name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Ideal.mulQuot._proof_1 | Mathlib.RingTheory.OrderOfVanishing.Basic | [
"CommRing",
"Algebra.to_smulCommClass",
"instSMulOfMul",
"CommSemiring.toSemiring",
"Algebra.toSMul",
"Algebra.id",
"instDistribOfSemiring",
"CommRing.toCommSemiring",
"Distrib.toMul",
"SMulCommClass"
] | false |
Lean.Meta.instHashableInfoCacheKey._private_1 | Lean.Meta.Basic | [
"mixHash",
"UInt64",
"Lean.Meta.InfoCacheKey",
"Lean.Expr",
"instHashableNat",
"Hashable.hash",
"Nat",
"Lean.Expr.instHashable",
"instHashableOption",
"instHashableUInt64",
"_private.Lean.Meta.Basic.0.Lean.Meta.instHashableInfoCacheKey.match_1",
"Option"
] | false |
CategoryTheory.hasExactLimitsOfShape_discrete_of_hasExactLimitsOfShape_finset_discrete_op | Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Functor",
"CategoryTheory.preservesFiniteColimits_liftToFinset",
"Opposite",
"CategoryTheory.HasExactLimitsOfShape.preservesFiniteColimits",
"CategoryTheory.Limits.HasLimitsOfShape",
"Finset",
"CategoryTheory.Limits.HasFiniteBiproducts",
"Par... | true |
RootPairing.Hom.weight_coweight_transpose | Mathlib.LinearAlgebra.RootSystem.Hom | [
"CommRing",
"Algebra.to_smulCommClass",
"Semiring.toModule",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"RootPairing.flip",
"RootPairing.isPerfPair_toLinearMap",
"RootPairing.toLinearMap",
"AddZeroClass.toAddZero",
"... | true |
Lean.IR.IRType.erased.elim | Lean.Compiler.IR.Basic | [
"PULift.up",
"Lean.IR.IRType.ctorIdx",
"Nat",
"Lean.IR.IRType",
"Lean.IR.IRType.erased",
"Lean.IR.IRType.ctorElim",
"Eq.symm",
"Eq"
] | false |
Batteries.Tactic.PrintPrefixConfig.showTypes._default | Batteries.Tactic.PrintPrefix | [
"id",
"Bool.true",
"Bool"
] | false |
LatticeCon.ctorIdx | Mathlib.Order.Lattice.Congruence | [
"Lattice",
"Nat",
"LatticeCon"
] | false |
CommSemiRingCat | Mathlib.Algebra.Category.Ring.Basic | [
"CommSemiRingCat.of"
] | true |
CategoryTheory.Limits.map_lift_equalizerComparison_assoc | Mathlib.CategoryTheory.Limits.Shapes.Equalizers | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Limits.equalizer",
"Eq.mp",
"id",
"CategoryTheory.Limits.equalizer.lift",
"CategoryTheory.Limits.HasEqualizer",
"Mathlib.Tactic.Reassoc.eq_whisker'",
"... | true |
CategoryTheory.Over.iteratedSliceForward_obj | Mathlib.CategoryTheory.Comma.Over.Basic | [
"CategoryTheory.Over",
"CategoryTheory.Over.Hom.left",
"CategoryTheory.Over.mk",
"CategoryTheory.instCategoryOver",
"CategoryTheory.Over.iteratedSliceForward",
"CategoryTheory.Over.left",
"Eq.refl",
"Eq",
"CategoryTheory.Over.hom",
"CategoryTheory.Functor.obj",
"CategoryTheory.Category"
] | true |
MeasureTheory.TendstoInMeasure.congr | Mathlib.MeasureTheory.Function.ConvergenceInMeasure | [
"MeasureTheory.ae",
"MeasureTheory.Measure",
"Filter.EventuallyEq",
"MeasureTheory.TendstoInMeasure",
"Filter.Eventually.of_forall",
"MeasurableSpace",
"MeasureTheory.TendstoInMeasure.congr'",
"EDist",
"Filter",
"MeasureTheory.Measure.instFunLike",
"MeasureTheory.Measure.instOuterMeasureClass"
] | true |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.Const.equiv_of_beq._simp_1_2 | Std.Data.DTreeMap.Internal.Lemmas | [
"Ord",
"beqOfOrd",
"Ordering",
"Std.DTreeMap.Internal.Impl.compare_ne_iff_beq_eq_false",
"Ordering.eq",
"Ne",
"Ord.compare",
"BEq.beq",
"propext",
"Bool",
"Bool.false",
"Eq"
] | false |
CoassocSimps.lid_comp_map_assoc | Mathlib.RingTheory.Coalgebra.CoassocSimps | [
"LinearMap.id",
"Semiring.toModule",
"LinearMap.comp.congr_simp",
"congrArg",
"CommSemiring.toSemiring",
"TensorProduct.addCommMonoid",
"CoassocSimps.lid_comp_map",
"TensorProduct.map",
"LinearMap",
"AddCommMonoid",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"LinearMap.comp... | true |
Algebra.PreSubmersivePresentation.jacobian_ofAlgEquiv | Mathlib.RingTheory.Extension.Presentation.Submersive | [
"Eq.mpr",
"AlgEquiv.instEquivLike",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"CommRing",
"Algebra.Generators.Ring",
"MvPolynomial.aeval",
"Algebra.algebraMap",
"AddMonoidAlgebra.commRing",
"congrArg",
"CommSemiring.toSemiring",
"Algebra.Generators.instRing",
"AlgHom",
"Finite",... | true |
CategoryTheory.AddMonObj.add_comp_assoc | Mathlib.CategoryTheory.Monoidal.Cartesian.Mon | [
"CategoryTheory.Category.assoc",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.AddMonObj.add_comp",
"CategoryTheory.Hom.addMonoid",
"CategoryTheory.IsAddMonHom",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"Eq.mp",
"id",
"Mathlib.Tactic.Reassoc.e... | true |
_private.Mathlib.Algebra.SkewMonoidAlgebra.Lift.0.SkewMonoidAlgebra.domCongr._simp_1 | Mathlib.Algebra.SkewMonoidAlgebra.Lift | [
"SkewMonoidAlgebra.equivMapDomain",
"Equiv.trans",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"Equiv",
"AddCommMonoid",
"AddZero.toZero",
"SkewMonoidAlgebra.equivMapDomain_trans",
"SkewMonoidAlgebra",
"AddCommMonoid.toAddMonoid",
"Eq.symm",
"Eq"
] | false |
_private.Init.Data.String.Basic.0.String.Pos.lt_of_le_of_ne._simp_1_1 | Init.Data.String.Basic | [
"String.instLTRaw",
"String",
"String.Pos.lt_iff",
"String.Pos.Raw",
"String.instLTPos",
"LT.lt",
"propext",
"String.Pos",
"Eq",
"String.Pos.offset"
] | false |
_private.Mathlib.Order.Filter.Map.0.Filter.frequently_comap._simp_1_2 | Mathlib.Order.Filter.Map | [
"And",
"propext",
"not_and",
"Eq",
"Not"
] | false |
AdicCompletion.of_ofAlgEquiv_symm | Mathlib.RingTheory.AdicCompletion.Algebra | [
"CommRing",
"Semiring.toModule",
"instSMulOfMul",
"AlgEquiv.symm",
"congrArg",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"LinearMap.instFunLike",
"AdicCompletion.instAddCommGroup",
"Algebra.id",
"AdicCompletion.instModuleOfIsScalarTower",
"Ideal",
"LinearMap",
"IsScalarTow... | true |
Lean.Meta.AbstractMVars.instMonadMCtxM | Lean.Meta.AbstractMVars | [
"Pure.pure",
"Lean.Meta.AbstractMVars.State.ngen",
"Lean.Meta.AbstractMVars.State.mvars",
"Lean.Meta.AbstractMVars.State.mctx",
"modify",
"Monad.toApplicative",
"Lean.MetavarContext",
"MonadState.get",
"Lean.MonadMCtx.mk",
"Lean.Meta.AbstractMVars.State.fvars",
"Lean.Meta.AbstractMVars.State.nex... | true |
LinearMap.cancel_right | Mathlib.Algebra.Module.LinearMap.Defs | [
"LinearMap.instFunLike",
"Function.Injective.eq_iff",
"RingHom",
"RingHomCompTriple",
"LinearMap",
"AddCommMonoid",
"LinearMap.comp",
"Iff",
"Semiring",
"Module",
"Semiring.toNonAssocSemiring",
"Eq",
"DFunLike.coe",
"Function.Surjective",
"Function.Surjective.injective_linearMapComp_righ... | true |
_private.Mathlib.Topology.MetricSpace.CoveringNumbers.0.Metric.encard_maximalSeparatedSet._proof_1_4 | Mathlib.Topology.MetricSpace.CoveringNumbers | [
"instDecidableNot",
"False",
"Set.encard",
"Exists.choose_spec",
"ENNReal.ofNNReal",
"dite_congr",
"Lean.Grind.nestedProof",
"eq_false",
"LinearOrder.toDecidableEq",
"instTopENat",
"instLinearOrderENat",
"congrArg",
"Classical.byContradiction",
"Metric.maximalSeparatedSet",
"Set.Finite",... | false |
MeasureTheory.Measure.restrict_mono_measure | Mathlib.MeasureTheory.Measure.Restrict | [
"MeasureTheory.Measure",
"MeasureTheory.Measure.restrict_mono",
"PartialOrder.toPreorder",
"Preorder.toLE",
"MeasureTheory.Measure.restrict",
"Set.instReflSubset",
"LE.le",
"MeasurableSpace",
"MeasureTheory.Measure.instPartialOrder",
"subset_rfl",
"Set.instHasSubset",
"Set"
] | true |
_private.Mathlib.RingTheory.AlgebraicIndependent.Transcendental.0.lift_trdeg_add_le._simp_1_1 | Mathlib.RingTheory.AlgebraicIndependent.Transcendental | [
"Cardinal",
"Cardinal.lift",
"Cardinal.mk",
"Sum",
"Cardinal.instAdd",
"instHAdd",
"HAdd.hAdd",
"Cardinal.mk_sum",
"Eq.symm",
"Eq"
] | false |
Ideal.mapCotangent | Mathlib.RingTheory.Ideal.Cotangent | [
"AlgHom.toLinearMap",
"Submodule",
"CommRing",
"instHSMul",
"Semiring.toModule",
"AlgHom.algHomClass",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"AlgHom",
"Submodule.addCommMonoid",
"Submodule.restrictScalars",
"AlgHom.funLike",
"PartialOrder.toPreorder",
"Ideal.Cotangent"... | true |
Ordnode.split3._unsafe_rec | Mathlib.Data.Ordmap.Ordnode | [
"Ordnode",
"Ordnode.split3.match_1",
"Option.some",
"Ordering",
"Ordnode.split3._unsafe_rec",
"Prod.mk",
"Ordnode.mem.match_1",
"cmpLE",
"LE",
"Option.none",
"DecidableLE",
"Unit",
"Ordnode.size.match_1",
"Nat",
"Ordnode.nil",
"Prod",
"Ordnode.link",
"Option"
] | false |
Lean.Lsp.RpcWireFormat.v1.elim | Lean.Server.Rpc.Basic | [
"PULift.up",
"Lean.Lsp.RpcWireFormat.ctorIdx",
"Lean.Lsp.RpcWireFormat.v1",
"Lean.Lsp.RpcWireFormat.ctorElim",
"Nat",
"Lean.Lsp.RpcWireFormat",
"Eq.symm",
"Eq"
] | false |
Cardinal.lt_aleph0_iff_finite | Mathlib.SetTheory.Cardinal.Basic | [
"Preorder.toLT",
"Cardinal",
"congrArg",
"Finite",
"PartialOrder.toPreorder",
"Cardinal.mk",
"Exists",
"Equiv",
"Cardinal.aleph0",
"Nat.cast",
"iff_self",
"funext",
"Cardinal.partialOrder",
"Iff",
"_private.Mathlib.SetTheory.Cardinal.Basic.0.Cardinal.lt_aleph0_iff_finite._simp_1_1",
"N... | true |
Matrix.trace_zero | Mathlib.LinearAlgebra.Matrix.Trace | [
"instHSMul",
"Finset.univ",
"DistribMulAction.toDistribSMul",
"Matrix",
"Nat.instMonoid",
"AddMonoid.toAddZeroClass",
"AddMonoid.toNSMul",
"smul_zero",
"AddZeroClass.toAddZero",
"Matrix.trace",
"DistribSMul.toSMulZeroClass",
"AddCommMonoid",
"AddZero.toZero",
"Fintype",
"Nat",
"Finset.... | true |
_private.Mathlib.RingTheory.PowerSeries.Basic.0.PowerSeries.coeff_one_pow._simp_1_5 | Mathlib.RingTheory.PowerSeries.Basic | [
"And",
"and_assoc",
"propext",
"Eq"
] | false |
RootPairing.root | Mathlib.LinearAlgebra.RootSystem.Defs | [
"CommRing",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"AddCommGroup",
"Function.Embedding",
"CommRing.toCommSemiring",
"Module",
"RootPairing"
] | true |
_private.Mathlib.Data.Int.Basic.0.Int.natCast_dvd._simp_1_2 | Mathlib.Data.Int.Basic | [
"Dvd.dvd",
"Int.instNegInt",
"Int",
"Int.instDvd",
"Int.dvd_neg",
"propext",
"Eq",
"Neg.neg"
] | false |
Turing.ListBlank.tail_mk | Mathlib.Computability.TuringMachine.Tape | [
"Turing.ListBlank.mk",
"List.tail",
"Turing.ListBlank.tail",
"List",
"Turing.ListBlank",
"Inhabited",
"Eq",
"rfl"
] | true |
_private.Lean.Elab.Tactic.BVDecide.Frontend.Normalize.Simproc.0._regBuiltin.Lean.Elab.Tactic.BVDecide.Frontend.Normalize.bv_extractLsb'_not.declare_198._@.Lean.Elab.Tactic.BVDecide.Frontend.Normalize.Simproc.2283078798._hygCtx._hyg.24 | Lean.Elab.Tactic.BVDecide.Frontend.Normalize.Simproc | [
"IO",
"Lean.Meta.DiscrTree.Key.star",
"Lean.Name.mkStr7",
"Lean.Meta.DiscrTree.Key",
"instOfNatNat",
"List.toArray",
"List.cons",
"Lean.Elab.Tactic.BVDecide.Frontend.Normalize.bv_extractLsb'_not",
"Unit",
"Nat",
"Lean.Meta.Simp.registerBuiltinSimproc",
"Lean.Name.mkStr2",
"OfNat.ofNat",
"L... | false |
CategoryTheory.Mat_.instAddCommGroupHom._proof_20 | Mathlib.CategoryTheory.Preadditive.Mat | [
"AddMonoid.toAddSemigroup",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Mat_.instAddCommGroupHom._proof_7",
"CategoryTheory.Mat_.instAddCommGroupHom._proof_3",
"Add.mk",
"CategoryTheory.Mat_.instAddCommGroupHom._aux_1",
"AddMonoid.mk",
"AddCommGroup.toAddGroup",
"Catego... | false |
Mathlib.Meta.FunProp.FunctionTheorem.appliedArgs | Mathlib.Tactic.FunProp.Theorems | [
"Mathlib.Meta.FunProp.FunctionTheorem",
"Nat"
] | true |
Nat.one_eq_digitChar | Init.Data.Nat.ToString | [
"Nat.digitChar",
"instOfNatNat",
"eq_comm",
"Nat.digitChar_eq_one",
"Iff",
"Nat",
"Iff.trans",
"Char",
"OfNat.ofNat",
"Eq",
"Char.ofNat"
] | true |
RestrictedProduct.instNSMul | Mathlib.Topology.Algebra.RestrictedProduct.Basic | [
"SetLike",
"instHSMul",
"SMul",
"Filter.Eventually",
"AddMonoid.toAddZeroClass",
"AddMonoid.toNSMul",
"Membership.mem",
"AddSubmonoidClass",
"SMul.mk",
"RestrictedProduct.instDFunLike",
"RestrictedProduct",
"Subtype.mk",
"SetLike.coe",
"Nat",
"AddMonoid",
"HSMul.hSMul",
"RestrictedPr... | true |
Lean.Grind.eq_true_of_and_eq_true_right | Init.Grind.Lemmas | [
"congrArg",
"iff_true",
"eq_iff_iff._simp_1",
"Eq.mp",
"id",
"And",
"Iff",
"True",
"eq_self",
"eq_true",
"of_eq_true",
"congrFun'",
"Eq",
"Eq.trans"
] | true |
_private.Init.Data.String.Iterator.0.String.Legacy.Iterator.remainingBytes.match_1 | Init.Data.String.Iterator | [
"String.Legacy.Iterator.mk",
"String",
"String.Pos.Raw",
"String.Legacy.Iterator.casesOn",
"String.Legacy.Iterator"
] | false |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.ordered_keys_toList._simp_1_2 | Std.Data.DTreeMap.Internal.Lemmas | [
"Ord",
"beqOfOrd",
"Ordering",
"Std.DTreeMap.Internal.Impl.compare_ne_iff_beq_eq_false",
"Ordering.eq",
"Ne",
"Ord.compare",
"BEq.beq",
"propext",
"Bool",
"Bool.false",
"Eq"
] | false |
WeierstrassCurve.Jacobian.Point.zero_def | Mathlib.AlgebraicGeometry.EllipticCurve.Jacobian.Point | [
"Nontrivial",
"Units.instMulAction",
"CommRing",
"CommSemiring.toSemiring",
"AddGroupWithOne.toAddMonoidWithOne",
"WeierstrassCurve.Jacobian.instMulActionForallFinOfNatNat",
"Units",
"WeierstrassCurve.Jacobian.Point.mk",
"MulAction.orbitRel",
"instOfNatNat",
"Units.instGroup",
"WeierstrassCurv... | true |
TestFunction.instAddCommGroup._proof_1 | Mathlib.Analysis.Distribution.TestFunction | [
"Real",
"NormedSpace",
"AddMonoid.toAddSemigroup",
"TestFunction.toTestFunctionClass",
"Function.Injective.addSemigroup._proof_2",
"PseudoMetricSpace.toUniformSpace",
"TopologicalSpace.Opens",
"AddCommGroup.toAddGroup",
"TestFunction.instAdd",
"instHAdd",
"SeminormedAddCommGroup.toPseudoMetricSp... | false |
MulAction.IsPreprimitive.of_surjective | Mathlib.GroupTheory.GroupAction.Primitive | [
"Eq.mpr",
"MulAction.IsBlock",
"congrArg",
"Group",
"MulAction.IsPretransitive",
"MulAction.IsBlock.preimage",
"id",
"DivInvMonoid.toMonoid",
"Set.image_preimage_eq",
"instFunLikeMulActionHom",
"Group.toDivInvMonoid",
"Set.preimage",
"MulAction",
"Monoid.toSemigroup",
"MulAction.IsPretra... | true |
Std.DTreeMap.Raw.Const.get!_diff | Std.Data.DTreeMap.Raw.Lemmas | [
"Inhabited.default",
"Std.DTreeMap.Internal.Impl.Const.get!_diff!",
"Std.DTreeMap.Raw.Const.get!",
"Ord.mk",
"Ordering",
"id",
"instDecidableEqBool",
"Std.TransCmp",
"Bool.true",
"SDiff.sdiff",
"Std.DTreeMap.Raw.WF.out",
"Std.DTreeMap.Raw.inner",
"Std.DTreeMap.Raw.contains",
"Bool",
"Inh... | true |
abs_sub_sup_add_abs_sub_inf | Mathlib.Algebra.Order.Group.Unbundled.Abs | [
"neg_add_rev",
"Eq.mpr",
"Lattice",
"Trans.trans",
"Lattice.toSemilatticeSup",
"add_neg_cancel_left",
"AddMonoid.toAddSemigroup",
"abs",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"add_assoc",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"sub_eq_add_neg",
"HSub.hSub",
"AddLe... | true |
Sigma.isPreconnected_iff | Mathlib.Topology.Connected.Clopen | [
"Continuous.continuousOn",
"IsConnected",
"Classical.choice",
"continuous_sigmaMk",
"IsPreconnected.image",
"Exists",
"instTopologicalSpaceSigma",
"Or.casesOn",
"And.casesOn",
"Set.eq_empty_or_nonempty",
"TopologicalSpace",
"And",
"Iff",
"Set.Nonempty",
"Exists.casesOn",
"IsConnected.i... | true |
Module.Basis.constr_basis | Mathlib.LinearAlgebra.Basis.Defs | [
"Pi.Function.module",
"NonAssocSemiring.toAddCommMonoidWithOne",
"instHSMul",
"Semiring.toModule",
"Pi.addCommMonoid",
"Finsupp.module",
"congrArg",
"DistribMulAction.toDistribSMul",
"Finsupp.sum_single_index",
"AddMonoid.toAddZeroClass",
"LinearMap.instFunLike",
"Module.toMulActionWithZero",
... | true |
CategoryTheory.Reflective.comparison_full | Mathlib.CategoryTheory.Monad.Adjunction | [
"CategoryTheory.Functor.preimage",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.Full.mk",
"CategoryTheory.Monad.comparison",
"CategoryTheory.Monad.Algebra.A",
"CategoryTheory.Functor.map",
"True",
"CategoryTheory.Monad.Alge... | true |
Finpartition.mem_part_ofSetSetoid_iff_rel | Mathlib.Order.Partition.Finpartition | [
"Eq.mpr",
"Finset.mem_filter._simp_1",
"congrArg",
"Finset",
"exists_exists_and_eq_and._simp_1",
"DecidableRel",
"Finset.mem_image._simp_1",
"Finpartition.part",
"Membership.mem",
"Exists",
"Setoid.trans'",
"Setoid.symm'",
"id",
"Setoid",
"Finset.decidableEq",
"Finpartition.parts",
"... | true |
_private.Mathlib.Probability.Process.LocalProperty.0.ProbabilityTheory.isPreLocalizingSequence_of_isLocalizingSequence_aux | Mathlib.Probability.Process.LocalProperty | [
"MeasureTheory.ae",
"Eq.mpr",
"OrderTopology",
"MeasureTheory.Measure",
"Preorder.toLT",
"Lattice.toSemilatticeSup",
"instHDiv",
"StrictMono",
"WithTop.instPreorder",
"congrArg",
"CommSemiring.toSemiring",
"SecondCountableTopology",
"Prop.le",
"ConditionallyCompleteLinearOrderBot",
"Part... | true |
USize.toUInt64 | Init.Data.UInt.Basic | [
"UInt64",
"BitVec.toNat",
"UInt64.ofNatLT",
"System.Platform.numBits",
"USize.toBitVec",
"USize.toUInt64._proof_1",
"USize"
] | true |
Aesop.initFn._@.Aesop.Options.Public.1260513527._hygCtx._hyg.4 | Aesop.Options.Public | [
"Lean.Option",
"IO",
"Lean.Name.mkStr3",
"Lean.Option.Decl.mk",
"Bool.true",
"Lean.KVMap.instValueBool",
"Lean.Option.register",
"Bool",
"Lean.Name.mkStr4"
] | false |
Vector.toArray_zipIdx | Init.Data.Vector.Lemmas | [
"Vector",
"instOfNatNat",
"Array.zipIdx",
"Array",
"Nat",
"optParam",
"Prod",
"OfNat.ofNat",
"Eq",
"Vector.toArray",
"rfl",
"Vector.zipIdx"
] | true |
CategoryTheory.Functor.Final.colimitCoconeComp_isColimit | Mathlib.CategoryTheory.Limits.Final | [
"CategoryTheory.Limits.ColimitCocone.cocone",
"CategoryTheory.Functor",
"Equiv.instEquivLike",
"CategoryTheory.Functor.comp",
"CategoryTheory.Limits.IsColimit",
"CategoryTheory.Functor.Final.colimitCoconeComp",
"CategoryTheory.Limits.Cocone.whisker",
"Equiv",
"CategoryTheory.Limits.ColimitCocone.isC... | true |
Topology.IsLowerSet.closure_singleton | Mathlib.Topology.Order.UpperLowerSetTopology | [
"Eq.mpr",
"Set.Ici",
"UpperSet",
"Topology.IsLowerSet.closure_eq_upperClosure",
"congrArg",
"UpperSet.instSetLike",
"upperClosure_singleton",
"Topology.IsLowerSet",
"upperClosure",
"Preorder.toLE",
"UpperSet.Ici",
"Set.instSingletonSet",
"id",
"TopologicalSpace",
"SetLike.coe",
"closur... | true |
List.prod_hom₂_nonempty | Mathlib.Algebra.BigOperators.Group.List.Basic | [
"Monoid",
"MulOne.toOne",
"False",
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"_private.Mathlib.Algebra.BigOperators.Group.List.Basic.0.List.prod_hom₂_nonempty.match_1_1",
"List.map",
"False.elim",
"instInhabitedTrue",
"noConfusion_of_Nat",
"Eq.mp",
"id",
"MulOne.toMul",
"Ne",
"L... | true |
_private.Init.Meta.Defs.0.Lean.Syntax.structEq._sparseCasesOn_3 | Init.Meta.Defs | [
"Lean.Syntax.node",
"Lean.Syntax.ident",
"Lean.Syntax.missing",
"Nat.ne_of_beq_eq_false",
"Lean.Syntax.ctorIdx",
"String",
"Lean.SourceInfo",
"Nat.shiftRight",
"Lean.Syntax.atom",
"Lean.Syntax",
"Nat.hasNotBit",
"instOfNatNat",
"Substring.Raw",
"Array",
"Nat.land",
"List",
"Lean.Synt... | false |
Vector3.nil | Mathlib.Data.Vector3 | [
"instOfNatNat",
"Vector3",
"Nat",
"Vector3.nil.match_1",
"OfNat.ofNat",
"Fin2"
] | true |
Mathlib.Meta.Positivity.evalInv | Mathlib.Algebra.Order.Field.Basic | [
"Qq.QuotedDefEq",
"Pure.pure",
"Lean.MonadError.mk",
"Lean.instMonadExceptOfExceptionCoreM",
"Lean.Meta.whnf",
"Mathlib.Meta.Positivity.Strictness",
"Mathlib.Meta.Positivity.PositivityExt",
"instMonadControlTOfPure",
"String",
"Lean.Meta.State",
"Lean.Expr.const",
"Lean.instAddErrorMessageCont... | true |
AddSubgroup.toAddSubmonoid | Mathlib.Algebra.Group.Subgroup.Defs | [
"AddMonoid.toAddZeroClass",
"AddSubmonoid",
"AddSubgroup",
"AddGroup",
"AddGroup.toSubNegMonoid",
"SubNegMonoid.toAddMonoid"
] | true |
_private.Lean.Elab.MutualInductive.0.Lean.Elab.Command.AccLevelState.mk.sizeOf_spec | Lean.Elab.MutualInductive | [
"_private.Lean.Elab.MutualInductive.0.Lean.Elab.Command.AccLevelState._sizeOf_inst",
"Std.HashMap._sizeOf_inst",
"_private.Lean.Elab.MutualInductive.0.Lean.Elab.Command.AccLevelState",
"Lean.Level._sizeOf_inst",
"instOfNatNat",
"Lean.Level",
"Int",
"instHAdd",
"HAdd.hAdd",
"_private.Lean.Elab.Mutu... | true |
Plausible.PNat.sampleableExt | Mathlib.Testing.Plausible.Sampleable | [
"inferInstance",
"Plausible.PNat.Arbitrary",
"Plausible.PNat.shrinkable",
"Plausible.SampleableExt.selfContained",
"instReprPNat",
"Plausible.SampleableExt",
"PNat"
] | true |
Std.ExtTreeSet.min!_insert_le_self | Std.Data.ExtTreeSet.Lemmas | [
"Unit.unit",
"Ordering",
"Std.ExtTreeSet.inner",
"Std.TransCmp",
"Bool.true",
"Unit",
"Std.ExtTreeMap.minKey!_insertIfNew_le_self",
"Std.ExtTreeSet.min!",
"Std.ExtTreeSet",
"Bool",
"Inhabited",
"Ordering.isLE",
"Eq",
"Std.ExtTreeSet.insert"
] | true |
NNReal.strictMono_rpow_of_pos | Mathlib.Analysis.SpecialFunctions.Pow.NNReal | [
"Real",
"Preorder.toLT",
"StrictMono",
"Real.instZero",
"NNReal.rpow_lt_rpow",
"PartialOrder.toPreorder",
"Real.instLT",
"NNReal",
"NNReal.instPartialOrder",
"HPow.hPow",
"NNReal.instPowReal",
"LT.lt",
"Zero.toOfNat0",
"instHPow",
"OfNat.ofNat"
] | true |
IsDedekindDomain.selmerGroup.valuation | Mathlib.RingTheory.DedekindDomain.SelmerGroup | [
"MulOne.toOne",
"MonoidHom.range",
"CommRing",
"IsDedekindDomain.HeightOneSpectrum.valuationOfNeZeroMod._proof_1",
"MonoidHom.instFunLike",
"CommMonoid.toCommSemigroup",
"ZMod.commRing",
"MonoidHom",
"Monoid.toMulOneClass",
"IsFractionRing",
"OneHom.mk",
"AddMonoid.toAddZeroClass",
"IsDedeki... | true |
ProofWidgets.Jsx.getJsxText | ProofWidgets.Data.Html | [
"Lean.TSyntax",
"String",
"Lean.Syntax",
"Lean.Name.mkStr3",
"Lean.TSyntax.raw",
"Lean.Syntax.getAtomVal",
"instOfNatNat",
"List.cons",
"GetElem.getElem",
"Nat",
"True",
"Lean.SyntaxNodeKind",
"OfNat.ofNat",
"Lean.Syntax.instGetElemNatTrue",
"True.intro",
"List.nil"
] | true |
_private.Batteries.Data.Array.Lemmas.0.Array.extract_append_of_stop_le_size_left._proof_1_2 | Batteries.Data.Array.Lemmas | [
"Lean.Grind.Nat.lt_eq",
"instOfNatNat",
"LE.le",
"instLENat",
"Array.extract",
"Array",
"instHAdd",
"HAdd.hAdd",
"Nat",
"LT.lt",
"Eq.substr",
"instAddNat",
"instLTNat",
"OfNat.ofNat",
"Array.size"
] | false |
CategoryTheory.Pseudofunctor.DescentData.pullFunctorObjHom_eq._proof_20 | Mathlib.CategoryTheory.Sites.Descent.DescentData | [
"Opposite",
"CategoryTheory.LocallyDiscrete.mk",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.CategoryStruct.opposite",
"Quiver.Hom.op",
"CategoryTheory.locallyDiscreteBicategory",
"CategoryTheory.Bicategory.toCategoryStruct",
"CategoryTheory.Pseudofunctor.DescentData.pull... | false |
_private.Mathlib.Tactic.Observe.0.Mathlib.Tactic.LibrarySearch._aux_Mathlib_Tactic_Observe___elabRules_Mathlib_Tactic_LibrarySearch_observe_1.match_7 | Mathlib.Tactic.Observe | [
"Option.ctorIdx",
"Lean.MetavarContext",
"Option.some",
"Lean.MVarId",
"Nat.hasNotBit",
"Array",
"List",
"_private.Mathlib.Tactic.Observe.0.Mathlib.Tactic.LibrarySearch._aux_Mathlib_Tactic_Observe___elabRules_Mathlib_Tactic_LibrarySearch_observe_1._sparseCasesOn_7",
"Prod",
"Option"
] | false |
CochainComplex.shiftShortComplexFunctorIso_add'_hom_app._proof_1 | Mathlib.Algebra.Homology.HomotopyCategory.ShiftSequence | [
"Int.instAddSemigroup",
"Eq.mpr",
"congrArg",
"add_assoc",
"id",
"Int",
"instHAdd",
"AddSemigroup.toAdd",
"HAdd.hAdd",
"Int.instAdd",
"Eq.refl",
"Eq.symm",
"Eq"
] | false |
Function.Even.left_comp | Mathlib.Algebra.Group.EvenFunction | [
"Function.Even",
"Function.comp",
"congr_arg",
"Neg",
"Neg.neg"
] | true |
_private.Mathlib.Analysis.Complex.AbelLimit.0.Complex.tendsto_tsum_powerSeries_nhdsWithin_stolzSet._simp_1_4 | Mathlib.Analysis.Complex.AbelLimit | [
"Real",
"Metric.tendsto_atTop",
"Real.instZero",
"PartialOrder.toPreorder",
"PseudoMetricSpace.toUniformSpace",
"Real.instLT",
"Preorder.toLE",
"Exists",
"nhds",
"GE.ge",
"Filter.atTop",
"GT.gt",
"PseudoMetricSpace",
"Filter.Tendsto",
"LT.lt",
"propext",
"Nonempty",
"Zero.toOfNat0"... | false |
Lean.JsonRpc.MessageMetaData._sizeOf_inst | Lean.Data.JsonRpc | [
"Lean.JsonRpc.MessageMetaData",
"Lean.JsonRpc.MessageMetaData._sizeOf_1",
"SizeOf.mk",
"SizeOf"
] | false |
ProofWidgets.RpcEncodablePacket.component.injEq._@.ProofWidgets.Data.Html.2686543190._hygCtx._hyg.1 | ProofWidgets.Data.Html | [
"ProofWidgets.RpcEncodablePacket.component._@.ProofWidgets.Data.Html.2686543190._hygCtx._hyg.1",
"Lean.Json",
"ProofWidgets.RpcEncodablePacket.component.inj._@.ProofWidgets.Data.Html.2686543190._hygCtx._hyg.1",
"Eq.propIntro",
"Lean.injEq_helper",
"And",
"Eq.ndrec",
"Eq.refl",
"ProofWidgets.RpcEncod... | false |
_private.Mathlib.GroupTheory.GroupAction.Basic.0.MulAction.fixedPoints_of_subsingleton._simp_1_1 | Mathlib.GroupTheory.GroupAction.Basic | [
"Monoid",
"instHSMul",
"Membership.mem",
"MulAction.mem_fixedPoints",
"MulAction",
"propext",
"Monoid.toSemigroup",
"HSMul.hSMul",
"SemigroupAction.toSMul",
"MulAction.fixedPoints",
"MulAction.toSemigroupAction",
"Eq",
"Set.instMembership",
"Set"
] | false |
CategoryTheory.Limits.CatCospanTransform.mkIso_hom_left | Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform | [
"CategoryTheory.Limits.CatCospanTransform.mkIso._auto_3",
"CategoryTheory.Functor",
"CategoryTheory.Limits.CatCospanTransform.mkIso._auto_1",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.whiskerLeft",
... | true |
Lean.Meta.SizeOfSpecNested.Context.mk.noConfusion | Lean.Meta.SizeOf | [
"Lean.Meta.SizeOfSpecNested.Context.mk",
"Lean.NameMap",
"Lean.Meta.SizeOfSpecNested.Context.noConfusion",
"Lean.Expr",
"id",
"Lean.Meta.SizeOfSpecNested.Context",
"Array",
"Lean.Name",
"Eq",
"Lean.InductiveVal"
] | false |
SeparationQuotient.lift'_mk | Mathlib.Topology.UniformSpace.Separation | [
"UniformContinuous",
"UniformSpace",
"Eq.mpr",
"congrArg",
"SeparationQuotient.lift'.eq_1",
"Classical.propDecidable",
"dif_pos",
"id",
"Nonempty.some",
"SeparationQuotient.lift_mk",
"dite",
"SeparationQuotient.lift'._proof_1",
"SeparationQuotient.lift'",
"SeparationQuotient",
"Separatio... | true |
ClosedAddSubgroup.instCoeAddSubgroup | Mathlib.Topology.Algebra.Group.ClosedSubgroup | [
"ClosedAddSubgroup",
"Coe.mk",
"ClosedAddSubgroup.toAddSubgroup",
"AddSubgroup",
"TopologicalSpace",
"AddGroup",
"Coe"
] | true |
CategoryTheory.FunctorToTypes.monoFactorisation_e | Mathlib.CategoryTheory.Limits.FunctorCategory.Shapes.Images | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Subfunctor.toFunctor",
"CategoryTheory.Subfunctor.range",
"CategoryTheory.types",
"CategoryTheory.Subfunctor.toRange",
"CategoryTheory.Limits.MonoFactorisation.e",
"... | true |
Std.HashMap.Raw.all_eq_false_iff_exists_mem_getElem | Std.Data.HashMap.RawLemmas | [
"GetElem?.toGetElem",
"Std.HashMap.Raw.WF.out",
"LawfulBEq",
"Membership.mem",
"Exists",
"Std.DHashMap.Raw.Const.all_eq_false_iff_exists_contains_get",
"Std.HashMap.Raw.WF",
"Std.HashMap.Raw",
"GetElem.getElem",
"Iff",
"Std.HashMap.Raw.instGetElem?Mem",
"Bool",
"Std.HashMap.Raw.inner",
"St... | true |
Array.partition | Init.Data.Array.Basic | [
"Pure.pure",
"Array.push",
"instForInOfForIn'",
"Monad.toApplicative",
"Array.instMembership",
"inferInstance",
"instDecidableEqBool",
"Prod.mk",
"ForIn.forIn",
"Id.run",
"Id",
"Applicative.toPure",
"Membership",
"ForInStep",
"Prod.fst",
"List.toArray",
"Array",
"Bool.true",
"Boo... | true |
CategoryTheory.Lax.LaxTrans.homCategory._proof_6 | Mathlib.CategoryTheory.Bicategory.Modification.Lax | [
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.Lax.LaxTrans.Modification.app",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Lax.LaxTrans.Hom.as",
"congrArg",
"CategoryTheory.Lax.LaxTrans.Hom.of",
"id",
"CategoryTheory.Bicategory.toCategoryStruct",
"Category... | false |
isAddRightRegular_ofColex | Mathlib.Algebra.Order.Group.Synonym | [
"IsAddRightRegular",
"Equiv.instEquivLike",
"Colex",
"ofColex",
"Iff.rfl",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"Equiv",
"instAddColex",
"Iff",
"AddMonoid",
"AddZero.toAdd",
"DFunLike.coe",
"EquivLike.toFunLike"
] | true |
_private.Mathlib.RingTheory.Ideal.Quotient.PowTransition.0.Submodule.powSMulQuotInclusion_injective._simp_1_3 | Mathlib.RingTheory.Ideal.Quotient.PowTransition | [
"Submodule",
"PartialOrder.toPreorder",
"Preorder.toLE",
"RingHom",
"Submodule.instPartialOrder",
"LE.le",
"LinearMap",
"AddCommMonoid",
"Submodule.comap",
"propext",
"Semiring",
"RingHomSurjective",
"Module",
"Submodule.map",
"Submodule.map_le_iff_le_comap",
"Semiring.toNonAssocSemiri... | false |
StrongFEPair.symm_Λ_eq | Mathlib.NumberTheory.LSeries.AbstractFuncEq | [
"WeakFEPair.g",
"NormedSpace",
"Complex.instNormedField",
"StrongFEPair.symm",
"StrongFEPair.Λ",
"StrongFEPair",
"StrongFEPair.toWeakFEPair",
"Complex",
"mellin",
"NormedAddCommGroup.toSeminormedAddCommGroup",
"Eq",
"rfl",
"NormedAddCommGroup"
] | true |
_private.Mathlib.NumberTheory.ModularForms.EisensteinSeries.Summable.0.EisensteinSeries.r_pos._simp_1_3 | Mathlib.NumberTheory.ModularForms.EisensteinSeries.Summable | [
"Real",
"UpperHalfPlane.im_pos",
"Real.instZero",
"Real.instLT",
"UpperHalfPlane.im",
"UpperHalfPlane",
"LT.lt",
"True",
"eq_true",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq"
] | false |
_private.Mathlib.NumberTheory.ArithmeticFunction.Defs.0.ArithmeticFunction.IsMultiplicative.mul._simp_1_3 | Mathlib.NumberTheory.ArithmeticFunction.Defs | [
"HMul.hMul",
"Nat.divisorsAntidiagonal",
"Finset",
"Nat.mem_divisorsAntidiagonal",
"Membership.mem",
"Ne",
"instMulNat",
"instOfNatNat",
"Prod.fst",
"And",
"Finset.instSetLike",
"Nat",
"propext",
"Prod",
"OfNat.ofNat",
"Eq",
"Prod.snd",
"SetLike.instMembership",
"instHMul"
] | false |
Std.Http.Body.instToByteArrayString | Std.Internal.Http.Data.Body.Basic | [
"Std.Http.Body.ToByteArray.mk",
"String",
"Std.Http.Body.ToByteArray",
"String.toUTF8"
] | true |
CategoryTheory.Endofunctor.Algebra.functorOfNatTrans | Mathlib.CategoryTheory.Endofunctor.Algebra | [
"CategoryTheory.Endofunctor.Algebra.functorOfNatTrans._proof_3",
"CategoryTheory.Functor",
"CategoryTheory.Endofunctor.Algebra",
"CategoryTheory.Endofunctor.Algebra.functorOfNatTrans._proof_4",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.mk",
"CategoryTheory.Functor... | true |
exists_continuous_add_one_of_isCompact_nnreal | Mathlib.MeasureTheory.Integral.RieszMarkovKakutani.Basic | [
"NNReal.instTopologicalSpace",
"Set.mem_union",
"exists_continuous_sum_one_of_isOpen_isCompact",
"Iff.mpr",
"Eq.mpr",
"Set.compl_subset_compl_of_subset",
"NonAssocSemiring.toAddCommMonoidWithOne",
"instNeZeroNatHAdd_1",
"MulOne.toOne",
"Real",
"Fintype.elems",
"NonUnitalCommRing.toNonUnitalNon... | true |
Std.Tactic.BVDecide.BVExpr.bitblast.AppendTarget.noConfusionType | Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Impl.Operations.Append | [
"instHAdd",
"Std.Tactic.BVDecide.BVExpr.bitblast.AppendTarget",
"Std.Tactic.BVDecide.BVExpr.bitblast.AppendTarget.casesOn",
"Std.Sat.AIG",
"HAdd.hAdd",
"Nat",
"instAddNat",
"HEq",
"Hashable",
"Std.Sat.AIG.RefVec",
"Eq",
"DecidableEq"
] | false |
Lie.Derivation.ofLieDerivation | Mathlib.Algebra.Lie.Derivation.BaseChange | [
"LieHom",
"LieAlgebra.toModule",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"LieDerivation",
"LieRing.toAddCommGroup",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Lie.Derivation.ofDerivation._proof_6",
"LieAlgebra.ExtendScalars.in... | true |
AddGroupNorm.casesOn | Mathlib.Analysis.Normed.Group.Seminorm | [
"AddGroup.toSubtractionMonoid",
"Real",
"Real.instZero",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"AddGroupSeminorm",
"AddGroup",
"AddGroupSeminorm.toFun",
"AddGroupNorm.rec",
"Zero.toOfNat0",
"OfNat.ofNat",
"NegZeroClass.toZero",
"Eq",
"AddGroupNorm",
"... | false |
Std.DTreeMap.Internal.Impl.glue.eq_3 | Std.Data.DTreeMap.Internal.Operations | [
"Std.DTreeMap.Internal.Impl.View",
"Std.DTreeMap.Internal.Impl.glue._proof_14",
"Std.DTreeMap.Internal.Impl.minView",
"Std.DTreeMap.Internal.Impl.Balanced",
"Std.DTreeMap.Internal.Impl.glue._proof_12",
"Std.DTreeMap.Internal.Impl.size",
"Std.DTreeMap.Internal.Impl.inner",
"Std.DTreeMap.Internal.Impl.m... | true |
OpenPartialHomeomorph.IsImage.restr._proof_3 | Mathlib.Topology.OpenPartialHomeomorph.IsImage | [
"PartialEquiv.target",
"Set.inter_subset_left",
"OpenPartialHomeomorph.toFun'",
"OpenPartialHomeomorph.IsImage",
"TopologicalSpace",
"OpenPartialHomeomorph.continuousOn",
"OpenPartialHomeomorph.IsImage.toPartialEquiv",
"PartialEquiv.source",
"ContinuousOn.mono",
"ContinuousOn",
"OpenPartialHomeo... | false |
_private.Mathlib.MeasureTheory.Measure.Stieltjes.0.StieltjesFunction.outer_trim._simp_1_1 | Mathlib.MeasureTheory.Measure.Stieltjes | [
"Preorder.toLT",
"iInf",
"PartialOrder.toPreorder",
"Exists",
"CompleteLattice.toCompleteSemilatticeInf",
"iInf_lt_iff",
"LT.lt",
"propext",
"CompleteLinearOrder",
"CompleteLattice.toCompleteSemilatticeSup",
"CompleteSemilatticeInf.toInfSet",
"CompleteSemilatticeSup.toPartialOrder",
"Eq",
... | false |
Lean.Lsp.instToJsonDiagnosticSeverity.match_1 | Lean.Data.Lsp.Diagnostics | [
"Lean.Lsp.DiagnosticSeverity.information",
"Unit.unit",
"Lean.Lsp.DiagnosticSeverity.warning",
"Lean.Lsp.DiagnosticSeverity",
"Lean.Lsp.DiagnosticSeverity.casesOn",
"Unit",
"Lean.Lsp.DiagnosticSeverity.hint",
"Lean.Lsp.DiagnosticSeverity.error"
] | false |
Vector.range'._proof_1 | Init.Data.Vector.Basic | [
"congrArg",
"Array.range'",
"Nat",
"True",
"eq_self",
"of_eq_true",
"congrFun'",
"Array.size_range'",
"Eq",
"Array.size",
"Eq.trans"
] | false |
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