name string | module string | deps list |
|---|---|---|
ContinuousMap.abs_mem_subalgebra_closure | Mathlib.Topology.ContinuousMap.StoneWeierstrass | [
"Subalgebra.instSetLike",
"NormedCommRing.toNormedRing",
"Norm.norm",
"NormedCommRing.toSeminormedCommRing",
"Real",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Real.lattice",
"ContinuousMap.instNorm",
"IsTopologicalRing.toIsTopologicalSemiring",
"continuous_subtype_val",
"abs",
"Continu... |
IsLprojection.instLatticeSubtypeOfFaithfulSMul | Mathlib.Analysis.Normed.Module.MStructure | [
"SemilatticeSup.mk",
"Lattice",
"IsLprojection",
"IsLprojection.Subtype.sup",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"IsLprojection.instLatticeSubtypeOfFaithfulSMul._proof_3",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"Subtype",
"DistribSMul.toSMulZeroClass... |
Nat.leRecOn_injective | Mathlib.Data.Nat.Basic | [
"Nat.le_refl",
"Nat.leRecOn_succ",
"congrArg",
"Eq.mp",
"instOfNatNat",
"LE.le",
"Nat.le.rec",
"instLENat",
"Nat.le.step",
"instHAdd",
"HAdd.hAdd",
"Nat.le",
"Nat.leRecOn",
"Nat",
"Nat.leRecOn_self",
"instAddNat",
"Nat.le.refl",
"Function.Injective",
"OfNat.ofNat",
"Nat.succ",
... |
Nat.Prime.dvd_choose_pow | Mathlib.Data.Nat.Multiplicity | [
"Nat.Prime.emultiplicity_choose_prime_pow_add_emultiplicity",
"Nat.Prime",
"Preorder.toLT",
"Dvd.dvd",
"Nat.choose",
"instAddMonoidWithOneENat",
"Nat.instSemigroupWithZero",
"ENat.instNatCast",
"congrArg",
"CommSemiring.toSemiring",
"Nat.instMonoid",
"AddMonoid.toAddZeroClass",
"PartialOrder... |
QuaternionAlgebra.Basis.casesOn | Mathlib.Algebra.QuaternionBasis | [
"CommRing",
"instHSMul",
"HMul.hMul",
"Ring.toNonAssocRing",
"AddGroupWithOne.toAddGroup",
"AddGroupWithOne.toAddMonoidWithOne",
"HSub.hSub",
"Algebra",
"Algebra.toSMul",
"Distrib.toAdd",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"NonAssocRing.toNonUnitalNonAssocRing",
"Quaternion... |
EMetric.NonemptyCompacts.isClosed_in_closeds | Mathlib.Topology.MetricSpace.Closeds | [
"TopologicalSpace.NonemptyCompacts.toCloseds",
"CompleteSpace",
"TopologicalSpace.NonemptyCompacts",
"TopologicalSpace.Closeds.uniformSpace",
"TopologicalSpace.NonemptyCompacts.isClosed_in_closeds",
"EMetricSpace.metrizableSpace",
"EMetricSpace.toPseudoEMetricSpace",
"EMetricSpace",
"IsClosed",
"P... |
LinearMap.isNilpotent_mulRight_iff | Mathlib.RingTheory.Nilpotent.Lemmas | [
"LinearMap.pow_mulRight",
"Eq.mpr",
"Module.End.instMonoid",
"IsScalarTower.right",
"congrArg",
"CommSemiring.toSemiring",
"Algebra",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"Algebra.toModule",
"Eq.mp",
"id",
"LinearMap",
"Monoid.toPow",
"CommSemiring",
"NonUnitalNonAssocSemiring.toA... |
Equiv.toIso_hom | Mathlib.CategoryTheory.Types.Basic | [
"Equiv.instEquivLike",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Equiv",
"Equiv.toIso",
"CategoryTheory.types",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Iso.hom",
"Eq",
"DFunLike.coe",
"rfl",
"EquivLike.toFunLike"
] |
_private.Mathlib.Data.Fin.Basic.0.Fin.cast_injective._simp_1_1 | Mathlib.Data.Fin.Basic | [
"Fin.val",
"Nat",
"propext",
"Eq.symm",
"Fin",
"Eq",
"Fin.val_eq_val"
] |
Lean.Language.Lean.CommandParsedSnapshot.below_1 | Lean.Language.Lean.Types | [
"Task",
"Lean.Language.Lean.CommandElaboratingSnapshot",
"Lean.Syntax",
"Lean.Parser.ModuleParserState",
"Lean.Language.SnapshotTask",
"PProd",
"PUnit",
"Lean.Language.SnapshotTask.ReportingRange",
"Lean.Language.Snapshot",
"Lean.Language.Lean.CommandParsedSnapshot",
"IO.CancelToken",
"Lean.La... |
_private.Lean.Meta.Tactic.Grind.Arith.Linear.PropagateEq.0.Lean.Meta.Grind.Arith.Linear.updateDiseqs.match_3 | Lean.Meta.Tactic.Grind.Arith.Linear.PropagateEq | [
"Lean.PArray",
"Prod.mk",
"Int",
"Array",
"Prod",
"Prod.casesOn",
"Lean.Meta.Grind.Arith.Linear.DiseqCnstr"
] |
TensorProduct.finsuppLeft._proof_1 | Mathlib.LinearAlgebra.DirectSum.Finsupp | [
"Finsupp.smulZeroClass",
"Finsupp.smulCommClass",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"AddMonoid.toAddZeroClass",
"Algebra",
"Algebra.toSMul",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"AddCommMonoid",
"CommSemiring",
"AddZero.toZero",... |
_private.Std.Tactic.BVDecide.LRAT.Internal.Formula.RupAddResult.0.Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula.nodup_insertRupUnits._proof_1_3 | Std.Tactic.BVDecide.LRAT.Internal.Formula.RupAddResult | [
"instOfNatNat",
"And",
"And.right",
"Nat",
"LT.lt",
"instLTNat",
"OfNat.ofNat",
"Subtype.val",
"Std.Tactic.BVDecide.LRAT.Internal.PosFin",
"Subtype.property"
] |
_private.Std.Tactic.BVDecide.LRAT.Internal.Formula.Lemmas.0.Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula.deleteOne_preserves_strongAssignmentsInvariant.match_1_3 | Std.Tactic.BVDecide.LRAT.Internal.Formula.Lemmas | [
"Option.casesOn",
"Option.some",
"Option.none",
"Nat",
"Eq.refl",
"Std.Tactic.BVDecide.LRAT.Internal.DefaultClause",
"Eq",
"Option"
] |
rieszContentAux_image_nonempty | Mathlib.MeasureTheory.Integral.RieszMarkovKakutani.Basic | [
"instWeaklyLocallyCompactSpaceOfLocallyCompactSpace",
"NNReal.instTopologicalSpace",
"Iff.mpr",
"Set.image_nonempty",
"Eq.mpr",
"Real.instLE",
"Real",
"IsTopologicalSemiring.toContinuousAdd",
"Semiring.toModule",
"interior_subset",
"Real.instZero",
"Real.instZeroLEOneClass",
"congrArg",
"S... |
Finset.orderIsoOfFin._proof_4 | Mathlib.Data.Finset.Sort | [
"Finset",
"LinearOrder",
"Finset.orderIsoOfFin._proof_2",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"LinearOrder.toDecidableLE",
"DistribLattice.toLattice",
"LE.le",
"instIsTransLe",
"Nat",
"Finset.card",
"Finset.orderIsoOfFin._proof_3",
"Finset.length_so... |
Lean.Meta.AbstractNestedProofs.Context | Lean.Meta.AbstractNestedProofs | [
"Lean.Meta.AbstractNestedProofs.Context.mk"
] |
MeasurableSpace.monotone_map | Mathlib.MeasureTheory.MeasurableSpace.Basic | [
"MeasurableSpace.map_mono",
"MeasurableSpace.instPartialOrder",
"PartialOrder.toPreorder",
"Monotone",
"MeasurableSpace.map",
"MeasurableSpace"
] |
List.pairwise_le_finRange | Batteries.Data.List.Lemmas | [
"List.Pairwise.pmap",
"Eq.mpr",
"List.Pairwise",
"congrArg",
"Membership.mem",
"Fin.mk",
"id",
"List.mem_range._simp_1",
"List.pairwise_le_range",
"List.range",
"LE.le",
"instLENat",
"imp_self._simp_1",
"instLEFin",
"List.pmap",
"List",
"List.instMembership",
"implies_congr",
"Na... |
HahnSeries.cardSuppLTAddSubgroup | Mathlib.RingTheory.HahnSeries.Cardinal | [
"AddGroup.toSubtractionMonoid",
"Cardinal",
"AddMonoid.toAddZeroClass",
"Fact",
"AddZeroClass.toAddZero",
"PartialOrder",
"AddSubmonoid",
"SubtractionMonoid.toSubNegZeroMonoid",
"Cardinal.aleph0",
"LE.le",
"SubNegZeroMonoid.toNegZeroClass",
"Cardinal.instLE",
"AddSubgroup",
"AddZero.toZero... |
CompositionAsSet.length.eq_1 | Mathlib.Combinatorics.Enumerative.Composition | [
"CompositionAsSet",
"HSub.hSub",
"instSubNat",
"instOfNatNat",
"CompositionAsSet.boundaries",
"instHSub",
"Nat",
"Finset.card",
"Eq.refl",
"OfNat.ofNat",
"Fin",
"Nat.succ",
"Eq",
"CompositionAsSet.length"
] |
VAddCon._sizeOf_inst | Mathlib.Algebra.Module.Congruence.Defs | [
"VAddCon._sizeOf_1",
"VAdd",
"VAddCon",
"SizeOf.mk",
"SizeOf"
] |
Filter.Tendsto.units._proof_1 | Mathlib.Topology.Algebra.Monoid | [
"Monoid",
"Units.val",
"MulOne.toOne",
"tendsto_const_nhds_iff._simp_1",
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"Filter.NeBot",
"nhds",
"Units",
"Eq.mp",
"MulOne.toMul",
"Units.mul_inv",
"Filter.Tendsto.mul",
"TopologicalSpace",
"funext",
"MulOneClass.toMulOne",
"Continuo... |
Lean.Meta.Grind.UnitLike.State.ctorIdx | Lean.Meta.Tactic.Grind.Types | [
"Lean.Meta.Grind.UnitLike.State",
"Nat"
] |
CommMonoidWithZero.rec | Mathlib.Algebra.GroupWithZero.Defs | [
"Semigroup.toMul",
"HMul.hMul",
"CommMonoid.toMonoid",
"CommMonoidWithZero.mk",
"CommMonoidWithZero",
"Monoid.toSemigroup",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq",
"CommMonoid",
"instHMul",
"Zero"
] |
GrpCat.ext_iff | Mathlib.Algebra.Category.Grp.Basic | [
"GrpCat.instConcreteCategoryMonoidHomCarrier",
"GrpCat",
"MonoidHom.instFunLike",
"CategoryTheory.CategoryStruct.toQuiver",
"MonoidHom",
"Quiver.Hom",
"GrpCat.str",
"Monoid.toMulOneClass",
"CategoryTheory.ConcreteCategory.hom",
"HEq.refl",
"Eq.casesOn",
"DivInvMonoid.toMonoid",
"Group.toDivI... |
ModN.natCard_eq | Mathlib.LinearAlgebra.FreeModule.ModN | [
"IsNoetherianRing.strongRankCondition",
"Nat.instMulZeroClass",
"ModN._proof_2",
"Semiring.toModule",
"PrincipalIdealRing.isNoetherianRing",
"Finsupp.module",
"ZMod.commRing",
"Submodule.Quotient.addCommGroup",
"congrArg",
"CommSemiring.toSemiring",
"Int.euclideanDomain",
"AddCommGroup.toAddCo... |
CategoryTheory.MonoidalCategory.prodMonoidal._proof_15 | Mathlib.CategoryTheory.Monoidal.Category | [
"CategoryTheory.MonoidalCategory.prodMonoidal.match_1",
"CategoryTheory.Category.assoc",
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.Iso.inv_hom_id",
"CategoryTheory.prod",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory.id_whiskerLeft"... |
Algebra.traceMatrix_reindex | Mathlib.RingTheory.Trace.Basic | [
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"Equiv.instEquivLike",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"congrArg",
"CommSemiring.toSemiring",
"Matrix",
"LinearMap.instFunLike",
"Algebra",
"Function.comp",
"Algebra.toModule",
"Equiv",
"NonUni... |
Algebra.instCompleteLatticeSubalgebra | Mathlib.Algebra.Algebra.Subalgebra.Lattice | [
"Subalgebra.instSetLike",
"Algebra.instCompleteLatticeSubalgebra._proof_3",
"Lattice.toSemilatticeSup",
"CompleteLattice.toLattice",
"CommSemiring.toSemiring",
"Algebra.instCompleteLatticeSubalgebra._proof_2",
"PartialOrder.toPreorder",
"Algebra",
"Preorder.toLE",
"Algebra.adjoin",
"CompleteLatt... |
Matrix.vecMulBilin._proof_6 | Mathlib.LinearAlgebra.Matrix.ToLin | [
"Pi.Function.module",
"instHSMul",
"Matrix.add",
"Pi.addCommMonoid",
"DistribMulAction.toDistribSMul",
"Matrix",
"AddMonoid.toAddZeroClass",
"Matrix.vecMul",
"AddZeroClass.toAddZero",
"Distrib.toAdd",
"DistribSMul.toSMulZeroClass",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"AddZero.toZero... |
_private.Init.Data.String.Lemmas.Pattern.Basic.0.String.Slice.Pattern.Model.matchesAt_iff_exists_isMatch._simp_1_5 | Init.Data.String.Lemmas.Pattern.Basic | [
"String.instLEPos_1",
"String.Slice.sliceFrom",
"String.Slice.Pos.ofSliceFrom_le_ofSliceFrom_iff",
"String.Slice",
"LE.le",
"String.Slice.Pos.ofSliceFrom",
"propext",
"String.Slice.Pos",
"Eq.symm",
"Eq"
] |
truncSigmaOfExists._proof_1 | Mathlib.Data.Fintype.Basic | [
"Exists",
"Nonempty.intro",
"PSigma.mk",
"Nonempty",
"PSigma",
"Exists.elim"
] |
Int.add_neg | Init.Data.Int.Order | [
"Eq.rec",
"Int",
"Int.instLTInt",
"instHAdd",
"instOfNat",
"HAdd.hAdd",
"LT.lt",
"Int.instAdd",
"Int.add_lt_add",
"OfNat.ofNat",
"Int.zero_add",
"Eq"
] |
LieAlgebra.polyCharpoly_coeff_rank_ne_zero | Mathlib.Algebra.Lie.Rank | [
"LieAlgebra.toModule",
"Nontrivial",
"Module.End.instRing",
"CommRing",
"LieAlgebra.rank",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"LieRing.toAddCommGroup",
"LinearMap.polyCharpoly",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"LieAlgebra... |
CategoryTheory.BasedCategory.whiskerLeft_toNatTrans | Mathlib.CategoryTheory.FiberedCategory.BasedCategory | [
"CategoryTheory.Functor",
"CategoryTheory.BasedFunctor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.BasedNatTrans.toNatTrans",
"CategoryTheory.Functor.comp",
"CategoryTheory.BasedCategory.whiskerLeft",
"CategoryTheory.instCategoryObj",
... |
Int.instTransLe | Init.Data.Int.Order | [
"Int",
"LE.le",
"Trans",
"Int.le_trans",
"Trans.mk",
"Int.instLEInt"
] |
List.forIn_map | Init.Data.List.Monadic | [
"Pure.pure",
"congrArg",
"instForInOfForIn'",
"Monad.toApplicative",
"List.map",
"inferInstance",
"LawfulMonad",
"ForIn.forIn",
"List.rec",
"Applicative.toPure",
"Membership",
"ForInStep",
"List.forIn_cons",
"List.cons",
"funext",
"List",
"List.instMembership",
"List.forIn'_cons.ma... |
Left.neg_lt_self | Mathlib.Algebra.Order.Group.Unbundled.Basic | [
"Iff.mpr",
"AddGroup.toSubtractionMonoid",
"NegZeroClass.toNeg",
"Preorder.toLT",
"Left.neg_neg_iff",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"AddGroup",
"AddLeftStrictMono",
"AddGroup.toSubNegMonoid",
"... |
Lean.Elab.Tactic.BVDecide.Frontend.Normalize.ult._regBuiltin.Lean.Elab.Tactic.BVDecide.Frontend.Normalize.ult.declare_1._@.Lean.Elab.Tactic.BVDecide.Frontend.Normalize.Simproc.2445608185._hygCtx._hyg.16 | Lean.Elab.Tactic.BVDecide.Frontend.Normalize.Simproc | [
"Lean.Elab.Tactic.BVDecide.Frontend.Normalize.ult",
"IO",
"Lean.Elab.Tactic.BVDecide.Frontend.addBVNormalizeProcBuiltinAttr",
"Lean.Name.mkStr7",
"Sum.inl",
"Bool.true",
"Unit",
"Lean.Meta.Simp.DSimproc",
"Lean.Meta.Simp.Simproc"
] |
BitVec.equivFin._proof_1 | Mathlib.Data.BitVec | [
"Function.LeftInverse",
"Nat.instMonoid",
"BitVec.ofFin",
"BitVec",
"BitVec.toFin",
"instOfNatNat",
"Monoid.toPow",
"HPow.hPow",
"Nat",
"Eq.refl",
"instHPow",
"OfNat.ofNat",
"Fin"
] |
EReal.neg_mul | Mathlib.Data.EReal.Operations | [
"EReal.bot_mul_coe_of_neg",
"Eq.mpr",
"NegZeroClass.toNeg",
"EReal.bot_mul_coe_of_pos",
"Real.partialOrder",
"Real",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"HMul.hMul",
"EReal.instMulZeroOneClass",
"CommRing.toNonUnitalCommRing",
"Real.instZero",
"EReal.top_mul_coe_of_pos",
"congrA... |
Std.IdempotentOp.idempotent | Init.Core | [
"Eq",
"Std.IdempotentOp"
] |
LinearEquiv.conjAlgEquiv | Mathlib.Algebra.Algebra.Equiv | [
"RingEquiv.toEquiv",
"LinearEquiv.conjAlgEquiv._proof_1",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"SMul",
"AddMonoid.toAddZeroClass",
"Module.End.instSemiring",
"Module.End.instMul",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"LinearMap.instA... |
Lean.Compiler.LCNF.Closure.State.rec | Lean.Compiler.LCNF.Closure | [
"Lean.Compiler.LCNF.Closure.State.mk",
"Lean.Compiler.LCNF.Purity.pure",
"Array",
"Lean.Compiler.LCNF.CodeDecl",
"Lean.Compiler.LCNF.Closure.State",
"Lean.Compiler.LCNF.Param",
"Lean.FVarIdHashSet"
] |
CategoryTheory.Monad.monadToMon._proof_2 | Mathlib.CategoryTheory.Monad.EquivMon | [
"CategoryTheory.Monad",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.NatTrans.ext'",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.id",
"id",
"CategoryTheory.MonadHom.app_η",
"CategoryTheory.MonObj.one",
"funext",
... |
HahnModule.instSMulZeroClass | Mathlib.RingTheory.HahnSeries.Multiplication | [
"HahnModule.instZero",
"SMulZeroClass",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"HahnModule.instSMul",
"Preorder.toLE",
"HahnModule",
"HahnModule.instSMulZeroClass._proof_1",
"AddZeroClass.toAddZero",
"PartialOrder",
"VAdd",
"SMulZeroClass.mk",
"AddCommMonoid",
"AddZero.toZe... |
_private.Init.Data.Range.Polymorphic.Lemmas.0.Std.Rcc.size_eq_if_roc._simp_1_2 | Init.Data.Range.Polymorphic.Lemmas | [
"Std.PRange.UpwardEnumerable",
"Std.Rxc.HasSize",
"Std.Rxc.LawfulHasSize",
"instOfNatNat",
"LE.le",
"LE",
"Nat",
"propext",
"Std.Rxc.size_eq_zero_iff_not_le",
"Std.Rxc.HasSize.size",
"OfNat.ofNat",
"Eq",
"Not"
] |
HasMFDerivAt.mdifferentiableAt | Mathlib.Geometry.Manifold.MFDeriv.Basic | [
"Eq.mpr",
"extChartAt",
"NormedSpace",
"mdifferentiableAt_iff",
"congrArg",
"ContinuousAt",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"MDifferentiableAt",
"HasFDerivWithinAt",
"NormedField.toField",
"HasMFDerivAt",
"id",
"instModuleTangen... |
CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryFst._proof_2 | Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Over",
"CategoryTheory.Comma.right",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Comma.left",
"CategoryTheory.Over.mk",
"CategoryTheory.Functor.id",
"CategoryTheory.SemiCartesianMonoidalCategory.snd",
"Categ... |
AddMonoidAlgebra.ofMagma | Mathlib.Algebra.MonoidAlgebra.Defs | [
"MulHom",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Equiv.instEquivLike",
"Equiv",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"AddMonoidAlgebra.ofMagma._proof_1",
"AddMonoidWithOne.toOne",
"AddMonoidAlgebra.instMul",
"Multiplicative",
"MulHom.mk",
"Semiring",
"One.toOfNat1",
"Multiplicativ... |
CategoryTheory.MorphismProperty.Over.map.congr_simp | Mathlib.CategoryTheory.MorphismProperty.OverAdjunction | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MorphismProperty.instCompleteBooleanAlgebra",
"CategoryTheory.MorphismProperty.Over.map",
"CategoryTheory.MorphismProperty.IsMultiplicative.instTop",
"CategoryTheory.Mor... |
CategoryTheory.Aut.autMulEquivOfIso._proof_13 | Mathlib.CategoryTheory.Endomorphism | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Iso.inv_hom_id",
"HMul.hMul",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Monoid.toMulOneClass",
"congrArg",
"CategoryTheory.CategoryStruct.id",
"MulOne.toMul",
"CategoryTheory.Iso",
"DivInvMonoid.toMonoid",
"CategoryTheory.Iso.mk",... |
MonoidWithZeroHom.funLike._proof_1 | Mathlib.Algebra.GroupWithZero.Hom | [
"MulOne.toOne",
"HMul.hMul",
"ZeroHom.toFun",
"ZeroHom.casesOn",
"MonoidWithZeroHom.toZeroHom",
"Eq.rec",
"MulOne.toMul",
"MulZeroOneClass",
"ZeroHom.mk",
"ZeroHom",
"MulZeroOneClass.toMulOneClass",
"MulOneClass.toMulOne",
"MonoidWithZeroHom",
"MonoidWithZeroHom.casesOn",
"Eq.ndrec",
"... |
Nonneg.one | Mathlib.Algebra.Order.Nonneg.Basic | [
"One",
"One.mk",
"Subtype",
"ZeroLEOneClass",
"LE.le",
"LE",
"zero_le_one",
"Subtype.mk",
"One.toOfNat1",
"Zero.toOfNat0",
"OfNat.ofNat",
"Zero"
] |
Nondet.bind.match_3 | Batteries.Control.Nondet.Basic | [
"Unit.unit",
"Option.casesOn",
"Option.some",
"Prod.mk",
"Option.none",
"Unit",
"Prod",
"Prod.casesOn",
"MLList",
"Option"
] |
_private.Mathlib.MeasureTheory.Function.UnifTight.0.MeasureTheory.unifTight_of_tendsto_Lp | Mathlib.MeasureTheory.Function.UnifTight | [
"MeasureTheory.UnifTight.add",
"Eq.mpr",
"MeasureTheory.Measure",
"Preorder.toLT",
"congrArg",
"MeasureTheory.AEStronglyMeasurable.sub",
"PartialOrder.toPreorder",
"HSub.hSub",
"PseudoMetricSpace.toUniformSpace",
"nhds",
"SeminormedAddGroup.toContinuousENorm",
"id",
"Ne",
"MeasureTheory.Me... |
Lean.Meta.Simp.registerBuiltinSimproc | Lean.Meta.Tactic.Simp.Simproc | [
"Lean.Meta.SimpTheoremKey",
"IO",
"Sum.inl",
"Array",
"Unit",
"Lean.Meta.Simp.registerBuiltinSimprocCore",
"Lean.Meta.Simp.DSimproc",
"Lean.Name",
"Lean.Meta.Simp.Simproc"
] |
_private.Mathlib.GroupTheory.Perm.Cycle.Type.0.Equiv.Perm.IsThreeCycle.nodup_iff_mem_support._proof_1_714 | Mathlib.GroupTheory.Perm.Cycle.Type | [
"List.countP",
"Finset.mem_singleton",
"of_eq_false",
"Lean.Grind.CommRing.le_norm_expr",
"Lean.Grind.instOrderedRingInt",
"Lean.RArray.leaf",
"False",
"_private.Mathlib.GroupTheory.Perm.Cycle.Type.0.Equiv.Perm.IsThreeCycle.nodup_iff_mem_support._proof_1_713",
"Equiv.instEquivLike",
"List.idxOfNth... |
_private.Mathlib.Data.Sign.Basic.0.sign_sum._simp_1_1 | Mathlib.Data.Sign.Basic | [
"LinearOrder",
"PartialOrder.toPreorder",
"SignType.instLinearOrder",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"SignType.instZero",
"OrderHom.instFunLike",
"LinearOrder.toDecidableLT",
"sign_eq_zero_iff",
"propext",
"SignType",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq",
"D... |
TopologicalSpace.CompactOpens.instInf._proof_1 | Mathlib.Topology.Sets.Compacts | [
"TopologicalSpace.CompactOpens.toCompacts",
"TopologicalSpace.Compacts.isCompact'",
"TopologicalSpace.Compacts.carrier",
"Set.instInter",
"TopologicalSpace.CompactOpens",
"Inter.inter",
"TopologicalSpace",
"TopologicalSpace.CompactOpens.isOpen'",
"QuasiSeparatedSpace.inter_isCompact",
"QuasiSepara... |
ZeroAtInftyContinuousMap.instStarModule | Mathlib.Topology.ContinuousMap.ZeroAtInfty | [
"instHSMul",
"ZeroAtInftyContinuousMap.instSMul",
"SMulWithZero.toSMulZeroClass",
"ContinuousStar",
"StarModule.star_smul",
"AddMonoid.toAddZeroClass",
"ZeroAtInftyContinuousMap.ext",
"AddZeroClass.toAddZero",
"ZeroAtInftyContinuousMap.instFunLike",
"ZeroAtInftyContinuousMap.instStar",
"Continuo... |
CategoryTheory.Limits.CategoricalPullback.mkIso._proof_3 | Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Iso.hom_inv_id",
"CategoryTheory.Limits.CategoricalPullback.fst",
"CategoryTheory.Iso",
"CategoryTheory.Limits.CategoricalPullback",
"CategoryTheory.Fun... |
PseudoEpimorphism.comp_apply | Mathlib.Topology.Order.Hom.Esakia | [
"PseudoEpimorphism.comp",
"PseudoEpimorphism.instFunLike",
"Eq",
"DFunLike.coe",
"PseudoEpimorphism",
"rfl",
"Preorder"
] |
AlgebraicGeometry.LocallyRingedSpace.Γevaluation_naturality | Mathlib.Geometry.RingedSpace.LocallyRingedSpace.ResidueField | [
"Lattice.toSemilatticeSup",
"Opposite",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CompleteLattice.toLattice",
"TopologicalSpace.Opens.instCompleteLattice",
"TopologicalSpace.Opens.instPartialOrder",
"CategoryTheory.ConcreteCategory.hom",
... |
CategoryTheory.ShortComplex.toCycles_comp_leftHomologyπ | Mathlib.Algebra.Homology.ShortComplex.LeftHomology | [
"Eq.mpr",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.ShortComplex.leftHomologyπ",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.X₁",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.ShortComplex.lef... |
NFA.Path.supp._sunfold | Mathlib.Computability.NFA | [
"NFA.step",
"Finset.instUnion",
"Finset",
"NFA.Path",
"NFA",
"Membership.mem",
"NFA.Path.supp.match_1",
"List",
"Union.union",
"Finset.instSingleton",
"Singleton.singleton",
"NFA.Path.supp",
"Set.instMembership",
"DecidableEq",
"Set"
] |
IntermediateField.add_mem | Mathlib.FieldTheory.IntermediateField.Basic | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"AddSubmonoidClass.toAddMemClass",
"CommRing.toNonUnitalCommRing",
"Ring.toNonAssocRing",
"IntermediateField",
"SubsemiringClass.toAddSubmonoidClass",
"AddMonoid.toAddZeroClass",
"Algebra",
"Membership.mem"... |
Order.IsPredPrelimit.subtypeVal | Mathlib.Order.SuccPred.Limit | [
"False",
"Preorder.toLT",
"congrArg",
"CovBy",
"IsUpperSet",
"Preorder.toLE",
"CovBy._to_dual_cast_4",
"Membership.mem",
"Exists",
"Eq.mp",
"Set.Elem",
"Subtype.mk",
"And.casesOn",
"And",
"Exists.casesOn",
"And.right",
"LT.lt",
"propext",
"Subtype.instLT",
"CovBy.lt",
"CovBy.... |
unitInterval.instLinearOrderedCommMonoidWithZeroElemReal._proof_1 | Mathlib.Topology.UnitInterval | [
"Real.instIsOrderedRing",
"Real.partialOrder",
"Real",
"HMul.hMul",
"MulZeroClass.toMul",
"MulZeroClass.zero_mul",
"Real.semiring",
"Set.Elem",
"Set.Icc.instMonoidWithZero",
"MonoidWithZero.toMulZeroOneClass",
"Zero.toOfNat0",
"MulZeroOneClass.toMulZeroClass",
"OfNat.ofNat",
"Eq",
"unitI... |
CategoryTheory.Limits.multicospanShapeEnd_fst | Mathlib.CategoryTheory.Limits.Shapes.End | [
"CategoryTheory.Comma.left",
"CategoryTheory.Functor.id",
"CategoryTheory.Limits.multicospanShapeEnd",
"CategoryTheory.Limits.MulticospanShape.fst",
"Eq.refl",
"CategoryTheory.Arrow",
"Eq",
"CategoryTheory.Category"
] |
Con.lift_funext | Mathlib.GroupTheory.Congruence.Hom | [
"Con.hom_ext",
"MonoidHom.instFunLike",
"MonoidHom",
"DFunLike.ext",
"MulOne.toMul",
"MonoidHom.comp",
"Con.mulOneClass",
"Con.Quotient",
"MulOneClass.toMulOne",
"Con.toQuotient",
"Con",
"MulOneClass",
"Eq",
"DFunLike.coe",
"Con.mk'"
] |
StrictConvex.is_linear_preimage | Mathlib.Analysis.Convex.Strict | [
"StrictConvex",
"Continuous",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"PartialOrder",
"DistribSMul.toSMulZeroClass",
"StrictConvex.linear_preimage",
"AddCommMonoid",
"TopologicalSpace",
"AddZero.toZero",
"Set.preimage",
"IsLinearMap",
"Semiri... |
mem_skewAdjointMatricesSubmodule._simp_1 | Mathlib.LinearAlgebra.Matrix.SesquilinearForm | [
"Submodule",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"CommRing.toNonUnitalCommRing",
"Matrix.module",
"CommSemiring.toSemiring",
"Matrix",
"Membership.mem",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"Matrix.addCommMonoid",
"NonUnitalNonAssoc... |
ContinuousMultilinearMap.compContinuousLinearMapL._proof_5 | Mathlib.Topology.Algebra.Module.Multilinear.Topology | [
"AddCommGroup.toAddCommMonoid",
"NormedField.toField",
"AddCommGroup",
"Field.toSemifield",
"Field.toCommRing",
"NormedField",
"smulCommClass_self",
"Semifield.toDivisionSemiring",
"CommMonoid.toMonoid",
"Monoid.toSemigroup",
"DivisionSemiring.toSemiring",
"Module.toDistribMulAction",
"Semig... |
ProofWidgets.RpcEncodablePacket.goals._@.ProofWidgets.Component.Panel.Basic.2840189264._hygCtx._hyg.1 | ProofWidgets.Component.Panel.Basic | [
"Lean.Json",
"ProofWidgets.RpcEncodablePacket._@.ProofWidgets.Component.Panel.Basic.2840189264._hygCtx._hyg.1"
] |
CategoryTheory.LaxMonoidalFunctor.isoOfComponents | Mathlib.CategoryTheory.Monoidal.NaturalTransformation | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.LaxMonoidal.ε",
"CategoryTheory.Iso",
"CategoryTheory.LaxMonoidalFunctor.isoOfComponents._proof_1",
"autoParam",
"CategoryTheory.Functor.map",
"CategoryTheory.LaxMonoidalFunctor.isoOfCo... |
UInt8.ofFin | Init.Data.UInt.Basic | [
"UInt8.size",
"BitVec.ofFin",
"instOfNatNat",
"Nat",
"OfNat.ofNat",
"UInt8.ofBitVec",
"UInt8",
"Fin"
] |
Affine.Simplex.points_mem_affineSpan_faceOpposite | Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic | [
"Nontrivial",
"Eq.mpr",
"Affine.Simplex.points",
"Nat.instMulZeroClass",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"Compl.compl",
"Finset",
"instDecidableEqFin",
"Finset.mem_compl._simp_1",
"HSub.hSub",
"AddCommGroup.toAddGroup",
"Membership.mem",
"BooleanAlgebra.toCompl",
"AddCommGrou... |
cfc_add_const._auto_1 | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] |
CategoryTheory.StrongEpi.of_arrow_iso | Mathlib.CategoryTheory.Limits.Shapes.StrongEpi | [
"Eq.mpr",
"CategoryTheory.Comma.right",
"CategoryTheory.Epi",
"CategoryTheory.Mono",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.epi_comp",
"CategoryTheory.StrongEpi.mk",
"CategoryTheory.Comma.left",
"CategoryTheory.Functor.id",
"inferInstance",
"id",
... |
ContinuousAffineMap.vadd_toAffineMap | Mathlib.Topology.Algebra.ContinuousAffineMap | [
"AffineMap.instAddCommGroup",
"AddMonoid.toAddSemigroup",
"AddCommGroup.toAddCommMonoid",
"IsTopologicalAddTorsor",
"AddCommGroup.toAddGroup",
"AddCommGroup",
"ContinuousAffineMap",
"addGroupIsAddTorsor",
"AffineMap",
"HVAdd.hVAdd",
"TopologicalSpace",
"AddAction.toAddSemigroupAction",
"Affi... |
_private.Lean.Elab.BuiltinNotation.0.Lean.Elab.Term.mkPairs.loop | Lean.Elab.BuiltinNotation | [
"Inhabited.default",
"instInhabitedOfMonad",
"EStateM.instMonad",
"Lean.Macro.Exception",
"Lean.Syntax.Term",
"Lean.MacroM",
"Lean.Macro.Context",
"Array",
"Lean.Macro.State",
"Nat",
"Inhabited",
"EStateM",
"instInhabitedReaderT",
"Inhabited.mk"
] |
CategoryTheory.IsHomLift.id_comp_lift | Mathlib.CategoryTheory.FiberedCategory.HomLift | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.IsHomLift",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Category.comp_id",
"True",
"CategoryTheory.CategoryStruct.comp",
"eq_true",
"of_eq_true",
"CategoryTheory.Catego... |
Std.DTreeMap.Internal.Impl.getEntryLE!_eq_get!_getEntryLE? | Std.Data.DTreeMap.Internal.Model | [
"Ord",
"Option.get!",
"Std.DTreeMap.Internal.Impl.getEntryLE!",
"Inhabited",
"Eq",
"Std.DTreeMap.Internal.Impl.getEntryLE?",
"Std.DTreeMap.Internal.Impl",
"Sigma",
"rfl"
] |
_private.Lean.ReservedNameAction.0.Lean.initFn._@.Lean.ReservedNameAction.2721971034._hygCtx._hyg.2 | Lean.ReservedNameAction | [
"IO.mkRef",
"instMonadLiftT",
"Lean.ReservedNameAction",
"IO",
"EIO",
"liftM",
"List.toArray",
"Array",
"IO.Error",
"IO.Ref",
"instMonadLiftTOfMonadLift",
"BaseIO",
"instMonadLiftBaseIOEIO",
"List.nil"
] |
DomMulAct.isInducing_mk_symm | Mathlib.Topology.Algebra.Constructions.DomMulAct | [
"Homeomorph.isInducing",
"DomMulAct",
"Equiv.instEquivLike",
"DomMulAct.mkHomeomorph",
"Equiv",
"DomMulAct.instTopologicalSpace",
"DomMulAct.mk",
"Topology.IsInducing",
"TopologicalSpace",
"Homeomorph.symm",
"Equiv.symm",
"DFunLike.coe",
"EquivLike.toFunLike"
] |
InnerProductSpace.Core.inner_add_left | Mathlib.Analysis.InnerProductSpace.Defs | [
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Inner.inner",
"AddCommGroup.toAddCommMonoid",
"NormedField.toField",
"AddCommGroup",
"Distrib.toAdd",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"PreInnerProductSpace.Core",
"NormedCommRing.toNonUnitalNormedCommRing",
"Field.toSemifield",... |
CategoryTheory.Abelian.SpectralObject.sc₃._auto_1 | Mathlib.Algebra.Homology.SpectralObject.Basic | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] |
Homeomorph.mulLeft | Mathlib.Topology.Algebra.Group.Basic | [
"Homeomorph.mk",
"Monoid.toMulOneClass",
"Group",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"Equiv.mulLeft",
"Group.toDivInvMonoid",
"Homeomorph.mulLeft._proof_1",
"TopologicalSpace",
"MulOneClass.toMulOne",
"Equiv.Perm",
"Homeomorph.mulLeft._proof_2",
"Homeomorph",
"SeparatelyContinuousMul... |
_private.Lean.Compiler.LCNF.Specialize.0.Lean.Compiler.LCNF.Specialize.loop._unsafe_rec | Lean.Compiler.LCNF.Specialize | [
"Pure.pure",
"Lean.Core.instMonadTraceCoreM",
"Lean.instMonadEnvOfMonadLift",
"Lean.MessageData",
"Lean.MonadError.mk",
"Unit.unit",
"Lean.instMonadExceptOfExceptionCoreM",
"_private.Lean.Compiler.LCNF.Specialize.0.Lean.Compiler.LCNF.Specialize.State.localSpecParamInfo",
"Lean.PersistentEnvExtension... |
AlgebraicGeometry.StructureSheaf.Localizations.comapFun._proof_9 | Mathlib.AlgebraicGeometry.StructureSheaf | [
"CommRing",
"instHSMul",
"Semiring.toModule",
"IsScalarTower.right",
"LocalizedModule",
"PrimeSpectrum.isPrime",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"AddCommGroup.toAddGroup",
"RingHom",
"Algebra.toSMul",
... |
BitVec.sshiftRight_xor_distrib | Init.Data.BitVec.Lemmas | [
"Eq.mpr",
"Decidable.casesOn",
"dite_congr",
"BitVec.instXorOp",
"BitVec.getElem_xor",
"BitVec.msb_xor",
"congrArg",
"Decidable",
"BitVec",
"dif_pos",
"id",
"LE.le",
"instLENat",
"dif_neg",
"dite",
"GetElem.getElem",
"instHAdd",
"Bool.xor",
"HAdd.hAdd",
"BitVec.sshiftRight",
... |
AddOreLocalization.zero_add | Mathlib.GroupTheory.OreLocalization.Basic | [
"AddOreLocalization.instZero",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"AddSubmonoid",
"AddOreLocalization",
"AddZero.toZero",
"instHAdd",
"AddOreLocalization.zero_vadd",
"HAdd.hAdd",
"AddOreLocalization.AddOreSet",
"AddMonoid.toAddAction",
"AddMonoid",
"AddOreLocalization.inst... |
AlgebraicTopology.DoldKan.N₁_obj_p | Mathlib.AlgebraicTopology.DoldKan.FunctorN | [
"ChainComplex",
"HomologicalComplex.instCategory",
"Opposite",
"CategoryTheory.Idempotents.Karoubi",
"Nat.instOne",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"AddRightCancelSemigroup.toAddSemigroup",
"AddCancelMonoid.toAddRightCancelMonoid",
"Nat.... |
GenContFract.convs'_succ | Mathlib.Algebra.ContinuedFractions.Computation.Translations | [
"GenContFract.s",
"AddGroup.toSubtractionMonoid",
"Int.cast",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"Stream'.Seq",
"GenContFract.Pair.b",
"DivInvMonoid.toInv",
"instHDiv",
"GroupWithZero.toDivisionMonoid",
"AddLeftCancelSemigroup.toIsLeftCancelAdd",
"GroupWithZero.toDivInvMonoid",
"Gen... |
_private.Std.Data.ExtDTreeMap.Lemmas.0.Std.ExtDTreeMap.Const.ofList_eq_empty_iff._simp_1_2 | Std.Data.ExtDTreeMap.Lemmas | [
"Bool.true",
"List",
"List.isEmpty",
"List.isEmpty_iff",
"propext",
"Bool",
"Eq.symm",
"Eq",
"List.nil"
] |
Aesop.FVarIdSubst.casesOn | Aesop.RuleTac.FVarIdSubst | [
"Lean.instBEqFVarId",
"Aesop.FVarIdSubst",
"Aesop.FVarIdSubst.rec",
"Lean.FVarId",
"Std.HashMap",
"Lean.instHashableFVarId",
"Aesop.FVarIdSubst.mk"
] |
Int.Linear.eq_def'_cert | Init.Data.Int.Linear | [
"Int.Linear.Poly.beq'",
"Int.instNegInt",
"Int",
"Int.Linear.Var",
"Int.Linear.Poly.add",
"Int.Linear.Expr",
"instOfNat",
"Int.Linear.Expr.norm",
"Bool",
"OfNat.ofNat",
"Neg.neg",
"Int.Linear.Poly"
] |
Set.powersetCard.mulActionHom_of_embedding.eq_1 | Mathlib.GroupTheory.GroupAction.SubMulAction.Combination | [
"Set.powersetCard.ofFinEmb",
"Finset",
"Group",
"Set.powersetCard.instMulActionElemFinset",
"Set.Elem",
"Set.powersetCard.mulActionHom_of_embedding",
"id",
"Function.Embedding.smul",
"Set.powersetCard.mulActionHom_of_embedding._proof_1",
"DivInvMonoid.toMonoid",
"MulActionHom.mk",
"Function.Em... |
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