented" .
wd:Q915906 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/FinitelyPresentedGroup.html#Group.IsFinitelyPresented> .
wd:Q863912 wl:formalizedAs "Ideal.IsPrime" .
wd:Q863912 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Ideal/Prime.html#Ideal.IsPrime> .
wd:Q863912 wl:formalizedAs "Ideal.span_singleton_prime" .
wd:Q863912 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Ideal/Maximal.html#Ideal.span_singleton_prime> .
wd:Q863912 wl:formalizedAs "Nat.Prime.dvd_mul" .
wd:Q863912 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/Prime/Defs.html#Nat.Prime.dvd_mul> .
wd:Q863912 wl:formalizedAs "PrimeSpectrum" .
wd:Q863912 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Spectrum/Prime/Defs.html#PrimeSpectrum> .
wd:Q863912 wl:formalizedAs "AlgebraicGeometry.AffineScheme" .
wd:Q863912 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/AlgebraicGeometry/AffineScheme.html#AlgebraicGeometry.AffineScheme> .
wd:Q863912 wl:formalizedAs "Ideal.IsPrime.mul_notMem" .
wd:Q863912 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Ideal/Prime.html#Ideal.IsPrime.mul_notMem> .
wd:Q863912 wl:formalizedAs "Ideal.primeCompl" .
wd:Q863912 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Ideal/Prime.html#Ideal.primeCompl> .
wd:Q863912 wl:formalizedAs "PrincipalIdealRing.isMaximal_of_irreducible" .
wd:Q863912 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/PrincipalIdealDomain.html#PrincipalIdealRing.isMaximal_of_irreducible> .
wd:Q863912 wl:formalizedAs "Polynomial.irreducible_of_eisenstein_criterion" .
wd:Q863912 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Polynomial/Eisenstein/Criterion.html#Polynomial.irreducible_of_eisenstein_criterion> .
wd:Q863912 wl:formalizedAs "Ideal.IsMaximal" .
wd:Q863912 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Ideal/Maximal.html#Ideal.IsMaximal> .
wd:Q863912 wl:formalizedAs "Ideal.IsMaximal.isPrime" .
wd:Q863912 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Ideal/Maximal.html#Ideal.IsMaximal.isPrime> .
wd:Q863912 wl:formalizedAs "Ideal.IsPrime.isMaximal_of_ne_bot" .
wd:Q863912 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/KrullDimension/Basic.html#Ideal.IsPrime.isMaximal_of_ne_bot> .
wd:Q863912 wl:formalizedAs "MvPolynomial.isMaximal_iff_eq_vanishingIdeal_singleton" .
wd:Q863912 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Nullstellensatz.html#MvPolynomial.isMaximal_iff_eq_vanishingIdeal_singleton> .
wd:Q863912 wl:formalizedAs "Ideal.Quotient.isDomain_iff_prime" .
wd:Q863912 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Ideal/Quotient/Basic.html#Ideal.Quotient.isDomain_iff_prime> .
wd:Q863912 wl:formalizedAs "Ideal.isPrime_bot" .
wd:Q863912 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Ideal/Prime.html#Ideal.isPrime_bot> .
wd:Q863912 wl:formalizedAs "PrimeSpectrum.instIsEmpty" .
wd:Q863912 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Spectrum/Prime/Basic.html#PrimeSpectrum.instIsEmpty> .
wd:Q863912 wl:formalizedAs "Ideal.exists_maximal" .
wd:Q863912 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Ideal/Maximal.html#Ideal.exists_maximal> .
wd:Q863912 wl:formalizedAs "Ideal.isPrime_of_maximally_disjoint" .
wd:Q863912 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Ideal/Maximal.html#Ideal.isPrime_of_maximally_disjoint> .
wd:Q863912 wl:formalizedAs "Ideal.IsPrime.comap" .
wd:Q863912 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Ideal/Maps.html#Ideal.IsPrime.comap> .
wd:Q863912 wl:formalizedAs "Ideal.IsMinimalPrime" .
wd:Q863912 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Ideal/MinimalPrime/Basic.html#Ideal.IsMinimalPrime> .
wd:Q863912 wl:formalizedAs "minimalPrimes.equivIrreducibleComponents" .
wd:Q863912 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Spectrum/Prime/Topology.html#minimalPrimes.equivIrreducibleComponents> .
wd:Q863912 wl:formalizedAs "UniqueFactorizationMonoid.iff_exists_prime_mem_of_isPrime" .
wd:Q863912 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/UniqueFactorizationDomain/Kaplansky.html#UniqueFactorizationMonoid.iff_exists_prime_mem_of_isPrime> .
wd:Q863912 wl:formalizedAs "PrimeSpectrum.isIrreducible_iff_vanishingIdeal_isPrime" .
wd:Q863912 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Spectrum/Prime/Topology.html#PrimeSpectrum.isIrreducible_iff_vanishingIdeal_isPrime> .
wd:Q863912 wl:formalizedAs "AlgebraicGeometry.Scheme" .
wd:Q863912 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/AlgebraicGeometry/Scheme.html#AlgebraicGeometry.Scheme> .
wd:Q863912 wl:formalizedAs "exists_le_isAssociatedPrime_of_isNoetherianRing" .
wd:Q863912 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Ideal/AssociatedPrime/Basic.html#exists_le_isAssociatedPrime_of_isNoetherianRing> .
wd:Q863912 wl:formalizedAs "Ideal.subset_union_prime" .
wd:Q863912 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Ideal/Operations.html#Ideal.subset_union_prime> .
wd:Q863912 wl:formalizedAs "Ideal.IsPrime.inf_le&#x27;" .
wd:Q863912 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Ideal/Operations.html#Ideal.IsPrime.inf_le'> .
wd:Q863912 wl:formalizedAs "Ideal.IsOka.isPrime_of_maximal_not" .
wd:Q863912 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Ideal/Oka.html#Ideal.IsOka.isPrime_of_maximal_not> .
wd:Q863912 wl:formalizedAs "Ideal.isOka_isPrincipal" .
wd:Q863912 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/PrincipalIdealDomainOfPrime.html#Ideal.isOka_isPrincipal> .
wd:Q207522 wl:formalizedAs "MeasureTheory.pdf" .
wd:Q207522 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Probability/Density.html#MeasureTheory.pdf> .
wd:Q207522 wl:formalizedAs "MeasureTheory.HasPDF" .
wd:Q207522 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Probability/Density.html#MeasureTheory.HasPDF> .
wd:Q207522 wl:formalizedAs "MeasureTheory.withDensity_eq_iff_of_sigmaFinite" .
wd:Q207522 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/MeasureTheory/Function/AEEqOfLIntegral.html#MeasureTheory.withDensity_eq_iff_of_sigmaFinite> .
wd:Q207522 wl:formalizedAs "MeasureTheory.pdf.IsUniform.pdf_eq" .
wd:Q207522 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Probability/Distributions/Uniform.html#MeasureTheory.pdf.IsUniform.pdf_eq> .
wd:Q207522 wl:formalizedAs "ProbabilityTheory.gaussianPDFReal" .
wd:Q207522 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Probability/Distributions/Gaussian/Real.html#ProbabilityTheory.gaussianPDFReal> .
wd:Q207522 wl:formalizedAs "MeasureTheory.pdf.integral_mul_eq_integral" .
wd:Q207522 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Probability/Density.html#MeasureTheory.pdf.integral_mul_eq_integral> .
wd:Q207522 wl:formalizedAs "MeasureTheory.noAtoms_withDensity" .
wd:Q207522 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/MeasureTheory/Measure/WithDensity.html#MeasureTheory.noAtoms_withDensity> .
wd:Q207522 wl:formalizedAs "MeasureTheory.pdf.indepFun_iff_pdf_prod_eq_pdf_mul_pdf" .
wd:Q207522 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Probability/Density.html#MeasureTheory.pdf.indepFun_iff_pdf_prod_eq_pdf_mul_pdf> .
wd:Q207522 wl:formalizedAs "MeasureTheory.pdf.integral_pdf_smul" .
wd:Q207522 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Probability/Density.html#MeasureTheory.pdf.integral_pdf_smul> .
wd:Q207522 wl:formalizedAs "ProbabilityTheory.IndepFun.pdf_add_eq_lconvolution_pdf" .
wd:Q207522 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Probability/Density.html#ProbabilityTheory.IndepFun.pdf_add_eq_lconvolution_pdf> .
wd:Q7246880 wl:formalizedAs "MeasureTheory.uniformOn_univ" .
wd:Q7246880 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Probability/UniformOn.html#MeasureTheory.uniformOn_univ> .
wd:Q7246880 wl:formalizedAs "ProbabilityTheory.strong_law_ae" .
wd:Q7246880 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Probability/StrongLaw.html#ProbabilityTheory.strong_law_ae> .
wd:Q623472 wl:formalizedAs "MeasureTheory.IsProbabilityMeasure" .
wd:Q623472 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/MeasureTheory/Measure/Typeclasses/Probability.html#MeasureTheory.IsProbabilityMeasure> .
wd:Q623472 wl:formalizedAs "MeasurableSpace" .
wd:Q623472 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/MeasureTheory/MeasurableSpace/Defs.html#MeasurableSpace> .
wd:Q623472 wl:formalizedAs "MeasurableSet" .
wd:Q623472 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/MeasureTheory/MeasurableSpace/Defs.html#MeasurableSet> .
wd:Q623472 wl:formalizedAs "MeasureTheory.ProbabilityMeasure" .
wd:Q623472 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/MeasureTheory/Measure/ProbabilityMeasure.html#MeasureTheory.ProbabilityMeasure> .
wd:Q623472 wl:formalizedAs "MeasureTheory.MeasureSpace" .
wd:Q623472 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/MeasureTheory/Measure/MeasureSpaceDef.html#MeasureTheory.MeasureSpace> .
wd:Q623472 wl:formalizedAs "MeasurableSet.iInter" .
wd:Q623472 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/MeasureTheory/MeasurableSpace/Defs.html#MeasurableSet.iInter> .
wd:Q623472 wl:formalizedAs "PMF" .
wd:Q623472 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Probability/ProbabilityMassFunction/Basic.html#PMF> .
wd:Q623472 wl:formalizedAs "MeasureTheory.Measure.IsComplete" .
wd:Q623472 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/MeasureTheory/Measure/NullMeasurable.html#MeasureTheory.Measure.IsComplete> .
wd:Q623472 wl:formalizedAs "Measurable" .
wd:Q623472 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/MeasureTheory/MeasurableSpace/Defs.html#Measurable> .
wd:Q623472 wl:formalizedAs "MeasureTheory.Measure.map" .
wd:Q623472 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/MeasureTheory/Measure/Map.html#MeasureTheory.Measure.map> .
wd:Q623472 wl:formalizedAs "MeasurableSpace.measurableSet_top" .
wd:Q623472 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/MeasureTheory/MeasurableSpace/Defs.html#MeasurableSpace.measurableSet_top> .
wd:Q623472 wl:formalizedAs "MeasureTheory.borel" .
wd:Q623472 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.html#MeasureTheory.borel> .
wd:Q623472 wl:formalizedAs "ProbabilityTheory.cond" .
wd:Q623472 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Probability/ConditionalProbability.html#ProbabilityTheory.cond> .
wd:Q623472 wl:formalizedAs "ProbabilityTheory.cond_isProbabilityMeasure" .
wd:Q623472 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Probability/ConditionalProbability.html#ProbabilityTheory.cond_isProbabilityMeasure> .
wd:Q623472 wl:formalizedAs "ProbabilityTheory.IndepSet" .
wd:Q623472 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Probability/Independence/Basic.html#ProbabilityTheory.IndepSet> .
wd:Q623472 wl:formalizedAs "ProbabilityTheory.IndepFun" .
wd:Q623472 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Probability/Independence/Basic.html#ProbabilityTheory.IndepFun> .
wd:Q623472 wl:formalizedAs "Disjoint" .
wd:Q623472 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/Disjoint.html#Disjoint> .
wd:Q623472 wl:formalizedAs "MeasureTheory.measure_union" .
wd:Q623472 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/MeasureTheory/Measure/MeasureSpace.html#MeasureTheory.measure_union> .
wd:Q623472 wl:formalizedAs "Set.inter" .
wd:Q623472 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Set/Defs.html#Set.inter> .
wd:Q5862903 wl:formalizedAs "MeasurableSet" .
wd:Q5862903 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/MeasureTheory/MeasurableSpace/Defs.html#MeasurableSet> .
wd:Q5862903 wl:formalizedAs "IsProbabilityMeasure" .
wd:Q5862903 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/MeasureTheory/Measure/Typeclasses/Probability.html#IsProbabilityMeasure> .
wd:Q5862903 wl:formalizedAs "ProbabilityMeasure" .
wd:Q5862903 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/MeasureTheory/Measure/ProbabilityMeasure.html#ProbabilityMeasure> .
wd:Q5862903 wl:formalizedAs "ProbabilityTheory.uniformOn" .
wd:Q5862903 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Probability/UniformOn.html#ProbabilityTheory.uniformOn> .
wd:Q5862903 wl:formalizedAs "PMF" .
wd:Q5862903 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Probability/ProbabilityMassFunction/Basic.html#PMF> .
wd:Q5862903 wl:formalizedAs "PMF.toMeasure_apply" .
wd:Q5862903 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Probability/ProbabilityMassFunction/Basic.html#PMF.toMeasure_apply> .
wd:Q5862903 wl:formalizedAs "ProbabilityTheory.cdf" .
wd:Q5862903 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Probability/CDF.html#ProbabilityTheory.cdf> .
wd:Q5862903 wl:formalizedAs "ProbabilityTheory.monotone_cdf" .
wd:Q5862903 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Probability/CDF.html#ProbabilityTheory.monotone_cdf> .
wd:Q5862903 wl:formalizedAs "MeasureTheory.pdf" .
wd:Q5862903 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Probability/Density.html#MeasureTheory.pdf> .
wd:Q5862903 wl:formalizedAs "ProbabilityTheory.cdf_measure_stieltjesFunction" .
wd:Q5862903 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Probability/CDF.html#ProbabilityTheory.cdf_measure_stieltjesFunction> .
wd:Q5862903 wl:formalizedAs "MeasureTheory.Measure" .
wd:Q5862903 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/MeasureTheory/Measure/MeasureSpaceDef.html#MeasureTheory.Measure> .
wd:Q5862903 wl:formalizedAs "MeasureTheory.Measure.rnDeriv" .
wd:Q5862903 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/MeasureTheory/Measure/Decomposition/Lebesgue.html#MeasureTheory.Measure.rnDeriv> .
wd:Q5862903 wl:formalizedAs "MeasureTheory.TendstoInDistribution" .
wd:Q5862903 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/MeasureTheory/Function/ConvergenceInDistribution.html#MeasureTheory.TendstoInDistribution> .
wd:Q5862903 wl:formalizedAs "MeasureTheory.TendstoInMeasure" .
wd:Q5862903 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/MeasureTheory/Function/ConvergenceInMeasure.html#MeasureTheory.TendstoInMeasure> .
wd:Q5862903 wl:formalizedAs "MeasureTheory.TendstoInMeasure.tendstoInDistribution" .
wd:Q5862903 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/MeasureTheory/Function/ConvergenceInDistribution.html#MeasureTheory.TendstoInMeasure.tendstoInDistribution> .
wd:Q5862903 wl:formalizedAs "ProbabilityTheory.strong_law_ae" .
wd:Q5862903 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Probability/StrongLaw.html#ProbabilityTheory.strong_law_ae> .
wd:Q5862903 wl:formalizedAs "ProbabilityTheory.tendstoInDistribution_inv_sqrt_mul_sum_sub" .
wd:Q5862903 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Probability/CentralLimitTheorem.html#ProbabilityTheory.tendstoInDistribution_inv_sqrt_mul_sum_sub> .
wd:Q942423 wl:formalizedAs "Module.Projective" .
wd:Q942423 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Module/Projective.html#Module.Projective> .
wd:Q942423 wl:formalizedAs "Module.Projective.of_free" .
wd:Q942423 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Module/Projective.html#Module.Projective.of_free> .
wd:Q942423 wl:formalizedAs "Module.projective_lifting_property" .
wd:Q942423 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Module/Projective.html#Module.projective_lifting_property> .
wd:Q942423 wl:formalizedAs "Module.Projective.iff_split_of_projective" .
wd:Q942423 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Module/Projective.html#Module.Projective.iff_split_of_projective> .
wd:Q942423 wl:formalizedAs "Module.Projective.iff_split" .
wd:Q942423 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Module/Projective.html#Module.Projective.iff_split> .
wd:Q942423 wl:formalizedAs "CategoryTheory.Projective.projective_iff_preservesEpimorphisms_preadditiveCoyoneda_obj" .
wd:Q942423 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Preadditive/Yoneda/Projective.html#CategoryTheory.Projective.projective_iff_preservesEpimorphisms_preadditiveCoyoneda_obj> .
wd:Q942423 wl:formalizedAs "Module.projective_def" .
wd:Q942423 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Module/Projective.html#Module.projective_def> .
wd:Q942423 wl:formalizedAs "Module.Projective.of_split" .
wd:Q942423 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Module/Projective.html#Module.Projective.of_split> .
wd:Q942423 wl:formalizedAs "Module.Free.of_divisionRing" .
wd:Q942423 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Basis/VectorSpace.html#Module.Free.of_divisionRing> .
wd:Q942423 wl:formalizedAs "Module.projective_of_isSemisimpleRing" .
wd:Q942423 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/SimpleModule/InjectiveProjective.html#Module.projective_of_isSemisimpleRing> .
wd:Q942423 wl:formalizedAs "Module.Flat.of_projective" .
wd:Q942423 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Flat/Basic.html#Module.Flat.of_projective> .
wd:Q942423 wl:formalizedAs "Module.Flat.projective_of_finitePresentation" .
wd:Q942423 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Flat/EquationalCriterion.html#Module.Flat.projective_of_finitePresentation> .
wd:Q942423 wl:formalizedAs "CategoryTheory.ProjectiveResolution" .
wd:Q942423 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Preadditive/Projective/Resolution.html#CategoryTheory.ProjectiveResolution> .
wd:Q942423 wl:formalizedAs "ModuleCat.enoughProjectives" .
wd:Q942423 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Category/ModuleCat/Projective.html#ModuleCat.enoughProjectives> .
wd:Q942423 wl:formalizedAs "CategoryTheory.projectiveDimension" .
wd:Q942423 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Abelian/Projective/Dimension.html#CategoryTheory.projectiveDimension> .
wd:Q942423 wl:formalizedAs "CategoryTheory.projective_iff_hasProjectiveDimensionLT_one" .
wd:Q942423 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Abelian/Projective/Dimension.html#CategoryTheory.projective_iff_hasProjectiveDimensionLT_one> .
wd:Q942423 wl:formalizedAs "Module.projective_of_isLocalizedModule" .
wd:Q942423 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/LocalProperties/Projective.html#Module.projective_of_isLocalizedModule> .
wd:Q942423 wl:formalizedAs "Module.freeLocus_eq_univ_iff" .
wd:Q942423 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Spectrum/Prime/FreeLocus.html#Module.freeLocus_eq_univ_iff> .
wd:Q942423 wl:formalizedAs "Module.rankAtStalk" .
wd:Q942423 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Spectrum/Prime/FreeLocus.html#Module.rankAtStalk> .
wd:Q942423 wl:formalizedAs "Module.isLocallyConstant_rankAtStalk" .
wd:Q942423 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Spectrum/Prime/FreeLocus.html#Module.isLocallyConstant_rankAtStalk> .
wd:Q877775 wl:formalizedAs "Projectivization.equivSubmodule" .
wd:Q877775 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Projectivization/Basic.html#Projectivization.equivSubmodule> .
wd:Q877775 wl:formalizedAs "projectivizationSetoid" .
wd:Q877775 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Projectivization/Basic.html#projectivizationSetoid> .
wd:Q877775 wl:formalizedAs "Projectivization" .
wd:Q877775 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Projectivization/Basic.html#Projectivization> .
wd:Q877775 wl:formalizedAs "Projectivization.Subspace" .
wd:Q877775 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Projectivization/Subspace.html#Projectivization.Subspace> .
wd:Q877775 wl:formalizedAs "Projectivization.Subspace.instInfSet" .
wd:Q877775 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Projectivization/Subspace.html#Projectivization.Subspace.instInfSet> .
wd:Q877775 wl:formalizedAs "Projectivization.Subspace.span" .
wd:Q877775 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Projectivization/Subspace.html#Projectivization.Subspace.span> .
wd:Q877775 wl:formalizedAs "Projectivization.Independent" .
wd:Q877775 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Projectivization/Independence.html#Projectivization.Independent> .
wd:Q877775 wl:formalizedAs "Complex.exists_root" .
wd:Q877775 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Complex/Polynomial/Basic.html#Complex.exists_root> .
wd:Q877775 wl:formalizedAs "AlgebraicGeometry.Proj" .
wd:Q877775 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Scheme.html#AlgebraicGeometry.Proj> .
wd:Q877775 wl:formalizedAs "littleWedderburn" .
wd:Q877775 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/LittleWedderburn.html#littleWedderburn> .
wd:Q877775 wl:formalizedAs "Projectivization.map" .
wd:Q877775 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Projectivization/Basic.html#Projectivization.map> .
wd:Q877775 wl:formalizedAs "Matrix.ProjGenLinGroup" .
wd:Q877775 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Matrix/GeneralLinearGroup/Projective.html#Matrix.ProjGenLinGroup> .
wd:Q877775 wl:formalizedAs "Module.Grassmannian" .
wd:Q877775 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Grassmannian.html#Module.Grassmannian> .
wd:Q837863 wl:formalizedAs "irrational_sqrt_two" .
wd:Q837863 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/Real/Irrational.html#irrational_sqrt_two> .
wd:Q15909572 wl:formalizedAs "quadratic_eq_zero_iff" .
wd:Q15909572 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/QuadraticDiscriminant.html#quadratic_eq_zero_iff> .
wd:Q15909572 wl:formalizedAs "discrim" .
wd:Q15909572 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/QuadraticDiscriminant.html#discrim> .
wd:Q472883 wl:formalizedAs "legendreSym.quadratic_reciprocity" .
wd:Q472883 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/LegendreSymbol/QuadraticReciprocity.html#legendreSym.quadratic_reciprocity> .
wd:Q472883 wl:formalizedAs "legendreSym.quadratic_reciprocity_one_mod_four" .
wd:Q472883 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/LegendreSymbol/QuadraticReciprocity.html#legendreSym.quadratic_reciprocity_one_mod_four> .
wd:Q472883 wl:formalizedAs "legendreSym.quadratic_reciprocity_three_mod_four" .
wd:Q472883 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/LegendreSymbol/QuadraticReciprocity.html#legendreSym.quadratic_reciprocity_three_mod_four> .
wd:Q472883 wl:formalizedAs "ZMod.exists_sq_eq_neg_one_iff" .
wd:Q472883 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/LegendreSymbol/Basic.html#ZMod.exists_sq_eq_neg_one_iff> .
wd:Q472883 wl:formalizedAs "ZMod.exists_sq_eq_two_iff" .
wd:Q472883 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/LegendreSymbol/QuadraticReciprocity.html#ZMod.exists_sq_eq_two_iff> .
wd:Q472883 wl:formalizedAs "legendreSym.at_neg_one" .
wd:Q472883 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/LegendreSymbol/Basic.html#legendreSym.at_neg_one> .
wd:Q472883 wl:formalizedAs "ZMod.pow_card_sub_one_eq_one" .
wd:Q472883 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/FieldTheory/Finite/Basic.html#ZMod.pow_card_sub_one_eq_one> .
wd:Q472883 wl:formalizedAs "legendreSym" .
wd:Q472883 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/LegendreSymbol/Basic.html#legendreSym> .
wd:Q472883 wl:formalizedAs "ZMod.exists_sq_eq_neg_two_iff" .
wd:Q472883 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/LegendreSymbol/QuadraticReciprocity.html#ZMod.exists_sq_eq_neg_two_iff> .
wd:Q472883 wl:formalizedAs "jacobiSym.quadratic_reciprocity" .
wd:Q472883 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/LegendreSymbol/JacobiSymbol.html#jacobiSym.quadratic_reciprocity> .
wd:Q472883 wl:formalizedAs "jacobiSym" .
wd:Q472883 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/LegendreSymbol/JacobiSymbol.html#jacobiSym> .
wd:Q918099 wl:formalizedAs "Finite.exists_infinite_fiber" .
wd:Q918099 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Fintype/Pigeonhole.html#Finite.exists_infinite_fiber> .
wd:Q23937546 wl:formalizedAs "Projectivization" .
wd:Q23937546 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Projectivization/Basic.html#Projectivization> .
wd:Q23937546 wl:formalizedAs "Projectivization.equivSubmodule" .
wd:Q23937546 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Projectivization/Basic.html#Projectivization.equivSubmodule> .
wd:Q23937546 wl:formalizedAs "projectivizationSetoid" .
wd:Q23937546 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Projectivization/Basic.html#projectivizationSetoid> .
wd:Q23937546 wl:formalizedAs "Matrix.op_smul_eq_vecMul" .
wd:Q23937546 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Matrix/Action.html#Matrix.op_smul_eq_vecMul> .
wd:Q23937546 wl:formalizedAs "Projectivization.generalLinearGroup_smul_def" .
wd:Q23937546 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Projectivization/Action.html#Projectivization.generalLinearGroup_smul_def> .
wd:Q23937546 wl:formalizedAs "Matrix.ProjGenLinGroup" .
wd:Q23937546 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Matrix/GeneralLinearGroup/Projective.html#Matrix.ProjGenLinGroup> .
wd:Q23937546 wl:formalizedAs "OnePoint.smul_some_eq_ite" .
wd:Q23937546 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Compactification/OnePoint/ProjectiveLine.html#OnePoint.smul_some_eq_ite> .
wd:Q7322955 wl:formalizedAs "TensorProduct.contractLeft" .
wd:Q7322955 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Contraction.html#TensorProduct.contractLeft> .
wd:Q7322955 wl:formalizedAs "Basis.ext_elem_iff" .
wd:Q7322955 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Basis/Defs.html#Basis.ext_elem_iff> .
wd:Q7322955 wl:formalizedAs "MultilinearMap.alternatization" .
wd:Q7322955 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Alternating/Basic.html#MultilinearMap.alternatization> .
wd:Q7322955 wl:formalizedAs "fderiv_mul" .
wd:Q7322955 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/FDeriv/Mul.html#fderiv_mul> .
wd:Q7322955 wl:formalizedAs "CovariantDerivative" .
wd:Q7322955 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Manifold/VectorBundle/CovariantDerivative/Basic.html#CovariantDerivative> .
wd:Q7322955 wl:formalizedAs "IsCovariantDerivativeOn.leibniz" .
wd:Q7322955 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Manifold/VectorBundle/CovariantDerivative/Basic.html#IsCovariantDerivativeOn.leibniz> .
wd:Q7322955 wl:formalizedAs "extDeriv" .
wd:Q7322955 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/DifferentialForm/Basic.html#extDeriv> .
wd:Q7322955 wl:formalizedAs "VectorField.mlieBracket_self" .
wd:Q7322955 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Manifold/VectorField/LieBracket.html#VectorField.mlieBracket_self> .
wd:Q7322955 wl:formalizedAs "Matrix.one_apply" .
wd:Q7322955 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Matrix/Diagonal.html#Matrix.one_apply> .
wd:Q7322955 wl:formalizedAs "CovariantDerivative.torsion" .
wd:Q7322955 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Manifold/VectorBundle/CovariantDerivative/Torsion.html#CovariantDerivative.torsion> .
wd:Q825857 wl:formalizedAs "onePointEquivSphereOfFinrankEq" .
wd:Q825857 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Compactification/OnePoint/Sphere.html#onePointEquivSphereOfFinrankEq> .
wd:Q825857 wl:formalizedAs "OnePoint.equivProjectivization" .
wd:Q825857 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Compactification/OnePoint/ProjectiveLine.html#OnePoint.equivProjectivization> .
wd:Q825857 wl:formalizedAs "stereographic" .
wd:Q825857 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Manifold/Instances/Sphere.html#stereographic> .
wd:Q825857 wl:formalizedAs "MeromorphicOn" .
wd:Q825857 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Meromorphic/Basic.html#MeromorphicOn> .
wd:Q825857 wl:formalizedAs "MDifferentiable.exists_eq_const_of_compactSpace" .
wd:Q825857 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Manifold/Complex.html#MDifferentiable.exists_eq_const_of_compactSpace> .
wd:Q753035 wl:formalizedAs "MDifferentiable.comp" .
wd:Q753035 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Manifold/MFDeriv/Basic.html#MDifferentiable.comp> .
wd:Q753035 wl:formalizedAs "MDifferentiable.exists_eq_const_of_compactSpace" .
wd:Q753035 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Manifold/Complex.html#MDifferentiable.exists_eq_const_of_compactSpace> .
wd:Q187235 wl:formalizedAs "riemannZeta" .
wd:Q187235 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/LSeries/RiemannZeta.html#riemannZeta> .
wd:Q187235 wl:formalizedAs "differentiableAt_riemannZeta" .
wd:Q187235 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/LSeries/RiemannZeta.html#differentiableAt_riemannZeta> .
wd:Q187235 wl:formalizedAs "riemannZeta_residue_one" .
wd:Q187235 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/LSeries/RiemannZeta.html#riemannZeta_residue_one> .
wd:Q187235 wl:formalizedAs "riemannZeta_eulerProduct_tprod" .
wd:Q187235 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/EulerProduct/DirichletLSeries.html#riemannZeta_eulerProduct_tprod> .
wd:Q187235 wl:formalizedAs "Nat.exists_infinite_primes" .
wd:Q187235 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/Prime/Infinite.html#Nat.exists_infinite_primes> .
wd:Q187235 wl:formalizedAs "not_summable_one_div_on_primes" .
wd:Q187235 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/SumPrimeReciprocals.html#not_summable_one_div_on_primes> .
wd:Q187235 wl:formalizedAs "riemannZeta_one_sub" .
wd:Q187235 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/LSeries/RiemannZeta.html#riemannZeta_one_sub> .
wd:Q187235 wl:formalizedAs "completedRiemannZeta_one_sub" .
wd:Q187235 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/LSeries/RiemannZeta.html#completedRiemannZeta_one_sub> .
wd:Q187235 wl:formalizedAs "RiemannHypothesis" .
wd:Q187235 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/LSeries/RiemannZeta.html#RiemannHypothesis> .
wd:Q187235 wl:formalizedAs "riemannZeta_ne_zero_of_one_le_re" .
wd:Q187235 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/LSeries/Nonvanishing.html#riemannZeta_ne_zero_of_one_le_re> .
wd:Q187235 wl:formalizedAs "riemannZeta_two_mul_nat" .
wd:Q187235 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/LSeries/HurwitzZetaValues.html#riemannZeta_two_mul_nat> .
wd:Q187235 wl:formalizedAs "riemannZeta_two" .
wd:Q187235 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/LSeries/HurwitzZetaValues.html#riemannZeta_two> .
wd:Q187235 wl:formalizedAs "riemannZeta_neg_nat_eq_bernoulli" .
wd:Q187235 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/LSeries/HurwitzZetaValues.html#riemannZeta_neg_nat_eq_bernoulli> .
wd:Q187235 wl:formalizedAs "riemannZeta_neg_two_mul_nat_add_one" .
wd:Q187235 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/LSeries/RiemannZeta.html#riemannZeta_neg_two_mul_nat_add_one> .
wd:Q187235 wl:formalizedAs "riemannZeta_zero" .
wd:Q187235 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/LSeries/RiemannZeta.html#riemannZeta_zero> .
wd:Q187235 wl:formalizedAs "LSeries_zeta_mul_Lseries_moebius" .
wd:Q187235 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/LSeries/Dirichlet.html#LSeries_zeta_mul_Lseries_moebius> .
wd:Q187235 wl:formalizedAs "mellin" .
wd:Q187235 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/MellinTransform.html#mellin> .
wd:Q187235 wl:formalizedAs "hurwitzZeta" .
wd:Q187235 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/LSeries/HurwitzZeta.html#hurwitzZeta> .
wd:Q1208658 wl:formalizedAs "CommRing" .
wd:Q1208658 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Ring/Defs.html#CommRing> .
wd:Q1208658 wl:formalizedAs "IsDomain" .
wd:Q1208658 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Ring/Defs.html#IsDomain> .
wd:Q1208658 wl:formalizedAs "IsPrincipalIdealRing" .
wd:Q1208658 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Ideal/Span.html#IsPrincipalIdealRing> .
wd:Q1208658 wl:formalizedAs "EuclideanDomain" .
wd:Q1208658 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/EuclideanDomain/Defs.html#EuclideanDomain> .
wd:Q1208658 wl:formalizedAs "MvPolynomial.isMaximal_iff_eq_vanishingIdeal_singleton" .
wd:Q1208658 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Nullstellensatz.html#MvPolynomial.isMaximal_iff_eq_vanishingIdeal_singleton> .
wd:Q1208658 wl:formalizedAs "PrimeSpectrum" .
wd:Q1208658 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Spectrum/Prime/Defs.html#PrimeSpectrum> .
wd:Q1208658 wl:formalizedAs "Module" .
wd:Q1208658 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Module/Defs.html#Module> .
wd:Q1208658 wl:formalizedAs "Matrix.instRing" .
wd:Q1208658 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Matrix/Mul.html#Matrix.instRing> .
wd:Q1208658 wl:formalizedAs "IsSimpleRing.exists_ringEquiv_matrix_divisionRing" .
wd:Q1208658 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/SimpleModule/WedderburnArtin.html#IsSimpleRing.exists_ringEquiv_matrix_divisionRing> .
wd:Q1208658 wl:formalizedAs "jacobson_density" .
wd:Q1208658 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/SimpleModule/Basic.html#jacobson_density> .
wd:Q1208658 wl:formalizedAs "IsSemiprimaryRing.isNoetherian_iff_isArtinian" .
wd:Q1208658 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/HopkinsLevitzki.html#IsSemiprimaryRing.isNoetherian_iff_isArtinian> .
wd:Q1208658 wl:formalizedAs "littleWedderburn" .
wd:Q1208658 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/LittleWedderburn.html#littleWedderburn> .
wd:Q1208658 wl:formalizedAs "ringKrullDim" .
wd:Q1208658 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/KrullDimension/Basic.html#ringKrullDim> .
wd:Q1208658 wl:formalizedAs "MvPolynomial.ringKrullDim_of_isNoetherianRing" .
wd:Q1208658 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/KrullDimension/Polynomial.html#MvPolynomial.ringKrullDim_of_isNoetherianRing> .
wd:Q1208658 wl:formalizedAs "IsMoritaEquivalent" .
wd:Q1208658 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Morita/Basic.html#IsMoritaEquivalent> .
wd:Q1208658 wl:formalizedAs "CommRing.Pic" .
wd:Q1208658 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/PicardGroup.html#CommRing.Pic> .
wd:Q1208658 wl:formalizedAs "Ring.jacobson" .
wd:Q1208658 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Jacobson/Radical.html#Ring.jacobson> .
wd:Q1208658 wl:formalizedAs "Quaternion" .
wd:Q1208658 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Quaternion.html#Quaternion> .
wd:Q1208658 wl:formalizedAs "MvPolynomial.IsSymmetric" .
wd:Q1208658 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/MvPolynomial/Symmetric/Defs.html#MvPolynomial.IsSymmetric> .
wd:Q1208658 wl:formalizedAs "MvPolynomial.esymmAlgEquiv" .
wd:Q1208658 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/MvPolynomial/Symmetric/FundamentalTheorem.html#MvPolynomial.esymmAlgEquiv> .
wd:Q534131 wl:formalizedAs "RootPairing.IsRootSystem" .
wd:Q534131 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/RootSystem/Defs.html#RootPairing.IsRootSystem> .
wd:Q534131 wl:formalizedAs "RootPairing.IsCrystallographic" .
wd:Q534131 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/RootSystem/IsValuedIn.html#RootPairing.IsCrystallographic> .
wd:Q534131 wl:formalizedAs "RootPairing.IsReduced" .
wd:Q534131 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/RootSystem/Reduced.html#RootPairing.IsReduced> .
wd:Q534131 wl:formalizedAs "RootPairing.IsIrreducible" .
wd:Q534131 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/RootSystem/Irreducible.html#RootPairing.IsIrreducible> .
wd:Q534131 wl:formalizedAs "RootPairing.Equiv" .
wd:Q534131 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/RootSystem/Hom.html#RootPairing.Equiv> .
wd:Q534131 wl:formalizedAs "RootPairing.rootSpan" .
wd:Q534131 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/RootSystem/IsValuedIn.html#RootPairing.rootSpan> .
wd:Q534131 wl:formalizedAs "RootPairing.weylGroup" .
wd:Q534131 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/RootSystem/WeylGroup.html#RootPairing.weylGroup> .
wd:Q534131 wl:formalizedAs "LieAlgebra.IsKilling.rootSystem" .
wd:Q534131 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Lie/Weights/RootSystem.html#LieAlgebra.IsKilling.rootSystem> .
wd:Q534131 wl:formalizedAs "RootPairing.pairingIn_pairingIn_mem_set_of_isCrystal_of_isRed" .
wd:Q534131 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/RootSystem/Finite/Lemmas.html#RootPairing.pairingIn_pairingIn_mem_set_of_isCrystal_of_isRed> .
wd:Q534131 wl:formalizedAs "RootPairing.Base" .
wd:Q534131 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/RootSystem/Base.html#RootPairing.Base> .
wd:Q534131 wl:formalizedAs "RootPairing.Base.toWeightBasis" .
wd:Q534131 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/RootSystem/Base.html#RootPairing.Base.toWeightBasis> .
wd:Q534131 wl:formalizedAs "RootPairing.coroot" .
wd:Q534131 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/RootSystem/Defs.html#RootPairing.coroot> .
wd:Q534131 wl:formalizedAs "RootPairing.flip" .
wd:Q534131 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/RootSystem/Defs.html#RootPairing.flip> .
wd:Q534131 wl:formalizedAs "RootPairing.flip_flip" .
wd:Q534131 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/RootSystem/Defs.html#RootPairing.flip_flip> .
wd:Q534131 wl:formalizedAs "RootPairing.Base.flip" .
wd:Q534131 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/RootSystem/Base.html#RootPairing.Base.flip> .
wd:Q534131 wl:formalizedAs "LieAlgebra.IsKilling.isSimple_iff_isIrreducible" .
wd:Q534131 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Lie/Weights/IsSimple.html#LieAlgebra.IsKilling.isSimple_iff_isIrreducible> .
wd:Q534131 wl:formalizedAs "RootPairing.InvariantForm.exists_apply_eq_or" .
wd:Q534131 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/RootSystem/Finite/Lemmas.html#RootPairing.InvariantForm.exists_apply_eq_or> .
wd:Q6500908 wl:formalizedAs "IsSelfAdjoint" .
wd:Q6500908 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Star/SelfAdjoint.html#IsSelfAdjoint> .
wd:Q6500908 wl:formalizedAs "LinearMap.IsSymmetric.eigenvectorBasis_apply_self_apply" .
wd:Q6500908 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/InnerProductSpace/Spectrum.html#LinearMap.IsSymmetric.eigenvectorBasis_apply_self_apply> .
wd:Q6500908 wl:formalizedAs "LinearPMap.graph" .
wd:Q6500908 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Algebra/Module/LinearPMap.html#LinearPMap.graph> .
wd:Q6500908 wl:formalizedAs "LinearPMap.adjoint" .
wd:Q6500908 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/InnerProductSpace/LinearPMap.html#LinearPMap.adjoint> .
wd:Q6500908 wl:formalizedAs "LinearMap.IsSymmetric" .
wd:Q6500908 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/InnerProductSpace/Symmetric.html#LinearMap.IsSymmetric> .
wd:Q6500908 wl:formalizedAs "LinearPMap.IsSelfAdjoint" .
wd:Q6500908 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/InnerProductSpace/LinearPMap.html#LinearPMap.IsSelfAdjoint> .
wd:Q6500908 wl:formalizedAs "LinearMap.IsSymmetric.continuous" .
wd:Q6500908 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/InnerProductSpace/Symmetric.html#LinearMap.IsSymmetric.continuous> .
wd:Q6500908 wl:formalizedAs "ContinuousLinearMap.isSelfAdjoint_iff_isSymmetric" .
wd:Q6500908 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/InnerProductSpace/Adjoint.html#ContinuousLinearMap.isSelfAdjoint_iff_isSymmetric> .
wd:Q6500908 wl:formalizedAs "realPart_add_I_smul_imaginaryPart" .
wd:Q6500908 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Complex/Module.html#realPart_add_I_smul_imaginaryPart> .
wd:Q6500908 wl:formalizedAs "ContinuousLinearMap.IsPositive.isSelfAdjoint" .
wd:Q6500908 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/InnerProductSpace/Positive.html#ContinuousLinearMap.IsPositive.isSelfAdjoint> .
wd:Q6500908 wl:formalizedAs "LinearMap.IsSymmetric.norm_eq_iSup_rayleighQuotient" .
wd:Q6500908 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/InnerProductSpace/Rayleigh.html#LinearMap.IsSymmetric.norm_eq_iSup_rayleighQuotient> .
wd:Q6500908 wl:formalizedAs "LinearMap.IsSymmetric.conj_eigenvalue_eq_self" .
wd:Q6500908 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/InnerProductSpace/Spectrum.html#LinearMap.IsSymmetric.conj_eigenvalue_eq_self> .
wd:Q6500908 wl:formalizedAs "ContinuousLinearMap.eq_zero_of_forall_hasEigenvalue_eq_zero" .
wd:Q6500908 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/InnerProductSpace/Spectrum.html#ContinuousLinearMap.eq_zero_of_forall_hasEigenvalue_eq_zero> .
wd:Q6500908 wl:formalizedAs "resolventSet" .
wd:Q6500908 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Algebra/Spectrum/Basic.html#resolventSet> .
wd:Q6500908 wl:formalizedAs "spectrum" .
wd:Q6500908 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Algebra/Spectrum/Basic.html#spectrum> .
wd:Q6500908 wl:formalizedAs "IsSelfAdjoint.val_re_map_spectrum" .
wd:Q6500908 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/CStarAlgebra/Spectrum.html#IsSelfAdjoint.val_re_map_spectrum> .
wd:Q6500908 wl:formalizedAs "QuasispectrumRestricts.isSelfAdjoint" .
wd:Q6500908 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/CStarAlgebra/ContinuousFunctionalCalculus/Instances.html#QuasispectrumRestricts.isSelfAdjoint> .
wd:Q6500908 wl:formalizedAs "LinearMap.IsSymmetric.eigenvectorBasis" .
wd:Q6500908 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/InnerProductSpace/Spectrum.html#LinearMap.IsSymmetric.eigenvectorBasis> .
wd:Q6500908 wl:formalizedAs "cfc" .
wd:Q6500908 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/CStarAlgebra/ContinuousFunctionalCalculus/Unital.html#cfc> .
wd:Q6500908 wl:formalizedAs "MeasureTheory.Measure.MutuallySingular" .
wd:Q6500908 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/MeasureTheory/Measure/MutuallySingular.html#MeasureTheory.Measure.MutuallySingular> .
wd:Q12482 wl:formalizedAs "Cardinal" .
wd:Q12482 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Defs.html#Cardinal> .
wd:Q12482 wl:formalizedAs "Cardinal.not_countable_real" .
wd:Q12482 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Real/Cardinality.html#Cardinal.not_countable_real> .
wd:Q12482 wl:formalizedAs "Cardinal.cantor" .
wd:Q12482 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Order.html#Cardinal.cantor> .
wd:Q12482 wl:formalizedAs "Ordinal" .
wd:Q12482 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Ordinal/Basic.html#Ordinal> .
wd:Q12482 wl:formalizedAs "Set.Mem" .
wd:Q12482 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Set/Defs.html#Set.Mem> .
wd:Q12482 wl:formalizedAs "Set.Subset" .
wd:Q12482 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Set/Defs.html#Set.Subset> .
wd:Q12482 wl:formalizedAs "Set.ssubset_iff_subset_ne" .
wd:Q12482 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Set/Basic.html#Set.ssubset_iff_subset_ne> .
wd:Q12482 wl:formalizedAs "Set.union" .
wd:Q12482 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Set/Defs.html#Set.union> .
wd:Q12482 wl:formalizedAs "Set.inter" .
wd:Q12482 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Set/Defs.html#Set.inter> .
wd:Q12482 wl:formalizedAs "Set.diff" .
wd:Q12482 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Set/Defs.html#Set.diff> .
wd:Q12482 wl:formalizedAs "Set.compl" .
wd:Q12482 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Set/Defs.html#Set.compl> .
wd:Q12482 wl:formalizedAs "symmDiff" .
wd:Q12482 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/SymmDiff.html#symmDiff> .
wd:Q12482 wl:formalizedAs "Set.prod" .
wd:Q12482 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Set/Operations.html#Set.prod> .
wd:Q12482 wl:formalizedAs "Set.instEmptyCollectionSet" .
wd:Q12482 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Set/Defs.html#Set.instEmptyCollectionSet> .
wd:Q12482 wl:formalizedAs "Set.powerset" .
wd:Q12482 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Set/Defs.html#Set.powerset> .
wd:Q12482 wl:formalizedAs "ZFSet.rank" .
wd:Q12482 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/ZFC/Rank.html#ZFSet.rank> .
wd:Q331350 wl:formalizedAs "Affine.Simplex" .
wd:Q331350 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/AffineSpace/Simplex/Basic.html#Affine.Simplex> .
wd:Q331350 wl:formalizedAs "Affine.Simplex.mkOfPoint" .
wd:Q331350 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/AffineSpace/Simplex/Basic.html#Affine.Simplex.mkOfPoint> .
wd:Q331350 wl:formalizedAs "stdSimplex_fin_two" .
wd:Q331350 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Convex/StdSimplex.html#stdSimplex_fin_two> .
wd:Q331350 wl:formalizedAs "Affine.Triangle" .
wd:Q331350 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/AffineSpace/Simplex/Basic.html#Affine.Triangle> .
wd:Q331350 wl:formalizedAs "stdSimplex" .
wd:Q331350 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Convex/StdSimplex.html#stdSimplex> .
wd:Q331350 wl:formalizedAs "Geometry.SimplicialComplex" .
wd:Q331350 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Convex/SimplicialComplex/Basic.html#Geometry.SimplicialComplex> .
wd:Q331350 wl:formalizedAs "AbstractSimplicialComplex" .
wd:Q331350 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/AlgebraicTopology/SimplicialComplex/Basic.html#AbstractSimplicialComplex> .
wd:Q331350 wl:formalizedAs "Affine.Simplex.face" .
wd:Q331350 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/AffineSpace/Simplex/Basic.html#Affine.Simplex.face> .
wd:Q331350 wl:formalizedAs "single_mem_stdSimplex" .
wd:Q331350 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Convex/StdSimplex.html#single_mem_stdSimplex> .
wd:Q331350 wl:formalizedAs "AffineBasis.coord" .
wd:Q331350 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/AffineSpace/Basis.html#AffineBasis.coord> .
wd:Q331350 wl:formalizedAs "stdSimplex_unique" .
wd:Q331350 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Convex/StdSimplex.html#stdSimplex_unique> .
wd:Q331350 wl:formalizedAs "Basis.addHaar_parallelepiped" .
wd:Q331350 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/MeasureTheory/Measure/Lebesgue/EqHaar.html#Basis.addHaar_parallelepiped> .
wd:Q331350 wl:formalizedAs "TopCat.toSSetObjEquiv" .
wd:Q331350 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/AlgebraicTopology/SingularSet.html#TopCat.toSSetObjEquiv> .
wd:Q331350 wl:formalizedAs "CategoryTheory.SimplicialObject" .
wd:Q331350 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/AlgebraicTopology/SimplicialObject/Basic.html#CategoryTheory.SimplicialObject> .
wd:Q420904 wl:formalizedAs "LinearMap.singularValues" .
wd:Q420904 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/InnerProductSpace/SingularValues.html#LinearMap.singularValues> .
wd:Q420904 wl:formalizedAs "LinearMap.card_support_singularValues" .
wd:Q420904 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/InnerProductSpace/SingularValues.html#LinearMap.card_support_singularValues> .
wd:Q420904 wl:formalizedAs "LinearMap.IsSymmetric.hasEigenvalue_iSup_of_finiteDimensional" .
wd:Q420904 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/InnerProductSpace/Rayleigh.html#LinearMap.IsSymmetric.hasEigenvalue_iSup_of_finiteDimensional> .
wd:Q420904 wl:formalizedAs "Matrix.IsHermitian.spectral_theorem" .
wd:Q420904 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Matrix/Spectrum.html#Matrix.IsHermitian.spectral_theorem> .
wd:Q420904 wl:formalizedAs "Matrix.frobenius_norm_def" .
wd:Q420904 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Matrix/Normed.html#Matrix.frobenius_norm_def> .
wd:Q190667 wl:formalizedAs "Real.log_mul" .
wd:Q190667 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Log/Basic.html#Real.log_mul> .
wd:Q190667 wl:formalizedAs "quadratic_eq_zero_iff" .
wd:Q190667 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/QuadraticDiscriminant.html#quadratic_eq_zero_iff> .
wd:Q190667 wl:formalizedAs "Real.logb" .
wd:Q190667 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Log/Base.html#Real.logb> .
wd:Q190667 wl:formalizedAs "div_add_one" .
wd:Q190667 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Field/Basic.html#div_add_one> .
wd:Q133327 wl:formalizedAs "EuclideanSpace.dist_eq" .
wd:Q133327 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/InnerProductSpace/PiL2.html#EuclideanSpace.dist_eq> .
wd:Q133327 wl:formalizedAs "Isometry.dist_eq" .
wd:Q133327 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/MetricSpace/Isometry.html#Isometry.dist_eq> .
wd:Q133327 wl:formalizedAs "IsRiemannianManifold" .
wd:Q133327 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Manifold/Riemannian/Basic.html#IsRiemannianManifold> .
wd:Q3503315 wl:formalizedAs "CategoryTheory.CohomologicalSpectralSequence" .
wd:Q3503315 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Homology/SpectralSequence/Basic.html#CategoryTheory.CohomologicalSpectralSequence> .
wd:Q3503315 wl:formalizedAs "CategoryTheory.SpectralSequence.page" .
wd:Q3503315 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Homology/SpectralSequence/Basic.html#CategoryTheory.SpectralSequence.page> .
wd:Q3503315 wl:formalizedAs "CategoryTheory.SpectralSequence" .
wd:Q3503315 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Homology/SpectralSequence/Basic.html#CategoryTheory.SpectralSequence> .
wd:Q3503315 wl:formalizedAs "CategoryTheory.SpectralSequence.Hom" .
wd:Q3503315 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Homology/SpectralSequence/Basic.html#CategoryTheory.SpectralSequence.Hom> .
wd:Q3503315 wl:formalizedAs "HomologicalComplex₂" .
wd:Q3503315 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Homology/HomologicalBicomplex.html#HomologicalComplex₂> .
wd:Q3503315 wl:formalizedAs "HomologicalComplex₂.total" .
wd:Q3503315 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Homology/TotalComplex.html#HomologicalComplex₂.total> .
wd:Q3503315 wl:formalizedAs "CategoryTheory.CohomologicalSpectralSequenceNat" .
wd:Q3503315 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Homology/SpectralSequence/Basic.html#CategoryTheory.CohomologicalSpectralSequenceNat> .
wd:Q1425077 wl:formalizedAs "Matrix.IsHermitian.spectral_theorem" .
wd:Q1425077 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Matrix/Spectrum.html#Matrix.IsHermitian.spectral_theorem> .
wd:Q1425077 wl:formalizedAs "LinearMap.IsSymmetric" .
wd:Q1425077 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/InnerProductSpace/Symmetric.html#LinearMap.IsSymmetric> .
wd:Q1425077 wl:formalizedAs "ContinuousLinearMap.isSelfAdjoint_iff_isSymmetric" .
wd:Q1425077 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/InnerProductSpace/Adjoint.html#ContinuousLinearMap.isSelfAdjoint_iff_isSymmetric> .
wd:Q1425077 wl:formalizedAs "LinearMap.IsSymmetric.conj_eigenvalue_eq_self" .
wd:Q1425077 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/InnerProductSpace/Spectrum.html#LinearMap.IsSymmetric.conj_eigenvalue_eq_self> .
wd:Q1425077 wl:formalizedAs "Module.End.HasEigenvector" .
wd:Q1425077 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Eigenspace/Basic.html#Module.End.HasEigenvector> .
wd:Q1425077 wl:formalizedAs "LinearMap.IsSymmetric.direct_sum_isInternal" .
wd:Q1425077 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/InnerProductSpace/Spectrum.html#LinearMap.IsSymmetric.direct_sum_isInternal> .
wd:Q1425077 wl:formalizedAs "Module.End.eigenspace" .
wd:Q1425077 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Eigenspace/Basic.html#Module.End.eigenspace> .
wd:Q1425077 wl:formalizedAs "LinearMap.IsSymmetric.eigenvectorBasis_apply_self_apply" .
wd:Q1425077 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/InnerProductSpace/Spectrum.html#LinearMap.IsSymmetric.eigenvectorBasis_apply_self_apply> .
wd:Q1425077 wl:formalizedAs "IsStarNormal" .
wd:Q1425077 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Star/Basic.html#IsStarNormal> .
wd:Q1425077 wl:formalizedAs "ContinuousLinearMap.orthogonalComplement_iSup_eigenspaces_eq_bot" .
wd:Q1425077 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/InnerProductSpace/Spectrum.html#ContinuousLinearMap.orthogonalComplement_iSup_eigenspaces_eq_bot> .
wd:Q1425077 wl:formalizedAs "cfc" .
wd:Q1425077 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/CStarAlgebra/ContinuousFunctionalCalculus/Unital.html#cfc> .
wd:Q2409122 wl:formalizedAs "resolventSet" .
wd:Q2409122 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Algebra/Spectrum/Basic.html#resolventSet> .
wd:Q2409122 wl:formalizedAs "spectrum" .
wd:Q2409122 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Algebra/Spectrum/Basic.html#spectrum> .
wd:Q2409122 wl:formalizedAs "resolvent" .
wd:Q2409122 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Algebra/Spectrum/Basic.html#resolvent> .
wd:Q2409122 wl:formalizedAs "Module.End.HasEigenvalue.mem_spectrum" .
wd:Q2409122 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Eigenspace/Basic.html#Module.End.HasEigenvalue.mem_spectrum> .
wd:Q2409122 wl:formalizedAs "IsSelfAdjoint.mem_spectrum_eq_re" .
wd:Q2409122 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/CStarAlgebra/Spectrum.html#IsSelfAdjoint.mem_spectrum_eq_re> .
wd:Q2409122 wl:formalizedAs "InnerProductSpace.rankOne" .
wd:Q2409122 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/InnerProductSpace/LinearMap.html#InnerProductSpace.rankOne> .
wd:Q2409122 wl:formalizedAs "Module.End.HasEigenvalue" .
wd:Q2409122 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Eigenspace/Basic.html#Module.End.HasEigenvalue> .
wd:Q2409122 wl:formalizedAs "OrthonormalBasis.sum_rankOne_eq_id" .
wd:Q2409122 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/InnerProductSpace/PiL2.html#OrthonormalBasis.sum_rankOne_eq_id> .
wd:Q2409122 wl:formalizedAs "OrthonormalBasis.sum_repr&#x27;" .
wd:Q2409122 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/InnerProductSpace/PiL2.html#OrthonormalBasis.sum_repr'> .
wd:Q2409122 wl:formalizedAs "IsSelfAdjoint.hasEigenvector_of_isMaxOn" .
wd:Q2409122 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/InnerProductSpace/Rayleigh.html#IsSelfAdjoint.hasEigenvector_of_isMaxOn> .
wd:Q203218 wl:formalizedAs "Metric.sphere" .
wd:Q203218 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/MetricSpace/Pseudo/Defs.html#Metric.sphere> .
wd:Q164 wl:formalizedAs "irrational_sqrt_two" .
wd:Q164 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/Real/Irrational.html#irrational_sqrt_two> .
wd:Q164 wl:formalizedAs "IsSquare" .
wd:Q164 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Even.html#IsSquare> .
wd:Q164 wl:formalizedAs "DihedralGroup" .
wd:Q164 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/SpecificGroups/Dihedral.html#DihedralGroup> .
wd:Q164 wl:formalizedAs "norm_add_sq_eq_norm_sq_add_norm_sq_iff_angle_eq_pi_div_two" .
wd:Q164 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Euclidean/Angle/Unoriented/RightAngle.html#norm_add_sq_eq_norm_sq_add_norm_sq_iff_angle_eq_pi_div_two> .
wd:Q389813 wl:formalizedAs "Real.sqrt" .
wd:Q389813 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Real/Sqrt.html#Real.sqrt> .
wd:Q389813 wl:formalizedAs "irrational_sqrt_two" .
wd:Q389813 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/Real/Irrational.html#irrational_sqrt_two> .
wd:Q389813 wl:formalizedAs "irrational_sqrt_natCast_iff" .
wd:Q389813 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/Real/Irrational.html#irrational_sqrt_natCast_iff> .
wd:Q389813 wl:formalizedAs "Real.cos_pi_div_four" .
wd:Q389813 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.html#Real.cos_pi_div_four> .
wd:Q193394 wl:formalizedAs "EuclideanSpace.volume_ball_fin_two" .
wd:Q193394 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/MeasureTheory/Measure/Lebesgue/VolumeOfBalls.html#EuclideanSpace.volume_ball_fin_two> .
wd:Q193394 wl:formalizedAs "intermediate_value_Icc" .
wd:Q193394 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Order/IntermediateValue.html#intermediate_value_Icc> .
wd:Q193394 wl:formalizedAs "integral_inv" .
wd:Q193394 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Integrals/Basic.html#integral_inv> .
wd:Q193394 wl:formalizedAs "irrational_pi" .
wd:Q193394 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Real/Pi/Irrational.html#irrational_pi> .
wd:Q7598372 wl:formalizedAs "MeasureTheory.Measure.map" .
wd:Q7598372 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/MeasureTheory/Measure/Map.html#MeasureTheory.Measure.map> .
wd:Q7598372 wl:formalizedAs "MeasurableSpace.CountablySeparated" .
wd:Q7598372 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/MeasureTheory/MeasurableSpace/CountablyGenerated.html#MeasurableSpace.CountablySeparated> .
wd:Q7598372 wl:formalizedAs "MeasurableSpace.CountablyGenerated" .
wd:Q7598372 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/MeasureTheory/MeasurableSpace/CountablyGenerated.html#MeasurableSpace.CountablyGenerated> .
wd:Q7598372 wl:formalizedAs "MeasureTheory.Measure.condKernel" .
wd:Q7598372 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Probability/Kernel/Disintegration/StandardBorel.html#MeasureTheory.Measure.condKernel> .
wd:Q2500758 wl:formalizedAs "IsLocalMin" .
wd:Q2500758 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Order/LocalExtr.html#IsLocalMin> .
wd:Q2500758 wl:formalizedAs "IsLocalMax" .
wd:Q2500758 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Order/LocalExtr.html#IsLocalMax> .
wd:Q2500758 wl:formalizedAs "IsLocalExtr" .
wd:Q2500758 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Order/LocalExtr.html#IsLocalExtr> .
wd:Q2500758 wl:formalizedAs "IsExtrOn" .
wd:Q2500758 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/Filter/Extr.html#IsExtrOn> .
wd:Q2500758 wl:formalizedAs "IsLocalExtr.deriv_eq_zero" .
wd:Q2500758 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/LocalExtr/Basic.html#IsLocalExtr.deriv_eq_zero> .
wd:Q2500758 wl:formalizedAs "isLocalMin_of_deriv_deriv_pos" .
wd:Q2500758 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/DerivativeTest.html#isLocalMin_of_deriv_deriv_pos> .
wd:Q80918 wl:formalizedAs "Nat.stirlingFirst" .
wd:Q80918 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Combinatorics/Enumerative/Stirling.html#Nat.stirlingFirst> .
wd:Q80918 wl:formalizedAs "Nat.stirlingSecond" .
wd:Q80918 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Combinatorics/Enumerative/Stirling.html#Nat.stirlingSecond> .
wd:Q80918 wl:formalizedAs "descPochhammer_zero" .
wd:Q80918 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Polynomial/Pochhammer.html#descPochhammer_zero> .
wd:Q80918 wl:formalizedAs "Ring.descPochhammer_eq_factorial_smul_choose" .
wd:Q80918 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Binomial.html#Ring.descPochhammer_eq_factorial_smul_choose> .
wd:Q484298 wl:formalizedAs "chartAt" .
wd:Q484298 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Manifold/ChartedSpace.html#chartAt> .
wd:Q484298 wl:formalizedAs "ModelWithCorners.IsBoundaryPoint" .
wd:Q484298 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Manifold/IsManifold/InteriorBoundary.html#ModelWithCorners.IsBoundaryPoint> .
wd:Q484298 wl:formalizedAs "ModelWithCorners.IsInteriorPoint" .
wd:Q484298 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Manifold/IsManifold/InteriorBoundary.html#ModelWithCorners.IsInteriorPoint> .
wd:Q484298 wl:formalizedAs "SmoothBumpCovering.exists_embedding_euclidean_of_compact" .
wd:Q484298 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Manifold/WhitneyEmbedding.html#SmoothBumpCovering.exists_embedding_euclidean_of_compact> .
wd:Q229102 wl:formalizedAs "Function.Surjective" .
wd:Q229102 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Logic/Function/Defs.html#Function.Surjective> .
wd:Q229102 wl:formalizedAs "Function.surjective_id" .
wd:Q229102 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Logic/Function/Defs.html#Function.surjective_id> .
wd:Q229102 wl:formalizedAs "Real.log_surjective" .
wd:Q229102 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Log/Basic.html#Real.log_surjective> .
wd:Q229102 wl:formalizedAs "Prod.fst_surjective" .
wd:Q229102 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Prod/Basic.html#Prod.fst_surjective> .
wd:Q229102 wl:formalizedAs "Function.Bijective" .
wd:Q229102 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Logic/Function/Defs.html#Function.Bijective> .
wd:Q229102 wl:formalizedAs "Function.RightInverse" .
wd:Q229102 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Logic/Function/Defs.html#Function.RightInverse> .
wd:Q229102 wl:formalizedAs "Function.surjective_iff_hasRightInverse" .
wd:Q229102 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Logic/Function/Basic.html#Function.surjective_iff_hasRightInverse> .
wd:Q229102 wl:formalizedAs "Set.image_preimage_eq" .
wd:Q229102 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Set/Image.html#Set.image_preimage_eq> .
wd:Q229102 wl:formalizedAs "Function.injective_comp_right_iff_surjective" .
wd:Q229102 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Logic/Function/Basic.html#Function.injective_comp_right_iff_surjective> .
wd:Q229102 wl:formalizedAs "CategoryTheory.Types.epi_iff_surjective" .
wd:Q229102 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Types/Basic.html#CategoryTheory.Types.epi_iff_surjective> .
wd:Q229102 wl:formalizedAs "CategoryTheory.IsSplitEpi.epi" .
wd:Q229102 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/EpiMono.html#CategoryTheory.IsSplitEpi.epi> .
wd:Q229102 wl:formalizedAs "CategoryTheory.SplitEpi.section_" .
wd:Q229102 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/EpiMono.html#CategoryTheory.SplitEpi.section_> .
wd:Q229102 wl:formalizedAs "CategoryTheory.IsSplitEpi" .
wd:Q229102 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/EpiMono.html#CategoryTheory.IsSplitEpi> .
wd:Q229102 wl:formalizedAs "Cardinal.mk_le_of_surjective" .
wd:Q229102 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Order.html#Cardinal.mk_le_of_surjective> .
wd:Q229102 wl:formalizedAs "Fintype.injective_iff_surjective_of_equiv" .
wd:Q229102 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Fintype/Card.html#Fintype.injective_iff_surjective_of_equiv> .
wd:Q229102 wl:formalizedAs "Function.Surjective.comp" .
wd:Q229102 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Logic/Function/Defs.html#Function.Surjective.comp> .
wd:Q229102 wl:formalizedAs "Set.rangeFactorization_surjective" .
wd:Q229102 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Set/Operations.html#Set.rangeFactorization_surjective> .
wd:Q229102 wl:formalizedAs "Setoid.quotientKerEquivOfSurjective" .
wd:Q229102 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Setoid/Basic.html#Setoid.quotientKerEquivOfSurjective> .
wd:Q849512 wl:formalizedAs "Equiv.Perm" .
wd:Q849512 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Logic/Equiv/Defs.html#Equiv.Perm> .
wd:Q849512 wl:formalizedAs "Fintype.card_perm" .
wd:Q849512 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Fintype/Perm.html#Fintype.card_perm> .
wd:Q849512 wl:formalizedAs "Equiv.Perm.subgroupOfMulAction" .
wd:Q849512 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/Perm/Subgroup.html#Equiv.Perm.subgroupOfMulAction> .
wd:Q849512 wl:formalizedAs "Equiv.permUnique" .
wd:Q849512 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Logic/Equiv/Defs.html#Equiv.permUnique> .
wd:Q849512 wl:formalizedAs "Equiv.Perm.permGroup" .
wd:Q849512 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/End.html#Equiv.Perm.permGroup> .
wd:Q849512 wl:formalizedAs "Equiv.Perm.mul_apply" .
wd:Q849512 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/Perm/Basic.html#Equiv.Perm.mul_apply> .
wd:Q849512 wl:formalizedAs "Equiv.Perm.IsSwap" .
wd:Q849512 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/Perm/Support.html#Equiv.Perm.IsSwap> .
wd:Q849512 wl:formalizedAs "Equiv.Perm.closure_isSwap" .
wd:Q849512 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/Perm/Sign.html#Equiv.Perm.closure_isSwap> .
wd:Q849512 wl:formalizedAs "Equiv.Perm.sign" .
wd:Q849512 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/Perm/Sign.html#Equiv.Perm.sign> .
wd:Q849512 wl:formalizedAs "Equiv.Perm.sign_prod_list_swap" .
wd:Q849512 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/Perm/Sign.html#Equiv.Perm.sign_prod_list_swap> .
wd:Q849512 wl:formalizedAs "Equiv.Perm.sign_mul" .
wd:Q849512 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/Perm/Sign.html#Equiv.Perm.sign_mul> .
wd:Q849512 wl:formalizedAs "alternatingGroup" .
wd:Q849512 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/SpecificGroups/Alternating.html#alternatingGroup> .
wd:Q849512 wl:formalizedAs "Equiv.Perm.alternatingGroup.index_eq_two" .
wd:Q849512 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/SpecificGroups/Alternating.html#Equiv.Perm.alternatingGroup.index_eq_two> .
wd:Q849512 wl:formalizedAs "Equiv.Perm.mclosure_swap_castSucc_succ" .
wd:Q849512 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/Perm/Sign.html#Equiv.Perm.mclosure_swap_castSucc_succ> .
wd:Q849512 wl:formalizedAs "Equiv.Perm.IsCycle" .
wd:Q849512 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/Perm/Cycle/Basic.html#Equiv.Perm.IsCycle> .
wd:Q849512 wl:formalizedAs "Equiv.Perm.IsCycle.orderOf" .
wd:Q849512 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/Perm/Cycle/Basic.html#Equiv.Perm.IsCycle.orderOf> .
wd:Q849512 wl:formalizedAs "Equiv.Perm.card_support_eq_two" .
wd:Q849512 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/Perm/Support.html#Equiv.Perm.card_support_eq_two> .
wd:Q849512 wl:formalizedAs "Equiv.Perm.Disjoint" .
wd:Q849512 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/Perm/Support.html#Equiv.Perm.Disjoint> .
wd:Q849512 wl:formalizedAs "Equiv.Perm.Disjoint.commute" .
wd:Q849512 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/Perm/Support.html#Equiv.Perm.Disjoint.commute> .
wd:Q849512 wl:formalizedAs "Equiv.Perm.truncCycleFactors" .
wd:Q849512 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/Perm/Cycle/Factors.html#Equiv.Perm.truncCycleFactors> .
wd:Q849512 wl:formalizedAs "Fin.revPerm" .
wd:Q849512 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/Fin/Basic.html#Fin.revPerm> .
wd:Q849512 wl:formalizedAs "Fin.rev_rev" .
wd:Q849512 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/Fin/Basic.html#Fin.rev_rev> .
wd:Q849512 wl:formalizedAs "Equiv.Perm.isConj_iff_cycleType_eq" .
wd:Q849512 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/Perm/Cycle/Type.html#Equiv.Perm.isConj_iff_cycleType_eq> .
wd:Q849512 wl:formalizedAs "Equiv.Perm.partition" .
wd:Q849512 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/Perm/Cycle/Type.html#Equiv.Perm.partition> .
wd:Q849512 wl:formalizedAs "Equiv.Perm.fin_5_not_solvable" .
wd:Q849512 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/Solvable.html#Equiv.Perm.fin_5_not_solvable> .
wd:Q849512 wl:formalizedAs "Equiv.Perm.alternatingGroup.isSimpleGroup" .
wd:Q849512 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/SpecificGroups/Alternating/Simple.html#Equiv.Perm.alternatingGroup.isSimpleGroup> .
wd:Q849512 wl:formalizedAs "Subgroup" .
wd:Q849512 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/Subgroup/Defs.html#Subgroup> .
wd:Q849512 wl:formalizedAs "Equiv.Perm.isCoatom_stabilizer" .
wd:Q849512 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/Perm/MaximalSubgroups.html#Equiv.Perm.isCoatom_stabilizer> .
wd:Q849512 wl:formalizedAs "Sylow.isPGroup&#x27;" .
wd:Q849512 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/Sylow.html#Sylow.isPGroup'> .
wd:Q849512 wl:formalizedAs "IteratedWreathProduct" .
wd:Q849512 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/RegularWreathProduct.html#IteratedWreathProduct> .
wd:Q849512 wl:formalizedAs "MulAction.IsPretransitive" .
wd:Q849512 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/GroupAction/Defs.html#MulAction.IsPretransitive> .
wd:Q849512 wl:formalizedAs "Polynomial.Gal.galAction_isPretransitive" .
wd:Q849512 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/FieldTheory/PolynomialGaloisGroup.html#Polynomial.Gal.galAction_isPretransitive> .
wd:Q849512 wl:formalizedAs "Subgroup.zpowers" .
wd:Q849512 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/Subgroup/ZPowers.html#Subgroup.zpowers> .
wd:Q849512 wl:formalizedAs "Equiv.Perm.lcm_cycleType" .
wd:Q849512 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/Perm/Cycle/Type.html#Equiv.Perm.lcm_cycleType> .
wd:Q849512 wl:formalizedAs "MonoidAlgebra.instIsSemisimpleModule (Maschke)" .
wd:Q849512 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RepresentationTheory/Maschke.html#MonoidAlgebra.instIsSemisimpleModule (Maschke)> .
wd:Q21030012 wl:formalizedAs "MulAction.stabilizer" .
wd:Q21030012 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/GroupAction/Defs.html#MulAction.stabilizer> .
wd:Q21030012 wl:formalizedAs "AffineIsometryEquiv.pointReflection" .
wd:Q21030012 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Normed/Affine/Isometry.html#AffineIsometryEquiv.pointReflection> .
wd:Q2431134 wl:formalizedAs "Function.Even" .
wd:Q2431134 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/EvenFunction.html#Function.Even> .
wd:Q2431134 wl:formalizedAs "Function.Odd" .
wd:Q2431134 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/EvenFunction.html#Function.Odd> .
wd:Q2431134 wl:formalizedAs "Matrix.IsSymm" .
wd:Q2431134 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Matrix/Symmetric.html#Matrix.IsSymm> .
wd:Q2431134 wl:formalizedAs "Matrix.IsSymm.apply" .
wd:Q2431134 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Matrix/Symmetric.html#Matrix.IsSymm.apply> .
wd:Q2431134 wl:formalizedAs "Matrix.isSymm_diagonal" .
wd:Q2431134 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Matrix/Symmetric.html#Matrix.isSymm_diagonal> .
wd:Q2431134 wl:formalizedAs "Matrix.isHermitian_iff_isSymmetric" .
wd:Q2431134 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Matrix/Hermitian.html#Matrix.isHermitian_iff_isSymmetric> .
wd:Q2431134 wl:formalizedAs "Equiv.Perm" .
wd:Q2431134 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Logic/Equiv/Defs.html#Equiv.Perm> .
wd:Q2431134 wl:formalizedAs "Fintype.card_perm" .
wd:Q2431134 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Fintype/Perm.html#Fintype.card_perm> .
wd:Q2431134 wl:formalizedAs "MvPolynomial.IsSymmetric" .
wd:Q2431134 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/MvPolynomial/Symmetric/Defs.html#MvPolynomial.IsSymmetric> .
wd:Q2431134 wl:formalizedAs "MvPolynomial.esymmAlgHom_surjective" .
wd:Q2431134 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/MvPolynomial/Symmetric/FundamentalTheorem.html#MvPolynomial.esymmAlgHom_surjective> .
wd:Q2431134 wl:formalizedAs "SymmetricPower" .
wd:Q2431134 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/TensorPower/Symmetric.html#SymmetricPower> .
wd:Q2431134 wl:formalizedAs "Polynomial.Gal.galActionHom" .
wd:Q2431134 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/FieldTheory/PolynomialGaloisGroup.html#Polynomial.Gal.galActionHom> .
wd:Q2431134 wl:formalizedAs "CategoryTheory.Aut" .
wd:Q2431134 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Endomorphism.html#CategoryTheory.Aut> .
wd:Q2431134 wl:formalizedAs "MulAut" .
wd:Q2431134 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Group/End.html#MulAut> .
wd:Q2431134 wl:formalizedAs "LinearMap.GeneralLinearGroup" .
wd:Q2431134 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/GeneralLinearGroup/Basic.html#LinearMap.GeneralLinearGroup> .
wd:Q2431134 wl:formalizedAs "RingAut" .
wd:Q2431134 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Ring/Aut.html#RingAut> .
wd:Q2431134 wl:formalizedAs "LinearMap.BilinForm.IsAlt.neg_eq" .
wd:Q2431134 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/BilinearForm/Properties.html#LinearMap.BilinForm.IsAlt.neg_eq> .
wd:Q2431134 wl:formalizedAs "Symmetric" .
wd:Q2431134 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/Defs/Unbundled.html#Symmetric> .
wd:Q2431134 wl:formalizedAs "Isometry" .
wd:Q2431134 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/MetricSpace/Isometry.html#Isometry> .
wd:Q2431134 wl:formalizedAs "Congruent" .
wd:Q2431134 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/MetricSpace/Congruence.html#Congruent> .
wd:Q11203 wl:formalizedAs "Matrix.mulVec_eq_sum" .
wd:Q11203 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Matrix/Mul.html#Matrix.mulVec_eq_sum> .
wd:Q11203 wl:formalizedAs "Matrix.mulVec" .
wd:Q11203 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Matrix/Mul.html#Matrix.mulVec> .
wd:Q11203 wl:formalizedAs "Matrix.mulVec_cramer" .
wd:Q11203 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Matrix/Adjugate.html#Matrix.mulVec_cramer> .
wd:Q11203 wl:formalizedAs "Matrix.inv_mulVec_eq_vec" .
wd:Q11203 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Matrix/NonsingularInverse.html#Matrix.inv_mulVec_eq_vec> .
wd:Q11203 wl:formalizedAs "Matrix.mulVec_zero" .
wd:Q11203 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Matrix/Mul.html#Matrix.mulVec_zero> .
wd:Q11203 wl:formalizedAs "Matrix.mulVec_add" .
wd:Q11203 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Matrix/Mul.html#Matrix.mulVec_add> .
wd:Q11203 wl:formalizedAs "Matrix.mulVecLin" .
wd:Q11203 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Matrix/ToLin.html#Matrix.mulVecLin> .
wd:Q11203 wl:formalizedAs "LinearMap.sub_mem_ker_iff" .
wd:Q11203 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Module/Submodule/Ker.html#LinearMap.sub_mem_ker_iff> .
wd:Q11203 wl:formalizedAs "LinearMap.mem_range" .
wd:Q11203 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Module/Submodule/Range.html#LinearMap.mem_range> .
wd:Q746550 wl:formalizedAs "TangentBundle" .
wd:Q746550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Manifold/IsManifold/Basic.html#TangentBundle> .
wd:Q746550 wl:formalizedAs "Bundle.TotalSpace.mk" .
wd:Q746550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/FiberBundle/Basic.html#Bundle.TotalSpace.mk> .
wd:Q746550 wl:formalizedAs "Bundle.TotalSpace.proj" .
wd:Q746550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/FiberBundle/Basic.html#Bundle.TotalSpace.proj> .
wd:Q746550 wl:formalizedAs "ContMDiff.contMDiff_tangentMap" .
wd:Q746550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Manifold/ContMDiffMFDeriv.html#ContMDiff.contMDiff_tangentMap> .
wd:Q746550 wl:formalizedAs "tangentBundleCore" .
wd:Q746550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Manifold/VectorBundle/Tangent.html#tangentBundleCore> .
wd:Q746550 wl:formalizedAs "TangentSpace.vectorBundle" .
wd:Q746550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Manifold/VectorBundle/Tangent.html#TangentSpace.vectorBundle> .
wd:Q746550 wl:formalizedAs "ContMDiffSection" .
wd:Q746550 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Manifold/VectorBundle/ContMDiffSection.html#ContMDiffSection> .
wd:Q909601 wl:formalizedAs "TangentSpace" .
wd:Q909601 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Manifold/IsManifold/Basic.html#TangentSpace> .
wd:Q909601 wl:formalizedAs "range_mfderiv_coe_sphere" .
wd:Q909601 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Manifold/Instances/Sphere.html#range_mfderiv_coe_sphere> .
wd:Q909601 wl:formalizedAs "TangentBundle" .
wd:Q909601 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Manifold/IsManifold/Basic.html#TangentBundle> .
wd:Q909601 wl:formalizedAs "ContMDiff" .
wd:Q909601 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Manifold/ContMDiff/Defs.html#ContMDiff> .
wd:Q909601 wl:formalizedAs "ContMDiffMap.algebra" .
wd:Q909601 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Manifold/Algebra/SmoothFunctions.html#ContMDiffMap.algebra> .
wd:Q909601 wl:formalizedAs "Derivation" .
wd:Q909601 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Derivation/Basic.html#Derivation> .
wd:Q909601 wl:formalizedAs "Derivation.map_algebraMap" .
wd:Q909601 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Derivation/Basic.html#Derivation.map_algebraMap> .
wd:Q909601 wl:formalizedAs "PointDerivation" .
wd:Q909601 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Manifold/DerivationBundle.html#PointDerivation> .
wd:Q909601 wl:formalizedAs "NormedSpace.fromTangentSpace" .
wd:Q909601 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Manifold/IsManifold/Basic.html#NormedSpace.fromTangentSpace> .
wd:Q909601 wl:formalizedAs "lineDeriv" .
wd:Q909601 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/LineDeriv/Basic.html#lineDeriv> .
wd:Q909601 wl:formalizedAs "tangentMap" .
wd:Q909601 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Manifold/MFDeriv/Defs.html#tangentMap> .
wd:Q1137206 wl:formalizedAs "taylor_mean_remainder_lagrange" .
wd:Q1137206 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/Taylor.html#taylor_mean_remainder_lagrange> .
wd:Q1137206 wl:formalizedAs "hasDerivAt_iff_isLittleO" .
wd:Q1137206 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/Deriv/Basic.html#hasDerivAt_iff_isLittleO> .
wd:Q1137206 wl:formalizedAs "taylorWithinEval" .
wd:Q1137206 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/Taylor.html#taylorWithinEval> .
wd:Q1137206 wl:formalizedAs "taylor_isLittleO" .
wd:Q1137206 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/Taylor.html#taylor_isLittleO> .
wd:Q1137206 wl:formalizedAs "taylorWithin" .
wd:Q1137206 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/Taylor.html#taylorWithin> .
wd:Q1137206 wl:formalizedAs "taylor_mean_remainder" .
wd:Q1137206 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/Taylor.html#taylor_mean_remainder> .
wd:Q1137206 wl:formalizedAs "taylor_integral_remainder" .
wd:Q1137206 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/Taylor.html#taylor_integral_remainder> .
wd:Q1137206 wl:formalizedAs "taylor_mean_remainder_bound" .
wd:Q1137206 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/Taylor.html#taylor_mean_remainder_bound> .
wd:Q1137206 wl:formalizedAs "exists_taylor_mean_remainder_bound" .
wd:Q1137206 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/Taylor.html#exists_taylor_mean_remainder_bound> .
wd:Q1137206 wl:formalizedAs "AnalyticAt" .
wd:Q1137206 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Analytic/Basic.html#AnalyticAt> .
wd:Q1137206 wl:formalizedAs "FormalMultilinearSeries.radius_inv_eq_limsup" .
wd:Q1137206 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Analytic/RadiusLiminf.html#FormalMultilinearSeries.radius_inv_eq_limsup> .
wd:Q1137206 wl:formalizedAs "HasFPowerSeriesOnBall.tendstoUniformlyOn" .
wd:Q1137206 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Analytic/Basic.html#HasFPowerSeriesOnBall.tendstoUniformlyOn> .
wd:Q1137206 wl:formalizedAs "expNegInvGlue.not_analyticAt_zero" .
wd:Q1137206 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/SmoothTransition.html#expNegInvGlue.not_analyticAt_zero> .
wd:Q1137206 wl:formalizedAs "DifferentiableOn.analyticOnNhd" .
wd:Q1137206 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Complex/CauchyIntegral.html#DifferentiableOn.analyticOnNhd> .
wd:Q1137206 wl:formalizedAs "Complex.circleIntegral_div_sub_of_differentiable_on_off_countable" .
wd:Q1137206 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Complex/CauchyIntegral.html#Complex.circleIntegral_div_sub_of_differentiable_on_off_countable> .
wd:Q1137206 wl:formalizedAs "DifferentiableOn.contDiffOn" .
wd:Q1137206 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Complex/CauchyIntegral.html#DifferentiableOn.contDiffOn> .
wd:Q1137206 wl:formalizedAs "Complex.norm_iteratedDeriv_le_of_forall_mem_sphere_norm_le" .
wd:Q1137206 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Complex/Liouville.html#Complex.norm_iteratedDeriv_le_of_forall_mem_sphere_norm_le> .
wd:Q1137206 wl:formalizedAs "HasFDerivAt" .
wd:Q1137206 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/FDeriv/Defs.html#HasFDerivAt> .
wd:Q1137206 wl:formalizedAs "fderiv" .
wd:Q1137206 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/FDeriv/Defs.html#fderiv> .
wd:Q214856 wl:formalizedAs "DiscreteTiling.Prototile" .
wd:Q214856 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Combinatorics/Tiling/Tile.html#DiscreteTiling.Prototile> .
wd:Q65943 wl:formalizedAs "EuclideanGeometry.angle_add_angle_add_angle_eq_pi" .
wd:Q65943 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Euclidean/Triangle.html#EuclideanGeometry.angle_add_angle_add_angle_eq_pi> .
wd:Q65943 wl:formalizedAs "FermatLastTheorem" .
wd:Q65943 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/FLT/Basic.html#FermatLastTheorem> .
wd:Q65943 wl:formalizedAs "even_iff_two_dvd" .
wd:Q65943 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Ring/Parity.html#even_iff_two_dvd> .
wd:Q65943 wl:formalizedAs "FirstOrder.Language.Theory" .
wd:Q65943 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Syntax.html#FirstOrder.Language.Theory> .
wd:Q65943 wl:formalizedAs "FirstOrder.Language.Sentence" .
wd:Q65943 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/ModelTheory/Syntax.html#FirstOrder.Language.Sentence> .
wd:Q1154787 wl:formalizedAs "jacobiTheta₂" .
wd:Q1154787 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/ModularForms/JacobiTheta/TwoVariable.html#jacobiTheta₂> .
wd:Q1154787 wl:formalizedAs "jacobiTheta₂_add_left&#x27;" .
wd:Q1154787 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/ModularForms/JacobiTheta/TwoVariable.html#jacobiTheta₂_add_left'> .
wd:Q1154787 wl:formalizedAs "jacobiTheta₂_add_left" .
wd:Q1154787 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/ModularForms/JacobiTheta/TwoVariable.html#jacobiTheta₂_add_left> .
wd:Q1154787 wl:formalizedAs "jacobiTheta_S_smul" .
wd:Q1154787 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/ModularForms/JacobiTheta/OneVariable.html#jacobiTheta_S_smul> .
wd:Q1154787 wl:formalizedAs "jacobiTheta₂_functional_equation" .
wd:Q1154787 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/ModularForms/JacobiTheta/TwoVariable.html#jacobiTheta₂_functional_equation> .
wd:Q1154787 wl:formalizedAs "Complex.betaIntegral" .
wd:Q1154787 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Gamma/Beta.html#Complex.betaIntegral> .
wd:Q1154787 wl:formalizedAs "Complex.betaIntegral_eq_Gamma_mul_div" .
wd:Q1154787 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Gamma/Beta.html#Complex.betaIntegral_eq_Gamma_mul_div> .
wd:Q1154787 wl:formalizedAs "Nat.Partition" .
wd:Q1154787 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Combinatorics/Enumerative/Partition/Basic.html#Nat.Partition> .
wd:Q1154787 wl:formalizedAs "Nat.Partition.hasProd_powerSeriesMk_card_restricted" .
wd:Q1154787 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Combinatorics/Enumerative/Partition/Glaisher.html#Nat.Partition.hasProd_powerSeriesMk_card_restricted> .
wd:Q1154787 wl:formalizedAs "pentagonal" .
wd:Q1154787 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Combinatorics/Enumerative/Pentagonal.html#pentagonal> .
wd:Q1154787 wl:formalizedAs "Nat.Partition.distincts" .
wd:Q1154787 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Combinatorics/Enumerative/Partition/Basic.html#Nat.Partition.distincts> .
wd:Q1154787 wl:formalizedAs "Nat.Partition.hasProd_powerSeriesMk_card_countRestricted" .
wd:Q1154787 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Combinatorics/Enumerative/Partition/Glaisher.html#Nat.Partition.hasProd_powerSeriesMk_card_countRestricted> .
wd:Q2393193 wl:formalizedAs "Turing.TM2ComputableInPolyTime" .
wd:Q2393193 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Computability/TuringMachine/Computable.html#Turing.TM2ComputableInPolyTime> .
wd:Q737279 wl:formalizedAs "irrational_sqrt_two" .
wd:Q737279 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/Real/Irrational.html#irrational_sqrt_two> .
wd:Q737279 wl:formalizedAs "Nat.exists_infinite_primes" .
wd:Q737279 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/Prime/Basic.html#Nat.exists_infinite_primes> .
wd:Q737279 wl:formalizedAs "ZMod.chineseRemainder" .
wd:Q737279 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/ZMod/Basic.html#ZMod.chineseRemainder> .
wd:Q737279 wl:formalizedAs "Real.sin" .
wd:Q737279 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Complex/Trigonometric.html#Real.sin> .
wd:Q737279 wl:formalizedAs "sq_add_sq_mul_sq_add_sq" .
wd:Q737279 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Ring/Identities.html#sq_add_sq_mul_sq_add_sq> .
wd:Q737279 wl:formalizedAs "EuclideanSpace.volume_ball" .
wd:Q737279 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/MeasureTheory/Measure/Lebesgue/VolumeOfBalls.html#EuclideanSpace.volume_ball> .
wd:Q737279 wl:formalizedAs "Real.arctan" .
wd:Q737279 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Trigonometric/Arctan.html#Real.arctan> .
wd:Q737279 wl:formalizedAs "add_pow" .
wd:Q737279 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/BigOperators/Ring.html#add_pow> .
wd:Q737279 wl:formalizedAs "fermatLastTheoremThree" .
wd:Q737279 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/FLT/Three.html#fermatLastTheoremThree> .
wd:Q737279 wl:formalizedAs "EuclideanGeometry.law_sin" .
wd:Q737279 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Euclidean/Triangle.html#EuclideanGeometry.law_sin> .
wd:Q737279 wl:formalizedAs "Nat.rec" .
wd:Q737279 wl:formalizedAs "Real.sin_add" .
wd:Q737279 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.html#Real.sin_add> .
wd:Q737279 wl:formalizedAs "pow_eq_pow_iff_of_ne_zero" .
wd:Q737279 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Order/Ring/Abs.html#pow_eq_pow_iff_of_ne_zero> .
wd:Q737279 wl:formalizedAs "exists_deriv_eq_zero" .
wd:Q737279 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/LocalExtr/Rolle.html#exists_deriv_eq_zero> .
wd:Q737279 wl:formalizedAs "Complex.hasSum_arctan" .
wd:Q737279 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Complex/Arctan.html#Complex.hasSum_arctan> .
wd:Q737279 wl:formalizedAs "exists_deriv_eq_slope" .
wd:Q737279 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/MeanValue.html#exists_deriv_eq_slope> .
wd:Q737279 wl:formalizedAs "intervalIntegral.integral_eq_sub_of_hasDeriv_right_of_le" .
wd:Q737279 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/MeasureTheory/Integral/FundThmCalculus.html#intervalIntegral.integral_eq_sub_of_hasDeriv_right_of_le> .
wd:Q737279 wl:formalizedAs "Real.hasSum_pow_div_log_of_abs_lt_1" .
wd:Q737279 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Log/Deriv.html#Real.hasSum_pow_div_log_of_abs_lt_1> .
wd:Q737279 wl:formalizedAs "taylor_mean_remainder_lagrange" .
wd:Q737279 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/Taylor.html#taylor_mean_remainder_lagrange> .
wd:Q737279 wl:formalizedAs "deriv.lhopital_zero_nhds" .
wd:Q737279 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/LHopital.html#deriv.lhopital_zero_nhds> .
wd:Q737279 wl:formalizedAs "bernoulli" .
wd:Q737279 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/Bernoulli.html#bernoulli> .
wd:Q737279 wl:formalizedAs "taylorWithin" .
wd:Q737279 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/Taylor.html#taylorWithin> .
wd:Q737279 wl:formalizedAs "Complex.cos_add_sin_mul_I_pow" .
wd:Q737279 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Complex/Trigonometric.html#Complex.cos_add_sin_mul_I_pow> .
wd:Q737279 wl:formalizedAs "ProbabilityTheory.gaussianReal" .
wd:Q737279 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Probability/Distributions/Gaussian/Real.html#ProbabilityTheory.gaussianReal> .
wd:Q737279 wl:formalizedAs "hasSum_zeta_two" .
wd:Q737279 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/ZetaValues.html#hasSum_zeta_two> .
wd:Q737279 wl:formalizedAs "ProbabilityTheory.cond_eq_inv_mul_cond_mul" .
wd:Q737279 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Probability/ConditionalProbability.html#ProbabilityTheory.cond_eq_inv_mul_cond_mul> .
wd:Q737279 wl:formalizedAs "irrational_pi" .
wd:Q737279 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Real/Pi/Irrational.html#irrational_pi> .
wd:Q737279 wl:formalizedAs "MeasureTheory.integral_divergence_of_hasFDerivAt_off_countable" .
wd:Q737279 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/MeasureTheory/Integral/DivergenceTheorem.html#MeasureTheory.integral_divergence_of_hasFDerivAt_off_countable> .
wd:Q737279 wl:formalizedAs "Complex.exists_root" .
wd:Q737279 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Complex/Polynomial/Basic.html#Complex.exists_root> .
wd:Q737279 wl:formalizedAs "intermediate_value_Icc" .
wd:Q737279 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Order/IntermediateValue.html#intermediate_value_Icc> .
wd:Q737279 wl:formalizedAs "Metric.tendsto_nhds_nhds" .
wd:Q737279 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/MetricSpace/Pseudo/Defs.html#Metric.tendsto_nhds_nhds> .
wd:Q737279 wl:formalizedAs "Complex.circleIntegral_sub_inv_smul_of_differentiable_on_off_countable" .
wd:Q737279 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Complex/CauchyIntegral.html#Complex.circleIntegral_sub_inv_smul_of_differentiable_on_off_countable> .
wd:Q737279 wl:formalizedAs "Nat.infinite_setOf_prime_and_eq_mod" .
wd:Q737279 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/LSeries/PrimesInAP.html#Nat.infinite_setOf_prime_and_eq_mod> .
wd:Q737279 wl:formalizedAs "TendstoUniformly" .
wd:Q737279 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/UniformSpace/UniformConvergence.html#TendstoUniformly> .
wd:Q737279 wl:formalizedAs "Quaternion" .
wd:Q737279 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Quaternion.html#Quaternion> .
wd:Q737279 wl:formalizedAs "BooleanAlgebra" .
wd:Q737279 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/BooleanAlgebra/Defs.html#BooleanAlgebra> .
wd:Q737279 wl:formalizedAs "IsRiemannianManifold" .
wd:Q737279 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Manifold/Riemannian/Basic.html#IsRiemannianManifold> .
wd:Q737279 wl:formalizedAs "RiemannHypothesis" .
wd:Q737279 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/LSeries/RiemannZeta.html#RiemannHypothesis> .
wd:Q737279 wl:formalizedAs "Cardinal.not_countable_real" .
wd:Q737279 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Real/Cardinality.html#Cardinal.not_countable_real> .
wd:Q737279 wl:formalizedAs "CommRing" .
wd:Q737279 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Ring/Defs.html#CommRing> .
wd:Q737279 wl:formalizedAs "MeasureTheory.IsProbabilityMeasure" .
wd:Q737279 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/MeasureTheory/Measure/Typeclasses/Probability.html#MeasureTheory.IsProbabilityMeasure> .
wd:Q737279 wl:formalizedAs "Computable" .
wd:Q737279 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Computability/Partrec.html#Computable> .
wd:Q42989 wl:formalizedAs "TopologicalSpace" .
wd:Q42989 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Defs/Basic.html#TopologicalSpace> .
wd:Q42989 wl:formalizedAs "Homeomorph" .
wd:Q42989 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Homeomorph/Defs.html#Homeomorph> .
wd:Q42989 wl:formalizedAs "ContinuousMap.HomotopyEquiv" .
wd:Q42989 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Homotopy/Equiv.html#ContinuousMap.HomotopyEquiv> .
wd:Q42989 wl:formalizedAs "IsOpen" .
wd:Q42989 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Defs/Basic.html#IsOpen> .
wd:Q42989 wl:formalizedAs "IsClosed" .
wd:Q42989 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Defs/Basic.html#IsClosed> .
wd:Q42989 wl:formalizedAs "IsClopen" .
wd:Q42989 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Defs/Basic.html#IsClopen> .
wd:Q42989 wl:formalizedAs "TopologicalSpace.OpenNhds" .
wd:Q42989 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Category/TopCat/OpenNhds.html#TopologicalSpace.OpenNhds> .
wd:Q42989 wl:formalizedAs "Continuous" .
wd:Q42989 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Defs/Basic.html#Continuous> .
wd:Q42989 wl:formalizedAs "ChartedSpace" .
wd:Q42989 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Manifold/ChartedSpace.html#ChartedSpace> .
wd:Q42989 wl:formalizedAs "IsCompact" .
wd:Q42989 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Defs/Filter.html#IsCompact> .
wd:Q42989 wl:formalizedAs "IsConnected" .
wd:Q42989 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Connected/Basic.html#IsConnected> .
wd:Q42989 wl:formalizedAs "MetricSpace" .
wd:Q42989 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/MetricSpace/Defs.html#MetricSpace> .
wd:Q42989 wl:formalizedAs "Metric.isOpen_iff" .
wd:Q42989 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/MetricSpace/Pseudo/Defs.html#Metric.isOpen_iff> .
wd:Q42989 wl:formalizedAs "subgroupIsFreeOfIsFree" .
wd:Q42989 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/GroupTheory/FreeGroup/NielsenSchreier.html#subgroupIsFreeOfIsFree> .
wd:Q42989 wl:formalizedAs "CategoryTheory.GrothendieckTopology" .
wd:Q42989 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/Sites/Grothendieck.html#CategoryTheory.GrothendieckTopology> .
wd:Q173091 wl:formalizedAs "Transcendental" .
wd:Q173091 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Algebraic/Defs.html#Transcendental> .
wd:Q173091 wl:formalizedAs "Transcendental.irrational" .
wd:Q173091 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/Real/Irrational.html#Transcendental.irrational> .
wd:Q173091 wl:formalizedAs "transcendental_liouvilleNumber" .
wd:Q173091 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/Transcendental/Liouville/LiouvilleNumber.html#transcendental_liouvilleNumber> .
wd:Q173091 wl:formalizedAs "Liouville" .
wd:Q173091 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/Transcendental/Liouville/Basic.html#Liouville> .
wd:Q173091 wl:formalizedAs "Liouville.transcendental" .
wd:Q173091 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/NumberTheory/Transcendental/Liouville/Basic.html#Liouville.transcendental> .
wd:Q173091 wl:formalizedAs "Algebraic.countable" .
wd:Q173091 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/AlgebraicCard.html#Algebraic.countable> .
wd:Q208216 wl:formalizedAs "dist_triangle" .
wd:Q208216 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/MetricSpace/Pseudo/Defs.html#dist_triangle> .
wd:Q208216 wl:formalizedAs "norm_add_le" .
wd:Q208216 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Normed/Group/Basic.html#norm_add_le> .
wd:Q208216 wl:formalizedAs "EuclideanGeometry.dist_sq_eq_dist_sq_add_dist_sq_iff_angle_eq_pi_div_two" .
wd:Q208216 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Euclidean/Angle/Unoriented/RightAngle.html#EuclideanGeometry.dist_sq_eq_dist_sq_add_dist_sq_iff_angle_eq_pi_div_two> .
wd:Q208216 wl:formalizedAs "dist_le_range_sum_dist" .
wd:Q208216 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/MetricSpace/Pseudo/Basic.html#dist_le_range_sum_dist> .
wd:Q208216 wl:formalizedAs "sameRay_iff_norm_add" .
wd:Q208216 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Convex/StrictConvexSpace.html#sameRay_iff_norm_add> .
wd:Q208216 wl:formalizedAs "Real.norm_eq_abs" .
wd:Q208216 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Normed/Group/Real.html#Real.norm_eq_abs> .
wd:Q208216 wl:formalizedAs "PiLp.norm_eq_sum" .
wd:Q208216 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Normed/Lp/PiLp.html#PiLp.norm_eq_sum> .
wd:Q208216 wl:formalizedAs "EuclideanSpace.norm_eq" .
wd:Q208216 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/InnerProductSpace/PiL2.html#EuclideanSpace.norm_eq> .
wd:Q208216 wl:formalizedAs "norm_inner_eq_norm_iff" .
wd:Q208216 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/InnerProductSpace/Basic.html#norm_inner_eq_norm_iff> .
wd:Q208216 wl:formalizedAs "Real.Lp_add_le" .
wd:Q208216 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/MeanInequalities.html#Real.Lp_add_le> .
wd:Q208216 wl:formalizedAs "Filter.Tendsto.cauchySeq" .
wd:Q208216 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/UniformSpace/Cauchy.html#Filter.Tendsto.cauchySeq> .
wd:Q208216 wl:formalizedAs "abs_norm_sub_norm_le" .
wd:Q208216 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Normed/Group/Basic.html#abs_norm_sub_norm_le> .
wd:Q208216 wl:formalizedAs "lipschitzWith_one_norm" .
wd:Q208216 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Normed/Group/Uniform.html#lipschitzWith_one_norm> .
wd:Q8084 wl:formalizedAs "Real.sin" .
wd:Q8084 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Complex/Trigonometric.html#Real.sin> .
wd:Q8084 wl:formalizedAs "Real.cos" .
wd:Q8084 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Complex/Trigonometric.html#Real.cos> .
wd:Q8084 wl:formalizedAs "Real.tan" .
wd:Q8084 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Complex/Trigonometric.html#Real.tan> .
wd:Q8084 wl:formalizedAs "Real.cos_pi_div_two_sub" .
wd:Q8084 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.html#Real.cos_pi_div_two_sub> .
wd:Q8084 wl:formalizedAs "Circle" .
wd:Q8084 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Complex/Circle.html#Circle> .
wd:Q8084 wl:formalizedAs "Real.arctan" .
wd:Q8084 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Trigonometric/Arctan.html#Real.arctan> .
wd:Q8084 wl:formalizedAs "Complex.hasSum_sin" .
wd:Q8084 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Trigonometric/Series.html#Complex.hasSum_sin> .
wd:Q8084 wl:formalizedAs "Complex.exp_mul_I" .
wd:Q8084 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Complex/Trigonometric.html#Complex.exp_mul_I> .
wd:Q8084 wl:formalizedAs "EuclideanGeometry.sin_angle_mul_dist_eq_sin_angle_mul_dist" .
wd:Q8084 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Euclidean/Triangle.html#EuclideanGeometry.sin_angle_mul_dist_eq_sin_angle_mul_dist> .
wd:Q8084 wl:formalizedAs "EuclideanGeometry.dist_sq_eq_dist_sq_add_dist_sq_sub_two_mul_dist_mul_dist_mul_cos_angle" .
wd:Q8084 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Euclidean/Triangle.html#EuclideanGeometry.dist_sq_eq_dist_sq_add_dist_sq_sub_two_mul_dist_mul_dist_mul_cos_angle> .
wd:Q8084 wl:formalizedAs "Real.sin_sq_add_cos_sq" .
wd:Q8084 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Complex/Trigonometric.html#Real.sin_sq_add_cos_sq> .
wd:Q8084 wl:formalizedAs "Complex.sin" .
wd:Q8084 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Complex/Trigonometric.html#Complex.sin> .
wd:Q163310 wl:formalizedAs "Turing.TM0.Machine" .
wd:Q163310 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Computability/TuringMachine/PostTuringMachine.html#Turing.TM0.Machine> .
wd:Q163310 wl:formalizedAs "ComputablePred.halting_problem" .
wd:Q163310 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Computability/Halting.html#ComputablePred.halting_problem> .
wd:Q163310 wl:formalizedAs "Turing.TM0.Cfg" .
wd:Q163310 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Computability/TuringMachine/PostTuringMachine.html#Turing.TM0.Cfg> .
wd:Q658429 wl:formalizedAs "VectorBundle" .
wd:Q658429 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/VectorBundle/Basic.html#VectorBundle> .
wd:Q658429 wl:formalizedAs "Bundle.Trivial.vectorBundle" .
wd:Q658429 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/VectorBundle/Constructions.html#Bundle.Trivial.vectorBundle> .
wd:Q658429 wl:formalizedAs "tangentBundleCore" .
wd:Q658429 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Manifold/VectorBundle/Tangent.html#tangentBundleCore> .
wd:Q658429 wl:formalizedAs "FiberBundle" .
wd:Q658429 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/FiberBundle/Basic.html#FiberBundle> .
wd:Q658429 wl:formalizedAs "Bundle.Trivialization" .
wd:Q658429 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/FiberBundle/Trivialization.html#Bundle.Trivialization> .
wd:Q658429 wl:formalizedAs "Bundle.Trivial" .
wd:Q658429 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/FiberBundle/Constructions.html#Bundle.Trivial> .
wd:Q658429 wl:formalizedAs "VectorBundleCore.coordChange" .
wd:Q658429 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/VectorBundle/Basic.html#VectorBundleCore.coordChange> .
wd:Q658429 wl:formalizedAs "FiberBundleCore.coordChange_comp" .
wd:Q658429 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/FiberBundle/Basic.html#FiberBundleCore.coordChange_comp> .
wd:Q658429 wl:formalizedAs "FiberBundleCore.fiberBundle" .
wd:Q658429 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/FiberBundle/Basic.html#FiberBundleCore.fiberBundle> .
wd:Q658429 wl:formalizedAs "VectorBundle.prod" .
wd:Q658429 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/VectorBundle/Constructions.html#VectorBundle.prod> .
wd:Q658429 wl:formalizedAs "Bundle.ContinuousLinearMap.vectorBundle" .
wd:Q658429 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/VectorBundle/Hom.html#Bundle.ContinuousLinearMap.vectorBundle> .
wd:Q658429 wl:formalizedAs "VectorBundle.pullback" .
wd:Q658429 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/VectorBundle/Constructions.html#VectorBundle.pullback> .
wd:Q658429 wl:formalizedAs "RiemannianBundle" .
wd:Q658429 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/VectorBundle/Riemannian.html#RiemannianBundle> .
wd:Q658429 wl:formalizedAs "ContMDiffVectorBundle" .
wd:Q658429 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Manifold/VectorBundle/Basic.html#ContMDiffVectorBundle> .
wd:Q200802 wl:formalizedAs "crossProduct" .
wd:Q200802 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/CrossProduct.html#crossProduct> .
wd:Q200802 wl:formalizedAs "triple_product_eq_det" .
wd:Q200802 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/CrossProduct.html#triple_product_eq_det> .
wd:Q200802 wl:formalizedAs "MeasureTheory.integral_divergence_prod_Icc_of_hasFDerivAt_off_countable_of_le" .
wd:Q200802 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/MeasureTheory/Integral/DivergenceTheorem.html#MeasureTheory.integral_divergence_prod_Icc_of_hasFDerivAt_off_countable_of_le> .
wd:Q200802 wl:formalizedAs "HasFDerivAt" .
wd:Q200802 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/FDeriv/Basic.html#HasFDerivAt> .
wd:Q200802 wl:formalizedAs "IsLocalExtr.fderiv_eq_zero" .
wd:Q200802 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/LocalExtr/Basic.html#IsLocalExtr.fderiv_eq_zero> .
wd:Q200802 wl:formalizedAs "EuclideanSpace" .
wd:Q200802 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/InnerProductSpace/PiL2.html#EuclideanSpace> .
wd:Q200802 wl:formalizedAs "TangentBundle" .
wd:Q200802 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Geometry/Manifold/VectorBundle/Tangent.html#TangentBundle> .
wd:Q1970172 wl:formalizedAs "VonNeumannAlgebra" .
wd:Q1970172 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/VonNeumannAlgebra/Basic.html#VonNeumannAlgebra> .
wd:Q1970172 wl:formalizedAs "WStarAlgebra" .
wd:Q1970172 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/VonNeumannAlgebra/Basic.html#WStarAlgebra> .
wd:Q1970172 wl:formalizedAs "IsStarProjection" .
wd:Q1970172 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Star/StarProjection.html#IsStarProjection> .
wd:Q37172 wl:formalizedAs "fourierIntegral_gaussian" .
wd:Q37172 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Gaussian/FourierTransform.html#fourierIntegral_gaussian> .
wd:Q831390 wl:formalizedAs "MeasureTheory.Lp" .
wd:Q831390 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/MeasureTheory/Function/LpSpace/Basic.html#MeasureTheory.Lp> .
wd:Q659746 wl:formalizedAs "IsWellOrder" .
wd:Q659746 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/RelClasses.html#IsWellOrder> .
wd:Q659746 wl:formalizedAs "WellOrder" .
wd:Q659746 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Ordinal/Basic.html#WellOrder> .
wd:Q659746 wl:formalizedAs "WellFounded.has_min" .
wd:Q659746 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/WellFounded.html#WellFounded.has_min> .
wd:Q659746 wl:formalizedAs "SuccOrder.ofLinearWellFoundedLT" .
wd:Q659746 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/SuccPred/Basic.html#SuccOrder.ofLinearWellFoundedLT> .
wd:Q659746 wl:formalizedAs "WellFoundedLT.conditionallyCompleteLinearOrderBot" .
wd:Q659746 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/ConditionallyCompleteLattice/Defs.html#WellFoundedLT.conditionallyCompleteLinearOrderBot> .
wd:Q659746 wl:formalizedAs "isWellOrder_lt" .
wd:Q659746 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/RelClasses.html#isWellOrder_lt> .
wd:Q659746 wl:formalizedAs "Ordinal.type" .
wd:Q659746 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Ordinal/Basic.html#Ordinal.type> .
wd:Q659746 wl:formalizedAs "exists_wellFoundedLT" .
wd:Q659746 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Cardinal/Order.html#exists_wellFoundedLT> .
wd:Q659746 wl:formalizedAs "WellFoundedLT.induction" .
wd:Q659746 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/RelClasses.html#WellFoundedLT.induction> .
wd:Q659746 wl:formalizedAs "type_nat_lt" .
wd:Q659746 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Ordinal/Basic.html#type_nat_lt> .
wd:Q659746 wl:formalizedAs "PrincipalSeg.ofElement" .
wd:Q659746 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/InitialSeg.html#PrincipalSeg.ofElement> .
wd:Q659746 wl:formalizedAs "InitialSeg.isLowerSet_range" .
wd:Q659746 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/InitialSeg.html#InitialSeg.isLowerSet_range> .
wd:Q659746 wl:formalizedAs "ZFSet.IsOrdinal" .
wd:Q659746 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/ZFC/Ordinal.html#ZFSet.IsOrdinal> .
wd:Q659746 wl:formalizedAs "PrincipalSeg.irrefl" .
wd:Q659746 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/InitialSeg.html#PrincipalSeg.irrefl> .
wd:Q659746 wl:formalizedAs "InitialSeg.total" .
wd:Q659746 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/InitialSeg.html#InitialSeg.total> .
wd:Q659746 wl:formalizedAs "InitialSeg.image_Iio" .
wd:Q659746 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/InitialSeg.html#InitialSeg.image_Iio> .
wd:Q659746 wl:formalizedAs "Ordinal" .
wd:Q659746 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Ordinal/Basic.html#Ordinal> .
wd:Q659746 wl:formalizedAs "Preorder.topology" .
wd:Q659746 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Order/Basic.html#Preorder.topology> .
wd:Q659746 wl:formalizedAs "IsCofinal" .
wd:Q659746 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/Cofinal.html#IsCofinal> .
wd:Q659746 wl:formalizedAs "Ordinal.type_fintype" .
wd:Q659746 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Ordinal/Basic.html#Ordinal.type_fintype> .
wd:Q576728 wl:formalizedAs "FundamentalGroup" .
wd:Q576728 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/AlgebraicTopology/FundamentalGroupoid/FundamentalGroup.html#FundamentalGroup> .
wd:Q3573180 wl:formalizedAs "Real.hasSum_arctan" .
wd:Q3573180 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Complex/Arctan.html#Real.hasSum_arctan> .
wd:Q3573180 wl:formalizedAs "Real.tendsto_sum_pi_div_four" .
wd:Q3573180 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Real/Pi/Leibniz.html#Real.tendsto_sum_pi_div_four> .
wd:Q3573180 wl:formalizedAs "Real.pi_lt_d20" .
wd:Q3573180 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Real/Pi/Bounds.html#Real.pi_lt_d20> .
wd:Q3573180 wl:formalizedAs "Real.hasSum_sin" .
wd:Q3573180 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Trigonometric/Series.html#Real.hasSum_sin> .
wd:Q3573180 wl:formalizedAs "Real.cos_add" .
wd:Q3573180 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Complex/Trigonometric.html#Real.cos_add> .
wd:Q3573180 wl:formalizedAs "taylor_mean_remainder_lagrange" .
wd:Q3573180 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Calculus/Taylor.html#taylor_mean_remainder_lagrange> .
wd:Q290810 wl:formalizedAs "zorn_le" .
wd:Q290810 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/Zorn.html#zorn_le> .
wd:Q290810 wl:formalizedAs "IsChain.exists_maxChain" .
wd:Q290810 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/Zorn.html#IsChain.exists_maxChain> .
wd:Q290810 wl:formalizedAs "PartialOrder" .
wd:Q290810 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/Defs/PartialOrder.html#PartialOrder> .
wd:Q290810 wl:formalizedAs "GE.ge" .
wd:Q290810 wl:formalizedAs "LinearOrder" .
wd:Q290810 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/Defs/LinearOrder.html#LinearOrder> .
wd:Q290810 wl:formalizedAs "Subtype.partialOrder" .
wd:Q290810 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/Basic.html#Subtype.partialOrder> .
wd:Q290810 wl:formalizedAs "IsChain" .
wd:Q290810 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/Preorder/Chain.html#IsChain> .
wd:Q290810 wl:formalizedAs "IsMax" .
wd:Q290810 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/Max.html#IsMax> .
wd:Q290810 wl:formalizedAs "upperBounds" .
wd:Q290810 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/Bounds/Defs.html#upperBounds> .
wd:Q290810 wl:formalizedAs "exists_maximal_of_chains_bounded" .
wd:Q290810 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/Zorn.html#exists_maximal_of_chains_bounded> .
wd:Q290810 wl:formalizedAs "zorn_le_nonempty_Ici₀" .
wd:Q290810 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/Zorn.html#zorn_le_nonempty_Ici₀> .
wd:Q290810 wl:formalizedAs "Module.Basis.exists_basis" .
wd:Q290810 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/LinearAlgebra/Basis/VectorSpace.html#Module.Basis.exists_basis> .
wd:Q290810 wl:formalizedAs "Ideal.exists_maximal" .
wd:Q290810 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Ideal/Maximal.html#Ideal.exists_maximal> .
wd:Q290810 wl:formalizedAs "isCompact_univ_pi" .
wd:Q290810 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Compactness/Compact.html#isCompact_univ_pi> .
wd:Q290810 wl:formalizedAs "ChainCompletePartialOrder.nonempty_fixedPoints_of_inflationary" .
wd:Q290810 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/BourbakiWitt.html#ChainCompletePartialOrder.nonempty_fixedPoints_of_inflationary> .
wd:Q290810 wl:formalizedAs "exists_extension_of_le_sublinear" .
wd:Q290810 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/Convex/Cone/Extension.html#exists_extension_of_le_sublinear> .
wd:Q290810 wl:formalizedAs "Ultrafilter.exists_le" .
wd:Q290810 rdfs:seeAlso <https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/Filter/Ultrafilter/Defs.html#Ultrafilter.exists_le> .