name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
AlgebraicGeometry.PresheafedSpace.GlueData.ιInvApp | Mathlib.Geometry.RingedSpace.PresheafedSpace.Gluing | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.MultispanShape.prod",
"AlgebraicGeometry.PresheafedSpace.GlueData.ιInvApp._proof_1",
"CategoryTheory.Limits.hasLimitsOfShapeOfHasLimits",
"Opposite",
"CategoryTheory.Limits.WalkingMultispan",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CategoryTheory.... | true |
Real.toNNReal_lt_toNNReal_iff | Mathlib.Data.NNReal.Defs | [
"Real",
"Preorder.toLT",
"Real.instZero",
"PartialOrder.toPreorder",
"and_iff_left",
"Real.instLT",
"NNReal",
"NNReal.instPartialOrder",
"And",
"Iff",
"LT.lt",
"Iff.trans",
"Zero.toOfNat0",
"OfNat.ofNat",
"Real.toNNReal_lt_toNNReal_iff'",
"Real.toNNReal"
] | true |
isLocallyClosed_Ioi | Mathlib.Topology.Order.IsLocallyClosed | [
"Set.Ioi",
"LinearOrder",
"PartialOrder.toPreorder",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"IsOpen.isLocallyClosed",
"IsLocallyClosed",
"ClosedIicTopology",
"TopologicalSpace",
"isOpen_Ioi",
"instDistribLatticeOfLinearOrder",
"Lattice.toSemilatticeInf"
] | true |
SimpleGraph.adjMatrix_hadamard_one | Mathlib.Combinatorics.SimpleGraph.AdjMatrix | [
"MulOne.toOne",
"MulZeroClass.toMul",
"Matrix",
"SimpleGraph.Adj",
"DecidableRel",
"SimpleGraph.adjMatrix_hadamard_diagonal",
"MulZeroOneClass",
"Matrix.hadamard",
"MulZeroOneClass.toMulOneClass",
"SimpleGraph",
"MulOneClass.toMulOne",
"SimpleGraph.adjMatrix",
"One.toOfNat1",
"Matrix.one",... | true |
ENNReal.funMulInvSnorm | Mathlib.MeasureTheory.Integral.MeanInequalities | [
"Real",
"MeasureTheory.Measure",
"instHDiv",
"HMul.hMul",
"CommSemiring.toSemiring",
"ENNReal.instPowReal",
"Real.instDivInvMonoid",
"HDiv.hDiv",
"ENNReal.instCommSemiring",
"instDistribOfSemiring",
"Real.instOne",
"MeasurableSpace",
"Inv.inv",
"HPow.hPow",
"Distrib.toMul",
"ENNReal",
... | true |
List.countP_attach | Init.Data.List.Attach | [
"List.countP",
"congrArg",
"List.map",
"Function.comp",
"Membership.mem",
"Subtype",
"funext",
"List",
"List.instMembership",
"Nat",
"True",
"eq_self",
"Bool",
"of_eq_true",
"Function.comp_apply",
"congrFun'",
"Eq.symm",
"Subtype.val",
"Eq",
"_private.Init.Data.List.Attach.0.Li... | true |
CategoryTheory.fieldEndOfFiniteDimensional._proof_5 | Mathlib.CategoryTheory.Preadditive.Schur | [
"DivisionRing.zpow_neg'",
"CategoryTheory.instDivisionRingEndOfHasKernelsOfSimple",
"inferInstance",
"Int",
"Nat.cast",
"CategoryTheory.End",
"CategoryTheory.Preadditive",
"DivisionRing.zpow",
"Inv.inv",
"Nat",
"CategoryTheory.Preadditive.preadditiveHasZeroMorphisms",
"CategoryTheory.Limits.Ha... | false |
Set.ite_inter_inter | Mathlib.Order.BooleanAlgebra.Set | [
"Iff.mpr",
"Set.ext",
"Eq.mpr",
"False",
"Set.ite",
"congrArg",
"False.elim",
"Classical.propDecidable",
"Membership.mem",
"Set.instUnion",
"id",
"Set.instInter",
"Or.casesOn",
"Inter.inter",
"And.casesOn",
"SDiff.sdiff",
"And",
"Iff",
"Classical.or_iff_not_imp_left",
"And.intr... | true |
Pi.basis._proof_1 | Mathlib.LinearAlgebra.StdBasis | [
"RingHomCompTriple",
"Semiring",
"RingHom.id",
"RingHomCompTriple.ids",
"Semiring.toNonAssocSemiring"
] | false |
Stream'.get.eq_1 | Mathlib.Data.Stream.Init | [
"Stream'",
"Stream'.get",
"Nat",
"Eq.refl",
"Eq"
] | true |
Int16.toNatClampNeg | Init.Data.SInt.Basic | [
"Int16",
"Nat",
"Int16.toInt",
"Int.toNat"
] | true |
_private.Mathlib.Algebra.GroupWithZero.NonZeroDivisors.0.mk_mem_nonZeroDivisors_associates.match_1_1 | Mathlib.Algebra.GroupWithZero.NonZeroDivisors | [
"HMul.hMul",
"MulZeroClass.toMul",
"Exists",
"Ne",
"CommMonoidWithZero.toMonoidWithZero",
"And.casesOn",
"And",
"Exists.casesOn",
"MonoidWithZero.toMulZeroOneClass",
"CommMonoidWithZero",
"And.intro",
"Exists.intro",
"Zero.toOfNat0",
"MulZeroOneClass.toMulZeroClass",
"OfNat.ofNat",
"Eq... | false |
Lean.Compiler.LCNF.FindUsed.Context._sizeOf_inst | Lean.Compiler.LCNF.ReduceArity | [
"Lean.Compiler.LCNF.FindUsed.Context",
"SizeOf.mk",
"Lean.Compiler.LCNF.FindUsed.Context._sizeOf_1",
"SizeOf"
] | false |
AddCommGrpCat.toCommGrp | Mathlib.Algebra.Category.Grp.EquivalenceGroupAddGroup | [
"AddCommGrpCat.toCommGrp._proof_1",
"CategoryTheory.Functor",
"AddCommGrpCat.toCommGrp._proof_2",
"Equiv.instEquivLike",
"CategoryTheory.CategoryStruct.toQuiver",
"AddCommGrpCat.instCategory",
"MonoidHom",
"Quiver.Hom",
"CategoryTheory.Functor.mk",
"AddMonoid.toAddZeroClass",
"AddMonoidHom.toMul... | true |
PseudoEMetricSpace.ofRiemannianMetric._proof_1 | Mathlib.Geometry.Manifold.Riemannian.Basic | [
"Real",
"NormedSpace",
"Real.denselyNormedField",
"instAddCommGroupTangentSpace",
"instIsTopologicalAddGroupTangentSpace",
"AddCommGroup.toAddGroup",
"instTopologicalSpaceTangentSpace",
"TopologicalSpace",
"ModelWithCorners",
"TangentSpace",
"Real.normedField",
"DenselyNormedField.toNontrivial... | false |
SimpleGraph.edge_le | Mathlib.Combinatorics.SimpleGraph.Operations | [
"Set.diff_subset_iff._simp_1",
"SimpleGraph.edge",
"Sym2.mk",
"congrArg",
"SimpleGraph.fromEdgeSet",
"SimpleGraph.Adj",
"Membership.mem",
"Set.instUnion",
"Set.instSingletonSet",
"SimpleGraph.fromEdgeSet_le._simp_1",
"HasSubset.Subset",
"LE.le",
"SimpleGraph.edgeSet",
"Sym2.mem_diagSet._si... | true |
Lean.JsonRpc.ResponseError.message | Lean.Data.JsonRpc | [
"String",
"Lean.JsonRpc.ResponseError"
] | true |
Complex.cos_sub_pi_div_two | Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic | [
"instHDiv",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Real.pi",
"HMul.hMul",
"Complex.cos_pi_div_two",
"Complex.cos",
"AddGroupWithOne.toAddGroup",
"congrArg",
"AddMonoid.toAddZeroClass",
"Complex.sin",
"Nat.instAtLeastTwoHAddOfNat",
"Complex.instNormedField",
"AddGroupWithOne.toAddM... | true |
TopologicalSpace.Compacts.topology | Mathlib.Topology.Sets.VietorisTopology | [
"TopologicalSpace.vietoris",
"TopologicalSpace",
"TopologicalSpace.induced",
"SetLike.coe",
"TopologicalSpace.Compacts.instSetLike",
"TopologicalSpace.Compacts",
"Set"
] | true |
_private.Mathlib.MeasureTheory.MeasurableSpace.Invariants.0.MeasurableSpace.measurable_invariants_dom._simp_1_2 | Mathlib.MeasureTheory.MeasurableSpace.Invariants | [
"And",
"propext",
"Eq.symm",
"Eq",
"forall_and"
] | false |
_private.Lean.Elab.MutualInductive.0.Lean.Elab.Command.FinalizeContext.mk.inj | Lean.Elab.MutualInductive | [
"Lean.Elab.Command.InductiveElabStep2",
"Lean.MetavarContext",
"_private.Lean.Elab.MutualInductive.0.Lean.Elab.Command.FinalizeContext.mk.noConfusion",
"Lean.Expr",
"Lean.Meta.MetaM",
"Array",
"List",
"And",
"_private.Lean.Elab.MutualInductive.0.Lean.Elab.Command.FinalizeContext.mk",
"And.intro",
... | true |
String.sliceFrom.eq_1 | Init.Data.String.Basic | [
"String.toSlice",
"String.sliceFrom",
"String",
"String.Slice.sliceFrom",
"String.Pos.toSlice",
"String.Slice",
"String.Pos",
"Eq.refl",
"Eq"
] | true |
_private.Mathlib.Data.Int.Interval.0.Finset.Ioo_succ_succ._simp_1_1 | Mathlib.Data.Int.Interval | [
"Preorder.toLT",
"Finset",
"Membership.mem",
"Finset.mem_Ioo",
"And",
"Finset.instSetLike",
"LT.lt",
"propext",
"LocallyFiniteOrder",
"Eq",
"Finset.Ioo",
"SetLike.instMembership",
"Preorder"
] | false |
CategoryTheory.Functor.mapConeMapConeInv | Mathlib.CategoryTheory.Limits.Cones | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cone",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.id",
"CategoryTheory.Iso",
"CategoryTheory.Equivalence.functor",
"CategoryTheory.Functor.asEquivalence",
"CategoryTheory.Limits.Cone.functorialityEquivalence",
"CategoryTheory.Iso.app",
"... | true |
Descriptive.Tree.tree_eq_bot._simp_1 | Mathlib.SetTheory.Descriptive.Tree | [
"Membership.mem",
"Subtype",
"Bot.bot",
"Descriptive.tree",
"List",
"CompleteSublattice.instSetLike",
"Descriptive.Tree.tree_eq_bot",
"CompleteSublattice",
"propext",
"CompleteBooleanAlgebra.toCompleteLattice",
"CompleteSublattice.instBot",
"Eq",
"Descriptive.instSetLikeSubtypeSetListMemComp... | false |
Convexity.StdSimplex.rec | Mathlib.Geometry.Convex.ConvexSpace.Defs | [
"Finsupp.instLE",
"One",
"AddMonoid.toAddZeroClass",
"Finsupp.sum",
"AddZeroClass.toAddZero",
"LE.le",
"LE",
"AddCommMonoid",
"AddZero.toZero",
"Convexity.StdSimplex",
"Convexity.StdSimplex.mk",
"One.toOfNat1",
"Zero.toOfNat0",
"AddCommMonoid.toAddMonoid",
"Finsupp.instZero",
"OfNat.of... | false |
_private.Init.Data.List.MapIdx.0.List.exists_of_mem_mapFinIdx._simp_1_2 | Init.Data.List.MapIdx | [
"Exists",
"Subtype.exists",
"Subtype",
"Subtype.mk",
"propext",
"Eq"
] | false |
ContinuousAddMonoidHom.rec | Mathlib.Topology.Algebra.ContinuousMonoidHom | [
"Continuous",
"ZeroHom.toFun",
"ContinuousAddMonoidHom",
"AddMonoid.toAddZeroClass",
"AddMonoidHom.toZeroHom",
"AddZeroClass.toAddZero",
"TopologicalSpace",
"AddZero.toZero",
"ContinuousAddMonoidHom.mk",
"AddMonoid",
"AddMonoidHom"
] | false |
InformationTheory.wrapped._@.Mathlib.InformationTheory.KullbackLeibler.Basic.2839050664._hygCtx._hyg.8 | Mathlib.InformationTheory.KullbackLeibler.Basic | [
"MeasureTheory.Measure",
"InformationTheory.definition._@.Mathlib.InformationTheory.KullbackLeibler.Basic.2839050664._hygCtx._hyg.8",
"Subtype",
"_private.Mathlib.InformationTheory.KullbackLeibler.Basic.0.InformationTheory.wrapped._proof_1._@.Mathlib.InformationTheory.KullbackLeibler.Basic.2839050664._hygCtx.... | false |
AddSubgroup.relIndex_comap | Mathlib.GroupTheory.Index | [
"AddSubgroup.comap",
"Eq.mpr",
"congrArg",
"AddSubgroup.index",
"AddMonoid.toAddZeroClass",
"AddMonoidHom.range",
"AddSubgroup.toAddGroup",
"Membership.mem",
"AddMonoidHom.map_range",
"AddZeroClass.toAddZero",
"AddSubgroup.range_subtype",
"AddSubgroup.relIndex.eq_1",
"id",
"Subtype",
"Ad... | true |
List.subperm.cons | Mathlib.Data.List.Perm.Subperm | [
"Iff.mpr",
"List.cons",
"List",
"List.Subperm",
"List.subperm_cons"
] | true |
OpenAddSubgroup.toOpens_inf._simp_1 | Mathlib.Topology.Algebra.OpenSubgroup | [
"OpenAddSubgroup.instInfOpenAddSubgroup",
"TopologicalSpace.Opens.instCompleteLattice",
"TopologicalSpace.Opens",
"CompleteLattice.toConditionallyCompleteLattice",
"OpenAddSubgroup.toOpens",
"SemilatticeInf.toMin",
"OpenAddSubgroup.toOpens_inf",
"TopologicalSpace",
"OpenAddSubgroup",
"AddGroup",
... | false |
Filter.tendsto_mul_self_atTop | Mathlib.Order.Filter.AtTopBot.Ring | [
"HMul.hMul",
"IsOrderedRing",
"Filter.tendsto_id",
"PartialOrder.toPreorder",
"PartialOrder",
"id",
"instDistribOfSemiring",
"Filter.atTop",
"Distrib.toMul",
"Filter.Tendsto",
"Semiring",
"Filter.Tendsto.atTop_mul_atTop₀",
"instHMul"
] | true |
WeierstrassCurve.twoTorsionPolynomial.eq_1 | Mathlib.AlgebraicGeometry.EllipticCurve.Weierstrass | [
"WeierstrassCurve.b₄._proof_1",
"CommRing",
"HMul.hMul",
"CommSemiring.toSemiring",
"AddGroupWithOne.toAddMonoidWithOne",
"WeierstrassCurve.b₂",
"AddMonoidWithOne.toNatCast",
"WeierstrassCurve.b₄",
"WeierstrassCurve.twoTorsionPolynomial",
"WeierstrassCurve",
"Cubic.mk",
"instDistribOfSemiring"... | true |
_private.Mathlib.Order.Monotone.MonovaryOrder.0.instIsStrictTotalOrderMonovaryOrder._simp_4 | Mathlib.Order.Monotone.MonovaryOrder | [
"And",
"Iff",
"propext",
"Eq",
"iff_and_self"
] | false |
IsLocalMinOn.hasFDerivWithinAt_nonneg | Mathlib.Analysis.Calculus.LocalExtr.Basic | [
"NormedCommRing.toNormedRing",
"AddGroup.toSubtractionMonoid",
"NegZeroClass.toNeg",
"IsLocalMaxOn.hasFDerivWithinAt_nonpos",
"Real.partialOrder",
"Real.instLE",
"Real",
"Semiring.toModule",
"NormedRing.toRing",
"NormedSpace",
"Real.denselyNormedField",
"Real.instZero",
"AddCommGroup.toAddCo... | true |
_private.Std.Data.Internal.List.Associative.0.Std.Internal.List.Const.length_filter_key_eq_length_iff._simp_1_1 | Std.Data.Internal.List.Associative | [
"Option.guard",
"List",
"List.filter",
"Bool",
"List.filterMap",
"Eq.symm",
"Eq",
"List.filterMap_eq_filter"
] | false |
HasFiniteFPowerSeriesOnBall.continuousOn | Mathlib.Analysis.Analytic.CPolynomialDef | [
"NormedCommRing.toSeminormedCommRing",
"NormedSpace.toIsBoundedSMul",
"UniformContinuousConstSMul.to_continuousConstSMul",
"NormedSpace",
"FormalMultilinearSeries",
"NormedAddCommGroup.toMetricSpace",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"AddMon... | true |
Int.zmultiples_natAbs | Mathlib.Algebra.Group.Subgroup.ZPowers.Basic | [
"AddSubgroup.zmultiples_le._simp_1",
"Dvd.dvd",
"congrArg",
"and_self",
"_private.Mathlib.Algebra.Group.Subgroup.ZPowers.Basic.0.Int.zmultiples_natAbs._simp_1_3",
"PartialOrder.toPreorder",
"AddSubgroup.instPartialOrder",
"Preorder.toLE",
"Membership.mem",
"dvd_refl._simp_1",
"Int",
"LE.le",
... | true |
MvPolynomial.isWeightedHomogeneous_zero | Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous | [
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"MvPolynomial.weightedHomogeneousSubmodule",
"Semiring.toModule",
"AddMonoidAlgebra.addAddCommMonoid",
"CommSemiring.toSemiring",
"Finsupp.instAddMonoid",
"Nat.instAddMonoid",
"AddCommMonoid",
"CommSemiring",
"Submodule.zero_mem",
"Nat",
"... | true |
symmDiff_right_inj._simp_1 | Mathlib.Order.SymmDiff | [
"Lattice.toSemilatticeSup",
"symmDiff_right_inj",
"SemilatticeSup.toMax",
"GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra",
"GeneralizedBooleanAlgebra",
"propext",
"GeneralizedCoheytingAlgebra.toLattice",
"GeneralizedBooleanAlgebra.toSDiff",
"Eq",
"symmDiff"
] | false |
_private.Batteries.Tactic.GeneralizeProofs.0.Batteries.Tactic.GeneralizeProofs.MAbs.findProof?._sparseCasesOn_1 | Batteries.Tactic.GeneralizeProofs | [
"Nat.ne_of_beq_eq_false",
"Option.ctorIdx",
"Nat.shiftRight",
"Option.some",
"Nat.hasNotBit",
"Option.rec",
"instOfNatNat",
"Nat.land",
"Option.none",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Bool.false",
"Option"
] | false |
Part.some_dom._simp_1 | Mathlib.Data.Part | [
"Part.some",
"True",
"eq_true",
"Part.Dom",
"Eq",
"Part.some_dom"
] | false |
CategoryTheory.HasProjectiveDimensionLT.recOn | Mathlib.CategoryTheory.Abelian.Projective.Dimension | [
"CategoryTheory.Abelian",
"LE.le",
"instLENat",
"Nat",
"CategoryTheory.Abelian.Ext",
"CategoryTheory.HasProjectiveDimensionLT",
"CategoryTheory.HasProjectiveDimensionLT.mk'",
"CategoryTheory.HasProjectiveDimensionLT.rec",
"Subsingleton",
"CategoryTheory.HasExt.standard",
"CategoryTheory.Category... | false |
Aesop.elabForwardRuleTerm | Aesop.Forward.Match | [
"Lean.NameMap",
"Lean.Elab.Term.LevelMVarErrorInfo",
"Lean.Elab.Term.Context.mk",
"Lean.Elab.Term.State.mk",
"Lean.MVarIdMap",
"ReaderT",
"Lean.Meta.State",
"Lean.Elab.AutoBoundImplicitContext",
"instMonadLiftT",
"List.instEmptyCollection",
"Lean.MVarId",
"Lean.Expr",
"Lean.Meta.MetaM",
"I... | true |
Nat.reduceLTLE | Lean.Meta.Tactic.Simp.BuiltinSimprocs.Nat | [
"Pure.pure",
"cond",
"_private.Lean.Meta.Tactic.Simp.BuiltinSimprocs.Nat.0.Nat.NatOffset",
"Lean.Expr.isAppOfArity",
"ReaderT",
"Lean.Meta.Simp.Step",
"Lean.Meta.State",
"Lean.Meta.Simp.evalPropStep",
"instMonadLiftT",
"HSub.hSub",
"Lean.Expr.appArg!",
"Lean.Meta.Simp.MethodsRef",
"Lean.Name... | true |
Lean.instBEqDeclaration | Lean.Declaration | [
"BEq.mk",
"Lean.Declaration",
"Lean.instBEqDeclaration.beq",
"BEq"
] | true |
Stream'.Seq.append_nil | Mathlib.Data.Seq.Basic | [
"Eq.mpr",
"Stream'.Seq",
"Stream'.Seq.coinduction2",
"congrArg",
"Option.some",
"Exists",
"id",
"Prod.mk",
"Stream'.Seq.nil",
"Stream'.Seq.recOn",
"And",
"And.intro",
"Stream'.Seq.cons",
"Exists.intro",
"Stream'.Seq.destruct_cons",
"Eq.ndrec",
"Stream'.Seq1",
"Stream'.Seq.cons_appe... | true |
MeasurableEquiv.refl_toEquiv | Mathlib.MeasureTheory.MeasurableSpace.Embedding | [
"MeasurableEquiv.toEquiv",
"MeasurableEquiv.refl",
"Equiv",
"MeasurableSpace",
"Eq.refl",
"Equiv.refl",
"Eq"
] | true |
Polynomial.divModByMonicAux | Mathlib.Algebra.Polynomial.Div | [
"Polynomial",
"Polynomial.Monic",
"PSigma.mk",
"Polynomial.divModByMonicAux._unary",
"Prod",
"PSigma",
"Ring.toSemiring",
"Ring"
] | true |
_private.Mathlib.Analysis.Distribution.TemperateGrowth.0.Function.hasTemperateGrowth_one_add_norm_sq_rpow._proof_1_2 | Mathlib.Analysis.Distribution.TemperateGrowth | [
"Nat.instAtLeastTwoHAddOfNat",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat.instNeZeroSucc",
"Nat",
"instAddNat",
"OfNat.ofNat",
"Nat.AtLeastTwo"
] | false |
DirSupInacc.of_isEmpty._simp_1 | Mathlib.Order.DirSupClosed | [
"DirSupInacc.of_isEmpty",
"IsEmpty",
"DirSupInacc",
"True",
"eq_true",
"Eq",
"Preorder",
"Set"
] | false |
Lean.Parser.Tactic.MRefinePat._sizeOf_2_eq | Std.Tactic.Do.Syntax | [
"congrArg",
"instOfNatNat",
"List.rec",
"List.cons",
"List",
"instHAdd",
"Lean.Parser.Tactic.MRefinePat",
"List.cons.sizeOf_spec",
"Lean.Parser.Tactic.MRefinePat._sizeOf_inst",
"HAdd.hAdd",
"Lean.Parser.Tactic.MRefinePat._sizeOf_2",
"Nat",
"List._sizeOf_inst",
"SizeOf.sizeOf",
"instAddNa... | false |
_private.Mathlib.MeasureTheory.Covering.Differentiation.0.VitaliFamily.ae_eventually_measure_pos._simp_1_2 | Mathlib.MeasureTheory.Covering.Differentiation | [
"Filter.Eventually",
"Filter.Frequently",
"Filter.not_eventually",
"propext",
"Eq",
"Not",
"Filter"
] | false |
PowerSeries.IsWeierstrassDivisorAt.isWeierstrassDivisionAt_div_mod | Mathlib.RingTheory.PowerSeries.WeierstrassPreparation | [
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"Mathlib.Tactic.Ring.Common.neg_zero",
"Eq.mpr",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Submodule",
"Mathlib.Tactic.Ring.Common.neg_mul",
"PowerSeries.coeff_trunc",
"CommRing",
"Mathlib.Meta.NormNum.instAddMonoidWithOne",
"inst... | true |
MvPowerSeries.LinearTopology.hasBasis_nhds_zero | Mathlib.RingTheory.MvPowerSeries.LinearTopology | [
"Filter.instMembership",
"Iff.mpr",
"Eq.mpr",
"Filter.HasBasis.pi_self",
"NegZeroClass.toNeg",
"SetLike.mem_coe._simp_1",
"Finsupp.instLE",
"Nat.instMulZeroClass",
"Nat.instLattice",
"Lattice.toSemilatticeSup",
"MvPowerSeries.instZero",
"Semiring.toModule",
"LinearOrderedCommMonoidWithZero.t... | true |
_private.Init.Prelude.0.Nat.mod_lt.match_1_3 | Init.Prelude | [
"False",
"HEq.refl",
"False.elim",
"noConfusion_of_Nat",
"instOfNatNat",
"Nat.le.step",
"Nat.le",
"Nat",
"LT.lt",
"Nat.ctorIdx",
"Nat.zero",
"Eq.refl",
"HEq",
"Nat.le.refl",
"instLTNat",
"Nat.le.casesOn",
"OfNat.ofNat",
"Nat.succ",
"Eq",
"Nat.casesOn"
] | false |
ULift.down_sdiff | Mathlib.Order.ULift | [
"ULift",
"ULift.instSDiff_mathlib",
"SDiff.sdiff",
"SDiff",
"Eq",
"ULift.down",
"rfl"
] | true |
AddCon.quotientKerEquivRange.match_1 | Mathlib.GroupTheory.Congruence.Basic | [
"AddMonoidHom.instAddMonoidHomClass",
"AddCon.addZeroClass",
"AddCon.kerLift",
"Subtype.casesOn",
"Membership.mem",
"AddZeroClass.toAddZero",
"Subtype",
"AddMonoidHom.mrange",
"AddSubmonoid",
"Subtype.mk",
"AddZeroClass",
"Exists.casesOn",
"AddMonoidHomClass.toAddHomClass",
"Exists.intro",... | false |
WithBot.instMonoidWithZero._proof_8 | Mathlib.Algebra.Order.Ring.WithTop | [
"Nontrivial",
"WithBot.instMonoidWithZero._proof_6",
"WithBot.instMonoidWithZero._proof_5",
"MulOne.toOne",
"Semigroup.toMul",
"WithBot",
"HMul.hMul",
"MulZeroClass.toMul",
"WithBot.zero",
"WithBot.instMonoidWithZero._aux_3",
"SemigroupWithZero.toSemigroup",
"WithBot.instMonoidWithZero._proof_... | false |
AlgebraicGeometry.Scheme.instIsStableUnderCompositionProetalePrecoverage | Mathlib.AlgebraicGeometry.Sites.Proetale | [
"AlgebraicGeometry.Scheme",
"AlgebraicGeometry.Scheme.instIsStableUnderCompositionProetalePrecoverage._proof_1",
"AlgebraicGeometry.Scheme.proetalePrecoverage",
"CategoryTheory.Precoverage.IsStableUnderComposition",
"AlgebraicGeometry.Scheme.instCategory"
] | true |
Function.isPeriodicPt_minimalPeriod | Mathlib.Dynamics.PeriodicPts.Defs | [
"Eq.mpr",
"congrArg",
"Classical.propDecidable",
"Membership.mem",
"dif_pos",
"id",
"Function.IsPeriodicPt.instDecidableOfDecidableEq",
"Function.isPeriodicPt_zero",
"instOfNatNat",
"dif_neg",
"dite",
"Function.IsPeriodicPt",
"GT.gt",
"And",
"And.right",
"Nat",
"Function.periodicPts"... | true |
Qq.unpackParensIdent._unsafe_rec | Qq.Match | [
"Lean.TSyntax",
"Lean.Syntax.matchesIdent",
"Lean.Syntax.isOfKind",
"Option.some",
"Lean.TSyntax.mk",
"Lean.Syntax",
"Lean.TSyntax.raw",
"instDecidableEqBool",
"instOfNatNat",
"List.cons",
"Lean.Name.anonymous",
"Qq.unpackParensIdent._unsafe_rec",
"Bool.true",
"Option.none",
"Lean.Syntax... | false |
PowerSeries.order_monomial | Mathlib.RingTheory.PowerSeries.Order | [
"Eq.mpr",
"MvPowerSeries.instZero",
"Semiring.toModule",
"instCharZeroENat",
"instAddMonoidWithOneENat",
"SemilinearMapClass.distribMulActionSemiHomClass",
"ENat.instNatCast",
"instTopENat",
"instLinearOrderENat",
"congrArg",
"CommSemiring.toSemiring",
"AddMonoid.toAddZeroClass",
"LinearMap.... | true |
_private.Init.Data.Int.DivMod.Lemmas.0.Int.add_one_tdiv_of_pos._proof_1_15 | Init.Data.Int.DivMod.Lemmas | [
"Int.instDiv",
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"Lean.Omega.Int.le_of_not_lt",
"instHDiv",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int.add_congr",
"Int.... | false |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.getKey!_inter._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 |
Real.pi_div_two_le_arcsin._simp_1 | Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse | [
"Real.instLE",
"Real",
"instHDiv",
"Real.pi",
"Real.arcsin",
"Real.instDivInvMonoid",
"Nat.instAtLeastTwoHAddOfNat",
"HDiv.hDiv",
"instOfNatNat",
"LE.le",
"Real.instOne",
"Nat.instNeZeroSucc",
"Nat",
"Real.pi_div_two_le_arcsin",
"propext",
"DivInvMonoid.toDiv",
"One.toOfNat1",
"OfN... | false |
instAlgebraPointedContMDiffMap._proof_6 | Mathlib.Geometry.Manifold.DerivationBundle | [
"NormedCommRing.toNormedRing",
"instHSMul",
"HMul.hMul",
"chartedSpaceSelf",
"NormedSpace",
"instAlgebraPointedContMDiffMap._aux_3",
"CommSemiring.toSemiring",
"PseudoMetricSpace.toUniformSpace",
"RingHom",
"NormedAlgebra.id",
"NormedField.toField",
"NormedRing.toNonUnitalNormedRing",
"instA... | false |
ConvexCone.carrier | Mathlib.Geometry.Convex.Cone.Basic | [
"SMul",
"PartialOrder",
"AddCommMonoid",
"ConvexCone",
"Semiring",
"Set"
] | true |
IsDenseInducing.tendsto_comap_nhds_nhds | Mathlib.Topology.DenseEmbedding | [
"Filter.map_mono",
"IsDenseInducing.nhds_eq_comap",
"congrArg",
"Filter.map",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Function.comp",
"nhds",
"Filter.map_map",
"Eq.mp",
"Filter.comap_mono",
"IsDenseInducing",
"LE.le",
"TopologicalSpace",
"Filter.Tendsto",
"propext",
"Filter.map_... | true |
Int64.lt_trans | Init.Data.SInt.Lemmas | [
"Eq.mpr",
"_private.Init.Data.SInt.Lemmas.0.Int64.lt_trans._simp_1_1",
"Int64.toInt",
"Int.lt_trans",
"instLTInt64",
"id",
"Int64",
"Int",
"Int.instLTInt",
"implies_congr",
"LT.lt",
"Eq"
] | true |
Aesop.SlotIndex.mk.sizeOf_spec | Aesop.Forward.SlotIndex | [
"Aesop.SlotIndex",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"Aesop.SlotIndex.mk",
"SizeOf.sizeOf",
"instAddNat",
"Eq.refl",
"Aesop.SlotIndex._sizeOf_inst",
"instSizeOfNat",
"OfNat.ofNat",
"Eq"
] | true |
integralClosure.coe_smul | Mathlib.RingTheory.IntegralClosure.Algebra.Basic | [
"Subalgebra.instSetLike",
"CommRing",
"instHSMul",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"AddGroupWithOne.toAddMonoidWithOne",
"Group",
"Algebra",
"instMulSemiringActionSubtypeMemSubalgebraIntegralClosure",
"Algebra.toSMul",
"Membership.mem",
... | true |
CategoryTheory.Bicategory.postcomp | Mathlib.CategoryTheory.Bicategory.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Bicategory.postcomp._proof_4",
"CategoryTheory.Functor.mk",
"CategoryTheory.Bicategory.whiskerRight",
"CategoryTheory.Bicategory.toCategoryStruct",
"CategoryTheory.Bicategory",
"CategoryTheory.CategoryS... | true |
Std.ExtDTreeMap.maxKey?_eq_some_iff_getKey?_eq_self_and_forall | Std.Data.ExtDTreeMap.Lemmas | [
"Std.ExtDTreeMap.getKey?",
"Std.DTreeMap",
"Option.some",
"Membership.mem",
"Ordering",
"Std.ExtDTreeMap.maxKey?",
"Std.TransCmp",
"Bool.true",
"And",
"Iff",
"Std.ExtDTreeMap.inductionOn",
"Std.ExtDTreeMap",
"Bool",
"Ordering.isLE",
"Eq",
"Std.ExtDTreeMap.instMembershipOfTransCmp",
"... | true |
CategoryTheory.Limits.ChosenPullback.LiftStruct.f_p._autoParam | Mathlib.CategoryTheory.Limits.Shapes.Pullback.ChosenPullback | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.Name.mkStr2",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
Module.basisOfFiniteTypeTorsionFree._proof_7 | Mathlib.LinearAlgebra.FreeModule.PID | [
"CommMonoidWithZero.toCommMonoid",
"Eq.mpr",
"Submodule",
"IsDomain",
"CommRing",
"instHSMul",
"IsDomain.to_noZeroDivisors",
"Finset.univ",
"congrArg",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"Finset",
"AddMonoid.toAddZeroClass",
"inst... | false |
Metric.nhds_basis_closedEBall | Mathlib.Topology.EMetricSpace.Defs | [
"Preorder.toLT",
"uniformity_basis_edist_le",
"PartialOrder.toPreorder",
"setOf",
"nhds",
"LE.le",
"PseudoEMetricSpace",
"Prod.fst",
"Filter.HasBasis",
"PseudoEMetricSpace.toEDist",
"PseudoEMetricSpace.toUniformSpace",
"LT.lt",
"ENNReal.instLE",
"ENNReal",
"ENNReal.instPartialOrder",
"... | true |
LinearIndependent.group_smul | Mathlib.LinearAlgebra.LinearIndependent.Basic | [
"Eq.mpr",
"instHSMul",
"smul_assoc",
"congrArg",
"DistribMulAction.toDistribSMul",
"Finset",
"IsScalarTower",
"SMul",
"AddMonoid.toAddZeroClass",
"Group",
"Membership.mem",
"AddZeroClass.toAddZero",
"Eq.mp",
"Group.isUnit",
"id",
"DistribSMul.toSMulZeroClass",
"DivInvMonoid.toMonoid"... | true |
mulRightEmbedding_apply | Mathlib.Algebra.Group.Embedding | [
"HMul.hMul",
"mulRightEmbedding",
"Mul",
"Function.Embedding",
"Eq.refl",
"Function.instFunLikeEmbedding",
"Eq",
"DFunLike.coe",
"IsRightCancelMul",
"instHMul"
] | true |
CategoryTheory.Localization.Construction.LocQuiver.mk.noConfusion | Mathlib.CategoryTheory.Localization.Construction | [
"CategoryTheory.MorphismProperty",
"HEq.refl",
"CategoryTheory.Localization.Construction.LocQuiver",
"id",
"CategoryTheory.Localization.Construction.LocQuiver.mk",
"heq_of_eq",
"CategoryTheory.Localization.Construction.LocQuiver.noConfusion",
"Eq.refl",
"HEq",
"CategoryTheory.Category.toCategorySt... | false |
ContinuousLinearMap.norm_single_le_one | Mathlib.Analysis.Normed.Operator.NormedSpace | [
"Norm.norm",
"ContinuousLinearMap.single",
"Real.instLE",
"Real",
"SeminormedAddCommGroup",
"Pi.addCommMonoid",
"NormedSpace",
"Pi.topologicalSpace",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"Pi.module",
"PseudoMetricSpace.toUniformSpace",
"NormedField.toField",
"LE.le",
"... | true |
Fiber.algEquivQuotient._proof_9 | Mathlib.RingTheory.LocalRing.ResidueField.Fiber | [
"Fiber.algEquivQuotient._proof_3",
"CommRing",
"Algebra.algebraMap",
"Localization.AtPrime.isLocalRing",
"CommSemiring.toSemiring",
"Algebra",
"IsLocalRing.maximalIdeal",
"RingHom",
"instAlgebraLocalizationAlgebraMapSubmonoid",
"Ideal.map",
"Localization",
"Ideal.IsTwoSided",
"Ideal",
"Ide... | false |
Lean.ParseImports.State.recOn | Lean.Elab.ParseImportsFast | [
"Lean.ParseImports.State.mk",
"Lean.Import",
"String",
"String.Pos.Raw",
"Array",
"Bool",
"Lean.ParseImports.State",
"Lean.ParseImports.State.rec",
"Option"
] | false |
CategoryTheory.Limits.IsColimit.ofCoconeEquiv_apply_desc | Mathlib.CategoryTheory.Limits.IsLimit | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"Equiv.instEquivLike",
"CategoryTheory.Limits.IsColimit.ofCoconeEquiv",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.CoconeMorphism.hom",
"CategoryTheory.Equivalence",
"CategoryTheory.Functor.comp",
"Catego... | true |
_private.Mathlib.Topology.UniformSpace.Basic.0.UniformContinuousOn.comp._simp_1_3 | Mathlib.Topology.UniformSpace.Basic | [
"Filter.Eventually",
"Membership.mem",
"Filter.eventually_principal",
"propext",
"Filter.principal",
"Eq",
"Set.instMembership",
"Set"
] | false |
IsLocalizedModule.mk'_eq_zero._simp_1 | Mathlib.Algebra.Module.LocalizedModule.Basic | [
"CommSemiring.toSemiring",
"AddMonoid.toAddZeroClass",
"IsLocalizedModule",
"LinearMap.instFunLike",
"Membership.mem",
"AddZeroClass.toAddZero",
"Subtype",
"LinearMap",
"AddCommMonoid",
"MulZeroOneClass.toMulOneClass",
"instMulZeroOneClassOfSemiring",
"CommSemiring",
"AddZero.toZero",
"pro... | false |
Lean.Elab.Term.Quotation.precheckAttribute | Lean.Elab.Quotation.Precheck | [
"Classical.ofNonempty",
"Lean.Elab.Term.Quotation.Precheck",
"Lean.KeyedDeclsAttribute",
"Lean.instNonemptyKeyedDeclsAttribute"
] | true |
_private.Mathlib.CategoryTheory.LocallyDirected.0.CategoryTheory.instIsLocallyDirectedWidePushoutShapeOfMonoObjNoneSomeMapInit._simp_2 | Mathlib.CategoryTheory.LocallyDirected | [
"forall_eq",
"propext",
"Eq"
] | false |
AddSubmonoid.LocalizationMap.exists_of_eq | Mathlib.GroupTheory.MonoidLocalization.Basic | [
"AddMonoid.toAddZeroClass",
"Membership.mem",
"Exists",
"AddSubmonoid.LocalizationMap",
"AddZeroClass.toAddZero",
"Subtype",
"AddSubmonoid.LocalizationMap.instFunLike",
"AddSubmonoid",
"AddCommMonoid",
"instHAdd",
"HAdd.hAdd",
"AddSubmonoid.IsLocalizationMap.exists_of_eq",
"AddZero.toAdd",
... | true |
_private.Mathlib.Algebra.Star.CHSH.0.tsirelson_inequality._proof_1_6 | Mathlib.Algebra.Star.CHSH | [
"instLawfulOrderLT_mathlib",
"IsRightCancelAdd.addRightStrictMono_of_addRightMono",
"NegZeroClass.toNeg",
"Lean.Grind.CommRing.le_norm_expr",
"Lean.RArray.leaf",
"MulOne.toOne",
"Lean.Grind.Field.toCommRing",
"False",
"Real.partialOrder",
"Real.instLE",
"Semigroup.toMul",
"Real",
"instHSMul"... | false |
Polynomial.eval₂_map | Mathlib.Algebra.Polynomial.Eval.Coeff | [
"Eq.mpr",
"Polynomial.eval",
"congrArg",
"RingHom",
"id",
"Polynomial.eval₂",
"Polynomial",
"RingHom.comp",
"Semiring",
"Eq.refl",
"Polynomial.map",
"Polynomial.map_map",
"Semiring.toNonAssocSemiring",
"Eq",
"Polynomial.eval₂_eq_eval_map"
] | true |
CategoryTheory.Limits.IsColimit.mk.sizeOf_spec | Mathlib.CategoryTheory.Limits.IsLimit | [
"CategoryTheory.Limits.IsColimit.fac._autoParam",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Limits.IsColimit.mk",
"CategoryTheory.Limits.IsColimit",
"instOfNatNat",
"autoParam... | true |
ContinuousLinearMap.restrictScalars_add | Mathlib.Topology.Algebra.Module.ContinuousLinearMap.RestrictScalars | [
"ContinuousLinearMap.restrictScalars",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"ContinuousLinearMap.add",
"AddCommMonoid",
"ContinuousLinearMap",
"TopologicalSpace",
"AddZero.toZero",
"instHAdd",
"HAdd.hAdd",
"Sem... | true |
CategoryTheory.Triangulated.AbelianSubcategory.ιK.congr_simp | Mathlib.CategoryTheory.Triangulated.TStructure.AbelianSubcategory | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.shiftFunctor",
"CategoryTheory.Triangulated.AbelianSubcategory.ιK",
"Eq.rec",
"Int",
"Int.instAddMonoid",
"instOfNat",
"Eq.refl",
"CategoryTheory.Category.toCategoryStruct",
"OfNat.ofNat",
"Cate... | true |
AlgebraicGeometry.StructureSheaf.isFractionPrelocal._proof_1 | Mathlib.AlgebraicGeometry.StructureSheaf | [
"AlgebraicGeometry.StructureSheaf.Localizations",
"CommRing",
"Semiring.toModule",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"TopologicalSpace.Opens.instPartialOrder",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"PartialOrder.toPreorder",
"TopologicalSpace.Opens",
"M... | false |
Std.DHashMap.Internal.Raw₀.Const.getD_insertManyIfNewUnit_list | Std.Data.DHashMap.Internal.RawLemmas | [
"Unit.unit",
"instForInOfForIn'",
"inferInstance",
"Std.DHashMap.Internal.Raw₀.Const.getD",
"Id",
"Membership",
"List",
"Unit",
"Std.DHashMap.Internal.Raw₀.Const.insertManyIfNewUnit",
"List.instMembership",
"eq_self",
"of_eq_true",
"Std.DHashMap.Internal.Raw₀.insertIfNew",
"Id.instMonad",
... | true |
Matrix.blockDiagAddMonoidHom._proof_1 | Mathlib.Data.Matrix.Block | [
"Matrix.blockDiag",
"Matrix",
"AddZeroClass.toAddZero",
"Matrix.blockDiag_zero",
"Pi.instZero",
"AddZero.toZero",
"AddZeroClass",
"Zero.toOfNat0",
"Prod",
"OfNat.ofNat",
"Eq",
"Matrix.zero"
] | false |
_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_28 | Mathlib.Data.List.TakeDrop | [
"of_eq_false",
"Lean.Grind.CommRing.le_norm_expr",
"Lean.Grind.instOrderedRingInt",
"Lean.RArray.leaf",
"HMul.hMul",
"Lean.Grind.CommRing.Expr.mul",
"Int.Linear.norm_le",
"eq_false",
"Lean.Grind.CommRing.Expr.var",
"Int.Linear.Expr.eq_of_norm_eq",
"_private.Mathlib.Data.List.TakeDrop.0.List.drop... | false |
Std.TreeMap.isSome_minKey?_of_mem | Std.Data.TreeMap.Lemmas | [
"Std.TreeMap.minKey?",
"Std.TreeMap.inner",
"Membership.mem",
"Ordering",
"Std.TransCmp",
"Bool.true",
"Std.TreeMap.instMembership",
"Bool",
"Std.DTreeMap.isSome_minKey?_of_mem",
"Option.isSome",
"Eq",
"Std.TreeMap"
] | true |
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