name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
CategoryTheory.Subobject.sup_factors_of_factors_left | Mathlib.CategoryTheory.Subobject.Lattice | [
"CategoryTheory.Subobject.Factors",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"le_sup_left",
"CategoryTheory.Limits.HasImages",
"SemilatticeSup.toMax",
"CategoryTheory.Subobject.semilatticeSup",
"Max.max",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Limits.HasBinaryCo... | true |
CategoryTheory.RelCat.opEquivalence._proof_2 | Mathlib.CategoryTheory.Category.RelCat | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.id",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.RelCat.instLargeCategory",
"CategoryTheory.... | false |
_private.Batteries.Data.String.Lemmas.0.Substring.Raw.Valid.nextn.match_1_1 | Batteries.Data.String.Lemmas | [
"Substring.Raw",
"Substring.Raw.toString",
"instHAppendOfAppend",
"List",
"Substring.Raw.Valid",
"String.toList",
"Char",
"List.instAppend",
"Eq",
"HAppend.hAppend"
] | false |
Equiv.Set.univPi | Mathlib.Logic.Equiv.Set | [
"Set.univ",
"Equiv.Set.univPi._proof_4",
"Membership.mem",
"Equiv.mk",
"Set.Elem",
"Equiv",
"Equiv.Set.univPi._proof_3",
"Subtype.mk",
"Equiv.Set.univPi._proof_1",
"Equiv.Set.univPi._proof_2",
"Set.pi",
"Subtype.val",
"Set.instMembership",
"Set"
] | true |
MeasureTheory.L1.edist_def | Mathlib.MeasureTheory.Function.L1Space.AEEqFun | [
"edist_eq_enorm_sub",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"False",
"MeasureTheory.Lp.edist_def",
"PseudoEMetricSpace.toWeakPseudoEMetricSpace",
"Real",
"MeasureTheory.Measure",
"instHDiv",
"GroupWithZero.toDivisionMonoid",
"InvOneClass.toOne",
"DivInvOneMonoid.toInvOneClass",
"Linear... | true |
CategoryTheory.sheafSections | Mathlib.CategoryTheory.Sites.Sheaf | [
"CategoryTheory.Functor.flip",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.Functor.category",
"CategoryTheory.GrothendieckTopology",
"CategoryTheory.Category.opposite",
"CategoryTheory.Presheaf.IsSheaf",
"CategoryTheory.Sheaf",
"CategoryTheory.ObjectProperty.FullSubcategory.category",
"C... | true |
PMF.bindOnSupport_pure | Mathlib.Probability.ProbabilityMassFunction.Monad | [
"PMF.bindOnSupport_eq_bind",
"congrArg",
"PMF",
"PMF.bind",
"Membership.mem",
"PMF.support",
"PMF.pure",
"True",
"eq_self",
"of_eq_true",
"congrFun'",
"PMF.bindOnSupport",
"PMF.bind_pure",
"Eq",
"Set.instMembership",
"Eq.trans",
"Set"
] | true |
_private.Mathlib.Combinatorics.SimpleGraph.Maps.0.SimpleGraph.support_induce_subset_coe_preimage_support.match_1_1 | Mathlib.Combinatorics.SimpleGraph.Maps | [
"SetRel",
"SimpleGraph.Adj",
"setOf",
"Membership.mem",
"Set.Elem",
"Prod.mk",
"SimpleGraph.support.match_1",
"SimpleGraph",
"Exists.casesOn",
"SimpleGraph.support",
"Exists.intro",
"SimpleGraph.induce",
"Prod",
"Set.instMembership",
"Set"
] | false |
WeierstrassCurve.Jacobian.Point.noConfusion | Mathlib.AlgebraicGeometry.EllipticCurve.Jacobian.Point | [
"CommRing",
"HEq.refl",
"WeierstrassCurve.Jacobian.NonsingularLift",
"WeierstrassCurve.Jacobian",
"WeierstrassCurve.Jacobian.Point",
"WeierstrassCurve.Jacobian.PointClass",
"eq_of_heq",
"Eq.ndrec",
"HEq",
"WeierstrassCurve.Jacobian.Point.casesOn",
"Eq",
"WeierstrassCurve.Jacobian.Point.noConfu... | false |
Subgroup.isCyclic | Mathlib.GroupTheory.SpecificGroups.Cyclic.Basic | [
"zpow_natCast",
"Iff.mpr",
"Eq.mpr",
"not_exists._simp_1",
"MulOne.toOne",
"Int.instDiv",
"DivInvMonoid.toInv",
"zpow_add",
"instHDiv",
"InvOneClass.toOne",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"IsCyclic.exists_generator",
"Bot.isCyclic",
"Monoid.toMulOneClass",
"congrArg",
... | true |
Nat.find_add | Mathlib.Data.Nat.Find | [
"Iff.mpr",
"Eq.mpr",
"congrArg",
"PartialOrder.toPreorder",
"HSub.hSub",
"Preorder.toLE",
"Nat.sub_le_iff_le_add",
"Exists",
"Nat.le_find_iff",
"id",
"Nat.find_le",
"instSubNat",
"Nat.add_le_of_le_sub",
"LE.le",
"instLENat",
"le_antisymm",
"instHAdd",
"instHSub",
"Nat.sub_add_can... | true |
ZeroHom.instSub | Mathlib.Algebra.Group.Hom.Basic | [
"ZeroHom.funLike",
"HSub.hSub",
"Sub.mk",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubtractionMonoid.toSubNegMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"ZeroHom.mk",
"ZeroHom",
"SubNegMonoid.toSub",
"ZeroHom.instSub._proof_1",
"instHSub",
"SubtractionMonoid",
"NegZeroClass.toZero",
"DFunL... | true |
Bool.and_not_self | Init.Data.Bool | [
"Bool.instDecidableForallOfDecidablePred",
"Bool.not",
"of_decide_eq_true",
"id",
"Bool.and",
"instDecidableEqBool",
"Bool.true",
"Bool",
"Eq.refl",
"Bool.false",
"Decidable.decide",
"Eq"
] | true |
AlgebraicGeometry.IsReduced.rec | Mathlib.AlgebraicGeometry.Properties | [
"AlgebraicGeometry.Scheme",
"Opposite",
"CommRingCat.carrier",
"AlgebraicGeometry.PresheafedSpace.carrier",
"TopologicalSpace.Opens.instPartialOrder",
"CommSemiring.toSemiring",
"CommRingCat",
"PartialOrder.toPreorder",
"TopologicalSpace.Opens",
"CommRingCat.instCategory",
"AlgebraicGeometry.IsR... | false |
_private.Mathlib.Algebra.Star.SelfAdjoint.0.skewAdjoint.conjugate._simp_1_1 | Mathlib.Algebra.Star.SelfAdjoint | [
"NegZeroClass.toNeg",
"skewAdjoint.mem_iff",
"AddCommGroup.toAddGroup",
"Membership.mem",
"AddCommGroup",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"StarAddMonoid.toInvolutiveStar",
"skewAdjoint",
"SubtractionCommMonoid.toSubtractionMonoid",
"AddSubgroup",
"Add... | false |
AlgebraicGeometry.Scheme.instIsOverFstOverInferInstanceOverClassId | Mathlib.AlgebraicGeometry.Pullbacks | [
"AlgebraicGeometry.Scheme.canonicallyOverPullback._proof_1",
"CategoryTheory.Limits.pullback",
"AlgebraicGeometry.Scheme",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Limits.pullback.snd",
"CategoryTheory.CategoryStruct.id",
"inferInstance",
"AlgebraicGeomet... | true |
List.forIn'_nil | Init.Data.List.Control | [
"Pure.pure",
"Monad.toApplicative",
"Membership.mem",
"ForIn'.forIn'",
"Applicative.toPure",
"ForInStep",
"List",
"List.instMembership",
"Monad",
"Eq",
"rfl",
"List.nil",
"List.instForIn'InferInstanceMembershipOfMonad"
] | true |
BoolRing.hasForgetToBoolAlg._proof_2 | Mathlib.Algebra.Category.BoolRing | [
"BoolRing.carrier",
"BoolAlg.of",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"BoolRing.booleanRing",
"BoolAlg",
"BoolRing",
"BoolRing.Hom.hom",
"AsBoolAlg",
"id",
"RingHom.asBoolAlg",
"CategoryTheory.CategoryStruct.comp",
"BoolAlg.instCategory",
"Eq.refl",
"BoolAlg.ofHom",
... | false |
cfcₙ_sum._auto_1 | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
_private.Init.Data.List.Sort.Impl.0.List.MergeSort.Internal.mergeSortTR.run.eq_1 | Init.Data.List.Sort.Impl | [
"instHDiv",
"List.MergeSort.Internal.mergeTR",
"Subtype",
"HDiv.hDiv",
"_private.Init.Data.List.Sort.Impl.0.List.MergeSort.Internal.mergeSortTR.run.eq_def",
"instOfNatNat",
"_private.Init.Data.List.Sort.Impl.0.List.MergeSort.Internal.mergeSortTR.run.match_1",
"List.cons",
"Subtype.mk",
"List",
"... | true |
WeierstrassCurve.Affine.Point.instAddCommGroup._proof_7 | Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point | [
"WeierstrassCurve.Affine.Point.instAddZeroClass",
"AddZeroClass.toAddZero",
"Field.toCommRing",
"AddZero.toZero",
"instHAdd",
"HAdd.hAdd",
"WeierstrassCurve.Affine",
"AddZero.toAdd",
"Zero.toOfNat0",
"WeierstrassCurve.Affine.Point",
"add_zero",
"OfNat.ofNat",
"Eq",
"Field",
"DecidableEq"... | false |
AddEquiv.val_neg_piAddUnits_symm_apply | Mathlib.Algebra.Group.Pi.Units | [
"AddUnits.val",
"Pi.instAdd",
"AddMonoid",
"AddEquiv",
"Eq.refl",
"AddUnits.instAdd",
"AddUnits.instNeg",
"Pi.addMonoid",
"AddEquiv.piAddUnits",
"AddUnits.neg",
"AddEquiv.instEquivLike",
"Eq",
"DFunLike.coe",
"Neg.neg",
"AddEquiv.symm",
"EquivLike.toFunLike",
"AddUnits"
] | true |
_private.Init.Data.Iterators.Lemmas.Combinators.FlatMap.0.Std.Iter.step_flatMapAfterM.match_3.eq_3 | Init.Data.Iterators.Lemmas.Combinators.FlatMap | [
"Std.IterStep",
"Std.Iter.step_flatMapAfterM.match_3",
"Std.IterM.IsPlausibleStep",
"Std.IterStep.skip",
"Std.Iterator",
"Subtype.mk",
"Std.IterStep.yield",
"Std.IterM.Step",
"Std.IterStep.done",
"Eq.refl",
"Std.IterM",
"Eq"
] | true |
CategoryTheory.RingObjCat.Hom | Mathlib.CategoryTheory.Monoidal.Ring | [
"CategoryTheory.RingObjCat.Hom.mk",
"CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory",
"CategoryTheory.RingObjCat",
"CategoryTheory.CartesianMonoidalCategory",
"CategoryTheory.BraidedCategory",
"CategoryTheory.Category",
"CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCa... | true |
MeasureTheory.Integrable.integral_norm_condKernel | Mathlib.Probability.Kernel.Disintegration.Integral | [
"MeasureTheory.ae",
"Norm.norm",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"StandardBorelSpace",
"Real",
"MeasureTheory.Measure",
"MeasureTheory.AEStronglyMeasurable.ae_integrable_condKernel_iff",
"Real.instRCLike",
"congrArg",
"Filter.Eventually",
"PseudoMetric... | true |
Std.Http.Internal.Char.qdtext | Std.Internal.Http.Internal.Char | [
"Std.Http.Internal.Char.qdtext.match_1",
"LE.le",
"Bool.true",
"And",
"Unit",
"Char.instLE",
"Bool",
"Bool.or",
"Char",
"Char.instDecidableLe",
"instDecidableAnd",
"Bool.false",
"Decidable.decide",
"Char.ofNat"
] | true |
Matrix.BlockTriangular.mul | Mathlib.LinearAlgebra.Matrix.Block | [
"Eq.mpr",
"Preorder.toLT",
"HMul.hMul",
"Finset.univ",
"congrArg",
"Matrix",
"Finset",
"LinearOrder",
"Matrix.instHMulOfFintypeOfMulOfAddCommMonoid",
"MulZeroClass.zero_mul",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"Finset.sum_eq_zero",
"NonUnitalNonAssocSemiring.toMulZeroCl... | true |
Order.cof_eq_one_iff | Mathlib.SetTheory.Cardinal.Cofinality.Basic | [
"Eq.mpr",
"Cardinal.instOne",
"LE.le.trans_eq",
"Cardinal",
"congrArg",
"PartialOrder.toPreorder",
"isCofinal_singleton_iff",
"_private.Mathlib.SetTheory.Cardinal.Cofinality.Basic.0.Order.cof_eq_one_iff.match_1_1",
"Preorder.toLE",
"Cardinal.mk",
"Exists",
"Eq.mp",
"Set.Elem",
"Cardinal.on... | true |
moduleTopology | Mathlib.Topology.Algebra.Module.ModuleTopology | [
"ContinuousSMul",
"SMul",
"setOf",
"CompleteLattice.toConditionallyCompleteLattice",
"TopologicalSpace.instCompleteLattice",
"TopologicalSpace",
"And",
"ConditionallyCompleteLattice.toConditionallyCompletePartialOrder",
"ConditionallyCompletePartialOrderInf.toInfSet",
"ContinuousAdd",
"InfSet.sI... | true |
Lean.instReprKVMap | Lean.Data.KVMap | [
"Repr.mk",
"Lean.instReprKVMap.repr",
"Lean.KVMap",
"Repr"
] | true |
_private.Mathlib.Algebra.Order.GroupWithZero.Lex.0.MonoidWithZeroHom.snd_mono._simp_1_2 | Mathlib.Algebra.Order.GroupWithZero.Lex | [
"Prod.instLE_mathlib",
"LE.le",
"Prod.fst",
"LE",
"And",
"propext",
"Prod",
"Eq",
"Prod.snd",
"Prod.le_def"
] | false |
Matroid.exists_isBasis._auto_1 | Mathlib.Combinatorics.Matroid.Basic | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.Name.mkStr2",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
AddSubmonoid.comap_surjective_of_injective | Mathlib.Algebra.Group.Submonoid.Operations | [
"PartialOrder.toPreorder",
"AddZeroClass.toAddZero",
"AddSubmonoid.comap",
"AddMonoidHomClass",
"AddSubmonoid",
"AddZeroClass",
"AddSubmonoid.map",
"AddSubmonoid.gciMapComap",
"Function.Injective",
"DFunLike.coe",
"Function.Surjective",
"GaloisCoinsertion.u_surjective",
"AddSubmonoid.instPar... | true |
Nat.count_eq_card_filter_range | Mathlib.Data.Nat.Count | [
"Eq.mpr",
"List.countP",
"congrArg",
"id",
"List.range",
"Finset.range",
"List.countP_eq_length_filter",
"Nat.count.eq_1",
"DecidablePred",
"Nat",
"List.filter",
"Nat.count",
"Finset.card",
"Eq.refl",
"Finset.filter",
"Decidable.decide",
"Eq",
"List.length"
] | true |
ContinuousAffineEquiv.instEquivLike._proof_2 | Mathlib.Topology.Algebra.ContinuousAffineEquiv | [
"Equiv.right_inv",
"AddCommGroup.toAddCommMonoid",
"AddCommGroup.toAddGroup",
"AddCommGroup",
"ContinuousAffineEquiv",
"Equiv.toFun",
"TopologicalSpace",
"Function.RightInverse",
"AddTorsor",
"AffineEquiv.toEquiv",
"ContinuousAffineEquiv.toAffineEquiv",
"Module",
"Ring.toSemiring",
"Ring",... | false |
CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.inverse_map_left_left | Mathlib.CategoryTheory.Comma.Over.Basic | [
"CategoryTheory.Over",
"CategoryTheory.Functor",
"CategoryTheory.Functor.toCostructuredArrow",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Over.Hom.left",
"CategoryTheory.Comma.left",
"CategoryTheory.Functor.comp",
"CategoryTheory.CostructuredArrow.hom",
"CategoryTheory... | true |
Turing.PartrecToTM2.instDecidableEqCont'.decEq._proof_2 | Mathlib.Computability.TuringMachine.ToPartrec | [
"Turing.PartrecToTM2.Cont'",
"Turing.PartrecToTM2.Cont'.cons₂",
"Eq",
"rfl"
] | false |
Filter.NeBot.coprodᵢ | Mathlib.Order.Filter.Pi | [
"Filter.coprodᵢ",
"Iff.mpr",
"Filter.NeBot",
"Exists",
"Filter.coprodᵢ_neBot_iff",
"Exists.intro",
"Nonempty",
"Filter"
] | true |
Lean.Elab.Tactic.Do.ProofMode.elabMLeft._regBuiltin.Lean.Elab.Tactic.Do.ProofMode.elabMLeft_1 | Lean.Elab.Tactic.Do.ProofMode.LeftRight | [
"Lean.Elab.Tactic.tacticElabAttribute",
"IO",
"Unit",
"Lean.Elab.Tactic.Tactic",
"Lean.Name.mkStr6",
"Lean.Name.mkStr4",
"Lean.KeyedDeclsAttribute.addBuiltin",
"Lean.Elab.Tactic.Do.ProofMode.elabMLeft"
] | false |
Lean.Linter.UnusedVariables.FVarDefinition.noConfusion | Lean.Linter.UnusedVariables | [
"Lean.Syntax",
"Lean.FVarId",
"Lean.Linter.UnusedVariables.FVarDefinition.casesOn",
"Array",
"Eq.ndrec",
"Lean.Name",
"Eq.refl",
"Lean.Linter.UnusedVariables.FVarDefinition.noConfusionType",
"Lean.Options",
"Eq",
"Lean.Linter.UnusedVariables.FVarDefinition"
] | false |
PiTensorProduct.instSemiring._proof_11 | Mathlib.RingTheory.PiTensorProduct | [
"HMul.hMul",
"AddMonoid.toAddSemigroup",
"PiTensorProduct.instNonUnitalSemiring",
"Algebra",
"PiTensorProduct.instSemiring._proof_4",
"Algebra.toModule",
"NonUnitalNonAssocSemiring.toMul",
"NonUnitalSemiring.toNonUnitalNonAssocSemiring",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",... | false |
_private.Mathlib.Data.Ordmap.Invariants.0.Ordnode.splitMin'.match_1.splitter | Mathlib.Data.Ordmap.Invariants | [
"Ordnode",
"Prod.mk",
"Ordnode.splitMin'.match_1",
"Prod"
] | true |
Finset.nsmul | Mathlib.Algebra.Group.Pointwise.Finset.Basic | [
"Finset",
"SMul",
"SMul.mk",
"nsmulRec",
"Nat",
"Finset.zero",
"Finset.add",
"Add",
"DecidableEq",
"Zero"
] | true |
MulPosReflectLE.toMulPosReflectLT | Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic | [
"Iff.mpr",
"False",
"le_of_mul_le_mul_of_pos_right",
"Preorder.toLT",
"MulPosReflectLT",
"HMul.hMul",
"MulZeroClass.toMul",
"False.elim",
"PartialOrder.toPreorder",
"lt_self_iff_false._simp_1",
"MulZeroClass",
"PartialOrder",
"Eq.mp",
"Subtype",
"LT.lt.le",
"LE.le.lt_of_ne",
"Contrav... | true |
BitVec.intMin_sle | Init.Data.BitVec.Lemmas | [
"instDecidableTrue",
"congrArg",
"Decidable.decide.congr_simp",
"Int.decLe",
"BitVec",
"Int",
"LE.le",
"BitVec.toInt_intMin_le",
"decide_true",
"Bool.true",
"BitVec.intMin",
"Nat",
"True",
"eq_self",
"eq_true",
"Bool",
"of_eq_true",
"BitVec.toInt",
"congrFun'",
"Decidable.decid... | true |
Std.Time.Formats.leanDate | Std.Time.Format | [
"Std.Time.FormatPart",
"Std.Time.FormatPart.string",
"Std.Time.Modifier.d",
"Std.Time.FormatPart.modifier",
"instOfNatNat",
"Sum.inl",
"List.cons",
"Std.Time.Awareness.any",
"Std.Time.GenericFormat.mk",
"Nat",
"Std.Time.Number",
"Std.Time.Modifier.MorL",
"Std.Time.Text",
"Std.Time.GenericF... | true |
AlgebraicGeometry.Scheme.Pullback.pullbackFstιToV_snd | Mathlib.AlgebraicGeometry.Pullbacks | [
"CategoryTheory.Limits.pullbackSymmetry",
"AlgebraicGeometry.Scheme.Pullback.pullbackFstιToV._proof_3",
"AlgebraicGeometry.Scheme.GlueData.ι",
"CategoryTheory.Limits.limit.π",
"CategoryTheory.GlueData.diagram",
"AlgebraicGeometry.Scheme.Pullback.v._proof_1",
"CategoryTheory.Category.assoc",
"CategoryT... | true |
Set.mem_finsetSum | Mathlib.Algebra.Group.Pointwise.Set.BigOperators | [
"Eq.mpr",
"_private.Mathlib.Algebra.Group.Pointwise.Set.BigOperators.0.Set.mem_finsetSum.match_1_2",
"Function.update",
"Finset.mem_insert_self",
"AddMonoid.toAddSemigroup",
"Iff.of_eq",
"congrArg",
"Finset",
"False.elim",
"AddMonoid.toAddZeroClass",
"Classical.propDecidable",
"Membership.mem"... | true |
MvPolynomial.supported_le_supported_iff._simp_1 | Mathlib.Algebra.MvPolynomial.Supported | [
"Nontrivial",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"CommSemiring.toSemiring",
"AddMonoidAlgebra.algebra",
"PartialOrder.toPreorder",
"Finsupp.instAddMonoid",
"Preorder.toLE",
"Nat.instAddMonoid",
"Algebra.id",
"HasSubset.Subset",
"LE.le",
"CommSemiring",
"Subalgebra.instPar... | false |
Complex.ofReal_one | Mathlib.Data.Complex.Basic | [
"Real",
"Complex.ofReal",
"Real.instOne",
"One.toOfNat1",
"Complex",
"OfNat.ofNat",
"Eq",
"Complex.instOne",
"rfl"
] | true |
Metric.preimage_mul_left_closedEBall | Mathlib.Topology.MetricSpace.IsometricSMul | [
"instSMulOfMul",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"Metric.preimage_smul_closedEBall",
"IsIsometricSMul",
"Group",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"PseudoEMetricSpace",
"Group.toDivInvM... | true |
_private.Init.Data.BitVec.Bitblast.0.BitVec.msb_srem._simp_1_6 | Init.Data.BitVec.Bitblast | [
"Decidable",
"decide_eq_false_iff_not",
"propext",
"Bool",
"Bool.false",
"Decidable.decide",
"Eq",
"Not"
] | false |
Lean.Compiler.LCNF.CompilerM.Context.noConfusionType | Lean.Compiler.LCNF.CompilerM | [
"Lean.Compiler.LCNF.CompilerM.Context.casesOn",
"Lean.Compiler.LCNF.ConfigOptions",
"Lean.Compiler.LCNF.Phase",
"Eq",
"Lean.Compiler.LCNF.CompilerM.Context"
] | false |
Multiset.decidableDexistsMultiset._proof_1 | Mathlib.Data.Multiset.Defs | [
"Multiset.decidableDexistsMultiset.match_3",
"Membership.mem",
"Exists",
"Multiset",
"Subtype",
"Subtype.mk",
"Multiset.instMembership",
"And",
"Iff",
"Multiset.mem_attach",
"And.intro",
"Iff.intro",
"Exists.intro",
"Subtype.val",
"Multiset.attach",
"Multiset.decidableDexistsMultiset.m... | false |
ExteriorAlgebra.ι_eq_zero_iff._simp_1 | Mathlib.LinearAlgebra.ExteriorAlgebra.Basic | [
"CommRing",
"ExteriorAlgebra.ι_eq_zero_iff",
"Semiring.toModule",
"QuadraticMap.instZero",
"Ring.toNonAssocRing",
"ExteriorAlgebra",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"instAlgebraCliffordAlgebra",
"QuadraticForm",
"LinearMap.instFunLike",
"AddCommGroup",
"Algebra.toM... | false |
_private.Std.Data.DHashMap.Lemmas.0.Std.DHashMap.get?_insertIfNew._simp_1_1 | Std.Data.DHashMap.Lemmas | [
"Membership.mem",
"Std.DHashMap.instMembership",
"Std.DHashMap.mem_iff_contains",
"Bool.true",
"Std.DHashMap.contains",
"propext",
"Bool",
"Hashable",
"BEq",
"Eq",
"Std.DHashMap"
] | false |
Std.Iterators.HetT.bind._proof_3 | Std.Data.Iterators.Lemmas.Equivalence.HetT | [
"Std.Internal.Small",
"Std.Iterators.HetT.Property",
"Exists",
"inferInstance",
"Subtype",
"Std.Iterators.HetT",
"And"
] | false |
iSup_himp_eq | Mathlib.Order.CompleteBooleanAlgebra | [
"iInf",
"CompleteLattice.toLattice",
"congrArg",
"iSup",
"le_himp_iff._simp_1",
"le_iInf_iff._simp_1",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"iSup_le_iff._simp_2",
"GeneralizedHeytingAlgebra.toHImp",
"SemilatticeInf.toMin",
"LE.le",
"inf_iSup_eq",
"... | true |
_private.Mathlib.Algebra.CharP.Pi.0.CharP.pi.match_1 | Mathlib.Algebra.CharP.Pi | [
"Nonempty.intro",
"Nonempty.casesOn",
"Nonempty"
] | false |
Std.IterM.DefaultConsumers.forIn'_eq_match_step | Init.Data.Iterators.Lemmas.Consumers.Monadic.Loop | [
"Pure.pure",
"PSigma.snd",
"Eq.mpr",
"Std.IterM.DefaultConsumers.forIn'_eq_match_step.match_3",
"bind_congr",
"Std.IterStep",
"Std.IterStep.successor",
"Std.IterM.IsPlausibleIndirectOutput.indirect",
"Std.IterM.DefaultConsumers.forIn'.match_1",
"congrArg",
"Std.Shrink",
"Std.IterM.DefaultConsu... | true |
_private.Mathlib.Algebra.Order.Module.Field.0.Mathlib.Meta.Positivity.evalSMul._sparseCasesOn_9 | Mathlib.Algebra.Order.Module.Field | [
"Lean.Name.rec",
"Nat.ne_of_beq_eq_false",
"String",
"Nat.shiftRight",
"Nat.hasNotBit",
"instOfNatNat",
"Lean.Name.num",
"Lean.Name.ctorIdx",
"Lean.Name.str",
"Lean.Name.anonymous",
"Nat.land",
"Nat",
"Bool",
"Lean.Name",
"Eq.refl",
"OfNat.ofNat",
"Bool.false"
] | false |
Finset.inf'_sup_distrib_right | Mathlib.Data.Finset.Lattice.Fold | [
"Eq.mpr",
"Lattice.toSemilatticeSup",
"Finset.inf'",
"congrArg",
"Finset.inf'_congr",
"Finset",
"Membership.mem",
"Eq.rec",
"SemilatticeSup.toMax",
"DistribLattice.toLattice",
"id",
"DistribLattice",
"sup_comm",
"Finset.instSetLike",
"Max.max",
"True",
"eq_self",
"Finset.Nonempty",... | true |
Valuation.IsUniformizer.val_lt_one | Mathlib.RingTheory.Valuation.Discrete.Basic | [
"Valuation.IsRankOneDiscrete.generator_lt_one",
"Units.val",
"GroupWithZero.toMonoidWithZero",
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"Valuation.IsUniformizer",
"Preorder.toLT",
"InvOneClass.toOne",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
... | true |
Real.cos_two_mul_eq_one_sub | Mathlib.Analysis.Complex.Trigonometric | [
"Real",
"HMul.hMul",
"Complex.cos",
"Real.cos",
"congrArg",
"Real.instSub",
"Complex.sin",
"Nat.instAtLeastTwoHAddOfNat",
"HSub.hSub",
"Complex.cos_two_mul_eq_one_sub",
"Complex.instMul",
"instOfNatNat",
"Complex.instNatCast",
"Complex.ofReal",
"Monoid.toPow",
"Real.instOne",
"Real.i... | true |
OrderMonoidHom.comp_apply | Mathlib.Algebra.Order.Hom.Monoid | [
"OrderMonoidHom",
"OrderMonoidHom.comp",
"MulOneClass",
"OrderMonoidHom.instFunLike",
"Eq",
"DFunLike.coe",
"rfl",
"Preorder"
] | true |
CategoryTheory.Limits.PreservesCofilteredLimitsOfSize.mk._flat_ctor | Mathlib.CategoryTheory.Limits.Preserves.Filtered | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.PreservesCofilteredLimitsOfSize",
"CategoryTheory.IsCofiltered",
"CategoryTheory.Limits.PreservesCofilteredLimitsOfSize.mk",
"CategoryTheory.Limits.PreservesLimitsOfShape",
"CategoryTheory.Category"
] | false |
_private.Mathlib.Algebra.Group.Action.Faithful.0.FaithfulSMul.trans._simp_1_1 | Mathlib.Algebra.Group.Action.Faithful | [
"MulOne.toOne",
"instHSMul",
"instSMulOfMul",
"IsScalarTower",
"SMul",
"MulOne.toMul",
"FaithfulSMul",
"MulOneClass.toMulOne",
"propext",
"faithfulSMul_iff_injective_smul_one",
"One.toOfNat1",
"HSMul.hSMul",
"Function.Injective",
"MulOneClass",
"OfNat.ofNat",
"Eq"
] | false |
TopCat.uliftFunctorFullyFaithful._proof_1 | Mathlib.Topology.Category.TopCat.ULift | [
"ULift.topologicalSpace",
"Continuous.comp'",
"Continuous",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ConcreteCategory.hom",
"TopCat.instCategory",
"ContinuousMap",
"ULift",
"continuous_uliftUp",
"Function.comp",
"ContinuousMap.instContinuousMapClass",
"TopCat.u... | false |
Lean.Meta.ParamInfo.backDeps | Lean.Meta.Basic | [
"Array",
"Lean.Meta.ParamInfo",
"Nat"
] | true |
LinearMap.BilinForm.dualSubmoduleToDual._proof_3 | Mathlib.LinearAlgebra.BilinearForm.DualLattice | [
"LinearMap.BilinForm.dualSubmoduleParing_spec",
"Submodule",
"RingHom.instRingHomClass",
"CommRing",
"instHSMul",
"Semiring.toModule",
"HMul.hMul",
"IsScalarTower.right",
"Algebra.algebraMap",
"LinearMap.BilinForm",
"congrArg",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"... | false |
OrderType.instNontrivial | Mathlib.Order.Types.Defs | [
"Nontrivial",
"OrderType.type_ne_zero",
"OrderType.instOne",
"Exists",
"instInhabitedPUnit",
"Ne",
"Nontrivial.mk",
"PUnit",
"instNonemptyOfInhabited",
"Exists.intro",
"One.toOfNat1",
"Zero.toOfNat0",
"OrderType",
"OrderType.instZero",
"OfNat.ofNat",
"PUnit.instLinearOrder"
] | true |
_private.Mathlib.Order.ConditionallyCompleteLattice.Basic.0.MonotoneOn.csInf_eq_of_subset_of_forall_exists_le._simp_1_2 | Mathlib.Order.ConditionallyCompleteLattice.Basic | [
"Set.mem_image",
"Membership.mem",
"Exists",
"And",
"propext",
"Set.image",
"Eq",
"Set.instMembership",
"Set"
] | false |
CategoryTheory.BasedNatTrans.comp_toNatTrans | Mathlib.CategoryTheory.FiberedCategory.BasedCategory | [
"CategoryTheory.NatTrans.vcomp",
"CategoryTheory.BasedFunctor",
"CategoryTheory.BasedNatTrans",
"CategoryTheory.BasedNatTrans.toNatTrans",
"CategoryTheory.instCategoryObj",
"CategoryTheory.BasedCategory.obj",
"CategoryTheory.BasedNatTrans.comp",
"CategoryTheory.BasedFunctor.toFunctor",
"Eq.refl",
... | true |
Option.getD.eq_2 | Init.Data.Array.Lemmas | [
"Option.getD",
"Option.none",
"Eq.refl",
"Eq"
] | true |
Filter.Eventually.choice | Mathlib.Order.Filter.Basic | [
"Exists.nonempty",
"Filter.NeBot",
"Filter.Eventually",
"Function.sometimes_spec",
"Exists",
"Function.sometimes",
"Filter.Eventually.mono",
"Classical.choose_spec",
"Filter.Eventually.exists",
"Exists.intro",
"Classical.choose",
"Nonempty",
"_private.Mathlib.Order.Filter.Basic.0.Filter.Even... | true |
MulActionHom.instAddZeroClass | Mathlib.GroupTheory.GroupAction.Hom | [
"Add.mk",
"SMul",
"AddZeroClass.mk",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"MulActionHom.mk",
"MulActionHom.instAddZeroClass._proof_1",
"instFunLikeMulActionHom",
"AddZero.toZero",
"instHAdd",
"AddZeroClass",
"Pi.instAdd",
"HAdd.hAdd",
"DistribSMul",
"AddZero.toAdd",
... | true |
CategoryTheory.prodFunctorToFunctorProd_obj | Mathlib.CategoryTheory.Products.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.prodFunctorToFunctorProd",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.prod'",
"Prod.fst",
"CategoryTheory.prod'",
"Eq.refl",
"Prod",
"Eq",
"Prod.snd",
"CategoryTheory.Functor.obj",
"CategoryTheory.Category"
] | true |
_private.Batteries.Data.List.Lemmas.0.List.getElem_idxOf_eq_idxOfNth_add._proof_1_78 | Batteries.Data.List.Lemmas | [
"cond",
"_private.Batteries.Data.List.Lemmas.0.List.getElem_idxOf_eq_idxOfNth_add._proof_1_28",
"Int.Linear.eq_of_core",
"List.idxsOf",
"Int.Linear.not_eq_norm_expr",
"List.countP",
"Lean.Grind.CommRing.le_norm_expr",
"Lean.Grind.instOrderedRingInt",
"Lean.RArray.leaf",
"GetElem",
"False",
"Le... | false |
_private.Batteries.Data.Random.MersenneTwister.0.Batteries.Random.MersenneTwister.State.twist._proof_4 | Batteries.Data.Random.MersenneTwister | [
"_private.Batteries.Data.Random.MersenneTwister.0.Batteries.Random.MersenneTwister.State.twist._proof_1",
"id",
"Fin.val",
"Batteries.Random.MersenneTwister.State",
"Batteries.Random.MersenneTwister.State.index",
"Batteries.Random.MersenneTwister.Config",
"Nat",
"LT.lt",
"Decidable.byContradiction",... | false |
Lean.PersistentHashMap.Node._sizeOf_2_eq | Lean.Data.PersistentHashMap | [
"Lean.PersistentHashMap.Entry",
"congrArg",
"Lean.PersistentHashMap.Node",
"Array.rec",
"instOfNatNat",
"Lean.PersistentHashMap.Node._sizeOf_3",
"Array.mk.sizeOf_spec",
"Array._sizeOf_inst",
"Array",
"List",
"instHAdd",
"HAdd.hAdd",
"Lean.PersistentHashMap.Node._sizeOf_3_eq",
"Nat",
"Lis... | false |
CategoryTheory.MorphismProperty.Under.instHasInitialTopOfContainsIdentities | Mathlib.CategoryTheory.Limits.MorphismProperty | [
"CategoryTheory.MorphismProperty.Under",
"CategoryTheory.MorphismProperty",
"CategoryTheory.MorphismProperty.instCompleteBooleanAlgebra",
"CategoryTheory.MorphismProperty.IsMultiplicative.instTop",
"CategoryTheory.MorphismProperty.Comma.instCategory",
"CategoryTheory.MorphismProperty.Under.mk",
"Categor... | true |
List.toFinset_range'_1 | Mathlib.Order.Interval.Finset.Nat | [
"List.mem_toFinset",
"Eq.mpr",
"Preorder.toLT",
"congrArg",
"Finset",
"Iff.rfl",
"List.range'",
"Finset.ext",
"Preorder.toLE",
"Nat.instLocallyFiniteOrder",
"Membership.mem",
"id",
"Finset.Ico",
"instOfNatNat",
"LE.le",
"instLENat",
"List.toFinset",
"List",
"instHAdd",
"And",
... | true |
HomotopicalAlgebra.fibration_unop_iff | Mathlib.AlgebraicTopology.ModelCategory.CategoryWithCofibrations | [
"Opposite",
"Quiver.opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"Quiver.Hom.unop",
"HomotopicalAlgebra.Cofibration",
"HomotopicalAlgebra.instCategoryWithCofibrationsOpposite",
"iff_self",
"Iff",
"congr",
"True",
"of_eq_true",
"HomotopicalAlgebra.cofibrati... | true |
MeasureTheory.Measure.mkMetric_mono | Mathlib.MeasureTheory.Measure.Hausdorff | [
"Eq.mpr",
"instHSMul",
"MeasureTheory.Measure",
"instSMulOfMul",
"Set.Ici",
"IsScalarTower.right",
"congrArg",
"CommSemiring.toSemiring",
"HEq.refl",
"NeZero.charZero_one",
"nhdsWithin",
"ENNReal.instCharZero",
"PartialOrder.toPreorder",
"Preorder.toLE",
"MeasureTheory.Measure.mkMetric",... | true |
CategoryTheory.InjectiveResolution.descFOne._proof_1 | Mathlib.CategoryTheory.Abelian.Injective.Resolution | [
"CategoryTheory.Abelian.toPreadditive",
"HomologicalComplex.instCategory",
"Nat.instOne",
"HomologicalComplex.Hom.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CochainComplex.single₀",
"CategoryTheory.InjectiveResolution.ι",
"AddRightCancelSemigroup.toAddSemigroup",
"AddCancelMonoid... | false |
Lean.Grind.CommRing.Poly.combine.go.eq_1 | Init.Grind.Ring.CommSolver | [
"Lean.Grind.CommRing.Poly",
"Lean.Grind.CommRing.Poly.combine.go",
"Lean.Grind.CommRing.Poly.concat",
"instOfNatNat",
"Nat",
"Eq.refl",
"OfNat.ofNat",
"Eq"
] | true |
Batteries.instReprRBColor | Batteries.Data.RBMap.Basic | [
"Repr.mk",
"Batteries.RBColor",
"Batteries.instReprRBColor.repr",
"Repr"
] | true |
Std.Internal.UV.System.PasswdInfo.casesOn | Std.Internal.UV.System | [
"UInt64",
"String",
"Std.Internal.UV.System.PasswdInfo",
"Std.Internal.UV.System.PasswdInfo.mk",
"Std.Internal.UV.System.PasswdInfo.rec",
"Option"
] | false |
cfcHom.congr_simp | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | [
"spectrum",
"Ring.toNonAssocRing",
"CommSemiring.toSemiring",
"IsTopologicalSemiring",
"ContinuousStar",
"ContinuousMap",
"cfcHom",
"PseudoMetricSpace.toUniformSpace",
"Algebra",
"Membership.mem",
"Eq.rec",
"Set.Elem",
"Algebra.id",
"ContinuousMap.instSemiringOfIsTopologicalSemiring",
"N... | true |
ProofWidgets.Penrose.DiagramProps.embeds | ProofWidgets.Component.PenroseDiagram | [
"ProofWidgets.Html",
"String",
"Array",
"ProofWidgets.Penrose.DiagramProps",
"Prod"
] | true |
ArithmeticFunction.carmichael_mul | Mathlib.NumberTheory.ArithmeticFunction.Carmichael | [
"Nat.lcm",
"Nat.Coprime",
"Nat.instMulZeroClass",
"HMul.hMul",
"ArithmeticFunction.instFunLikeNat",
"Eq.rec",
"instMulNat",
"ArithmeticFunction.carmichael",
"Nat",
"Nat.Coprime.lcm_eq_mul",
"ArithmeticFunction",
"Eq",
"DFunLike.coe",
"ArithmeticFunction.carmichael_lcm",
"MulZeroClass.toZ... | true |
inv_nonpos' | Mathlib.Algebra.Order.Field.Basic | [
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"PartialOrder.toPreorder",
"IsStrictOrderedRing",
"Preorder.toLE",
"DivisionMonoid.toDivInvOneMonoid",
"PartialOrder",
"LE.le",
"Field.toSemifield",
"instDistribOfSemiring",
"Iff",
"Inv.inv",
"Semifield.toDivisionSemirin... | true |
Std.Http.URI.Builder.setPort | Std.Internal.Http.Data.URI.Basic | [
"Std.Http.URI.Builder.userInfo",
"Std.Http.URI.Builder.query",
"Std.Http.URI.Builder.scheme",
"Std.Http.URI.Port.value",
"UInt16",
"Std.Http.URI.Builder",
"Std.Http.URI.Builder.pathSegments",
"Std.Http.URI.Builder.fragment",
"Std.Http.URI.Builder.host",
"Std.Http.URI.Builder.mk"
] | true |
_private.Mathlib.MeasureTheory.Covering.Besicovitch.0.Mathlib.Meta.Positivity.evalBesicovitchSatelliteConfigR._sparseCasesOn_1 | Mathlib.MeasureTheory.Covering.Besicovitch | [
"Lean.Level.ctorIdx",
"Nat.ne_of_beq_eq_false",
"Nat.shiftRight",
"Lean.Level.mvar",
"Lean.Level.param",
"Nat.hasNotBit",
"Lean.Level.imax",
"instOfNatNat",
"Lean.Level",
"Nat.land",
"Lean.Level.zero",
"Nat",
"Bool",
"Lean.Level.rec",
"Lean.Name",
"Eq.refl",
"Lean.Level.succ",
"OfN... | false |
InnerProductSpace.Core.inner_self_ne_zero | Mathlib.Analysis.InnerProductSpace.Defs | [
"InnerProductSpace.Core",
"InnerProductSpace.Core.toInner'",
"Inner.inner",
"AddCommGroup.toAddCommMonoid",
"NormedField.toField",
"AddCommGroup",
"InnerProductSpace.Core.inner_self_eq_zero",
"Iff.not",
"Ne",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"Subtracti... | true |
CategoryTheory.Grp.instGrpObj._proof_2 | Mathlib.CategoryTheory.Monoidal.Cartesian.Grp | [
"Eq.mpr",
"CategoryTheory.Grp.instMonoidalCategory",
"CategoryTheory.GrpObj.inv",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Mon.Hom.hom",
"CategoryTheory.Grp.instMonObj",
"CategoryTheory.Grp.instCategory",
"CategoryTheory.CategoryStruct.id",
"CategoryThe... | false |
MulRingNorm.mulRingNormEquivAbsoluteValue.congr_simp | Mathlib.Analysis.Normed.Unbundled.SpectralNorm | [
"Nontrivial",
"Real.partialOrder",
"Real",
"Ring.toNonAssocRing",
"MulRingNorm",
"Real.semiring",
"Equiv",
"MulRingNorm.mulRingNormEquivAbsoluteValue",
"Eq.refl",
"Ring.toSemiring",
"Eq",
"Ring",
"AbsoluteValue"
] | true |
_private.Mathlib.Algebra.Homology.SpectralObject.Basic.0.CategoryTheory.Abelian.SpectralObject._proof_9 | Mathlib.Algebra.Homology.SpectralObject.Basic | [
"False",
"False.elim",
"Classical.byContradiction",
"Nat.not_le_eq",
"noConfusion_of_Nat",
"False.casesOn",
"instOfNatNat",
"LE.le",
"instLENat",
"instHAdd",
"HAdd.hAdd",
"Nat.le_zero_eq",
"Nat",
"Nat.ctorIdx",
"Lean.Grind.intro_with_eq",
"instAddNat",
"OfNat.ofNat",
"eq_false'",
... | false |
IsFractionRing.definition._proof_1._@.Mathlib.RingTheory.Localization.FractionRing.1935392398._hygCtx._hyg.2 | Mathlib.RingTheory.Localization.FractionRing | [
"Iff.mpr",
"IsLocalization.sec",
"IsDomain",
"CommRing",
"IsDomain.to_noZeroDivisors",
"CommSemiring.toSemiring",
"IsFractionRing",
"Algebra",
"Membership.mem",
"nonZeroDivisors",
"Subtype",
"Ne",
"Prod.fst",
"MulZeroOneClass.toMulOneClass",
"instMulZeroOneClassOfSemiring",
"CommRing.t... | false |
HShiftRight.mk | Init.Prelude | [
"HShiftRight.mk",
"outParam",
"HShiftRight"
] | true |
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