name
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2
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stringlengths
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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