name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Dilation.ratioHom | Mathlib.Topology.MetricSpace.Dilation | [
"Dilation.instMonoid",
"Dilation.ratio_one",
"MulOne.toOne",
"Dilation.funLike",
"MonoidHom",
"Monoid.toMulOneClass",
"Dilation.ratio_mul",
"OneHom.mk",
"MonoidHom.mk",
"NNReal",
"PseudoEMetricSpace",
"Dilation.ratio",
"MulZeroOneClass.toMulOneClass",
"instMulZeroOneClassOfSemiring",
"Mu... | true |
irrational_ratCast_add_iff | Mathlib.NumberTheory.Real.Irrational | [
"Real",
"Real.instRatCast",
"Rat",
"Rat.cast",
"Real.instAdd",
"Irrational.ratCast_add",
"instHAdd",
"Iff",
"Irrational",
"HAdd.hAdd",
"Iff.intro",
"Irrational.of_ratCast_add"
] | true |
MeasurableEquiv.shearAddRight | Mathlib.MeasureTheory.Group.Prod | [
"AddGroup.toSubtractionMonoid",
"NegZeroClass.toNeg",
"MeasurableEquiv.shearAddRight._proof_4",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"Equiv",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"MeasurableSpace",
"AddGroup",
"AddGroup.toSubNegMonoid",
"M... | true |
lie_abelian_iff_equiv_lie_abelian | Mathlib.Algebra.Lie.Abelian | [
"LieEquiv.injective",
"CommRing",
"LieRing.toAddCommGroup",
"LieEquiv.toLieHom",
"LieEquiv",
"Function.Injective.isLieAbelian",
"SubtractionMonoid.toSubNegZeroMonoid",
"LieRingModule.toBracket",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",
"IsLieAbelian",
"Li... | true |
_private.Mathlib.Topology.DiscreteSubset.0.mem_codiscrete_accPt._simp_1_1 | Mathlib.Topology.DiscreteSubset | [
"Filter.instMembership",
"Compl.compl",
"Filter.instCompleteLatticeFilter",
"nhdsWithin",
"PartialOrder.toPreorder",
"mem_codiscrete",
"Preorder.toLE",
"Disjoint",
"Membership.mem",
"CompleteLattice.toBoundedOrder",
"Set.instSingletonSet",
"Set.instCompl",
"TopologicalSpace",
"BoundedOrder... | false |
Lean.Grind.CommRing.Poly.NonnegCoeffs.below.casesOn | Init.Grind.Ring.CommSemiringAdapter | [
"Lean.Grind.CommRing.Poly.NonnegCoeffs",
"Lean.Grind.CommRing.Poly.NonnegCoeffs.below.rec",
"Lean.Grind.CommRing.Poly",
"Lean.Grind.CommRing.Poly.add",
"Lean.Grind.CommRing.Poly.NonnegCoeffs.below.add",
"Lean.Grind.CommRing.Poly.NonnegCoeffs.num",
"Lean.Grind.CommRing.Poly.NonnegCoeffs.below.num",
"GE... | false |
_private.Mathlib.CategoryTheory.Sites.Coherent.RegularTopology.0.CategoryTheory.regularTopology.instEffectiveEpiComp.match_1 | Mathlib.CategoryTheory.Sites.Coherent.RegularTopology | [
"Unit.unit",
"PUnit.casesOn",
"Unit",
"PUnit.unit"
] | false |
UniqueDiffWithinAt.inter' | Mathlib.Analysis.Calculus.TangentCone.Basic | [
"Filter.instMembership",
"Iff.mpr",
"AddCommGroup.toAddCommMonoid",
"nhdsWithin",
"UniqueDiffWithinAt",
"Membership.mem",
"AddCommGroup",
"Set.instInter",
"Inter.inter",
"TopologicalSpace",
"Semiring",
"AddCommSemigroup.toAddCommMagma",
"Module",
"ContinuousAdd",
"AddCommMonoid.toAddComm... | true |
Polynomial.Monic.pow | Mathlib.Algebra.Polynomial.Monic | [
"Nat.brecOn",
"Polynomial",
"Monoid.toPow",
"Polynomial.Monic",
"HPow.hPow",
"Polynomial.Monic.pow._f",
"Polynomial.semiring",
"Nat",
"Semiring.toMonoid",
"Semiring",
"instHPow"
] | true |
WithLp.noConfusion | Mathlib.Analysis.Normed.Lp.WithLp | [
"WithLp",
"HEq.refl",
"WithLp.noConfusionType",
"ENNReal",
"eq_of_heq",
"Eq.ndrec",
"HEq",
"WithLp.casesOn",
"Eq"
] | false |
instPreorderShrink | Mathlib.Order.Shrink | [
"Equiv.instEquivLike",
"Preorder.lift",
"Equiv",
"Shrink",
"Equiv.symm",
"equivShrink",
"DFunLike.coe",
"Preorder",
"Small",
"EquivLike.toFunLike"
] | true |
_private.Std.Data.DHashMap.Internal.Defs.0.Std.DHashMap.Internal.Raw₀.interSmallerFn.match_1 | Std.Data.DHashMap.Internal.Defs | [
"Unit.unit",
"Option.casesOn",
"Option.some",
"Option.none",
"Unit",
"Sigma",
"Option"
] | false |
Multiset.exists_multiset_eq_map_quot_mk | Mathlib.Data.Multiset.MapFold | [
"Multiset.map_cons",
"Multiset.map",
"_private.Mathlib.Data.Multiset.MapFold.0.Multiset.exists_multiset_eq_map_quot_mk.match_1_1",
"Exists",
"Quot.inductionOn",
"Eq.rec",
"Multiset",
"Multiset.cons",
"Multiset.induction_on",
"Exists.intro",
"Zero.toOfNat0",
"Quot",
"OfNat.ofNat",
"Eq.symm"... | true |
CliffordAlgebra.reverse_mem_evenOdd_iff._simp_1 | Mathlib.LinearAlgebra.CliffordAlgebra.Conjugation | [
"Submodule",
"CommRing",
"CliffordAlgebra.reverse",
"Ring.toNonAssocRing",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"CliffordAlgebra",
"instAlgebraCliffordAlgebra",
"QuadraticForm",
"LinearMap.instFunLike",
"Membership.mem",
"AddCommGroup",
"Algebra.toModule",
"CliffordAl... | false |
CommGroup.monoidHomMonoidHomEquiv._proof_5 | Mathlib.GroupTheory.FiniteAbelian.Duality | [
"MulOne.toOne",
"MonoidHom.instFunLike",
"MonoidHom",
"Monoid.toMulOneClass",
"Units",
"DivInvMonoid.toMonoid",
"CommGroup",
"Group.toDivInvMonoid",
"MulOneClass.toMulOne",
"CommMonoid.toMonoid",
"One.toOfNat1",
"MonoidHom.one_apply",
"CommGroup.toGroup",
"OfNat.ofNat",
"Eq",
"CommMono... | false |
FractionalIdeal.coeIdeal_inj | Mathlib.RingTheory.FractionalIdeal.Operations | [
"CommRing",
"le_rfl",
"CommSemiring.toSemiring",
"IsFractionRing",
"PartialOrder.toPreorder",
"Algebra",
"nonZeroDivisors",
"Ideal",
"Field.toSemifield",
"Field.toCommRing",
"MulZeroOneClass.toMulOneClass",
"instMulZeroOneClassOfSemiring",
"FractionalIdeal",
"FractionalIdeal.coeIdeal_inj'"... | true |
_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.supp_injective._simp_1_2 | Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected | [
"Membership.mem",
"Iff",
"propext",
"Set.ext_iff",
"Eq",
"Set.instMembership",
"Set"
] | false |
Std.Time.OffsetO | Std.Time.Format.Basic | [
"Std.Time.OffsetO.full",
"Std.Time.OffsetO.short"
] | true |
_private.Mathlib.Analysis.Meromorphic.IsolatedZeros.0.MeromorphicAt.eventually_nhdsSet_eventuallyEq_codiscreteWithin._simp_1_1 | Mathlib.Analysis.Meromorphic.IsolatedZeros | [
"imp_self",
"True",
"propext",
"Eq"
] | false |
QuotientGroup.Quotient.group._proof_13 | Mathlib.GroupTheory.QuotientGroup.Defs | [
"Con.mk",
"DivInvMonoid.toInv",
"Con.inv",
"Monoid.toMulOneClass",
"Group",
"QuotientGroup.leftRel",
"MulOne.toMul",
"QuotientGroup.instHasQuotientSubgroup",
"DivInvMonoid.toMonoid",
"Subgroup",
"Setoid",
"Int",
"Nat.cast",
"autoParam",
"Group.toDivInvMonoid",
"HasQuotient.Quotient",
... | false |
CategoryTheory.Limits.biprod.lift_desc_assoc | Mathlib.CategoryTheory.Preadditive.Biproducts | [
"CategoryTheory.Category.assoc",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"CategoryTheory.Limits.biprod.desc",
"Eq.mp",
"CategoryTheory.Limits.HasBinaryBiproduct",
"id",
"Mathlib.Tactic.Reassoc.eq_whisker'",
"CategoryTheory.Limits.biprod... | true |
inl_coprodIsoPushout_hom_assoc | Mathlib.CategoryTheory.Limits.Constructions.BinaryProducts | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.WalkingSpan",
"CategoryTheory.Limits.HasBinaryCoproduct",
"CategoryTheory.Limits.hasColimitOfHasColimitsOfShape",
"inl_coprodIsoPushout_hom",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"Eq.mp",
"id",
"CategoryTheory... | true |
CategoryTheory.Bicategory.whiskerLeftIso | Mathlib.CategoryTheory.Bicategory.Basic | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Bicategory.whiskerLeftIso._proof_4",
"CategoryTheory.Bicategory.whiskerLeftIso._proof_2",
"CategoryTheory.Iso",
"CategoryTheory.Bicategory.toCategoryStruct",
"CategoryTheory.Iso.mk",
"CategoryTheory.Bicategory",
"CategoryTheory.... | true |
CategoryTheory.MonoidalCategory.DayConvolution.isPointwiseLeftKanExtensionUnit | Mathlib.CategoryTheory.Monoidal.DayConvolution | [
"CategoryTheory.MonoidalCategory.DayConvolution.convolution",
"CategoryTheory.Functor",
"CategoryTheory.MonoidalCategory.DayConvolution",
"CategoryTheory.Functor.LeftExtension.mk",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.MonoidalCategory.tensor",
"CategoryTheory.prod'",
"CategoryTheory.Mono... | true |
CategoryTheory.ShortComplex.Homotopy.ofEq._proof_10 | Mathlib.Algebra.Homology.ShortComplex.Preadditive | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"CategoryTheory.ShortComplex",
"AddCommGroup.toAddGroup",
"CategoryTheory.ShortComplex.instCategory",
"zero_add",
"CategoryTheory.Limits.HasZeroMorphisms.zero",
"Catego... | false |
Lean.Firefox.ProfileMeta.product._default | Lean.Util.Profiler | [
"String",
"id"
] | false |
IsPrimitiveRoot.integralPowerBasis_dim | Mathlib.NumberTheory.NumberField.Cyclotomic.Basic | [
"Nat.instMulZeroClass",
"LinearOrderedCommMonoidWithZero.toIsBotZeroClass",
"PowerBasis.dim",
"NumberField.instCommRingRingOfIntegers",
"congrArg",
"CommSemiring.toSemiring",
"Polynomial.natDegree_cyclotomic",
"Rat",
"AddGroupWithOne.toAddMonoidWithOne",
"Int.instNontrivial",
"Polynomial.cycloto... | true |
curveIntegral | Mathlib.MeasureTheory.Integral.CurveIntegral.Basic | [
"NormedSpace",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"NormedField.toField",
"Field.toSemifield",
"RCLike.toDenselyNormedField",
"ContinuousLinearMap",
"RCLike",
"Semifield.toDivisionSemiring",
"SeminormedAddCommGroup.toPseudoMetricSpace",
"... | true |
_private.Mathlib.Algebra.Module.Presentation.Tensor.0.Module.Relations.Solution.tensor.match_1.splitter | Mathlib.Algebra.Module.Presentation.Tensor | [
"CommRing",
"Prod.mk",
"Module.Relations.G",
"Module.Relations.Solution.tensor.match_1",
"CommRing.toRing",
"Module.Relations",
"Module.Relations.tensor"
] | true |
termSudoSet_option___In_ | Mathlib.Tactic.SudoSetOption | [
"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 |
_private.Mathlib.Analysis.SpecialFunctions.Artanh.0.Real.strictMonoOn_one_add_div_one_sub._simp_1_4 | Mathlib.Analysis.SpecialFunctions.Artanh | [
"False",
"eq_false",
"instOfNatNat",
"Nat",
"Zero.toOfNat0",
"three_ne_zero",
"NeZero",
"OfNat.ofNat",
"Eq",
"OfNat",
"Zero"
] | false |
String.front_eq | Init.Data.String.Lemmas.Search | [
"String.toSlice",
"Inhabited.default",
"String.Slice.front?",
"String.front?",
"congrArg",
"String",
"Option.getD",
"String.front?_toSlice",
"_private.Init.Data.String.Lemmas.Search.0.String.front_eq._simp_1_1",
"Char.instInhabited",
"String.front",
"True",
"eq_self",
"of_eq_true",
"cong... | true |
Metric.ediam_pi_le_of_le | Mathlib.Topology.EMetricSpace.Diam | [
"Iff.mpr",
"PseudoEMetricSpace.toWeakPseudoEMetricSpace",
"congrArg",
"Set.univ",
"Membership.mem",
"Eq.mp",
"pseudoEMetricSpacePi",
"LE.le",
"PseudoEMetricSpace",
"Metric.ediam",
"Fintype",
"WeakPseudoEMetricSpace.toEDist",
"PseudoEMetricSpace.toUniformSpace",
"Metric.ediam_le",
"ENNRea... | true |
DenseRange.zpow_of_ergodic_mul_left | Mathlib.Dynamics.Ergodic.Action.OfMinimal | [
"Filter.instMembership",
"Continuous.comp'",
"Iff.mpr",
"Set.instSProd",
"Eq.mpr",
"not_exists._simp_1",
"Ergodic",
"MulOne.toOne",
"False",
"instHSMul",
"MeasureTheory.Measure",
"zpow_add",
"instHDiv",
"instSMulOfMul",
"_private.Mathlib.Dynamics.Ergodic.Action.OfMinimal.0.DenseRange.zpo... | true |
CategoryTheory.Sigma.descUniq_inv_app | Mathlib.CategoryTheory.Sigma.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Sigma.incl",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Iso",
"CategoryTheory.Sigma.sigma",
"CategoryTheory.Sigma.desc",
"CategoryTheory.Category.toCategoryStruc... | true |
groupCohomology.isMulCoboundary₁_of_isMulCocycle₁_of_aut_to_units | Mathlib.RepresentationTheory.Homological.GroupCohomology.Hilbert90 | [
"Finsupp.instFunLike",
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Units.val",
"Eq.mpr",
"Pi.Function.module",
"GroupWithZero.toMonoidWithZero",
"AlgEquiv.instEquivLike",
"MonoidHom.instMonoidHomClass",
"_private.Mathlib.RepresentationTheory.Homological.GroupCohomology.Hilbert90.0.... | true |
continuousOn_union_iff_of_isOpen | Mathlib.Topology.ContinuousOn | [
"Set.subset_union_right",
"Set.instUnion",
"ContinuousOn.union_of_isOpen",
"Set.subset_union_left",
"TopologicalSpace",
"And",
"Iff",
"And.right",
"And.left",
"And.intro",
"Iff.intro",
"ContinuousOn.mono",
"ContinuousOn",
"IsOpen",
"Union.union",
"Set"
] | true |
Finmap.lookup_toFinmap | Mathlib.Data.Finmap | [
"Finmap.lookup",
"AList.lookup",
"AList",
"Eq",
"AList.toFinmap",
"rfl",
"Option",
"DecidableEq"
] | true |
Unitary.mulRight_apply | Mathlib.Analysis.CStarAlgebra.Unitary.Maps | [
"LinearIsometryEquiv.instEquivLike",
"instSMulOfMul",
"NormedRing.toRing",
"HMul.hMul",
"Ring.toNonAssocRing",
"Monoid.toMulOneClass",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"unitary",
"AddMonoid.toAddZeroClass",
"AddGroupWithOne.toAddMonoidWithOne",
"Membership.mem",
"NormedRing... | true |
_private.Mathlib.Combinatorics.Graph.Delete.0.Graph.restrict_isLoopAt._simp_1_2 | Mathlib.Combinatorics.Graph.Delete | [
"and_comm",
"And",
"propext",
"Eq"
] | false |
AffineSubspace.instNontrivial | Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs | [
"Nontrivial",
"Lattice.toSemilatticeSup",
"CompleteLattice.toLattice",
"AddCommGroup.toAddCommMonoid",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Preorder.toLE",
"AddCommGroup.toAddGroup",
"Exists",
"CompleteLattice.toBoundedOrder",
"AddCommGroup",
"Ne",
"Bot.bot",
"Nontrivial.mk",
"A... | true |
IsStarNormal.recOn | Mathlib.Algebra.Star.SelfAdjoint | [
"IsStarNormal.mk",
"IsStarNormal",
"Mul",
"Commute",
"IsStarNormal.rec",
"Star",
"Star.star"
] | false |
AugmentedSimplexCategory.inl'_eval | Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Monoidal | [
"OrderEmbedding.monotone",
"Fin.castOrderIso",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.WithInitial.of",
"Fin.castAdd",
"congrArg",
"OrderIso.toOrderEmbedding",
"CategoryTheory.eqToHom",
"AugmentedSimplexCategory.tensorHomOf._proof_6",
"PartialOrder.toPreorder",
... | true |
Quiver.reverse | Mathlib.Combinatorics.Quiver.Symmetric | [
"Quiver.Hom",
"Quiver.HasReverse.reverse'",
"Quiver",
"Quiver.HasReverse"
] | true |
Std.Time.PlainDateTime.toPlainTime | Std.Time.DateTime | [
"Std.Time.PlainTime",
"Std.Time.PlainDateTime",
"Std.Time.PlainDateTime.time"
] | true |
Parser.Attr.mfld_simps_proc | Mathlib.Tactic.Attr.Register | [
"Lean.ParserDescr.nonReservedSymbol",
"Lean.Name.mkStr3",
"instOfNatNat",
"Lean.ParserDescr.binary",
"Lean.ParserDescr",
"Lean.ParserDescr.unary",
"Lean.Parser.Tactic.simpPre",
"Lean.ParserDescr.node",
"Nat",
"Lean.Parser.Tactic.simpPost",
"OfNat.ofNat",
"Bool.false",
"Lean.Name.mkStr1"
] | true |
CategoryTheory.RetractArrow.right_i | Mathlib.CategoryTheory.Retract | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.id",
"CategoryTheory.Retract.i",
"CategoryTheory.instCategoryArrow",
"CategoryTheory.RetractArrow.right",
"CategoryTheory.CommaMorphism.right",
"Eq.refl",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Arr... | true |
ENat.floor_le._simp_1 | Mathlib.Algebra.Order.Floor.Extended | [
"ENNReal.instAdd",
"Preorder.toLT",
"instTopENat",
"PartialOrder.toPreorder",
"ENat.toENNReal",
"Ne",
"LE.le",
"instLEENat",
"instHAdd",
"ENat.floor",
"HAdd.hAdd",
"ENat",
"LT.lt",
"ENNReal",
"propext",
"One.toOfNat1",
"ENNReal.instPartialOrder",
"ENNReal.instOne",
"Top.top",
"... | false |
Nat.isCompl_even_odd | Mathlib.Algebra.Order.Ring.Nat | [
"congrArg",
"Compl.compl",
"Odd",
"setOf",
"SemilatticeInf.toPartialOrder",
"BiheytingAlgebra.toCoheytingAlgebra",
"Set.instCompl",
"BooleanAlgebra.toBiheytingAlgebra",
"_private.Mathlib.Algebra.Order.Ring.Nat.0.Nat.isCompl_even_odd._simp_1_3",
"funext",
"IsCompl",
"Set.instBoundedOrder",
"S... | true |
_private.Mathlib.CategoryTheory.Sites.Hypercover.Zero.0.CategoryTheory.Precoverage.RespectsIso.of_forall_exists_iso.match_1_7 | Mathlib.CategoryTheory.Sites.Hypercover.Zero | [
"CategoryTheory.PreZeroHypercover.mk",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Presieve",
"CategoryTheory.Presieve.uncurry",
"Membership.mem",
"Sum.casesOn",
"Set.Elem",
"Sum",
"CategoryTheory.Iso",
"Sigma.fst",
"Sum.inl",
"CategoryTheory.PreZeroHypercover.I₀"... | false |
Subspace.orderIsoFiniteCodimDim._proof_5 | Mathlib.LinearAlgebra.Dual.Lemmas | [
"Iff.mpr",
"Submodule",
"Submodule.Quotient.addCommMonoid",
"Algebra.to_smulCommClass",
"Subspace.dualQuotDistrib._proof_1",
"Semiring.toModule",
"Equiv.instEquivLike",
"OrderDual.ofDual",
"Submodule.dualCoannihilator",
"Submodule.Quotient.addCommGroup",
"CommSemiring.toSemiring",
"DistribMulA... | false |
SSet.chainComplexFunctorAdjunction._proof_1 | Mathlib.AlgebraicTopology.SimplicialSet.Homology.Basic | [
"CategoryTheory.Limits.hasColimitOfHasColimitsOfShape",
"Opposite",
"CategoryTheory.Functor.category",
"CategoryTheory.Discrete.functor",
"SSet",
"SSet.stdSimplex",
"CategoryTheory.Limits.HasCoproducts",
"CategoryTheory.discreteCategory",
"SimplexCategory.mk",
"Opposite.op",
"Nat",
"CategoryTh... | false |
Metric.eventually_notMem_thickening_of_infEDist_pos | Mathlib.Topology.MetricSpace.Thickening | [
"Eq.mpr",
"Real",
"Preorder.toLT",
"Lattice.toSemilatticeSup",
"Real.instZero",
"ENNReal.ofReal",
"Filter.Eventually",
"PartialOrder.toPreorder",
"instClosedIciTopology",
"setOf",
"PseudoMetricSpace.toUniformSpace",
"Real.instLT",
"eventually_lt_nhds",
"Preorder.toLE",
"Membership.mem",
... | true |
_private.Mathlib.MeasureTheory.Integral.DivergenceTheorem.0.MeasureTheory.«_aux_Mathlib_MeasureTheory_Integral_DivergenceTheorem___macroRules__private_Mathlib_MeasureTheory_Integral_DivergenceTheorem_0_MeasureTheory_term__¹_1» | Mathlib.MeasureTheory.Integral.DivergenceTheorem | [
"Pure.pure",
"Lean.TSyntax",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Name.mkNum",
"Lean.Syntax.ident",
"instMonadExceptOfMonadExceptOf",
"String",
"Lean.SourceInfo",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Macro.Exception",
"Lean.Syntax.atom",
"Lean.TSyntax.... | false |
SSet.horn.isCompatible_zero_iff_true._simp_1 | Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | [
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"SSet.horn.IsCompatible",
"Ne",
"instOfNatNat",
"SSet",
"SSet.stdSimplex",
"SSet.horn.isCompatible_zero_iff_true",
"SimplexCategory.mk",
"Nat",
"True",
"CategoryTheory.types",
"propext"... | false |
PosNum.shiftl | Mathlib.Data.Num.Bitwise | [
"PosNum.shiftl._f",
"Nat.brecOn",
"Nat",
"PosNum"
] | true |
_private.Mathlib.RingTheory.MvPowerSeries.LinearTopology.0.MvPowerSeries.LinearTopology.hasBasis_nhds_zero.match_1_5 | Mathlib.RingTheory.MvPowerSeries.LinearTopology | [
"Nat.instMulZeroClass",
"Ring.toNonAssocRing",
"TwoSidedIdeal",
"Prod.mk",
"NonAssocRing.toNonUnitalNonAssocRing",
"Nat",
"Prod",
"Prod.casesOn",
"Ring",
"Finsupp",
"MulZeroClass.toZero"
] | false |
CategoryTheory.Limits.Cone.functoriality.eq_1 | Mathlib.CategoryTheory.Limits.Cones | [
"CategoryTheory.Limits.Cone.functoriality._proof_5",
"CategoryTheory.Limits.ConeMorphism.mk",
"CategoryTheory.Limits.Cone.π",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cone",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.mk",
"CategoryTheory.Functor.category"... | true |
_private.Mathlib.NumberTheory.ModularForms.DedekindEta.0.ModularForm.one_sub_eta_logDeriv_eq | Mathlib.NumberTheory.ModularForms.DedekindEta | [
"logDeriv",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra",
"instHDiv",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"Real.pi",
"ModularForm.eta_q",
"HMul.hMul",
"Complex.instNormedAddCommGroup",
"congrArg",
"deri... | true |
CategoryTheory.Over.map_map_left | Mathlib.CategoryTheory.Comma.Over.Basic | [
"CategoryTheory.Over.map",
"CategoryTheory.Over",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Over.Hom.left",
"CategoryTheory.instCategoryOver",
"CategoryTheory.Functor.map",
"CategoryTheory.Over.left",
"CategoryTheory.Category.toCategoryStruct",
"Eq",
"CategoryTheory... | true |
_private.Mathlib.Algebra.Group.Prod.0.Prod.instCancelMonoid._simp_3 | Mathlib.Algebra.Group.Prod | [
"propext",
"Nonempty",
"forall_const",
"Eq"
] | false |
Std.DTreeMap.Const.getD_ofList_of_contains_eq_false | Std.Data.DTreeMap.Lemmas | [
"Std.DTreeMap.Const.getD",
"List.map",
"List.contains",
"Ord.mk",
"Ordering",
"Std.DTreeMap.Const.ofList",
"Std.TransCmp",
"Prod.fst",
"List",
"Std.LawfulBEqCmp",
"Bool",
"Prod",
"Bool.false",
"BEq",
"Eq",
"Std.DTreeMap.Internal.Impl.Const.getD_insertMany_empty_list_of_contains_eq_fals... | true |
_private.Lean.Elab.Tactic.BVDecide.Frontend.BVDecide.ReifiedBVPred.0.Lean.Elab.Tactic.BVDecide.Frontend.ReifiedBVPred.mkGetLsbD.match_1 | Lean.Elab.Tactic.BVDecide.Frontend.BVDecide.ReifiedBVPred | [
"Option.ctorIdx",
"Option.some",
"Lean.Expr",
"Nat.hasNotBit",
"_private.Lean.Elab.Tactic.BVDecide.Frontend.BVDecide.ReifiedBVPred.0.Lean.Elab.Tactic.BVDecide.Frontend.ReifiedBVPred.mkBinPred._sparseCasesOn_1",
"Option"
] | false |
_private.Lean.Elab.Tactic.BVDecide.Frontend.BVDecide.Reflect.0.Lean.Elab.Tactic.BVDecide.Frontend.LemmaM.withBVLogicalCache.match_1 | Lean.Elab.Tactic.BVDecide.Frontend.BVDecide.Reflect | [
"Unit.unit",
"Lean.Elab.Tactic.BVDecide.Frontend.ReifiedBVLogical",
"Option.casesOn",
"Option.some",
"Option.none",
"Unit",
"Option"
] | false |
Mathlib.Tactic.AtomM.Recurse.Config.zetaDelta | Mathlib.Util.AtomM.Recurse | [
"Bool",
"Mathlib.Tactic.AtomM.Recurse.Config"
] | true |
Std.DTreeMap.Internal.Impl.insertMin!._sunfold | Std.Data.DTreeMap.Internal.Operations | [
"Std.DTreeMap.Internal.Impl.inner",
"instOfNatNat",
"Std.DTreeMap.Internal.Impl.minView!.match_1",
"Unit",
"Std.DTreeMap.Internal.Impl.leaf",
"Nat",
"Std.DTreeMap.Internal.Impl.insertMin!",
"Std.DTreeMap.Internal.Impl.balanceL!",
"OfNat.ofNat",
"Std.DTreeMap.Internal.Impl"
] | false |
_private.Std.Data.Internal.List.Associative.0.Std.Internal.List.Const.minKey?_modifyKey_beq._simp_1_1 | Std.Data.Internal.List.Associative | [
"Option.eq_some_iff_get_eq",
"Option.some",
"Exists",
"Bool.true",
"Option.get",
"propext",
"Bool",
"Option.isSome",
"Eq",
"Option"
] | false |
Std.Net.SocketAddressV6.mk.noConfusion | Std.Net.Addr | [
"Std.Net.SocketAddressV6.noConfusion",
"Std.Net.IPv6Addr",
"Std.Net.SocketAddressV6.mk",
"id",
"UInt16",
"Std.Net.SocketAddressV6",
"Eq"
] | false |
CategoryTheory.Abelian.SpectralObject.zero₂ | Mathlib.Algebra.Homology.SpectralObject.Basic | [
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Abelian.SpectralObject._proof_8",
"CategoryTheory.Abelian.SpectralObject.H",
"PartialOrder.toPreorder",
"CategoryTheory.Functor.category",
"CategoryTheory.Abelian",
"CategoryTheory.Composa... | true |
_private.Mathlib.NumberTheory.ModularForms.NormTrace.0.ModularForm.eq_const_of_weight_zero₀._simp_1_6 | Mathlib.NumberTheory.ModularForms.NormTrace | [
"AddGroup.toSubtractionMonoid",
"sub_eq_zero",
"HSub.hSub",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubNegMonoid.toSub",
"AddGroup",
"instHSub",
"AddGroup.toSubNegMonoid",
"propext",
"Zero.toOfNat0",
"OfNat.ofNat",
"NegZeroClass.toZero",
"Eq"
] | false |
IO.Process.SpawnArgs.inheritEnv._default | Init.System.IO | [
"id",
"Bool.true",
"Bool"
] | false |
PartialEquiv.trans' | Mathlib.Logic.Equiv.PartialEquiv | [
"PartialEquiv.trans'._proof_4",
"PartialEquiv.target",
"PartialEquiv",
"Function.comp",
"Membership.mem",
"PartialEquiv.symm",
"PartialEquiv.trans'._proof_3",
"PartialEquiv.source",
"PartialEquiv.toFun",
"PartialEquiv.mk",
"Eq",
"Set.instMembership",
"PartialEquiv.trans'._proof_2",
"Partia... | true |
IsLocalHomeomorph.localInverseAt_apply_self | Mathlib.Topology.IsLocalHomeomorph | [
"IsLocalHomeomorph.self_mem_localInverseAt_target",
"PartialEquiv.target",
"IsLocalHomeomorph.localInverseAt",
"IsLocalHomeomorph.apply_self_mem_localInverseAt_source",
"Membership.mem",
"OpenPartialHomeomorph.toFun'",
"IsLocalHomeomorph.apply_self_mem_localInverseAt_source._simp_1",
"IsLocalHomeomorp... | true |
Std.Internal.IO.Process.ResourceUsageStats.messagesSent | Std.Internal.Async.Process | [
"UInt64",
"Std.Internal.IO.Process.ResourceUsageStats"
] | true |
Perfection.instCommSemiring._proof_21 | Mathlib.RingTheory.Perfection | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Semigroup.toMul",
"Perfection.instCommSemiring._proof_10",
"Nat.Prime",
"HMul.hMul",
"Perfection",
"Perfection.instCommMonoid",
"Perfection.instCommSemiring._proof_12",
"CommSemiring.toSemiring",
"Subsemiring.toCommSemiring._proof_1",
"Add.mk",
"Perf... | false |
CategoryTheory.Functor.PreOneHypercoverDenseData.multicospanShape | Mathlib.CategoryTheory.Sites.DenseSubsite.OneHypercoverDense | [
"CategoryTheory.Functor",
"CategoryTheory.Functor.PreOneHypercoverDenseData.I₁",
"CategoryTheory.Functor.PreOneHypercoverDenseData",
"Sigma.fst",
"Prod.fst",
"CategoryTheory.Limits.MulticospanShape.mk",
"CategoryTheory.Limits.MulticospanShape",
"Prod",
"Prod.snd",
"CategoryTheory.Functor.PreOneHyp... | true |
FiberBundleCore.rec | Mathlib.Topology.FiberBundle.Basic | [
"Set.instSProd",
"SProd.sprod",
"Set.univ",
"instTopologicalSpaceProd",
"Membership.mem",
"FiberBundleCore.mk",
"Set.instInter",
"Prod.fst",
"Inter.inter",
"TopologicalSpace",
"ContinuousOn",
"IsOpen",
"Prod",
"FiberBundleCore",
"Eq",
"Set.instMembership",
"Prod.snd",
"Set"
] | false |
Asymptotics.IsEquivalent.mono | Mathlib.Analysis.Asymptotics.AsymptoticEquivalent | [
"PartialOrder.toPreorder",
"HSub.hSub",
"Preorder.toLE",
"AddCommGroup.toAddGroup",
"LE.le",
"SubNegMonoid.toSub",
"SeminormedAddCommGroup.toNorm",
"Asymptotics.IsEquivalent",
"instHSub",
"AddGroup.toSubNegMonoid",
"SeminormedAddCommGroup.toAddCommGroup",
"Pi.instSub",
"NormedAddCommGroup.to... | true |
Sylow.noConfusionType | Mathlib.GroupTheory.Sylow | [
"Sylow",
"PartialOrder.toPreorder",
"IsPGroup",
"Group",
"Preorder.toLE",
"Membership.mem",
"Subtype",
"Subgroup",
"LE.le",
"Sylow.casesOn",
"Nat",
"Subgroup.instPartialOrder",
"HEq",
"Subgroup.toGroup",
"Eq",
"SetLike.instMembership",
"Subgroup.instSetLike"
] | false |
_private.Lean.Elab.MutualDef.0.Lean.Elab.Term.MutualClosure.mkClosureForAux._unsafe_rec | Lean.Elab.MutualDef | [
"Pure.pure",
"Lean.Core.instMonadTraceCoreM",
"Lean.Elab.Term.MutualClosure.ClosureState",
"Lean.instBEqFVarId",
"Lean.MessageData",
"Unit.unit",
"Inhabited.default",
"Lean.Elab.Term.instMonadMacroAdapterTermElabM",
"Bool.not",
"Lean.LocalDecl.ldecl",
"_private.Lean.Elab.MutualDef.0.Lean.Elab.Te... | false |
Distribution.IsVanishingOn.disjoint_dsupport | Mathlib.Analysis.Distribution.Support | [
"Eq.mpr",
"ChainCompletePartialOrder.instOfCompleteLattice",
"Distribution.dsupport",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"congrArg",
"Compl.compl",
"Set.subset_compl_iff_disjoint_right",
"setOf",
"Set.sUnion",
"Disjoint",
"SemilatticeInf.toPartialOrder",
"id",
"BiheytingAlgeb... | true |
_private.Mathlib.Tactic.Translate.TagUnfoldBoundary.0.Mathlib.Tactic.Translate.elabInsertCastAux | Mathlib.Tactic.Translate.TagUnfoldBoundary | [
"Applicative.toSeqLeft",
"Pure.pure",
"Lean.instMonadEnvOfMonadLift",
"Lean.instantiateMVars",
"_private.Mathlib.Tactic.Translate.TagUnfoldBoundary.0.Mathlib.Tactic.Translate.CastKind.mkProof",
"Lean.MonadError.mk",
"Mathlib.Tactic.Translate.applyReplacementFun",
"Lean.instMonadExceptOfExceptionCoreM"... | true |
CategoryTheory.Triangulated.TStructure.isIso_truncLE_map_iff | Mathlib.CategoryTheory.Triangulated.TStructure.TruncLEGT | [
"CategoryTheory.IsIso",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.Additive",
"CategoryTheory.Triangulated.TStructure.isIso_truncLT_map_iff",
"CategoryTheory.shiftFunctor",
"Membership.mem",
"Exists",
"CategoryTheory.Functor.id",
"Int",
"Int.instAddMonoid",
... | true |
Quotient.outRelEmbedding_apply | Mathlib.Order.RelIso.Basic | [
"Quotient.lift₂",
"Quotient.out",
"Setoid",
"RelEmbedding",
"Quotient",
"HasEquiv.Equiv",
"instHasEquivOfSetoid",
"Quotient.outRelEmbedding",
"Eq.refl",
"Eq",
"DFunLike.coe",
"RelEmbedding.instFunLike"
] | true |
ContinuousLinearMap.coprod_apply | Mathlib.Topology.Algebra.Module.ContinuousLinearMap.PiProd | [
"ContinuousLinearMap.funLike",
"instTopologicalSpaceProd",
"Prod.fst",
"AddCommMonoid",
"ContinuousLinearMap",
"TopologicalSpace",
"instHAdd",
"HAdd.hAdd",
"ContinuousLinearMap.coprod",
"Semiring",
"Eq.refl",
"AddCommSemigroup.toAddCommMagma",
"Module",
"ContinuousAdd",
"Prod",
"Prod.i... | true |
Std.HashMap.getKey!_union_of_not_mem_left | Std.Data.HashMap.Lemmas | [
"Membership.mem",
"Std.HashMap",
"Std.DHashMap.getKey!_union_of_not_mem_left",
"Std.HashMap.instUnion",
"LawfulHashable",
"Std.HashMap.getKey!",
"EquivBEq",
"Inhabited",
"Hashable",
"Union.union",
"Std.HashMap.inner",
"BEq",
"Eq",
"Not",
"Std.HashMap.instMembership"
] | true |
CategoryTheory.NatTrans.shift_app | Mathlib.CategoryTheory.Shift.CommShift | [
"Eq.mpr",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.shiftFunctor",
"id",
"CategoryTheory.Functor.map",
"CategoryTheory.NatTrans.CommShift",
"AddMonoid",
"Cate... | true |
_private.Mathlib.Logic.Denumerable.0.nonempty_denumerable_iff.match_1_1 | Mathlib.Logic.Denumerable | [
"Nonempty.intro",
"Nonempty.casesOn",
"Nonempty",
"Denumerable"
] | false |
List.TProd.elim'.congr_simp | Mathlib.Data.Prod.TProd | [
"instSubsingletonDecidable",
"Decidable",
"Membership.mem",
"Eq.rec",
"Pi.instSubsingleton",
"List.TProd.elim'",
"List",
"List.instMembership",
"Eq.ndrec",
"List.TProd",
"Eq.refl",
"Subsingleton.elim",
"Eq",
"DecidableEq"
] | true |
CategoryTheory.MonoidalCategory.tensorHom_def'_assoc | Mathlib.CategoryTheory.Monoidal.Category | [
"CategoryTheory.Category.assoc",
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.MonoidalCategory",
"Eq.mp",
"id",
"Mathlib.Tactic.Reassoc.eq_whisker'",
"CategoryTheory.MonoidalCategory.tensorHom_def'",
"Cat... | true |
TopologicalSpace.NonemptyCompacts.continuous_singleton | Mathlib.Topology.Sets.VietorisTopology | [
"Continuous",
"TopologicalSpace.NonemptyCompacts",
"TopologicalSpace.NonemptyCompacts.isEmbedding_singleton",
"TopologicalSpace",
"TopologicalSpace.NonemptyCompacts.topology",
"Singleton.singleton",
"TopologicalSpace.NonemptyCompacts.instSingleton",
"Topology.IsEmbedding.continuous"
] | true |
Subarray.array.eq_1 | Init.Data.Slice.Array.Lemmas | [
"Subarray",
"Std.Slice.internalRepresentation",
"Array",
"Std.Slice.Internal.SubarrayData",
"Std.Slice.Internal.SubarrayData.array",
"Eq.refl",
"Eq",
"Subarray.array"
] | true |
stalkSkyscraperSheafAdjunction._proof_1 | Mathlib.Topology.Sheaves.Skyscraper | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"TopologicalSpace.Opens.instPartialOrder",
"TopCat.instCategoryPresheaf",
"PartialOrder.toPreorder",
"CategoryTheory.Functor.category",
"Decidable",
"CategoryTheory.Functor.comp",
"TopologicalSpace.Open... | false |
Std.DTreeMap.minKey?_eq_some_iff_getKey?_eq_self_and_forall | Std.Data.DTreeMap.Lemmas | [
"Std.DTreeMap",
"Ord.mk",
"Option.some",
"Membership.mem",
"Ordering",
"Std.DTreeMap.Internal.Impl.minKey?_eq_some_iff_getKey?_eq_self_and_forall",
"Std.DTreeMap.inner",
"Std.TransCmp",
"Std.DTreeMap.getKey?",
"Std.DTreeMap.instMembership",
"Bool.true",
"And",
"Iff",
"Std.DTreeMap.wf",
"... | true |
Nat.ceil_add_le | Mathlib.Algebra.Order.Floor.Semiring | [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"AddMonoid.toAddSemigroup",
"congrArg",
"LinearOrder",
"covariant_swap_add_of_covariant_add",
"add_le_add",
"PartialOrder.toPreorder",
"IsStrictOrderedRing",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"id... | true |
_private.Mathlib.CategoryTheory.Monoidal.Category.0.CategoryTheory.MonoidalCategory.whisker_exchange._simp_1_1 | Mathlib.CategoryTheory.Monoidal.Category | [
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory.id_tensorHom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.MonoidalCategoryStruct.tensorObj",
"CategoryTheory.Monoida... | false |
CategoryTheory.Functor.PreOneHypercoverDenseData.multicospanIndex | Mathlib.CategoryTheory.Sites.DenseSubsite.OneHypercoverDense | [
"CategoryTheory.Limits.MulticospanShape.snd",
"CategoryTheory.Functor",
"CategoryTheory.Functor.PreOneHypercoverDenseData.p₂",
"Opposite",
"CategoryTheory.Limits.MulticospanShape.L",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.Functor.PreOneHypercoverDenseData.I₁",
"Quiver.Hom.op",
"Ca... | true |
_private.Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap.0.Std.IterM.step_filterM.match_1.eq_2 | Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap | [
"ULift",
"Subtype",
"Subtype.mk",
"Bool.true",
"MonadAttach",
"Bool",
"Eq.refl",
"ULift.up",
"Bool.false",
"Eq",
"MonadAttach.CanReturn",
"Std.IterM.step_filterM.match_1"
] | true |
FormalMultilinearSeries.compChangeOfVariables_blocksFun | Mathlib.Analysis.Analytic.Composition | [
"Finset.univ",
"Composition.mk",
"Composition.length",
"congrArg",
"Finset",
"List.ofFn",
"Composition.blocksFun",
"Fin.isLt",
"Membership.mem",
"FormalMultilinearSeries.compPartialSumSource",
"Eq.rec",
"Fin.mk",
"id",
"Sigma.fst",
"Composition",
"FormalMultilinearSeries.compChangeOfVa... | true |
Set.infinite_of_finite_compl | Mathlib.Data.Set.Finite.Basic | [
"Set.Finite.union",
"congrArg",
"Compl.compl",
"Set.univ",
"Set.Finite",
"Set.instUnion",
"Eq.mp",
"Set.instCompl",
"Set.infinite_univ",
"Set.compl_union_self",
"Infinite",
"Union.union",
"Set.Infinite",
"Set"
] | true |
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