name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
CategoryTheory.ObjectProperty.preservesLimit_iff | Mathlib.CategoryTheory.ObjectProperty.FunctorCategory.PreservesLimits | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.PreservesLimit",
"Iff.rfl",
"Iff",
"CategoryTheory.Category",
"CategoryTheory.ObjectProperty.preservesLimit"
] | true |
CategoryTheory.Limits.IsLimit.ofIsZero | Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Limits.IsLimit.ofIsZero._proof_1",
"CategoryTheory.Functor",
"CategoryTheory.Limits.IsLimit.mk",
"CategoryTheory.Limits.Cone",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Limits.I... | true |
_private.Mathlib.Data.Nat.Totient.0.Mathlib.Meta.Positivity.evalNatTotient.match_4 | Mathlib.Data.Nat.Totient | [
"Lean.Level.ctorIdx",
"Mathlib.Meta.Positivity.Strictness",
"Lean.Expr.const",
"Lean.Meta.MetaM",
"Nat.hasNotBit",
"Lean.Expr.sort",
"Lean.Level",
"List.cons",
"Qq.Quoted",
"Lean.Level.zero",
"Lean.Expr.app",
"Lean.Level.succ",
"Lean.Level.instOfNat",
"_private.Mathlib.Data.Nat.Totient.0.M... | false |
String.Slice.Pos.prevAux._proof_6 | Init.Data.String.Basic | [
"_private.Init.Data.String.Basic.0.String.Slice.Pos.prevAux._proof_5",
"String.Slice",
"instOfNatNat",
"String.Slice.utf8ByteSize",
"instHAdd",
"HAdd.hAdd",
"Nat",
"LT.lt",
"Decidable.byContradiction",
"Nat.decLt",
"instAddNat",
"instLTNat",
"OfNat.ofNat",
"Not"
] | false |
_private.Mathlib.NumberTheory.Dioph.0.Dioph.diophFn_compn.match_1_1 | Mathlib.NumberTheory.Dioph | [
"Dioph",
"Sum",
"instOfNatNat",
"Vector3",
"Nat",
"Nat.zero",
"OfNat.ofNat",
"Nat.succ",
"Nat.casesOn",
"Fin2",
"Set"
] | false |
Std.DTreeMap.Internal.Impl.toListModel_interSmallerFn | Std.Data.DTreeMap.Internal.WF.Lemmas | [
"Std.DTreeMap.Internal.Impl.interSmallerFn",
"Eq.mpr",
"Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl",
"Ord",
"congrArg",
"Std.DTreeMap.Internal.Impl.interSmallerFn.match_3",
"Std.DTreeMap.Internal.Impl.getEntry?",
"Std.DTreeMap.Internal.Impl.Ordered.distinctKeys",
"Std.TransOrd",
"Std.DTreeM... | true |
_private.Mathlib.Algebra.Homology.HomotopyCategory.ShiftSequence.0.CochainComplex.instShiftSequenceHomologicalComplexIntUpHomologyFunctorOfNat._simp_4 | Mathlib.Algebra.Homology.HomotopyCategory.ShiftSequence | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.HasHomology",
"CategoryTheory.ShortComplex.instCategory",
"CategoryTheory.ShortComplex.homology",
"CategoryTheory.ShortComplex.homologyMap_comp"... | false |
MonoidHom.op._proof_5 | Mathlib.Algebra.Group.Equiv.Opposite | [
"MulOne.toOne",
"MonoidHom.instFunLike",
"MonoidHom",
"congrArg",
"MulOpposite",
"Function.comp",
"MulOneClass.toMulOne",
"MonoidHom.map_one",
"One.toOfNat1",
"MulOpposite.unop",
"PreOpposite.op'",
"MulOneClass",
"OfNat.ofNat",
"Eq",
"DFunLike.coe",
"MulOpposite.op",
"MulOpposite.ins... | false |
Std.DHashMap.Internal.Raw.Const.ofList_eq | Std.Data.DHashMap.Internal.Raw | [
"dite_cond_eq_true",
"Std.DHashMap.Raw.Const.ofList",
"Eq.mpr",
"Std.DHashMap.Raw.instEmptyCollection",
"Std.DHashMap.Raw.WF.empty",
"congrArg",
"instForInOfForIn'",
"Std.DHashMap.Raw",
"Eq.rec",
"inferInstance",
"id",
"Subtype",
"instOfNatNat",
"Std.DHashMap.Raw.WF.size_buckets_pos",
"I... | true |
definition._@.Mathlib.MeasureTheory.Measure.Typeclasses.Finite.588747923._hygCtx._hyg.2 | Mathlib.MeasureTheory.Measure.Typeclasses.Finite | [
"MeasureTheory.Measure",
"SecondCountableTopology",
"setOf",
"definition._proof_3._@.Mathlib.MeasureTheory.Measure.Typeclasses.Finite.588747923._hygCtx._hyg.2",
"Nonempty.some",
"MeasurableSpace",
"TopologicalSpace",
"MeasureTheory.IsLocallyFiniteMeasure",
"Nonempty",
"IsOpen",
"MeasureTheory.Me... | false |
IsBaseChange.endHom._proof_2 | Mathlib.RingTheory.TensorProduct.IsBaseChangeHom | [
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"LinearMap.instSMulCommClass",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"SMulCommClass.symm",
"IsBaseChange.linearMapRightBaseChangeHom._proof_1",
"LinearMap.module",
"LinearMap",
"smulCommCl... | false |
CategoryTheory.Limits.Fan.combPairHoms | Mathlib.CategoryTheory.Limits.Shapes.CombinedProducts | [
"CategoryTheory.Limits.Fan.proj",
"CategoryTheory.Limits.BinaryFan.fst",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.BinaryFan",
"CategoryTheory.Limits.Fan",
"CategoryTheory.Discrete.functor",
"CategoryTheory.Limits.WalkingPair.right",
"Sum",
"CategoryTheory.Limi... | true |
Lean.Elab.Term.Quotation.elabMatchSyntax._regBuiltin.Lean.Elab.Term.Quotation.elabMatchSyntax.declRange_3 | Lean.Elab.Quotation | [
"Lean.addBuiltinDeclarationRanges",
"Lean.DeclarationRange.mk",
"Lean.Name.mkStr5",
"IO",
"instOfNatNat",
"Unit",
"Lean.Position.mk",
"Nat",
"OfNat.ofNat",
"Lean.DeclarationRanges.mk"
] | false |
Submodule.isTopCompl_bot_top | Mathlib.Topology.Algebra.Module.Complement | [
"Submodule",
"RingHomSurjective.ids",
"IsIdempotentElem.zero",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"LinearMap.range_zero",
"LinearMap.ker",
"LinearMap.range",
"AddCommGroup",
"Eq.mp",
"ContinuousLinearMap.toLinearMap",
"ContinuousLinearMap.IsIdempotentElem.isTopCompl",
"ContinuousLin... | true |
IncidenceAlgebra.instNonAssocSemiring | Mathlib.Combinatorics.Enumerative.IncidenceAlgebra | [
"IncidenceAlgebra.instNonAssocSemiring._proof_4",
"NonAssocSemiring.mk",
"NonAssocSemiring.toAddCommMonoidWithOne",
"AddMonoid.toAddSemigroup",
"AddMonoid.toZero",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"Preorder.toLE",
"IncidenceAlgebra.instNonAssocSemiring._proof_3",
"AddCommMonoidWithOne.toA... | true |
Matrix.of_symm_apply | Mathlib.LinearAlgebra.Matrix.Defs | [
"Equiv.instEquivLike",
"Matrix",
"Matrix.of",
"Equiv",
"Equiv.symm",
"Eq",
"DFunLike.coe",
"rfl",
"EquivLike.toFunLike"
] | true |
Mathlib.Meta.Positivity.prod_ne_zero | Mathlib.Algebra.Order.BigOperators.Ring.Finset | [
"Nontrivial",
"CommMonoidWithZero.toCommMonoid",
"Iff.mpr",
"MulZeroClass.toMul",
"Finset",
"Membership.mem",
"Ne",
"Finset.prod_ne_zero_iff",
"CommMonoidWithZero.toMonoidWithZero",
"Finset.prod",
"NoZeroDivisors",
"MonoidWithZero.toMulZeroOneClass",
"Finset.instSetLike",
"CommMonoidWithZe... | true |
instAddCancelMonoidLex | Mathlib.Algebra.Order.Group.Synonym | [
"Lex",
"AddCancelMonoid"
] | true |
_private.Mathlib.Combinatorics.Graph.Delete.0.Graph.deleteEdges_isLoopAt._simp_1_1 | Mathlib.Combinatorics.Graph.Delete | [
"Graph",
"Graph.deleteEdges",
"Graph.restrict_edgeSet_diff_eq_deleteEdges",
"SDiff.sdiff",
"Graph.edgeSet",
"Eq.symm",
"Eq",
"Set.instSDiff",
"Graph.restrict",
"Set"
] | false |
Aesop.Iteration | Aesop.Tree.Data | [
"Nat"
] | true |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.Const.equiv_iff_toList_perm._simp_1_3 | Std.Data.DTreeMap.Internal.Lemmas | [
"Ord",
"Membership.mem",
"Bool.true",
"Std.DTreeMap.Internal.Impl.contains",
"propext",
"Bool",
"Std.DTreeMap.Internal.Impl.mem_iff_contains",
"Eq",
"Std.DTreeMap.Internal.Impl",
"Std.DTreeMap.Internal.Impl.instMembershipOfOrd"
] | false |
NFA.eval | Mathlib.Computability.NFA | [
"NFA.evalFrom",
"NFA",
"NFA.start",
"List",
"Set"
] | true |
Units.oneSub.eq_1 | Mathlib.Analysis.Analytic.Constructions | [
"Norm.norm",
"Real",
"NormedRing.toRing",
"Ring.toNonAssocRing",
"AddGroupWithOne.toAddGroup",
"HasSummableGeomSeries",
"AddGroupWithOne.toAddMonoidWithOne",
"HSub.hSub",
"PseudoMetricSpace.toUniformSpace",
"mul_neg_geom_series",
"Real.instLT",
"Units",
"NonUnitalNonAssocRing.toNonUnitalNonA... | true |
_private.Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics.0.tendsto_rpow_div_mul_add._simp_1_1 | Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics | [
"Set.Ioi",
"Preorder.toLT",
"Membership.mem",
"Set.mem_Ioi",
"LT.lt",
"propext",
"Eq",
"Set.instMembership",
"Preorder",
"Set"
] | false |
instOneMulHom._proof_1 | Mathlib.Algebra.Group.Hom.Defs | [
"MulOne.toOne",
"HMul.hMul",
"MulOne.toMul",
"MulOneClass.toMulOne",
"One.toOfNat1",
"MulOneClass",
"OfNat.ofNat",
"Eq.symm",
"Eq",
"one_mul",
"instHMul"
] | false |
AddGroupExtension.quotientKerRightHomEquivRight.eq_1 | Mathlib.GroupTheory.GroupExtension.Basic | [
"AddMonoidHom.normal_ker",
"AddGroupExtension",
"AddMonoid.toAddZeroClass",
"AddGroupExtension.rightHom",
"QuotientAddGroup.Quotient.addGroup",
"AddZeroClass.toAddZero",
"AddSubgroup",
"AddGroupExtension.quotientKerRightHomEquivRight",
"HasQuotient.Quotient",
"AddGroup",
"AddGroup.toSubNegMonoid... | true |
_private.Mathlib.Algebra.Homology.ExactSequence.0.CategoryTheory.ComposableArrows.isComplex₂_iff._proof_3 | Mathlib.Algebra.Homology.ExactSequence | [
"Nat.lt_of_not_le",
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.LinearCombo.eval",
"Option.some",
"id",
"instDecidableEqBool",
"Int.instNegInt",
"Int.sub_nonne... | false |
Lean.Elab.Term.Do.ToCodeBlock.doReassignArrowToCode | Lean.Elab.Do.Legacy | [
"Inhabited.default",
"Lean.Elab.Term.instInhabitedTermElabM",
"Lean.Syntax",
"Lean.Elab.Term.Do.CodeBlock",
"List",
"Lean.Elab.Term.TermElabM",
"Lean.Elab.Term.Do.ToCodeBlock.M",
"instInhabitedReaderT",
"Lean.Elab.Term.Do.ToCodeBlock.Context"
] | true |
SSet.RelativeMorphism.Homotopy.mk | Mathlib.AlgebraicTopology.SimplicialSet.RelativeMorphism | [
"SSet.Subcomplex.toSSet",
"SSet.RelativeMorphism.Homotopy.h₀._autoParam",
"SSet.RelativeMorphism",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.typesCartesianMonoidalCategory",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"SSet.RelativeMorphism.Homotopy",
"SSet.Relativ... | true |
MeasureTheory.Measure.MutuallySingular.compProd_of_left | Mathlib.Probability.Kernel.Composition.MeasureCompProd | [
"Set.instSProd",
"Eq.mpr",
"MeasureTheory.Measure.MutuallySingular.zero_left._simp_1",
"MeasureTheory.Measure",
"MeasurableSet",
"Set.union_empty",
"SProd.sprod",
"congrArg",
"Compl.compl",
"Set.univ",
"MeasureTheory.Measure.MutuallySingular.zero_right._simp_1",
"ProbabilityTheory.IsSFiniteKer... | true |
_private.Mathlib.AlgebraicTopology.SimplicialSet.Horn.0.SSet.horn.primitiveTriangle._proof_27 | Mathlib.AlgebraicTopology.SimplicialSet.Horn | [
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"LT.lt",
"instAddNat",
"SSet.horn.primitiveTriangle._proof_19",
"instLTNat",
"OfNat.ofNat"
] | false |
_private.Mathlib.Combinatorics.SimpleGraph.Trails.0.SimpleGraph.Walk.IsTrail.even_countP_edges_iff._simp_1_4 | Mathlib.Combinatorics.SimpleGraph.Trails | [
"Exists",
"propext",
"Classical.not_forall",
"Eq",
"Not"
] | false |
WittVector.one_coeff_zero | Mathlib.RingTheory.WittVector.Defs | [
"Finsupp.instAddZeroClass",
"WittVector.instOne",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"CommRing",
"Nat.Prime",
"AlgHom.algHomClass",
"MvPolynomial.aeval",
"congrArg",
"CommSemiring.toSemiring",
"AlgHom",
"AlgHom.funLike",
"AddMonoid.toAddZeroClass",
"AddMonoidAlgebra.algeb... | true |
CategoryTheory.ShortComplex.epi_homologyMap_of_epi_cyclesMap' | Mathlib.Algebra.Homology.ShortComplex.Homology | [
"Eq.mpr",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.ShortComplex.homologyπ",
"CategoryTheory.Epi",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.epi_of_epi",
"CategoryTheory.epi_comp",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortCompl... | true |
_private.Mathlib.Analysis.CStarAlgebra.ApproximateUnit.0.Set.InvOn.one_sub_one_add_inv._simp_1_6 | Mathlib.Analysis.CStarAlgebra.ApproximateUnit | [
"GroupWithZero.toMonoidWithZero",
"False",
"GroupWithZero.toDivInvMonoid",
"eq_false",
"GroupWithZero",
"DivInvMonoid.toZPow",
"Ne",
"Int",
"MonoidWithZero.toMulZeroOneClass",
"HPow.hPow",
"Zero.toOfNat0",
"zpow_ne_zero",
"instHPow",
"MulZeroOneClass.toMulZeroClass",
"OfNat.ofNat",
"Eq... | false |
dense_of_nonempty_smul_invariant | Mathlib.Dynamics.Minimal | [
"Iff.mpr",
"Monoid",
"instHSMul",
"Membership.mem",
"Dense",
"Dense.mono",
"HasSubset.Subset",
"MulAction.dense_orbit",
"_private.Mathlib.Dynamics.Minimal.0.dense_of_nonempty_smul_invariant.match_1_1",
"MulAction.IsMinimal",
"TopologicalSpace",
"And",
"Set.Nonempty",
"MulAction",
"And.in... | true |
List.drop_modifyHead_of_pos | Init.Data.List.Nat.Modify | [
"List.modifyHead_nil",
"False",
"congrArg",
"False.elim",
"Eq.mp",
"instOfNatNat",
"List.cons",
"Nat.casesAuxOn",
"List",
"instHAdd",
"List.drop",
"HAdd.hAdd",
"List.drop_nil",
"Nat",
"congr",
"LT.lt",
"True",
"List.casesOn",
"eq_self",
"List.modifyHead_cons",
"of_eq_true",
... | true |
div_eq_inv_self | Mathlib.Algebra.Group.Basic | [
"Eq.mpr",
"MulOne.toOne",
"CancelMonoid.toRightCancelMonoid",
"DivInvMonoid.toInv",
"instHDiv",
"InvOneClass.toOne",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"mul_eq_right",
"Monoid.toMulOneClass",
"congrArg",
"Iff.rfl",
"Group",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOne... | true |
Finset.min_mem_image_coe | Mathlib.Data.Finset.Max | [
"Finset.min'",
"Iff.mpr",
"LinearOrder.toDecidableEq",
"Finset.mem_image",
"Finset",
"LinearOrder",
"Finset.min'_mem",
"WithTop.decidableEq",
"Membership.mem",
"Exists",
"Finset.min",
"Finset.coe_min'",
"WithTop.some",
"And",
"Finset.instSetLike",
"And.intro",
"Exists.intro",
"Fins... | true |
_private.Init.Data.Rat.Lemmas.0.Rat.divInt.match_3.eq_1 | Init.Data.Rat.Lemmas | [
"Int.ofNat",
"Int",
"Nat",
"Rat.divInt.match_3",
"Eq.refl",
"Int.negSucc",
"Eq"
] | true |
Rep.coindFunctor_map | Mathlib.RepresentationTheory.Coinduced | [
"Monoid",
"CommRing",
"CategoryTheory.CategoryStruct.toQuiver",
"MonoidHom",
"Quiver.Hom",
"Monoid.toMulOneClass",
"CommSemiring.toSemiring",
"Rep.instCategory",
"CategoryTheory.Functor.map",
"Rep.coind",
"MulOneClass.toMulOne",
"CommRing.toCommSemiring",
"Rep",
"Rep.coindMap",
"Eq.refl"... | true |
_private.Mathlib.Algebra.Ring.Subring.Defs.0.intCast_mem._simp_1_1 | Mathlib.Algebra.Ring.Subring.Defs | [
"Int.cast",
"instHSMul",
"AddGroupWithOne.toAddGroup",
"AddGroupWithOne.toAddMonoidWithOne",
"Int",
"AddGroupWithOne.toIntCast",
"AddMonoidWithOne.toOne",
"AddGroup.toSubNegMonoid",
"One.toOfNat1",
"AddGroupWithOne",
"HSMul.hSMul",
"zsmul_one",
"OfNat.ofNat",
"Eq.symm",
"Eq",
"SubNegMo... | false |
Algebra.Extension | Mathlib.RingTheory.Extension.Basic | [
"CommRing",
"CommSemiring.toSemiring",
"Algebra",
"CommRing.toCommSemiring",
"Algebra.Extension.mk"
] | true |
isOfFinAddOrder_ofMul_iff | Mathlib.GroupTheory.OrderOfElement | [
"Monoid",
"Equiv.instEquivLike",
"Additive",
"Iff.rfl",
"Equiv",
"Additive.ofMul",
"IsOfFinAddOrder",
"Iff",
"Additive.addMonoid",
"DFunLike.coe",
"IsOfFinOrder",
"EquivLike.toFunLike"
] | true |
SeparationQuotient.preimage_image_mk_closed | Mathlib.Topology.Inseparable | [
"Set.Subset.antisymm",
"SeparationQuotient.mk_eq_mk",
"Membership.mem",
"Inseparable.mem_closed_iff",
"And.casesOn",
"IsClosed",
"TopologicalSpace",
"And",
"Exists.casesOn",
"Set.preimage",
"SeparationQuotient",
"SeparationQuotient.mk",
"Iff.mp",
"Set.image",
"Eq",
"Set.instMembership"... | true |
IsCompact.compl_mem_coclosedCompact_of_isClosed | Mathlib.Topology.Compactness.Compact | [
"Filter.instMembership",
"Compl.compl",
"Membership.mem",
"Filter.hasBasis_coclosedCompact",
"Filter.coclosedCompact",
"Set.instCompl",
"IsClosed",
"TopologicalSpace",
"And",
"And.intro",
"Filter.HasBasis.mem_of_mem",
"Filter",
"IsCompact",
"Set"
] | true |
Lean.Elab.Tactic.BVDecide.Frontend.BVDecideConfig.maxSteps._default | Std.Tactic.BVDecide.Syntax | [
"id",
"Nat",
"Lean.Meta.Simp.defaultMaxSteps"
] | false |
ContinuousLinearEquiv.continuousAlternatingMapCongrLeft._proof_1 | Mathlib.Topology.Algebra.Module.Alternating.Topology | [
"ContinuousLinearEquiv.symm",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"ContinuousAlternatingMap.compContinuousLinearMapCLM",
"AddCommGroup.toAddGroup",
"NormedField.toField",
"AddZeroClass.toAddZero",
"AddCommGroup",
"ContinuousLinearMap.toLine... | false |
Sigma.curry_update | Mathlib.Data.Sigma.Basic | [
"Eq.mpr",
"Function.update",
"congrArg",
"mt",
"Sigma.mk.noConfusion",
"id",
"Ne",
"Sigma.fst",
"Ne.symm",
"Sigma.instDecidableEqSigma",
"ne_of_apply_ne",
"Or.casesOn",
"funext",
"Sigma.curry",
"congrFun",
"congr",
"True",
"eq_self",
"of_eq_true",
"eq_of_heq",
"Eq.ndrec",
"... | true |
_private.Lean.Meta.Tactic.Cbv.BuiltinCbvSimprocs.Array.0.Lean.Meta.Tactic.Cbv.simpArrayGetElem.match_1 | Lean.Meta.Tactic.Cbv.BuiltinCbvSimprocs.Array | [
"OptionT",
"Option.ctorIdx",
"Option.some",
"Nat.hasNotBit",
"Id",
"Nat",
"_private.Lean.Meta.Tactic.Cbv.BuiltinCbvSimprocs.Array.0.Lean.Meta.Tactic.Cbv.simpArrayGetElem._sparseCasesOn_1"
] | false |
Matrix.cRank_one | Mathlib.LinearAlgebra.Matrix.Rank | [
"Nontrivial",
"Eq.mpr",
"Pi.Function.module",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Submodule",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"Pi.addCommMonoid",
"CommRing.toNonUnitalCommRing",
"Cardinal",
"congrArg",
"CommSemiring.toSemiring",
"Ma... | true |
NonUnitalRing.sub._inherited_default | Mathlib.Algebra.Ring.Defs | [
"Add.mk",
"Neg.mk",
"AddMonoid.mk",
"SubNegMonoid.sub'",
"id",
"instOfNatNat",
"AddSemigroup.mk",
"instHAdd",
"HAdd.hAdd",
"Nat",
"Zero.mk",
"instAddNat",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq"
] | false |
ContDiff.fun_comp_contDiffOn | Mathlib.Analysis.Calculus.ContDiff.Comp | [
"Iff.mpr",
"Set.mapsTo_univ",
"NormedSpace",
"ContDiffOn.comp",
"Set.univ",
"ContDiffOn",
"ContDiff",
"ENat",
"NontriviallyNormedField",
"NontriviallyNormedField.toNormedField",
"NormedAddCommGroup.toSeminormedAddCommGroup",
"contDiffOn_univ",
"NormedAddCommGroup",
"WithTop",
"Set"
] | true |
IsLowerSet.isOpen | Mathlib.Topology.Order.Basic | [
"OrderTopology",
"Preorder.toLT",
"Compl.compl",
"LinearOrder",
"WellFoundedLT",
"PartialOrder.toPreorder",
"isClosed_compl_iff._simp_1",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"Eq.mp",
"DistribLattice.toLattice",
"IsLowerSet.compl",
"Set.instCompl",
"IsClosed",
"TopologicalSp... | true |
_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.subgraphOfAdj_eq_induce._simp_1_4 | Mathlib.Combinatorics.SimpleGraph.Subgraph | [
"Membership.mem",
"Set.instSingletonSet",
"Set.mem_singleton_iff",
"propext",
"Singleton.singleton",
"Eq",
"Set.instMembership",
"Set"
] | false |
ProbabilityTheory.Kernel.ae_comp_of_ae_ae | Mathlib.Probability.Kernel.Composition.Comp | [
"MeasureTheory.ae",
"Eq.mpr",
"MeasureTheory.Measure",
"MeasurableSet",
"congrArg",
"ProbabilityTheory.Kernel.comp",
"Filter.Eventually",
"setOf",
"Eq.mp",
"ProbabilityTheory.Kernel.instFunLike",
"Filter.EventuallyEq",
"id",
"Pi.instZero",
"MeasurableSet.compl",
"MeasurableSpace",
"Mea... | true |
_private.Mathlib.MeasureTheory.Integral.Bochner.Basic.0.Mathlib.Meta.Positivity.evalIntegral.match_1 | Mathlib.MeasureTheory.Integral.Bochner.Basic | [
"Lean.Level.ctorIdx",
"Mathlib.Meta.Positivity.Strictness",
"Lean.Expr.const",
"Lean.Meta.MetaM",
"Nat.hasNotBit",
"Lean.Expr.sort",
"Lean.Level",
"List.cons",
"_private.Mathlib.MeasureTheory.Integral.Bochner.Basic.0.Mathlib.Meta.Positivity.evalIntegral._sparseCasesOn_1",
"Qq.Quoted",
"Lean.Leve... | false |
Filter.mem_zero | Mathlib.Order.Filter.Pointwise | [
"Filter.instMembership",
"Membership.mem",
"Iff",
"Filter.instZero",
"Zero.toOfNat0",
"OfNat.ofNat",
"Set.instMembership",
"Filter",
"Filter.mem_pure",
"Zero",
"Set"
] | true |
Std.DTreeMap.Internal.Impl.Const.get?_union_of_contains_eq_false_left | Std.Data.DTreeMap.Internal.Lemmas | [
"Std.DTreeMap.Internal.Impl.WF.union",
"Eq.mpr",
"Std.Internal.List.DistinctKeys",
"Std.DTreeMap.Internal.Impl.toListModel_union_list",
"Std.Internal.List.insertList",
"Ord",
"Std.instLawfulBEqOrd",
"congrArg",
"Std.DTreeMap.Internal.Impl.contains_eq_containsKey",
"beqOfOrd",
"Std.DTreeMap.Inter... | true |
CategoryTheory.AddMon.Hom.mk | Mathlib.CategoryTheory.Monoidal.Mon | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.IsAddMonHom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.AddMon.Hom",
"CategoryTheory.AddMon.Hom.mk",
"CategoryTheory.AddMon.addMon",
"CategoryTheory.AddMon.X",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheo... | true |
Lean.Doc.Data.instTypeNameTactic | Lean.Elab.DocString.Builtin | [
"TypeName",
"Lean.Doc.Data.Tactic",
"Lean.Doc.Data.inst._@.Lean.Elab.DocString.Builtin.1563348410._hygCtx._hyg.8"
] | true |
LieRinehartAlgebra.Hom.comp._proof_1 | Mathlib.Algebra.LieRinehartAlgebra.Defs | [
"LieHom",
"CommRing",
"instHSMul",
"LieRing.toAddCommGroup",
"congrArg",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AlgHom",
"AlgHom.funLike",
"AddMonoid.toAddZeroClass",
"Algebra",
"AddCommGroup.toAddGroup",
"AddZeroClass.toAddZero",
"D... | false |
CategoryTheory.GrothendieckTopology.sheafify.eq_1 | Mathlib.CategoryTheory.Sites.CompatibleSheafification | [
"CategoryTheory.GrothendieckTopology.Cover.shape",
"CategoryTheory.Functor",
"CategoryTheory.GrothendieckTopology.sheafify",
"Opposite",
"CategoryTheory.Limits.HasColimitsOfShape",
"CategoryTheory.GrothendieckTopology.instPreorderCover",
"Preorder.smallCategory",
"CategoryTheory.GrothendieckTopology.C... | true |
_private.Std.Internal.Http.Data.Body.Stream.0.Std.Http.Body.Channel.Consumer.noConfusion | Std.Internal.Http.Data.Body.Stream | [
"Std.Http.Chunk",
"_private.Std.Internal.Http.Data.Body.Stream.0.Std.Http.Body.Channel.Consumer.casesOn",
"Std.Internal.IO.Async.Waiter",
"_private.Std.Internal.Http.Data.Body.Stream.0.Std.Http.Body.Channel.Consumer.noConfusionType",
"IO.Promise",
"Eq.ndrec",
"Eq.refl",
"Eq",
"_private.Std.Internal.... | false |
multipliable_of_exists_eq_zero | Mathlib.Topology.Algebra.InfiniteSum.Basic | [
"CommMonoidWithZero.toCommMonoid",
"SummationFilter",
"HasProd",
"Exists",
"CommMonoidWithZero.toMonoidWithZero",
"Multipliable",
"hasProd_zero_of_exists_eq_zero",
"TopologicalSpace",
"MonoidWithZero.toMulZeroOneClass",
"CommMonoidWithZero",
"Exists.intro",
"SummationFilter.LeAtTop",
"Zero.t... | true |
_private.Init.Data.String.Lemmas.FindPos.0.String.Slice.posGE_le_iff._simp_1_3 | Init.Data.String.Lemmas.FindPos | [
"String.instLEPos_1",
"String.Slice.Pos.offset",
"String.Slice",
"LE.le",
"String.Pos.Raw",
"String.Slice.Pos.le_iff",
"String.instLERaw",
"propext",
"String.Slice.Pos",
"Eq"
] | false |
CharTwo.add_cancel_right | Mathlib.Algebra.CharP.Two | [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"AddMonoid.toAddSemigroup",
"congrArg",
"add_assoc",
"AddMonoid.toAddZeroClass",
"CharTwo.add_self_eq_zero",
"AddZeroClass.toAddZero",
"id",
"Distrib.toAdd",
"instOfNatNat",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"instDistribOfSemiring... | true |
Mathlib.Tactic.Contrapose.contrapose.negate_iff | Mathlib.Tactic.Contrapose | [
"Inhabited.default",
"instInhabitedBool",
"Lean.Option",
"Lean.instInhabitedOption",
"Bool"
] | true |
_private.Mathlib.GroupTheory.Coxeter.Basic.0.CoxeterSystem.getElem_alternatingWord._proof_1_5 | Mathlib.GroupTheory.Coxeter.Basic | [
"Nat.succ_lt_succ_iff",
"Lean.Grind.instOrderedRingInt",
"Lean.RArray.leaf",
"Lean.Grind.nestedProof",
"Lean.Grind.Order.lt_eq_true_of_lt_k",
"Lean.Grind.CommRing.Expr.var",
"congrArg",
"Lean.Grind.Order.le_of_eq_2_k",
"Lean.Grind.Order.lt_le_trans_k",
"PartialOrder.toPreorder",
"HSub.hSub",
"... | false |
convex_halfSpace_le | Mathlib.Analysis.Convex.Basic | [
"convex_Iic",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"setOf",
"Preorder.toLE",
"AddZeroClass.toAddZero",
"PartialOrder",
"Convex.is_linear_preimage",
"DistribSMul.toSMulZeroClass",
"PosSMulMono",
"LE.le",
"AddCommMonoid",
"AddZero.toZero",
... | true |
Sym2.sortEquiv_apply_coe | Mathlib.Data.Sym.Sym2.Order | [
"Lattice.toSemilatticeSup",
"Equiv.instEquivLike",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"Equiv",
"Subtype",
"Prod.mk",
"LE.le",
"Sym2.inf",
"Prod.fst",
"Sym2.sup",
"Eq.refl",
"Sym2.sortEquiv",
"Prod",
... | true |
CategoryTheory.Limits.ProductsFromFiniteCofiltered.finiteSubproductsCone._proof_1 | Mathlib.CategoryTheory.Limits.Constructions.Filtered | [
"Opposite",
"Finset",
"CategoryTheory.Discrete.functor",
"CategoryTheory.Limits.HasLimit",
"Membership.mem",
"Subtype",
"CategoryTheory.Limits.ProductsFromFiniteCofiltered.liftToFinsetObj._proof_1",
"CategoryTheory.discreteCategory",
"Finset.instSetLike",
"Subtype.val",
"CategoryTheory.Limits.Ha... | false |
Antisymmetrization.induction_on | Mathlib.Order.Antisymmetrization | [
"AntisymmRel.setoid",
"Quotient.inductionOn'",
"Antisymmetrization",
"IsPreorder",
"toAntisymmetrization"
] | true |
Std.Tactic.BVDecide.BVUnOp.ctorElimType | Std.Tactic.BVDecide.Bitblast.BVExpr.Basic | [
"cond",
"Std.Tactic.BVDecide.BVUnOp.clz",
"Nat.ble",
"Std.Tactic.BVDecide.BVUnOp",
"Std.Tactic.BVDecide.BVUnOp.cpop",
"Std.Tactic.BVDecide.BVUnOp.not",
"PULift",
"Std.Tactic.BVDecide.BVUnOp.rotateLeft",
"Nat",
"Std.Tactic.BVDecide.BVUnOp.reverse",
"Std.Tactic.BVDecide.BVUnOp.arithShiftRightConst... | false |
_private.Mathlib.CategoryTheory.Sites.Coherent.Comparison.0.CategoryTheory.extensive_regular_generate_coherent.match_1_4 | Mathlib.CategoryTheory.Sites.Coherent.Comparison | [
"CategoryTheory.IsIso",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Presieve",
"Finite",
"Membership.mem",
"Exists",
"And.casesOn",
"CategoryTheory.extensiveCoverage",
"And",
"Exists.casesOn",
"CategoryTheory.extensiveCoverage._proof_1",
"And.intro",
"Exists.int... | false |
_private.Mathlib.Testing.Plausible.Functions.0.Plausible.TotalFunction.zeroDefault.match_1.splitter | Mathlib.Testing.Plausible.Functions | [
"Plausible.TotalFunction.zeroDefault.match_1",
"List",
"Plausible.TotalFunction.withDefault",
"Plausible.TotalFunction",
"Sigma"
] | true |
Std.DTreeMap.Const.mergeWith._proof_1 | Std.Data.DTreeMap.Basic | [
"Std.DTreeMap",
"Ord.mk",
"Ordering",
"Std.DTreeMap.Internal.Impl.Const.mergeWith",
"Std.DTreeMap.inner",
"Std.DTreeMap.Const.getThenInsertIfNew?._proof_1",
"Std.DTreeMap.Internal.Impl.WF.constMergeWith",
"Std.DTreeMap.Internal.Impl.WF",
"Std.DTreeMap.Internal.Impl.WF.balanced",
"Std.DTreeMap.wf",... | false |
NormedSpace.exp_op | Mathlib.Analysis.Normed.Algebra.Exponential | [
"Eq.mpr",
"False",
"RingEquiv.toEquiv",
"instHSMul",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"Ring.toNonAssocRing",
"congrArg",
"IsEmpty.elim",
"NormedSpace.exp_eq_tsum",
"NormedSpace.exp",
"MulOpposite.instAlgebra",
"Rat",
"MulOpposite",
"AddGroupWithOne.... | true |
Module.Basis.linearMap | Mathlib.LinearAlgebra.Matrix.ToLin | [
"LinearEquiv.symm",
"Semiring.toModule",
"Matrix.module",
"Matrix.stdBasis",
"CommSemiring.toSemiring",
"Matrix",
"Module.Basis.map",
"LinearMap.toMatrix'._proof_5",
"Matrix.addCommMonoid",
"Finite.of_fintype",
"LinearMap.module",
"LinearMap",
"smulCommClass_self",
"AddCommMonoid",
"Comm... | true |
Topology.IsLower.tendsto_nhds_iff_not_le | Mathlib.Topology.Order.LowerUpperTopology | [
"Filter.instMembership",
"_private.Mathlib.Topology.Order.LowerUpperTopology.0.Topology.IsLower.tendsto_nhds_iff_not_le._simp_1_1",
"Set.Ici",
"congrArg",
"Compl.compl",
"Topology.IsLower.topology_eq_lowerTopology",
"Filter.Eventually",
"setOf",
"Preorder.toLE",
"Membership.mem",
"Exists",
"nh... | true |
_private.Mathlib.Algebra.Order.Round.0.round_eq_div._simp_1_3 | Mathlib.Algebra.Order.Round | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"HMul.hMul",
"Nat.instAtLeastTwoHAddOfNat",
"two_mul",
"Distrib.toAdd",
"AddMonoidWithOne.toNatCast",
"instOfNatNat",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"instHAdd",
"NonAssocSemiring",
"Distrib.toMul",
"HAdd.hAdd",
"Nat.instNeZeroSucc",
"N... | false |
ContinuousAlternatingMap.instContinuousEval | Mathlib.Analysis.Normed.Module.Alternating.Basic | [
"SeminormedAddCommGroup",
"NormedSpace",
"Pi.topologicalSpace",
"ContinuousEval",
"AddCommGroup.toAddCommMonoid",
"Finite",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"AddCommGroup.toAddGroup",
"ContinuousMultilinearMap",
"NormedField.toField",
"AddCommGroup",
"ContinuousMul... | true |
_private.Mathlib.GroupTheory.Nilpotent.0.Group.nilpotencyClass_pi._simp_1_2 | Mathlib.GroupTheory.Nilpotent | [
"Group",
"Subgroup",
"Bot.bot",
"LE.le",
"Group.nilpotencyClass",
"instLENat",
"Subgroup.lowerCentralSeries",
"Nat",
"propext",
"Subgroup.lowerCentralSeries_eq_bot_iff_nilpotencyClass_le",
"Subgroup.instBot",
"Group.IsNilpotent",
"Eq.symm",
"Eq"
] | false |
MeasureTheory.setIntegral_abs_condExp_le | Mathlib.MeasureTheory.Function.ConditionalExpectation.Real | [
"MeasureTheory.ae",
"AddGroup.toSubtractionMonoid",
"Norm.norm",
"SeminormedAddGroup.toNorm",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"MeasureTheory.integral_indicator",
"MeasureTheory.integral_nonneg",
"Real.partialOrder",
"Real.instLE",
"Real",
"... | true |
Lean.Elab.Do.map1TermElabM | Lean.Elab.Do.Basic | [
"Lean.Elab.Do.controlAtTermElabM",
"Lean.Elab.Term.TermElabM",
"Lean.Elab.Do.DoElabM"
] | true |
CompactT2.Projective | Mathlib.Topology.ExtremallyDisconnected | [
"Continuous",
"Function.comp",
"Exists",
"CompactSpace",
"TopologicalSpace",
"And",
"T2Space",
"Eq",
"Function.Surjective"
] | true |
Pi.zero_mono | Mathlib.Algebra.Group.Pi.Lemmas | [
"monotone_const",
"Zero.zero",
"Monotone",
"Pi.instZero",
"Zero.toOfNat0",
"OfNat.ofNat",
"Preorder",
"Zero"
] | true |
Lean.IR.LitVal.str.elim | Lean.Compiler.IR.Basic | [
"PULift.up",
"String",
"Lean.IR.LitVal.str",
"Lean.IR.LitVal.ctorIdx",
"Nat",
"Lean.IR.LitVal.ctorElim",
"Eq.symm",
"Eq",
"Lean.IR.LitVal"
] | false |
LinearMap.tensorEqLocus_coe | Mathlib.RingTheory.Flat.Equalizer | [
"Submodule",
"IsScalarTower.to_smulCommClass'",
"CommRing",
"SemilinearMapClass.distribMulActionSemiHomClass",
"congrArg",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"IsScalarTower",
"Submodule.addCommMonoid",
"TensorProduct.addCommMonoid",
"Ad... | true |
CategoryTheory.Factorisation.casesOn | Mathlib.CategoryTheory.Category.Factorisation | [
"CategoryTheory.Factorisation",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Factorisation.rec",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryStruct",
"Eq",
"CategoryTheory.Factorisation.mk",
"CategoryTheory.Category"
] | false |
Subgroup.inv_mem | Mathlib.Algebra.Group.Subgroup.Defs | [
"Subgroup.instSubgroupClass",
"DivInvOneMonoid.toInvOneClass",
"Group",
"Group.toDivisionMonoid",
"Membership.mem",
"DivisionMonoid.toDivInvOneMonoid",
"Subgroup",
"SubgroupClass.toInvMemClass",
"Group.toDivInvMonoid",
"InvMemClass.inv_mem",
"Inv.inv",
"InvOneClass.toInv",
"SetLike.instMembe... | true |
RingQuot.mkRingHom_def | Mathlib.Algebra.RingQuot | [
"Eq.mpr",
"RingQuot.definition._proof_1._@.Mathlib.Algebra.RingQuot.3469094938._hygCtx._hyg.2",
"RingQuot.definition._@.Mathlib.Algebra.RingQuot.3469094938._hygCtx._hyg.2",
"MulOne.toOne",
"RingHom.mk",
"congrArg",
"OneHom.mk",
"RingHom",
"RingQuot.instSemiring",
"RingQuot.definition._proof_2._@.M... | true |
Std.IterM.step_intermediateDropWhile._proof_4 | Std.Data.Iterators.Lemmas.Combinators.Monadic.DropWhile | [
"Pure.pure",
"Eq.mpr",
"Monad.toApplicative",
"ULift",
"ULift.up.injEq",
"Function.comp",
"Std.Iterators.PostconditionT.Property",
"id",
"Std.Iterators.PostconditionT.property_pure",
"Applicative.toPure",
"Std.Iterators.instMonadPostconditionT",
"congrFun",
"Bool",
"Std.Iterators.Postcondi... | false |
Multiplicative.ofAdd.eq_1 | Mathlib.Algebra.BigOperators.Group.Finset.Defs | [
"Equiv.mk",
"Equiv",
"Additive.ofMul._proof_1",
"Multiplicative.ofAdd._proof_1",
"Multiplicative",
"Eq.refl",
"Multiplicative.ofAdd",
"Eq"
] | true |
Lean.Grind.Nat.lo_lo | Init.Grind.Offset | [
"_private.Init.Grind.Offset.0.Lean.Grind.Nat.lo_lo._proof_1_1",
"LE.le",
"instLENat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"Decidable.byContradiction",
"instAddNat",
"Not",
"Nat.decLe"
] | true |
Int.instLocallyFiniteOrder._proof_6 | Mathlib.Data.Int.Interval | [
"addLeftEmbedding",
"Eq.mpr",
"_private.Mathlib.Data.Int.Interval.0.Int.instLocallyFiniteOrder._simp_2",
"congrArg",
"instIsLeftCancelAddOfAddLeftReflectLE",
"Finset",
"_private.Mathlib.Data.Int.Interval.0.Int.instLocallyFiniteOrder._proof_4",
"PartialOrder.toPreorder",
"AddGroupWithOne.toAddMonoidW... | false |
_private.Init.Data.String.Decode.0.String.toBitVec_getElem_utf8EncodeChar_zero_of_utf8Size_eq_two | Init.Data.String.Decode | [
"BitVec.setWidth_ofNat_of_le_of_lt",
"UInt32.toUInt8",
"Eq.mpr",
"UInt32.toBitVec",
"BitVec.setWidth",
"BitVec.instHShiftRight",
"instHOrOfOrOp",
"BitVec.instAndOp",
"BitVec.instHShiftRightNat",
"UInt8.instOfNat",
"Nat.zero_lt_succ._simp_1",
"BitVec.extractLsb'",
"BitVec.instOfNat",
"congr... | true |
List.Shortlex.of_length_lt | Mathlib.Data.List.Shortlex | [
"List",
"Nat",
"LT.lt",
"List.Shortlex",
"instLTNat",
"Prod.Lex.left",
"List.length",
"List.Lex"
] | true |
LinearEquiv.cast | Mathlib.Algebra.Module.Equiv.Defs | [
"LinearEquiv.cast._proof_1",
"LinearEquiv.cast._proof_4",
"LinearEquiv.mk",
"LinearEquiv.cast._proof_3",
"AddEquiv.cast",
"Equiv.toFun",
"AddCommMonoid",
"RingHomInvPair.ids",
"LinearEquiv",
"LinearMap.mk",
"Semiring",
"AddEquiv",
"AddCommSemigroup.toAddCommMagma",
"AddHom.mk",
"AddEquiv... | true |
_private.Lean.Structure.0.Lean.findParentProjStruct?.go._unsafe_rec | Lean.Structure | [
"Pure.pure",
"Lean.getStructureParentInfo",
"Lean.NameSet",
"modify",
"Monad.toApplicative",
"MonadState.get",
"Option.some",
"Lean.StructureParentInfo.structName",
"instDecidableEqBool",
"Id",
"Applicative.toPure",
"Array",
"Bool.true",
"Lean.StructureParentInfo",
"Option.none",
"Lean... | false |
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