name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
_private.Mathlib.Tactic.Simps.Basic.0.Lean.Meta.mkSimpContextResult._sparseCasesOn_1 | Mathlib.Tactic.Simps.Basic | [
"Nat.ne_of_beq_eq_false",
"Lean.Elab.Tactic.Simp.DischargeWrapper.default",
"Nat.shiftRight",
"Lean.Elab.Tactic.Simp.DischargeWrapper.rec",
"Nat.hasNotBit",
"instOfNatNat",
"Nat.land",
"Lean.Elab.Tactic.Simp.DischargeWrapper.custom",
"Lean.Elab.Tactic.Simp.DischargeWrapper.ctorIdx",
"Nat",
"Bool... | false |
IsSemitopologicalSemiring.continuousNeg_of_mul | Mathlib.Topology.Algebra.Ring.Basic | [
"NegZeroClass.toNeg",
"ContinuousNeg.mk",
"Continuous",
"HMul.hMul",
"congrArg",
"NonUnitalNonAssocRing.toAddCommGroup",
"AddGroupWithOne.toAddMonoidWithOne",
"Eq.mp",
"id",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"SubtractionMonoid.toSubNegZeroMonoid",
"NonAssocSemiring.toMulZero... | true |
PowerSeries.coe_orderHom | Mathlib.RingTheory.PowerSeries.Order | [
"Nontrivial",
"MonoidHom.instFunLike",
"instAddMonoidWithOneENat",
"MonoidHom",
"AddMonoid.toAddZeroClass",
"Multiplicative.mulOneClass",
"MulZeroOneClass.toMulOneClass",
"instDistribOfSemiring",
"instMulZeroOneClassOfSemiring",
"MvPowerSeries.instSemiring",
"Multiplicative",
"MulOneClass.toMu... | true |
Finset.Ico_diff_Ico_left | Mathlib.Order.Interval.Finset.Basic | [
"Lattice.toSemilatticeSup",
"LinearOrder.toDecidableEq",
"_private.Mathlib.Order.Interval.Finset.Basic.0.Finset.Ico_diff_Ico_left._proof_1_1",
"Finset",
"LinearOrder",
"PartialOrder.toPreorder",
"Finset.instSDiff",
"SemilatticeInf.toPartialOrder",
"SemilatticeSup.toMax",
"DistribLattice.toLattice"... | true |
_private.Batteries.Data.List.Lemmas.0.List.getElem_filter_eq_getElem_getElem_findIdxs_sub._proof_1_49 | Batteries.Data.List.Lemmas | [
"List.countP",
"Lean.Grind.CommRing.le_norm_expr",
"Lean.Grind.instOrderedRingInt",
"Lean.RArray.leaf",
"GetElem",
"_private.Batteries.Data.List.Lemmas.0.List.getElem_filter_eq_getElem_getElem_findIdxs_sub._proof_1_9",
"HMul.hMul",
"Lean.Grind.CommRing.Expr.mul",
"Int.Linear.norm_le",
"Lean.Grind.... | false |
CategoryTheory.ShortComplex.exact_of_f_is_kernel | Mathlib.Algebra.Homology.ShortComplex.Exact | [
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.KernelFork.ofι",
"CategoryTheory.Epi",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.WalkingParallelPair",
"congrArg",
"CategoryTheory.ShortComplex.iCycles_g",
"CategoryTheory.instIsRegularEpiOfIsSpl... | true |
CoxeterSystem.map_simple | Mathlib.GroupTheory.Coxeter.Basic | [
"MulEquiv.instEquivLike",
"Monoid.toMulOneClass",
"CoxeterSystem.map",
"Group",
"MulOne.toMul",
"CoxeterSystem.simple",
"DivInvMonoid.toMonoid",
"CoxeterMatrix",
"Group.toDivInvMonoid",
"MulOneClass.toMulOne",
"MulEquiv",
"CoxeterSystem",
"Eq",
"DFunLike.coe",
"rfl",
"EquivLike.toFunLi... | true |
ENNReal.mul_inv_le_one | Mathlib.Data.ENNReal.Inv | [
"HMul.hMul",
"CommSemiring.toSemiring",
"ENNReal.div_self_le_one",
"ENNReal.instCommSemiring",
"LE.le",
"instDistribOfSemiring",
"Inv.inv",
"Distrib.toMul",
"ENNReal.instLE",
"ENNReal",
"One.toOfNat1",
"ENNReal.instOne",
"ENNReal.instInv",
"OfNat.ofNat",
"instHMul"
] | true |
Std.DHashMap.Raw.Const.get_unitOfList | Std.Data.DHashMap.RawLemmas | [
"Std.DHashMap.Raw.instMembershipOfBEqOfHashable",
"Unit.unit",
"Std.DHashMap.Raw.Const.get",
"Std.DHashMap.Raw",
"Membership.mem",
"Std.DHashMap.Raw.Const.unitOfList",
"List",
"Unit",
"eq_self",
"of_eq_true",
"Hashable",
"BEq",
"Eq"
] | true |
WeierstrassCurve._sizeOf_1 | Mathlib.AlgebraicGeometry.EllipticCurve.Weierstrass | [
"instOfNatNat",
"WeierstrassCurve",
"WeierstrassCurve.rec",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"SizeOf",
"OfNat.ofNat"
] | false |
Codisjoint.eq_top_of_le | Mathlib.Order.Disjoint | [
"Iff.mpr",
"Codisjoint",
"le_rfl",
"eq_top_iff",
"PartialOrder.toPreorder",
"Preorder.toLE",
"PartialOrder",
"LE.le",
"OrderTop",
"OrderTop.toTop",
"Top.top",
"Eq"
] | true |
Array.find?_range_eq_some._simp_1 | Init.Data.Array.Range | [
"Bool.not",
"Array.instMembership",
"Option.some",
"Membership.mem",
"Array",
"Bool.true",
"And",
"Array.range",
"Nat",
"LT.lt",
"propext",
"Bool",
"instLTNat",
"Eq",
"Array.find?_range_eq_some",
"Option",
"Array.find?"
] | false |
CategoryTheory.NatTrans.IsMonoidal.hcomp | Mathlib.CategoryTheory.Monoidal.NaturalTransformation | [
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.LaxMonoidal.ε",
"CategoryTheory.NatTrans.IsMonoidal.unit",
"Categ... | true |
Aesop.Script.LazyStep.postGoals | Aesop.Script.Step | [
"Lean.MVarId",
"Array",
"Aesop.Script.LazyStep"
] | true |
ContinuousMap.instSemigroupWithZeroOfContinuousMul | Mathlib.Topology.ContinuousMap.Algebra | [
"SemigroupWithZero",
"ContinuousMap.instSemigroupWithZeroOfContinuousMul._proof_2",
"MulZeroClass.toMul",
"ContinuousMap.instSemigroupWithZeroOfContinuousMul._proof_1",
"ContinuousMap",
"SemigroupWithZero.toMulZeroClass",
"SemigroupWithZero.toSemigroup",
"TopologicalSpace",
"ContinuousMul",
"Semig... | true |
IsLocalizedModule.map_surjective._simp_1 | Mathlib.Algebra.Module.LocalizedModule.Basic | [
"CommSemiring.toSemiring",
"IsLocalizedModule",
"LinearMap.instFunLike",
"LinearMap.module",
"LinearMap",
"smulCommClass_self",
"AddCommMonoid",
"MulZeroOneClass.toMulOneClass",
"instMulZeroOneClassOfSemiring",
"CommSemiring",
"CommMonoid.toMonoid",
"IsLocalizedModule.map",
"True",
"Linear... | false |
IsPrimitiveRoot.integralPowerBasisOfPrimePow.eq_1 | Mathlib.NumberTheory.NumberField.Cyclotomic.Basic | [
"Subalgebra.instSetLike",
"PowerBasis",
"Nat.Prime",
"NumberField.instCommRingRingOfIntegers",
"CommSemiring.toSemiring",
"Nat.instMonoid",
"IsPrimitiveRoot.integralPowerBasisOfPrimePow._proof_2",
"Rat",
"AddGroupWithOne.toAddMonoidWithOne",
"Algebra.adjoin",
"Membership.mem",
"Field.toDivisio... | true |
_private.Mathlib.CategoryTheory.WithTerminal.Cone.0.CategoryTheory.WithTerminal.id.match_1.eq_1 | Mathlib.CategoryTheory.WithTerminal.Cone | [
"CategoryTheory.WithTerminal.id.match_1",
"CategoryTheory.WithTerminal",
"CategoryTheory.WithTerminal.of",
"Unit",
"CategoryTheory.WithTerminal.star",
"Eq.refl",
"Eq"
] | true |
Tree.brecOn.go | Mathlib.Data.Tree.Basic | [
"Tree.node",
"PProd.mk",
"Tree.rec",
"Tree.nil",
"Tree.below",
"Tree",
"PProd",
"PUnit",
"PUnit.unit"
] | true |
Subgroup.commutator | Mathlib.GroupTheory.Commutator.Basic | [
"Subgroup.closure",
"Bracket.bracket",
"setOf",
"Group",
"Membership.mem",
"Exists",
"Bracket",
"Subgroup",
"commutatorElement",
"And",
"Eq",
"SetLike.instMembership",
"Bracket.mk",
"Subgroup.instSetLike"
] | true |
Submodule.tensorSpanEquivSpan._proof_1 | Mathlib.LinearAlgebra.Span.TensorProduct | [
"CommSemiring.toSemiring",
"RingHomCompTriple",
"CommSemiring",
"RingHom.id",
"RingHomCompTriple.ids",
"Semiring.toNonAssocSemiring"
] | false |
ContinuousLinearMap.opNNNorm_mul_flip_apply | Mathlib.Analysis.CStarAlgebra.Unitization | [
"NormedCommRing.toSeminormedCommRing",
"Real.instLE",
"Real",
"instSMulOfMul",
"NormedSpace.toIsBoundedSMul",
"UniformContinuousConstSMul.to_continuousConstSMul",
"NormedSpace",
"ContinuousLinearMap.opNorm_mul_flip_apply",
"ContinuousLinearMap.topologicalSpace",
"Real.instZero",
"DistribMulActio... | true |
_private.Mathlib.Topology.Sets.VietorisTopology.0.TopologicalSpace.IsTopologicalBasis.compacts._proof_1_12 | Mathlib.Topology.Sets.VietorisTopology | [
"False",
"eq_false",
"Classical.byContradiction",
"setOf",
"Membership.mem",
"Exists",
"Eq.mp",
"id",
"Set.mem_setOf_eq",
"Set.instInter",
"Inter.inter",
"TopologicalSpace",
"And",
"Set.Nonempty",
"Exists.casesOn",
"SetLike.coe",
"TopologicalSpace.Compacts.instSetLike",
"True",
"... | false |
Mathlib.Tactic.Bicategory.StructuralOfExpr_bicategoricalComp | Mathlib.Tactic.CategoryTheory.Bicategory.Datatypes | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Iso",
"CategoryTheory.Bicategory.toCategoryStruct",
"CategoryTheory.BicategoricalCoherence",
"CategoryTheory.Bicategory",
"CategoryTheory.BicategoricalCoherence.iso",
"CategoryTheory.Iso.trans",
"congr",
"True",
... | true |
_private.Plausible.Tactic.0._aux_Plausible_Tactic___elabRules_plausibleSyntax_1.match_6 | Plausible.Tactic | [
"Lean.MVarId",
"Lean.FVarId",
"Prod.mk",
"Array",
"Prod",
"Prod.casesOn"
] | false |
_private.Lean.Compiler.LCNF.JoinPoints.0.Lean.Compiler.LCNF.JoinPointContextExtender.extend.go._unsafe_rec | Lean.Compiler.LCNF.JoinPoints | [
"Lean.Compiler.LCNF.JoinPointContextExtender.ExtendM",
"_private.Lean.Compiler.LCNF.JoinPoints.0.Lean.Compiler.LCNF.JoinPointContextExtender.extend.goFVar",
"Pure.pure",
"Lean.Compiler.LCNF.LetDecl.updateValue",
"Lean.instBEqFVarId",
"Array.instAppend",
"Unit.unit",
"Array.mapMonoM",
"Lean.Compiler.... | false |
CategoryTheory.ObjectProperty.tStructure._proof_8 | Mathlib.CategoryTheory.Triangulated.TStructure.Induced | [
"CategoryTheory.Functor",
"CategoryTheory.ObjectProperty.IsTriangulated.toIsStableUnderShift",
"CategoryTheory.ObjectProperty.ι",
"CategoryTheory.Functor.Additive",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.ObjectProperty.hasShift",
"CategoryTheory.shiftFunctor"... | false |
HomogeneousLocalization.NumDenSameDeg.instCommMonoid._proof_5 | Mathlib.RingTheory.GradedAlgebra.HomogeneousLocalization | [
"SetLike",
"HomogeneousLocalization.NumDenSameDeg.num",
"CommRing",
"HomogeneousLocalization.NumDenSameDeg",
"HomogeneousLocalization.NumDenSameDeg.ext",
"HMul.hMul",
"CommSemiring.toSemiring",
"AddMonoid.toAddZeroClass",
"AddGroupWithOne.toAddMonoidWithOne",
"Membership.mem",
"AddSubmonoidClass... | false |
Rack.toEnvelGroup.mapAux.eq_2 | Mathlib.Algebra.Quandle | [
"Quandle.toRack",
"ShelfHom",
"Rack.toShelf",
"Rack",
"Group",
"Quandle.Conj.quandle",
"Quandle.Conj",
"Rack.toEnvelGroup.mapAux",
"Rack.PreEnvelGroup.incl",
"Eq.refl",
"Eq",
"DFunLike.coe",
"ShelfHom.instFunLike"
] | true |
ContinuousMonoidHom.mk._flat_ctor | Mathlib.Topology.Algebra.ContinuousMonoidHom | [
"Monoid",
"MulOne.toOne",
"Continuous",
"HMul.hMul",
"Monoid.toMulOneClass",
"ContinuousMonoidHom.mk",
"OneHom.mk",
"MulOne.toMul",
"MonoidHom.mk",
"autoParam",
"TopologicalSpace",
"MulOneClass.toMulOne",
"ContinuousMap.continuous_toFun._autoParam",
"One.toOfNat1",
"ContinuousMonoidHom",... | false |
_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.rankFinite_iff_cRank_lt_aleph0.match_1_1 | Mathlib.Combinatorics.Matroid.Rank.Cardinal | [
"Set.Finite",
"Exists",
"Matroid.IsBase",
"Matroid.RankFinite.mk",
"And.casesOn",
"And",
"Exists.casesOn",
"Matroid.RankFinite.casesOn",
"And.intro",
"Exists.intro",
"Matroid.RankFinite",
"Matroid",
"Set"
] | false |
ProbabilityTheory.covarianceBilinDual_apply | Mathlib.Probability.Moments.CovarianceBilinDual | [
"Iff.mpr",
"ContinuousSub.measurableSub",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"ENNReal.instIsOrderedRing",
"NormedCommRing.toSeminormedCommRing",
"Continuous.comp_aestronglyMeasurable",
"Real",
"Algebra.to_smulCommClass",
"MeasureTheory.Measure",
"NonUnitalCommRing.toNonUnitalNonAssocCo... | true |
SSet.Subcomplex.Pairing.op._proof_2 | Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.Op | [
"SSet.Subcomplex.N.opEquiv",
"SSet.op",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SSet.Subcomplex.N",
"OrderIso",
"SSet.Subcomplex.N.instPartialOrder",
"SSet",
"Set.instInter",
"SSet.Subcomplex.Pairing",
"Inter.inter",
"SSet.Subcomplex.Pairing.I",
"instFunLikeOrderIso",
"S... | false |
StateTransition.EvalsTo.mk | Mathlib.Computability.StateTransition | [
"Option.some",
"flip",
"Nat.iterate",
"instMonadOption",
"StateTransition.EvalsTo",
"Nat",
"Monad.toBind",
"Bind.bind",
"Eq",
"Option",
"StateTransition.EvalsTo.mk"
] | true |
Real.nonempty_algEquiv_or | Mathlib.Analysis.Complex.Polynomial.Basic | [
"NormedCommRing.toSeminormedCommRing",
"Real",
"RCLike.toNormedAlgebra",
"Complex.instNormedField",
"Algebra",
"Field.toDivisionRing",
"Real.semiring",
"Algebra.id",
"DivisionRing.toRing",
"Complex.instRCLike",
"Algebra.IsAlgebraic",
"Real.commRing",
"Field.toSemifield",
"Semifield.toDivis... | true |
deriv_fun_mul | Mathlib.Analysis.Calculus.Deriv.Mul | [
"NormedCommRing.toNormedRing",
"NormedCommRing.toSeminormedCommRing",
"Semiring.toModule",
"NormedRing.toRing",
"HMul.hMul",
"DifferentiableAt.hasDerivAt",
"DifferentiableAt",
"deriv",
"NormedSpace.toModule",
"HasDerivAt.deriv",
"PseudoMetricSpace.toUniformSpace",
"NormedField.toField",
"Nor... | true |
TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIsoApp | Mathlib.Topology.Sheaves.SheafCondition.EqualizerProducts | [
"TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIsoApp._proof_2",
"CategoryTheory.Limits.ConeMorphism.mk",
"CategoryTheory.Functor.op",
"CategoryTheory.Limits.Cone",
"Opposite",
"CategoryTheory.Limits.WalkingParallelPair",
"TopologicalSpace.Opens.instCompleteLattice",
"CategoryTheory... | true |
Graph.IsSubgraph.isLoopAt_congr | Mathlib.Combinatorics.Graph.Subgraph | [
"Eq.mpr",
"Graph.IsLoopAt",
"congrArg",
"Graph.IsSubgraph.isLink_iff",
"Iff.rfl",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"id",
"Graph",
"LE.le",
"Graph.IsLink",
"Iff",
"Graph.edgeSet",
"propext",
"Graph.instPartialOrder",
"Eq",
"Set.instMembership",
"Set"
] | true |
_private.Std.Data.DHashMap.Internal.RawLemmas.0.Std.DHashMap.Internal.Raw₀.Const.mem_toArray_iff_get?_eq_some._simp_1_1 | Std.Data.DHashMap.Internal.RawLemmas | [
"Std.DHashMap.Raw.Const.toList",
"Std.DHashMap.Raw",
"Std.DHashMap.Raw.Const.toArray",
"instOfNatNat",
"List.toArray",
"Array",
"Nat",
"Std.DHashMap.Raw.buckets",
"LT.lt",
"Std.DHashMap.Internal.Raw₀.Const.toArray_toList_eq_toArray",
"Std.DHashMap.Internal.AssocList",
"instLTNat",
"Prod",
... | false |
Lean.Parser.«command_Builtin_cbv_simproc_decl_(_):=_» | Init.CbvSimproc | [
"Lean.Name.mkStr3",
"instOfNatNat",
"Lean.ParserDescr.binary",
"Lean.ParserDescr",
"Lean.ParserDescr.unary",
"Lean.ParserDescr.node",
"Nat",
"Lean.ParserDescr.symbol",
"Lean.ParserDescr.const",
"Lean.ParserDescr.cat",
"OfNat.ofNat",
"Lean.Name.mkStr1"
] | true |
Aesop.Script.LazyStep.tacticBuilders_ne._autoParam | Aesop.Script.Step | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
CategoryTheory.NonPreadditiveAbelian.monoIsKernelOfCokernel | Mathlib.CategoryTheory.Abelian.NonPreadditive | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.KernelFork.ofι",
"CategoryTheory.Mono",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.WalkingParallelPair",
"CategoryTheory.Abelian.factorThruImage",
"CategoryTheory.Functor.category",
"CategoryTheory.Limits.WalkingPar... | true |
Set.mul_subset_mul | Mathlib.Algebra.Group.Pointwise.Set.Basic | [
"Set.image2_subset",
"HMul.hMul",
"Mul",
"HasSubset.Subset",
"Set.mul",
"Set.instHasSubset",
"instHMul",
"Set"
] | true |
CategoryTheory.Functor.CoreMonoidal.toOplaxMonoidal._proof_4 | Mathlib.CategoryTheory.Monoidal.Functor | [
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"CategoryTheory.Functor.CoreMonoidal.μIso",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.CoreMonoidal.εIso",
"congrArg",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.CoreMonoidal.l... | false |
_private.Mathlib.Topology.Semicontinuity.Hemicontinuity.0.lowerHemicontinuous_iff_isOpen_compl_preimage_Iic_compl._simp_1_6 | Mathlib.Topology.Semicontinuity.Hemicontinuity | [
"Filter.instMembership",
"Membership.mem",
"nhds",
"TopologicalSpace",
"propext",
"isOpen_iff_mem_nhds",
"IsOpen",
"Eq",
"Set.instMembership",
"Filter",
"Set"
] | false |
Function.Even.eq_1 | Mathlib.Analysis.Fourier.ZMod | [
"Function.Even",
"Neg",
"Eq.refl",
"Eq",
"Neg.neg"
] | true |
SupHom.copy._proof_1 | Mathlib.Order.Hom.Lattice | [
"SupHom.instFunLike",
"Eq.rec",
"Max",
"Max.max",
"SupHom.map_sup'",
"SupHom",
"Eq.symm",
"Eq",
"DFunLike.coe"
] | false |
SignType.LE | Mathlib.Data.Sign.Defs | [
"SignType.LE.of_pos",
"SignType.LE.of_neg",
"SignType.LE.zero",
"SignType"
] | true |
Tree.numNodes._sunfold | Mathlib.Data.Tree.Basic | [
"Tree.numNodes",
"instOfNatNat",
"Tree",
"instHAdd",
"Unit",
"HAdd.hAdd",
"Nat",
"Tree.traverse.match_1",
"instAddNat",
"OfNat.ofNat"
] | false |
_private.Mathlib.Analysis.InnerProductSpace.Rayleigh.0.ContinuousLinearMap.bddAbove_rayleighQuotient.match_1_1 | Mathlib.Analysis.InnerProductSpace.Rayleigh | [
"InnerProductSpace.toNormedSpace",
"Real",
"Real.lattice",
"abs",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"Membership.mem",
"NormedField.toField",
"Real.instAddGroup",
"Field.toSemifield",
"RCLike.toDenselyNormedField",
"ContinuousLinearMap... | false |
Profinite.toCompHaus.reflective._proof_2 | Mathlib.Topology.Category.Profinite.Basic | [
"Profinite.toCompHaus.reflective._proof_1",
"CompHausLike.toCompHausLike",
"TotallyDisconnectedSpace",
"CompHausLike",
"TopCat.str",
"TopCat.carrier",
"True",
"compHausLikeToCompHaus._proof_1",
"CompHausLike.category",
"CompHausLike.instFullToCompHausLike",
"TopCat",
"CategoryTheory.Functor.Fu... | false |
Lean.Meta.reduceNatNativeUnsafe | Lean.Meta.WHNF | [
"Lean.MonadError.mk",
"Lean.instMonadExceptOfExceptionCoreM",
"Lean.Meta.State",
"Lean.instAddErrorMessageContextOfAddMessageContextOfMonad",
"Lean.Core.instMonadOptionsCoreM",
"Lean.MonadQuotation.toMonadRef",
"Lean.instMonadOptionsOfMonadLift",
"Lean.Meta.MetaM",
"IO.RealWorld",
"StateRefT'.inst... | true |
Matrix.Pivot.reindex_exists_list_transvec_mul_mul_list_transvec_eq_diagonal | Mathlib.LinearAlgebra.Matrix.Transvection | [
"Eq.mpr",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Matrix.submatrix",
"Equiv.instEquivLike",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"Equiv.symm_comp_self",
"congrArg",
"CommSemiring.toSemiring",
"Matrix.instMulOfFintypeOfAddCommMonoid",
"Matrix",
"List.map",
"Matrix.instHMulOf... | true |
Matrix.discr | Mathlib.LinearAlgebra.Matrix.Charpoly.Disc | [
"CommRing",
"Matrix",
"Fintype",
"Polynomial.discr",
"Matrix.charpoly",
"DecidableEq"
] | true |
CategoryTheory.Pseudofunctor.whiskerLeft_mapId_hom | Mathlib.CategoryTheory.Bicategory.Functor.Pseudofunctor | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Pseudofunctor.mapId",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Bicategory.rightUnitor",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Iso.hom_inv_id",
"CategoryTheory.PrelaxFunctorStruct.map₂",
"Categ... | true |
_private.Lean.Compiler.LCNF.EmitC.0.Lean.Compiler.LCNF.emitLetDecl.emitLhs | Lean.Compiler.LCNF.EmitC | [
"String",
"_private.Lean.Compiler.LCNF.EmitC.0.Lean.Compiler.LCNF.emit",
"_private.Lean.Compiler.LCNF.EmitC.0.Lean.Compiler.LCNF.State",
"ReaderT.instMonad",
"_private.Lean.Compiler.LCNF.EmitC.0.Lean.Compiler.LCNF.EmitM",
"IO.RealWorld",
"_private.Lean.Compiler.LCNF.EmitC.0.Lean.Compiler.LCNF.instEmitTo... | true |
_private.Mathlib.Algebra.MonoidAlgebra.Module.0.MonoidAlgebra.mem_supported'._simp_1_1 | Mathlib.Algebra.MonoidAlgebra.Module | [
"MonoidAlgebra.addCommMonoid",
"Submodule",
"MonoidAlgebra.coeff",
"Finset",
"Finsupp.support",
"Membership.mem",
"HasSubset.Subset",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"SetLike.coe",
"Finset.instSetLike",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"MonoidAlgebra",
"Submodule.... | false |
Monoid.Coprod.swap_bijective | Mathlib.GroupTheory.Coprod.Basic | [
"MonoidHom.instFunLike",
"Monoid.Coprod.swap_surjective",
"MonoidHom",
"Monoid.Coprod.swap",
"Monoid.Coprod.swap_injective",
"MulOneClass.toMulOne",
"Monoid.Coprod.instMulOneClass",
"And.intro",
"Function.Bijective",
"Function.Injective",
"MulOneClass",
"Monoid.Coprod",
"DFunLike.coe",
"Fu... | true |
IsLeftCancelMul.mk | Mathlib.Algebra.Group.Defs | [
"IsLeftCancelMul",
"Mul",
"IsLeftRegular",
"IsLeftCancelMul.mk"
] | true |
Associates.instCommMonoid._proof_4 | Mathlib.Algebra.GroupWithZero.Associated | [
"MulOne.toOne",
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"MulOne.toMul",
"Quotient.mk",
"Associated.setoid",
"MulOneClass.toMulOne",
"Quotient",
"CommMonoid.toMonoid",
"True",
"eq_self",
"of_eq_true",
"One.toOfNat1",
"congrFun'",
"OfNat.ofNat",
"Eq",
"CommMonoid",
"one_mu... | false |
Set.inv_smul_set_distrib₀ | Mathlib.Algebra.GroupWithZero.Action.Pointwise.Set | [
"Set.ext",
"inv_eq_zero._simp_1",
"GroupWithZero.toMonoidWithZero",
"False",
"DivInvMonoid.toInv",
"instHSMul",
"instSMulOfMul",
"GroupWithZero.toDivisionMonoid",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"eq_false",
"MulOpposite.instInvolutiveInv",
"MulZeroClass.toMul",
"Monoid.toMulO... | true |
DFA.recOn | Mathlib.Computability.DFA | [
"DFA.mk",
"DFA",
"DFA.rec",
"Set"
] | false |
_private.Mathlib.RingTheory.Extension.Cotangent.Basis.0.Algebra.Generators.PresentationOfFreeCotangent.Aux.span_range_mk_kerGen | Mathlib.RingTheory.Extension.Cotangent.Basis | [
"Algebra.Generators.ker",
"Algebra.Extension.Cotangent.span_eq_top_of_span_eq_ker",
"NegZeroClass.toNeg",
"Submodule",
"Submodule.Quotient.instZeroQuotient",
"_private.Mathlib.RingTheory.Extension.Cotangent.Basis.0.Algebra.Generators.PresentationOfFreeCotangent.Aux.presLeft._proof_2",
"Nat.instMulZeroCl... | true |
Fin.partialProd_succ' | Mathlib.Algebra.BigOperators.Fin | [
"Monoid",
"Eq.mpr",
"instNeZeroNatHAdd_1",
"MulOne.toOne",
"HMul.hMul",
"Fin.succ",
"Monoid.toMulOneClass",
"congrArg",
"List.ofFn",
"id",
"Fin.instOfNat",
"MulOne.toMul",
"instOfNatNat",
"Fin.val",
"List.cons",
"List",
"instHAdd",
"MulOneClass.toMulOne",
"HAdd.hAdd",
"Nat.inst... | true |
Heyting.Regular.toRegular._proof_1 | Mathlib.Order.Heyting.Regular | [
"Compl.compl",
"Heyting.IsRegular",
"Heyting.isRegular_compl",
"HeytingAlgebra",
"HeytingAlgebra.toCompl"
] | false |
RatFunc.valuationIdeal._proof_2 | Mathlib.NumberTheory.RatFunc.Ostrowski | [
"Submodule.span_eq_bot._simp_1",
"Eq.mpr",
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"Submodule",
"RatFunc.uniformizingPolynomial",
"Semiring.toModule",
"InvOneClass.toOne",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"congrArg",
"CommSemirin... | false |
SecondCountableTopology.recOn | Mathlib.Topology.Bases | [
"SecondCountableTopology",
"Exists",
"SecondCountableTopology.mk",
"TopologicalSpace.generateFrom",
"SecondCountableTopology.rec",
"TopologicalSpace",
"And",
"Set.Countable",
"Eq",
"Set"
] | false |
Vector.set_append | Init.Data.Vector.Lemmas | [
"Array.instAppend",
"Eq.mpr",
"Decidable.casesOn",
"dite_congr",
"Vector.instHAppendHAddNat",
"Vector",
"congrArg",
"Array.set",
"Vector.set_mk._proof_2",
"HSub.hSub",
"Decidable",
"Vector.casesOn",
"Eq.rec",
"Array.set_append",
"dif_pos",
"id",
"instSubNat",
"Vector.getElem_append... | true |
Std.Http.Response.ok | Std.Internal.Http.Data.Response | [
"Std.Http.Status.ok",
"Std.Http.Response.Builder.status",
"Std.Http.Response.Builder.new",
"Std.Http.Response.Builder"
] | true |
CategoryTheory.IsVanKampenColimit.map_reflective | Mathlib.CategoryTheory.Limits.VanKampen | [
"CategoryTheory.Limits.PreservesColimitsOfShape.preservesColimit",
"Eq.mpr",
"CategoryTheory.Limits.IsColimit.fac",
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.PreservesColimitsOfSize",
"CategoryTheory.Functor.mapCocone_ι_app",
"CategoryTheory.Functor",
"CategoryTheory.Limits.colimit.cocon... | true |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.isSome_maxKey?_of_isSome_maxKey?_erase._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 |
TopologicalSpace.Compacts.isometry_toCloseds | Mathlib.Topology.MetricSpace.Closeds | [
"PseudoEMetricSpace.toWeakPseudoEMetricSpace",
"TopologicalSpace.Compacts.instEMetricSpace",
"TopologicalSpace.Compacts.toCloseds",
"EMetricSpace.metrizableSpace",
"EMetricSpace.toPseudoEMetricSpace",
"EMetricSpace",
"WeakPseudoEMetricSpace.toEDist",
"PseudoEMetricSpace.toUniformSpace",
"ENNReal",
... | true |
EisensteinSeries.gammaSetEquiv._proof_4 | Mathlib.NumberTheory.ModularForms.EisensteinSeries.Defs | [
"Eq.mpr",
"MulOne.toOne",
"Subtype.mk.congr_simp",
"Nat.instMulZeroClass",
"Matrix.SpecialLinearGroup",
"MonoidHom.instFunLike",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"inv_mul_cancel",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"ZMod.commRing",
"MonoidHom",
"Monoid.toMulOneClass... | false |
Mathlib.Meta.Positivity.pos_of_isNNRat | Mathlib.Tactic.Positivity.Core | [
"Iff.mpr",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Preorder.toLT",
"Nat.cast_pos",
"HMul.hMul",
"of_decide_eq_true",
"congrArg",
"LinearOrder",
"PartialOrder.toPreorder",
"Invertible.invOf",
"IsStrictOrderedRing",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
... | true |
_private.Lean.Meta.Tactic.Grind.Split.0.Lean.Meta.Grind.Action.getFalseProof?.go._f | Lean.Meta.Tactic.Grind.Split | [
"Pure.pure",
"Unit.unit",
"Lean.Expr.isApp",
"Lean.Meta.State",
"Lean.Expr.cleanupAnnotations",
"Option.some",
"Lean.Expr",
"Lean.Meta.MetaM",
"IO.RealWorld",
"instDecidableEqBool",
"Lean.Expr.appArg",
"Applicative.toPure",
"Lean.Expr.appFnCleanup",
"Lean.Expr.hasLooseBVars",
"dite",
"... | false |
Lean.Meta.ReduceMatcherResult.casesOn | Lean.Meta.WHNF | [
"Lean.Meta.ReduceMatcherResult.rec",
"Lean.Meta.ReduceMatcherResult.notMatcher",
"Lean.Expr",
"Lean.Meta.ReduceMatcherResult.stuck",
"Lean.Meta.ReduceMatcherResult.reduced",
"Lean.Meta.ReduceMatcherResult",
"Lean.Meta.ReduceMatcherResult.partialApp"
] | false |
OpenPartialHomeomorph.singletonChartedSpace._proof_2 | Mathlib.Geometry.Manifold.HasGroupoid | [
"Membership.mem",
"Set.instSingletonSet",
"TopologicalSpace",
"Eq.refl",
"Singleton.singleton",
"Set.instMembership",
"OpenPartialHomeomorph",
"Set"
] | false |
ContinuousCohomology.homogeneousCochains._proof_3 | Mathlib.Algebra.Category.ContinuousCohomology.Basic | [
"Nat.instOne",
"AddCancelMonoid.toAddRightCancelMonoid",
"Nat.instAddCancelCommMonoid",
"instOfNatNat",
"Nat",
"ComplexShape.up'",
"ContinuousCohomology.homogeneousCochains._proof_1",
"ComplexShape.instIsRelIffEmbeddingUp'Add",
"One.toOfNat1",
"AddRightCancelMonoid.toAddRightCancelSemigroup",
"A... | false |
OpenPartialHomeomorph.coe_ofContinuousOpen | Mathlib.Topology.OpenPartialHomeomorph.Basic | [
"PartialEquiv",
"IsOpenMap",
"OpenPartialHomeomorph.toFun'",
"OpenPartialHomeomorph.ofContinuousOpen",
"TopologicalSpace",
"PartialEquiv.source",
"ContinuousOn",
"IsOpen",
"PartialEquiv.toFun",
"Eq",
"rfl"
] | true |
Nat.strongRecOn'_beta | Mathlib.Data.Nat.Init | [
"Nat.strongRecOn'",
"Nat.strongRec'_spec",
"Nat",
"LT.lt",
"instLTNat",
"Eq"
] | true |
_private.Plausible.Gen.0.Plausible.test | Plausible.Gen | [
"Pure.pure",
"Plausible.GenError.genError",
"Nat.zero_le",
"Plausible.Gen.getSize",
"ReaderT",
"Monad.toApplicative",
"MonadExcept.throw",
"ULift",
"ReaderT.instMonad",
"Subtype",
"Nat.instMod",
"instDecidableEqBool",
"instHMod",
"instOfNatNat",
"LE.le",
"instLENat",
"Id",
"Applica... | true |
CategoryTheory.GradedObject.TriangleIndexData.p₂₃ | Mathlib.CategoryTheory.GradedObject.Unitor | [
"CategoryTheory.GradedObject.TriangleIndexData",
"Prod",
"Zero"
] | true |
Filter.empty_notMem._simp_1 | Mathlib.Order.Filter.Basic | [
"Filter.instMembership",
"False",
"eq_false",
"Filter.NeBot",
"Filter.empty_notMem",
"Membership.mem",
"Set.instEmptyCollection",
"EmptyCollection.emptyCollection",
"Eq",
"Filter",
"Set"
] | false |
MulSemiringAction.toAlgEquiv.congr_simp | Mathlib.FieldTheory.Galois.Basic | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"MulSemiringAction.toAlgEquiv",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"Group",
"Algebra",
"Algebra.toSMul",
"Eq.rec",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"DivInvMonoid.toMonoid",
"AddCommMonoidWithOne.toAdd... | true |
GroupNorm.coe_sup._simp_2 | Mathlib.Analysis.Normed.Group.Seminorm | [
"GroupNorm",
"Real",
"Group",
"GroupNorm.coe_sup",
"GroupNorm.funLike",
"Real.instMax",
"Pi.instMaxForall_mathlib",
"Max.max",
"Eq.symm",
"Eq",
"DFunLike.coe",
"GroupNorm.instMax"
] | false |
ULift.down_ratCast | Mathlib.Algebra.Field.ULift | [
"Rat",
"ULift",
"Rat.cast",
"RatCast",
"Eq",
"ULift.instRatCast",
"ULift.down",
"rfl"
] | true |
RelIso.relEmbeddingCongr_symm_apply | Mathlib.Order.RelIso.Basic | [
"Equiv.instEquivLike",
"Equiv",
"RelIso.symm",
"RelIso",
"RelEmbedding",
"Eq.refl",
"RelIso.relEmbeddingCongr",
"RelIso.toRelEmbedding",
"RelEmbedding.trans",
"Equiv.symm",
"Eq",
"DFunLike.coe",
"EquivLike.toFunLike"
] | true |
_private.Mathlib.Tactic.MoveAdd.0.Lean.Expr.getExprInputs._sparseCasesOn_1 | Mathlib.Tactic.MoveAdd | [
"Nat.ne_of_beq_eq_false",
"Lean.Expr.const",
"Lean.Expr.letE",
"Lean.Expr.mvar",
"Nat.shiftRight",
"Lean.MVarId",
"Lean.Expr",
"Lean.FVarId",
"Nat.hasNotBit",
"instOfNatNat",
"Lean.Expr.sort",
"Lean.Expr.bvar",
"Lean.Level",
"Lean.Literal",
"Lean.Expr.mdata",
"Lean.Expr.fvar",
"Lean.... | false |
CategoryTheory.instComonadicLeftAdjointCoalgebraForget | Mathlib.CategoryTheory.Monad.Adjunction | [
"CategoryTheory.Comonad",
"CategoryTheory.Comonad.forget",
"CategoryTheory.ComonadicLeftAdjoint",
"CategoryTheory.instComonadicLeftAdjointCoalgebraForget._proof_4",
"CategoryTheory.Comonad.adj",
"CategoryTheory.ComonadicLeftAdjoint.mk",
"CategoryTheory.Comonad.cofree",
"CategoryTheory.Comonad.Coalgebr... | true |
Chebyshev.integral_theta_div_log_sq_isLittleO | Mathlib.NumberTheory.Chebyshev | [
"Iff.mpr",
"NormedCommRing.toNormedRing",
"Real.instIsOrderedRing",
"Mathlib.Tactic.FieldSimp.zpow'_one",
"Mathlib.Tactic.FieldSimp.NF.div_eq_eval₁",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"InnerProductSpace.toNormedSpace",
"instDecidableNot",
"NormedCommRing.toSeminormedCommRing",
"NonAsso... | true |
typeToPointed._proof_3 | Mathlib.CategoryTheory.Category.Pointed | [
"CategoryTheory.ConcreteCategory.hom",
"TypeCat.instFunLikeFun",
"CategoryTheory.CategoryStruct.id",
"Pointed.point",
"Option.none",
"Option.map",
"Pointed.mk",
"TypeCat.Fun",
"CategoryTheory.types",
"CategoryTheory.Category.toCategoryStruct",
"Pointed.X",
"Eq",
"DFunLike.coe",
"rfl",
"i... | false |
MeasureTheory.lintegral_sub_right_eq_self | Mathlib.MeasureTheory.Group.LIntegral | [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"NegZeroClass.toNeg",
"MeasureTheory.Measure",
"congrArg",
"AddMonoid.toAddZeroClass",
"sub_eq_add_neg",
"HSub.hSub",
"AddZeroClass.toAddZero",
"id",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"MeasurableAdd",
"SubNe... | true |
Std.HashSet.Raw.mem_toList._simp_1 | Std.Data.HashSet.RawLemmas | [
"LawfulBEq",
"Membership.mem",
"Std.HashSet.Raw.WF",
"Std.HashSet.Raw.toList",
"List",
"Std.HashSet.Raw.instMembershipOfBEqOfHashable",
"List.instMembership",
"Std.HashSet.Raw.mem_toList",
"propext",
"Hashable",
"BEq",
"Eq",
"Std.HashSet.Raw"
] | false |
WithTop.measurable_of_measurable_comp_coe | Mathlib.MeasureTheory.Constructions.BorelSpace.WithTop | [
"MeasurableEquiv.instEquivLike",
"OrderTopology",
"TopologicalSpace.instOrderTopologyWithTop",
"LinearOrder",
"WithTop.instBorelSpace",
"PartialOrder.toPreorder",
"Measurable",
"setOf",
"WithTop.instMeasurableSpace",
"T5Space.toT1Space",
"Function.comp",
"Membership.mem",
"SemilatticeInf.toP... | true |
_private.Std.Data.DTreeMap.Internal.Model.0.Ordering.swap.match_1.splitter | Std.Data.DTreeMap.Internal.Model | [
"Ordering.gt",
"Ordering.swap.match_1",
"Ordering",
"Ordering.eq",
"Unit",
"Ordering.lt"
] | true |
Option.pfilter_filter | Init.Data.Option.Lemmas | [
"Iff.mpr",
"Eq.mpr",
"Decidable.casesOn",
"Option.pfilter",
"congrArg",
"Option.filter_eq_some_iff",
"Option.casesOn",
"Decidable",
"Bool.false_eq_true",
"Option.pfilter_none",
"Option.some",
"dif_pos",
"id",
"instDecidableEqBool",
"Option.pfilter_congr",
"if_pos",
"dif_neg",
"dite... | true |
Lean.Compiler.LCNF.Check.Pure.State.all | Lean.Compiler.LCNF.Check | [
"Lean.Compiler.LCNF.Check.Pure.State",
"Lean.FVarIdHashSet"
] | true |
Lean.Meta.LazyDiscrTree.instEmptyCollectionTrie | Lean.Meta.LazyDiscrTree | [
"Lean.Meta.LazyDiscrTree.instBEqKey",
"Lean.Meta.LazyDiscrTree.Trie.node",
"instOfNatNat",
"EmptyCollection.mk",
"Std.HashMap",
"Std.HashMap.instEmptyCollection",
"List.toArray",
"Lean.Meta.LazyDiscrTree.TrieIndex",
"Lean.Meta.LazyDiscrTree.Key.instHashable",
"Lean.Meta.LazyDiscrTree.LazyEntry",
... | true |
Lean.Lsp.CompletionItemTag.deprecated.sizeOf_spec | Lean.Data.Lsp.LanguageFeatures | [
"Lean.Lsp.CompletionItemTag.deprecated",
"Lean.Lsp.CompletionItemTag",
"instOfNatNat",
"Lean.Lsp.CompletionItemTag._sizeOf_inst",
"Nat",
"SizeOf.sizeOf",
"Eq.refl",
"OfNat.ofNat",
"Eq"
] | true |
LowerSet.mem_Iic_iff._simp_1 | Mathlib.Order.UpperLower.Principal | [
"Preorder.toLE",
"Membership.mem",
"LE.le",
"LowerSet.mem_Iic_iff",
"propext",
"LowerSet",
"Eq",
"SetLike.instMembership",
"Preorder",
"LowerSet.Iic",
"LowerSet.instSetLike"
] | false |
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