Documentation Verification Report

Unique

πŸ“ Source: Mathlib/Logic/Unique.lean

Statistics

MetricCount
DefinitionsinstUnique, unique, unique, uniqueOfSurjectiveConst, instUniqueOfIsEmpty, instUnique, unique, uniqueOfIsEmpty, instInhabited, mk', subtypeEq, subtypeEq', toInhabited, instUniqueTrue, uniqueElim, uniqueOfSubsingleton, uniqueProp
17
Theoremssubsingleton, subsingleton, subsingleton_iff_isEmpty, default_eq_unit, default_apply, default_def, bijective, default_eq, eq_default, exists_iff, ext, ext_iff, forall_iff, instSubsingleton, subsingleton_unique, subsingleton_unique', subsingleton_unique'_iff, uniq, eq_const_of_subsingleton, eq_const_of_unique, heq_const_of_unique, nonempty_unique, uniqueElim_const, uniqueElim_default, unique_iff_existsUnique, unique_iff_subsingleton_and_nonempty, unique_subtype_iff_existsUnique
27
Total44

Fin

Definitions

NameCategoryTheorems
instUnique πŸ“–CompOp
3 mathmath: Rep.diagonalOneIsoLeftRegular_inv_hom, succFunEquiv_symm_apply, Rep.diagonalOneIsoLeftRegular_hom_hom

Function.Injective

Definitions

NameCategoryTheorems
unique πŸ“–CompOpβ€”

Theorems

NameKindAssumesProvesValidatesDepends On
subsingleton πŸ“–β€”β€”β€”β€”β€”

Function.Surjective

Definitions

NameCategoryTheorems
unique πŸ“–CompOpβ€”
uniqueOfSurjectiveConst πŸ“–CompOpβ€”

Theorems

NameKindAssumesProvesValidatesDepends On
subsingleton πŸ“–β€”β€”β€”β€”forallβ‚‚

Option

Definitions

NameCategoryTheorems
instUniqueOfIsEmpty πŸ“–CompOpβ€”

Theorems

NameKindAssumesProvesValidatesDepends On
subsingleton_iff_isEmpty πŸ“–mathematicalβ€”IsEmptyβ€”β€”

PUnit

Definitions

NameCategoryTheorems
instUnique πŸ“–CompOp
3 mathmath: AddEquiv.finsuppUnique_symm, MeasureTheory.volume_preserving_pi_empty, MeasureTheory.measurePreserving_pi_empty

Theorems

NameKindAssumesProvesValidatesDepends On
default_eq_unit πŸ“–β€”β€”β€”β€”β€”

Pi

Definitions

NameCategoryTheorems
unique πŸ“–CompOpβ€”
uniqueOfIsEmpty πŸ“–CompOp
3 mathmath: MeasureTheory.volume_preserving_pi_empty, Fintype.piFinset_of_isEmpty, MeasureTheory.measurePreserving_pi_empty

Theorems

NameKindAssumesProvesValidatesDepends On
default_apply πŸ“–β€”β€”β€”β€”β€”
default_def πŸ“–β€”β€”β€”β€”β€”

Unique

Definitions

NameCategoryTheorems
instInhabited πŸ“–CompOp
177 mathmath: CategoryTheory.Limits.limitConeOfUnique_cone_Ο€, SetTheory.PGame.default_nim_one_rightMoves_eq, Equiv.uniqueProd_symm_apply, UniformEquiv.funUnique_apply, DFinsupp.lex_lt_iff_of_unique, Matrix.permanent_unique, ciSup_unique, Ordinal.Iio_one_default_eq, Fintype.sum_unique, MeasureTheory.integral_unique, Finset.Nonempty.eq_singleton_default, IsometryEquiv.withLpUniqueProd_symm_apply, Set.uniqueElim_preimage, unique_zero, Pi.Colex.lt_iff_of_unique, Pi.lex_le_iff_of_unique, MeasureTheory.measurable_uniqueElim_cylinderEvents, AddEquiv.piUnique_apply, Matrix.uniqueAddEquiv_apply, Ordinal.one_toPGame_leftMoves_default_eq, Set.range_unique, Equiv.prodUnique_symm_apply, Matrix.uniqueRingEquiv_apply, AddMonoidAlgebra.uniqueRingEquiv_apply, MonoidAlgebra.uniqueRingEquiv_apply, default_eq, Finsupp.LinearEquiv.finsuppUnique_symm_apply, ContinuousLinearEquiv.piUnique_symm_apply, ContinuousLinearEquiv.uniqueProd_symm_apply, CategoryTheory.Limits.productUniqueIso_hom, Equiv.uniqueSigma_apply, hasSum_unique, Pi.colex_le_iff_of_unique, AlgEquiv.default_apply, Equiv.equivPUnit_symm_apply, AddEquiv.uniqueProd_symm_apply, ContinuousLinearEquiv.piUnique_apply, Finsupp.unique_single, Finsupp.lex_iff_of_unique, LinearEquiv.piUnique_symm_apply, MonomialOrder.lex_lt_iff_of_unique, DFinsupp.colex_lt_iff_of_unique, Homeomorph.funUnique_apply, uniformEquicontinuousOn_unique, AddEquiv.piUnique_symm_apply, LinearEquiv.piUnique_apply, AddEquiv.funUnique_apply, DFinsupp.Lex.le_iff_of_unique, CategoryTheory.Limits.coproductUniqueIso_hom, CategoryTheory.Limits.limitBiconeOfUnique_bicone_Ο€, unique_one, CategoryTheory.Limits.limitBiconeOfUnique_isBilimit_isColimit, CategoryTheory.sectionsFunctorNatIsoCoyoneda_inv_app_coe, MulEquiv.prodUnique_symm_apply, Equiv.finsuppUnique_apply, AddEquiv.finsuppUnique_apply, CategoryTheory.Limits.productUniqueIso_inv, Finset.univ_unique, FiniteDimensional.basisSingleton_repr_apply, uniformEquicontinuous_unique, DFinsupp.Colex.le_iff_of_unique, IsCompactOpenCovered.iff_of_unique, Matrix.uniqueAlgEquiv_apply, finsum_unique, Pi.lex_lt_iff_of_unique, DFinsupp.lex_iff_of_unique, SetTheory.PGame.default_nim_one_leftMoves_eq, Set.eq_empty_or_singleton_of_unique, forall_iff, OrderIso.ofUnique_symm_apply, AlgebraicGeometry.Scheme.Cover.toSigma_sβ‚€, Pi.lex_iff_of_unique, Equiv.funUnique_apply, Homeomorph.continuousMapOfUnique_symm_apply, Equiv.sigmaUnique_symm_apply, AlgHom.default_apply, CategoryTheory.Limits.limitConeOfUnique_cone_pt, Finsupp.Colex.le_iff_of_unique, Finsupp.Lex.le_iff_of_unique, MulEquiv.uniqueProd_symm_apply, EuclideanGeometry.orthogonalProjection_affineSpan_singleton, Finsupp.lex_lt_iff_of_unique, eq_default, MeasurableEquiv.piUnique_symm_apply, MeasurableEquiv.piUnique_apply, Set.default_coe_singleton, LinearEquiv.uniqueProd_symm_apply, OrderIso.ofUnique_apply, Finset.default_singleton, Finsupp.linearCombination_unique, ContinuousLinearEquiv.prodUnique_symm_apply, Equiv.sigmaSigmaSubtype_apply, MeasurableEquiv.funUnique_apply, IsometryEquiv.funUnique_apply, MeasureTheory.measurePreserving_piUnique, Homeomorph.prodUnique_symm_apply_snd, CategoryTheory.Limits.biproductUniqueIso_inv, RingEquiv.piUnique_symm_apply, CompleteOrthogonalIdempotents.unique_iff, equicontinuous_unique, DFinsupp.Lex.lt_iff_of_unique, Homeomorph.piUnique_apply, CategoryTheory.Limits.limitBiconeOfUnique_isBilimit_isLimit, MeasureTheory.lintegral_unique, equicontinuousWithinAt_unique, Equiv.uniqueSigma_symm_apply, CategoryTheory.Bimon.trivialTo_hom, MulEquiv.piUnique_apply, Homeomorph.homeomorphOfUnique_symm_apply, LinearEquiv.prodUnique_symm_apply, AlgebraicGeometry.Scheme.default_asIdeal, DFinsupp.lex_le_iff_of_unique, AlgebraicGeometry.Scheme.Cover.Hom.sigma_hβ‚€, OrderIso.funUnique_apply, Finset.sum_unique_nonempty, Equiv.ofUnique_apply, CategoryTheory.Limits.limitConeOfUnique_isLimit_lift, LinearEquiv.funUnique_apply, Pi.Lex.lt_iff_of_unique, CategoryTheory.Limits.biproductUniqueIso_hom, measurable_uniqueElim, CategoryTheory.Presieve.ofArrows_of_unique, CategoryTheory.Limits.limitBiconeOfUnique_bicone_pt, finprod_unique, iInf_unique, CategoryTheory.Limits.coproductUniqueIso_inv, IsometryEquiv.withLpProdUnique_symm_apply, Finsupp.LinearEquiv.finsuppUnique_apply, LinearIsometryEquiv.withLpProdUnique_symm_apply, Finsupp.lex_le_iff_of_unique, AlgebraicGeometry.Scheme.Cover.Hom.sigma_sβ‚€, MulEquiv.piUnique_symm_apply, AffineSubspace.signedInfDist_singleton, iSup_unique, Finset.nonempty_iff_eq_singleton_default, Homeomorph.piUnique_symm_apply, CategoryTheory.SemiCartesianMonoidalCategory.default_eq_toUnit, ciInf_unique, Homeomorph.homeomorphOfUnique_apply, equicontinuousOn_unique, CommRingCat.coyonedaUnique_hom_app_hom_apply, MeasureTheory.volume_preserving_piUnique, Fintype.prod_unique, Finsupp.unique_ext_iff, uniqueElim_default, CategoryTheory.Limits.colimitCoconeOfUnique_cocone_pt, MulEquiv.funUnique_apply, Matrix.diagonal_unique, HahnSeries.SummableFamily.hsum_unique, AddEquiv.prodUnique_symm_apply, exists_iff, Matrix.det_unique, CategoryTheory.Limits.colimitCoconeOfUnique_cocone_ΞΉ, hasProd_unique, Matrix.uniqueEquiv_apply, Pi.colex_lt_iff_of_unique, Equiv.ofUnique_symm_apply, CategoryTheory.Limits.MulticospanIndex.multiforkOfParallelHomsEquivFork_functor_obj_ΞΉ, Ordinal.lsub_unique, CategoryTheory.Limits.limitBiconeOfUnique_bicone_ΞΉ, CategoryTheory.Limits.colimitCoconeOfUnique_isColimit_desc, RingEquiv.piUnique_apply, Finsupp.Colex.lt_iff_of_unique, Finset.prod_unique_nonempty, Set.univ_unique, Equiv.piUnique_symm_apply, LinearIsometryEquiv.withLpUniqueProd_symm_apply, Equiv.piUnique_apply, equicontinuousAt_unique, heq_const_of_unique, OrthogonalIdempotents.unique, Finsupp.Lex.lt_iff_of_unique, algebraicIndependent_unique_type_iff, ContinuousLinearEquiv.coe_funUnique, MonomialOrder.lex_le_iff_of_unique, eq_const_of_unique, Equiv.listUniqueEquiv_symm_apply
mk' πŸ“–CompOpβ€”
subtypeEq πŸ“–CompOpβ€”
subtypeEq' πŸ“–CompOpβ€”
toInhabited πŸ“–CompOp
5 mathmath: ext_iff, CategoryTheory.Comon.uniqueHomToTrivial_default_hom, chartedSpace_of_discreteTopology_chartAt, CategoryTheory.Mon.uniqueHomFromTrivial_default_hom, uniq

Theorems

NameKindAssumesProvesValidatesDepends On
bijective πŸ“–mathematicalβ€”Function.Bijectiveβ€”Function.bijective_iff_has_inverse
instSubsingleton
default_eq πŸ“–mathematicalβ€”instInhabitedβ€”uniq
eq_default πŸ“–mathematicalβ€”instInhabitedβ€”uniq
exists_iff πŸ“–mathematicalβ€”instInhabitedβ€”eq_default
ext πŸ“–β€”toInhabitedβ€”β€”β€”
ext_iff πŸ“–mathematicalβ€”toInhabitedβ€”ext
forall_iff πŸ“–mathematicalβ€”instInhabitedβ€”eq_default
instSubsingleton πŸ“–β€”β€”β€”β€”eq_default
subsingleton_unique πŸ“–mathematicalβ€”Uniqueβ€”subsingleton_unique'
subsingleton_unique' πŸ“–β€”β€”β€”β€”β€”
subsingleton_unique'_iff πŸ“–β€”β€”β€”β€”subsingleton_unique'
uniq πŸ“–mathematicalβ€”toInhabitedβ€”β€”

(root)

Definitions

NameCategoryTheorems
instUniqueTrue πŸ“–CompOpβ€”
uniqueElim πŸ“–CompOp
23 mathmath: Function.update_eq_updateFinset, Set.uniqueElim_preimage, Equiv.finsuppUnique_symm_apply_support_val, MeasureTheory.measurable_uniqueElim_cylinderEvents, Function.update_updateFinset, MeasurableEquiv.funUnique_symm_apply, ContinuousLinearEquiv.piUnique_symm_apply, AddEquiv.piUnique_symm_apply, MeasurableEquiv.piUnique_symm_apply, uniqueElim_const, Fin.succFunEquiv_symm_apply, RingEquiv.piUnique_symm_apply, UniformEquiv.funUnique_symm_apply, measurable_uniqueElim, MonoidAlgebra.uniqueRingEquiv_symm_apply, AddMonoidAlgebra.uniqueRingEquiv_symm_apply, MulEquiv.piUnique_symm_apply, Homeomorph.piUnique_symm_apply, AddEquiv.finsuppUnique_symm_apply_support_val, uniqueElim_default, Equiv.funUnique_symm_apply, Homeomorph.funUnique_symm_apply, Equiv.piUnique_symm_apply
uniqueOfSubsingleton πŸ“–CompOp
2 mathmath: Rep.ofMulActionSubsingletonIsoTrivial_inv_hom, Rep.ofMulActionSubsingletonIsoTrivial_hom_hom
uniqueProp πŸ“–CompOpβ€”

Theorems

NameKindAssumesProvesValidatesDepends On
eq_const_of_subsingleton πŸ“–β€”β€”β€”β€”β€”
eq_const_of_unique πŸ“–mathematicalβ€”Unique.instInhabitedβ€”eq_const_of_subsingleton
Unique.instSubsingleton
heq_const_of_unique πŸ“–mathematicalβ€”Unique.instInhabitedβ€”Function.hfunext
Unique.instSubsingleton
nonempty_unique πŸ“–mathematicalβ€”Uniqueβ€”β€”
uniqueElim_const πŸ“–mathematicalβ€”uniqueElimβ€”β€”
uniqueElim_default πŸ“–mathematicalβ€”uniqueElim
Unique.instInhabited
β€”β€”
unique_iff_existsUnique πŸ“–mathematicalβ€”Unique
ExistsUnique
β€”Unique.uniq
unique_iff_subsingleton_and_nonempty πŸ“–mathematicalβ€”Uniqueβ€”Unique.instSubsingleton
nonempty_unique
unique_subtype_iff_existsUnique πŸ“–mathematicalβ€”Unique
ExistsUnique
β€”Unique.uniq

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