name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
DirectLimit.NonUnitalRing.lift_of | Mathlib.Algebra.Colimit.DirectLimit | [
"DirectLimit.NonUnitalRing.lift",
"Preorder.toLE",
"LE.le",
"NonUnitalRingHom.instFunLike",
"DirectLimit",
"IsDirectedOrder",
"Nonempty",
"NonUnitalRingHomClass",
"DirectedSystem",
"NonUnitalRingHom",
"NonUnitalNonAssocSemiring",
"Eq",
"DFunLike.coe",
"DirectLimit.instNonUnitalNonAssocSemi... | true |
Multiset.countP_congr | Mathlib.Data.Multiset.Count | [
"Eq.mpr",
"_private.Mathlib.Data.Multiset.Count.0.Multiset.countP_congr._simp_1_1",
"List.Perm.countP_congr",
"Multiset.mem_coe._simp_1",
"eq_iff_iff._simp_1",
"Membership.mem",
"Multiset",
"Eq.mp",
"id",
"List.Perm",
"Quot.induction_on₂",
"Multiset.instMembership",
"List",
"Multiset.ofLis... | true |
instToStringFloat32 | Init.Data.Float32 | [
"ToString",
"Float32.toString",
"ToString.mk",
"Float32"
] | true |
Std.Tactic.BVDecide.BVExpr.bitblast.blastUdiv.ShiftConcatInput.lhs | Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Impl.Operations.Udiv | [
"Std.Sat.AIG",
"Nat",
"Std.Tactic.BVDecide.BVExpr.bitblast.blastUdiv.ShiftConcatInput",
"Hashable",
"Std.Sat.AIG.RefVec",
"DecidableEq"
] | true |
Lean.Server.RequestHandler._sizeOf_inst | Lean.Server.Requests | [
"Lean.Server.RequestHandler",
"SizeOf.mk",
"Lean.Server.RequestHandler._sizeOf_1",
"SizeOf"
] | false |
BddOrd.instConcreteCategoryBoundedOrderHomCarrier._proof_2 | Mathlib.Order.Category.BddOrd | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"id",
"BddOrd",
"BddOrd.instCategory",
"Eq.refl",
"CategoryTheory.Category.toCategoryStruct",
"_private.Mathlib.Order.Category.BddOrd.0.BddOrd.Hom.mk",
"Eq",
"BddOrd.Hom.hom'"
] | false |
Set.coe_snd_biUnionEqSigmaOfDisjoint | Mathlib.Data.Set.Pairwise.Lattice | [
"Equiv.instEquivLike",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"congrArg",
"Set.PairwiseDisjoint",
"Set.biUnionEqSigmaOfDisjoint._proof_1",
"Equiv.subtypeEquiv._proof_3",
"Membership.mem",
"Set.Elem",
"Equiv.subtypeEquivProp._proof_1",
"Equiv",
"Sigma.fst",
"Set.biUnionEqSigmaOfDisj... | true |
Quaternion.instNormedAddCommGroupReal._proof_3 | Mathlib.Analysis.Quaternion | [
"Quaternion.re_star",
"Quaternion.algebra",
"NegZeroClass.toNeg",
"instTrivialStarReal",
"Real",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"QuaternionAlgebra.imI",
"Semiring.toModule",
"HMul.hMul",
"Inner.inner",
"Real.instZero",
"Real.instRCLike",
"AddGroupWithOne.toAd... | false |
Aesop.TraceOption.mk.noConfusion | Aesop.Tracing | [
"Lean.Option",
"Aesop.TraceOption.mk",
"Aesop.TraceOption.noConfusion",
"id",
"Aesop.TraceOption",
"Bool",
"Lean.Name",
"Eq"
] | false |
MvPolynomial.killCompl_monomial_eq_monomial_comapDomain_of_subset | Mathlib.Algebra.MvPolynomial.Rename | [
"Eq.mpr",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"Semiring.toModule",
"MvPolynomial.killCompl",
"AddMonoidAlgebra.addAddCommMonoid",
"congrArg",
"CommSemiring.toSemiring",
"Function.Injective.injOn",
"AlgHom",
"Finset",
"Finsupp.mapDomain",
"AlgHom.funLike",
"AddMonoid.toAddZ... | true |
CategoryTheory.Functor.Elements.initialOfCorepresentableBy | Mathlib.CategoryTheory.Elements | [
"CategoryTheory.Functor.Elements",
"CategoryTheory.Functor",
"Equiv.instEquivLike",
"CategoryTheory.Functor.CorepresentableBy",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.CorepresentableBy.homEquiv",
"CategoryTheory.CategoryStruct.id",
"Equiv",
"CategoryTheory.... | true |
torusMap_zero_radius | Mathlib.MeasureTheory.Integral.TorusIntegral | [
"Iff.mpr",
"Real",
"Real.instZero",
"torusMap_eq_center_iff",
"torusMap",
"Pi.instZero",
"funext",
"Nat",
"Function.const",
"Zero.toOfNat0",
"Complex",
"OfNat.ofNat",
"Fin",
"Eq",
"rfl"
] | true |
Ordinal.inductionOnWellOrder | Mathlib.SetTheory.Ordinal.Basic | [
"Preorder.toLT",
"isWellOrder_lt",
"LinearOrder",
"WellFoundedLT",
"PartialOrder.toPreorder",
"Classical.propDecidable",
"SemilatticeInf.toPartialOrder",
"Ordinal.type",
"inferInstance",
"DistribLattice.toLattice",
"IsWellOrder",
"IsWellOrder.toIsWellFounded",
"LT.lt",
"linearOrderOfSTO",
... | true |
MeasureTheory.MemLp.exists_boundedContinuous_integral_rpow_sub_le | Mathlib.MeasureTheory.Function.ContinuousMapDense | [
"Iff.mpr",
"Norm.norm",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"MulOne.toOne",
"Real.instPow",
"MeasureTheory.integral_nonneg",
"Real.partialOrder",
"Real.instLE",
"Real.rpow_pos_of_pos",
"Real",
"ENNReal.ofNNReal",
"DivInvMonoid.toInv",
"MeasureTheory.Measure",
"Preorder.toLT",
"... | true |
ContinuousOpenMap._sizeOf_inst | Mathlib.Topology.Hom.Open | [
"ContinuousOpenMap._sizeOf_1",
"TopologicalSpace",
"SizeOf.mk",
"SizeOf",
"ContinuousOpenMap"
] | false |
indicator_ae_eq_zero_of_restrict_ae_eq_zero | Mathlib.MeasureTheory.Measure.Restrict | [
"MeasureTheory.ae",
"False",
"MeasureTheory.Measure",
"MeasurableSet",
"eq_false",
"congrArg",
"Set.indicator",
"Filter.Eventually",
"setOf",
"Classical.propDecidable",
"Membership.mem",
"Filter.mp_mem",
"MeasureTheory.Measure.restrict",
"Eq.mp",
"Filter.EventuallyEq",
"Filter.Eventual... | true |
AlgebraicGeometry.pointEquivClosedPoint._proof_4 | Mathlib.AlgebraicGeometry.AlgClosed.Basic | [
"AlgebraicGeometry.Spec",
"Subtype.mk.congr_simp",
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"AlgebraicGeometry.Scheme",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
... | false |
CategoryTheory.CommMon.X | Mathlib.CategoryTheory.Monoidal.CommMon_ | [
"CategoryTheory.MonoidalCategory",
"CategoryTheory.BraidedCategory",
"CategoryTheory.CommMon",
"CategoryTheory.Category"
] | true |
CategoryTheory.Limits.WalkingMulticospan.ctorElim | Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer | [
"CategoryTheory.Limits.MulticospanShape.L",
"CategoryTheory.Limits.WalkingMulticospan.ctorElimType",
"CategoryTheory.Limits.WalkingMulticospan.casesOn",
"CategoryTheory.Limits.WalkingMulticospan.right",
"Nat",
"CategoryTheory.Limits.WalkingMulticospan",
"Eq.ndrec",
"CategoryTheory.Limits.WalkingMultic... | false |
Lean.Doc.Block.brecOn_7 | Lean.DocString.Types | [
"Lean.Doc.Block",
"Lean.Doc.Block.below_2",
"Lean.Doc.Block.brecOn_7.go",
"Lean.Doc.Block.below_6",
"Lean.Doc.DescItem",
"Lean.Doc.Block.below_7",
"Array",
"Lean.Doc.Block.below",
"List",
"Lean.Doc.Block.below_1",
"Lean.Doc.ListItem",
"Lean.Doc.Block.below_5",
"Lean.Doc.Block.below_3",
"Le... | false |
AddMonoidAlgebra.single_mem_grade | Mathlib.Algebra.MonoidAlgebra.Grading | [
"Submodule",
"Semiring.toModule",
"AddMonoidAlgebra.addAddCommMonoid",
"CommSemiring.toSemiring",
"Membership.mem",
"id",
"AddMonoidAlgebra.grade",
"CommSemiring",
"Submodule.setLike",
"AddMonoidAlgebra",
"AddMonoidAlgebra.single",
"AddMonoidAlgebra.single_mem_gradeBy",
"SetLike.instMembersh... | true |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.Equiv.entryAtIdx_eq._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 |
MeasureTheory.LocallyIntegrable.mono_measure._gcongr_1 | Mathlib.MeasureTheory.Function.LocallyIntegrable | [
"MeasureTheory.Measure",
"PartialOrder.toPreorder",
"MeasureTheory.LocallyIntegrable",
"Preorder.toLE",
"MeasureTheory.LocallyIntegrable.mono_measure",
"LE.le",
"ContinuousENorm",
"MeasurableSpace",
"TopologicalSpace",
"MeasureTheory.Measure.instPartialOrder"
] | false |
TopCat.instAbelianPresheaf._proof_4 | Mathlib.Topology.Sheaves.Abelian | [
"CategoryTheory.Abelian.toPreadditive",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"TopologicalSpace.Opens.instPartialOrder",
"AddCommGroup.toAddCommMonoid",
"TopCat.instCategoryPresheaf",
"PartialOrder.toPreorder",
"TopologicalSpace.Opens",
"CategoryTheory.Abelian",
"To... | false |
Equiv.invFun | Mathlib.Logic.Equiv.Defs | [
"Equiv"
] | true |
Mathlib.TacticAnalysis.Pass._sizeOf_inst | Mathlib.Tactic.TacticAnalysis | [
"Mathlib.TacticAnalysis.Pass._sizeOf_1",
"SizeOf.mk",
"Mathlib.TacticAnalysis.Pass",
"SizeOf"
] | false |
Matrix.vecMul_empty | Mathlib.LinearAlgebra.Matrix.Notation | [
"Matrix",
"Matrix.vecMul",
"instOfNatNat",
"Matrix.empty_eq",
"Fintype",
"Nat",
"Matrix.vecEmpty",
"NonUnitalNonAssocSemiring",
"OfNat.ofNat",
"Fin",
"Eq"
] | true |
_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_24 | Mathlib.Data.List.Cycle | [
"List.getLast",
"Lean.Grind.nestedProof",
"Membership.mem",
"Ne",
"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4",
"List",
"List.instMembership",
"List.getLast_mem",
"Eq",
"Not",
"List.nil"
] | false |
NumberField.basisOfFractionalIdeal._proof_2 | Mathlib.NumberTheory.NumberField.FractionalIdeal | [
"Units.val",
"Submodule",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"NumberField.RingOfIntegers.instIsFractionRing",
"NumberField.instCommRingRingOfIntegers",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"NumberField.RingOfIntegers.instAlgebra_1",... | false |
AddUnits.leftOfAdd.eq_1 | Mathlib.Algebra.Group.Commute.Units | [
"AddUnits.leftOfAdd",
"AddUnits.val",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"AddUnits.leftOfAdd._proof_2",
"AddCommute",
"instHAdd",
"HAdd.hAdd",
"AddMonoid",
"AddZero.toAdd",
"Eq.refl",
"AddUnits.instNeg",
"Eq",
"Neg.neg",
"AddUnits.leftOfAdd._proof_1",
"AddUnits",
"... | true |
Subring.instField._proof_13 | Mathlib.Algebra.Ring.Subring.Basic | [
"Subring.instField._proof_7",
"Semiring.toNatCast",
"NNRat.castRec",
"Semigroup.toMul",
"instHDiv",
"GroupWithZero.toDivisionMonoid",
"HMul.hMul",
"Subring.instSetLike",
"Ring.toNonAssocRing",
"Subring.center",
"DivisionSemiring.toGroupWithZero",
"Membership.mem",
"DivisionRing.toDivisionSem... | false |
List.prod_inv_reverse | Mathlib.Algebra.BigOperators.Group.List.Basic | [
"List.brecOn",
"InvOneClass.toOne",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"List.map",
"Group",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"List.prod_inv_reverse._f",
"Group.toDivInvMonoid",
"List",
"MulOneClass.... | true |
Equiv.prodAssoc.match_3 | Mathlib.Logic.Equiv.Prod | [
"Prod.mk",
"Prod",
"Prod.casesOn"
] | false |
Ordinal.CNF.rec_pos | Mathlib.SetTheory.Ordinal.CantorNormalForm | [
"Eq.mpr",
"Ordinal.instLinearOrder",
"LinearOrder.toDecidableEq",
"_private.Mathlib.SetTheory.Ordinal.CantorNormalForm.0.Ordinal.CNF.rec._proof_4",
"congrArg",
"_private.Mathlib.SetTheory.Ordinal.CantorNormalForm.0.Ordinal.CNF.rec.eq_1",
"Eq.rec",
"Ordinal.mod",
"id",
"instHMod",
"Ne",
"dif_ne... | true |
Bundle.TotalSpace.toProd._proof_1 | Mathlib.Data.Bundle | [
"Function.LeftInverse",
"Bundle.TotalSpace.mk",
"Prod.mk",
"Prod.fst",
"Bundle.TotalSpace.proj",
"Bundle.TotalSpace",
"Eq.refl",
"Bundle.TotalSpace.snd",
"Prod",
"Prod.snd"
] | false |
Affine.Simplex.isCompact_closedInterior | Mathlib.Analysis.Convex.Topology | [
"Eq.mpr",
"instNeZeroNatHAdd_1",
"Affine.Simplex.points",
"AffineMap.instFunLike",
"ChainCompletePartialOrder.instOfCompleteLattice",
"ContinuousSMul",
"congrArg",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"IsTopologicalAddTorsor",
"LinearOrder",
"AffineEquiv.vaddConst"... | true |
_private.Mathlib.Algebra.BigOperators.ModEq.0.Int.prod_modEq_single._simp_1_1 | Mathlib.Algebra.BigOperators.ModEq | [
"Int.cast",
"ZMod.commRing",
"Int",
"AddGroupWithOne.toIntCast",
"Nat.cast",
"ZMod",
"ZMod.intCast_eq_intCast_iff",
"Nat",
"Int.ModEq",
"propext",
"instNatCastInt",
"CommRing.toRing",
"Eq.symm",
"Eq",
"Ring.toAddGroupWithOne"
] | false |
CategoryTheory.Comma.unopFunctor_map | Mathlib.CategoryTheory.Comma.Basic | [
"CategoryTheory.Comma.unopFunctor._proof_4",
"CategoryTheory.Functor.op",
"CategoryTheory.Functor",
"CategoryTheory.Comma.right",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Comma.unopFunctor",
"CategoryTheory.Comma.left",
"Quiver.Hom.unop",
"CategoryTheor... | true |
AddCommMonCat.recOn | Mathlib.Algebra.Category.MonCat.Basic | [
"AddCommMonCat",
"AddCommMonoid",
"AddCommMonCat.rec",
"AddCommMonCat.mk"
] | false |
Subfield.sInf_toSubring | Mathlib.Algebra.Field.Subfield.Basic | [
"iInf",
"Subring.instSetLike",
"Ring.toNonAssocRing",
"congrArg",
"Membership.mem",
"Subring.mem_iInf._simp_1",
"Subfield.mem_sInf._simp_1",
"DivisionRing.toRing",
"Subfield.instSetLike",
"iff_self",
"Iff",
"Subring",
"implies_congr",
"Subring.instInfSet",
"congr",
"True",
"of_eq_tru... | true |
himp_iff_imp._simp_1 | Mathlib.Order.Heyting.Basic | [
"himp_iff_imp",
"Prop.instHeytingAlgebra",
"GeneralizedHeytingAlgebra.toHImp",
"HeytingAlgebra.toGeneralizedHeytingAlgebra",
"propext",
"Eq",
"HImp.himp"
] | false |
WeierstrassCurve.Projective.negDblY_eq' | Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Formula | [
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"AddGroup.toSubtractionMonoid",
"Finsupp.instAddZeroClass",
"WeierstrassCurve.Projective.negY",
"Mathlib.Tactic.Ring.Common.neg_zero",
"Eq.mpr",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Mathlib.Tactic.Ring.Common.neg_mul",
"Weierst... | true |
HasFiniteFPowerSeriesOnBall.rec | Mathlib.Analysis.Analytic.CPolynomialDef | [
"NormedCommRing.toSeminormedCommRing",
"NormedSpace.toIsBoundedSMul",
"UniformContinuousConstSMul.to_continuousConstSMul",
"NormedSpace",
"FormalMultilinearSeries",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"IsBoundedSMul.... | false |
_private.Mathlib.Probability.Distributions.SetBernoulli.0.ProbabilityTheory.setBernoulli_ae_subset._simp_1_2 | Mathlib.Probability.Distributions.SetBernoulli | [
"Set.not_subset_iff_exists_mem_notMem",
"Membership.mem",
"Exists",
"HasSubset.Subset",
"And",
"propext",
"Eq",
"Set.instMembership",
"Not",
"Set.instHasSubset",
"Set"
] | false |
Set.biUnion_diff_biUnion_eq | Mathlib.Data.Set.Pairwise.Lattice | [
"Iff.mpr",
"Eq.mpr",
"Set.biUnion_diff_biUnion_subset",
"Disjoint.le_bot",
"False",
"Set.iUnion₂_subset",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"CompleteLattice.toLattice",
"congrArg",
"Set.PairwiseDisjoint",
"Membership.mem",
"Exists",
"Set.instUnion",
"id",
"Ne.symm",
"S... | true |
_private.Mathlib.CategoryTheory.Limits.Shapes.Images.0.CategoryTheory.Limits.image.map_id._simp_1_1 | Mathlib.CategoryTheory.Limits.Shapes.Images | [
"True",
"propext",
"Subsingleton",
"Eq",
"eq_iff_true_of_subsingleton"
] | false |
_private.Mathlib.Data.Finset.NAry.0.Finset.mem_image₂._simp_1_2 | Mathlib.Data.Finset.NAry | [
"And",
"and_assoc",
"propext",
"Eq"
] | false |
Mathlib.Tactic.WLOGResult.reductionGoal | Mathlib.Tactic.WLOG | [
"Lean.MVarId",
"Mathlib.Tactic.WLOGResult"
] | true |
NumberField.RingOfIntegers.mapAlgEquiv._proof_1 | Mathlib.NumberTheory.NumberField.Basic | [
"Algebra",
"AlgEquivClass.toAlgHomClass",
"Field.toSemifield",
"AlgHomClass",
"Semifield.toDivisionSemiring",
"EquivLike",
"DivisionSemiring.toSemiring",
"Semifield.toCommSemiring",
"Field",
"AlgEquivClass",
"EquivLike.toFunLike"
] | false |
Std.HashMap.getD_eq_fallback_of_contains_eq_false | Std.Data.HashMap.Lemmas | [
"Std.HashMap.contains",
"Std.HashMap",
"LawfulHashable",
"EquivBEq",
"Bool",
"Hashable",
"Std.DHashMap.Const.getD_eq_fallback_of_contains_eq_false",
"Std.HashMap.inner",
"Bool.false",
"BEq",
"Eq",
"Std.HashMap.getD"
] | true |
_private.Mathlib.Analysis.InnerProductSpace.Dual.0.InnerProductSpace.toDual._simp_5 | Mathlib.Analysis.InnerProductSpace.Dual | [
"False",
"eq_false",
"pow_ne_zero",
"Ne",
"Monoid.toPow",
"MonoidWithZero",
"MonoidWithZero.toMulZeroOneClass",
"HPow.hPow",
"Nat",
"Zero.toOfNat0",
"instHPow",
"MulZeroOneClass.toMulZeroClass",
"OfNat.ofNat",
"Eq",
"MonoidWithZero.toMonoid",
"MulZeroClass.toZero",
"IsReduced"
] | false |
CategoryTheory.Functor.isoWhiskerRight_twice | Mathlib.CategoryTheory.Whiskering | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.NatTrans.ext'",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Functor.associator",
"CategoryTheory.Iso",
"Category... | true |
ContinuousMap.concat | Mathlib.Topology.ContinuousMap.Interval | [
"OrderTopology",
"Continuous",
"ContinuousMap.mk",
"LinearOrder",
"ContinuousMap",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Classical.propDecidable",
"Preorder.toLE",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"Fact",
"LinearOrder.toDecidableLE",
"Set.Elem",
"DistribLattice.... | true |
Tactic.mkComp._sunfold | Mathlib.Tactic.HigherOrder | [
"guard",
"Pure.pure",
"Lean.MonadError.mk",
"Lean.instMonadExceptOfExceptionCoreM",
"Lean.Meta.mkAppOptM",
"String",
"Lean.Meta.State",
"Lean.instAddErrorMessageContextOfAddMessageContextOfMonad",
"Option.some",
"Lean.throwError",
"_private.Mathlib.Tactic.HigherOrder.0.Tactic.mkComp.match_1",
... | false |
GaussianInt.abs_natCast_norm | Mathlib.NumberTheory.Zsqrtd.GaussianInt | [
"GaussianInt",
"Int.instNegInt",
"Int",
"Nat.cast",
"Int.natAbs_of_nonneg",
"instOfNat",
"Int.natAbs",
"Zsqrtd.norm",
"instNatCastInt",
"OfNat.ofNat",
"Eq",
"GaussianInt.norm_nonneg",
"Neg.neg"
] | true |
instAddGroupObjOppositeOpensCarrierOfPresheafSmoothSheaf._aux_8 | Mathlib.Geometry.Manifold.Sheaf.Smooth | [
"instHSMul",
"Opposite",
"NormedSpace",
"instTopENat",
"TopologicalSpace.Opens.instPartialOrder",
"TopologicalSpace.Opens.instChartedSpace",
"PartialOrder.toPreorder",
"TopologicalSpace.Opens",
"Membership.mem",
"Subtype",
"Preorder.smallCategory",
"TopologicalSpace.Opens.instSetLike",
"With... | false |
StarAlgEquiv.trans_apply | Mathlib.Algebra.Star.StarAlgHom | [
"SMul",
"Mul",
"StarAlgEquiv",
"StarAlgEquiv.instFunLike",
"Star",
"StarAlgEquiv.trans",
"Eq",
"DFunLike.coe",
"Add",
"rfl"
] | true |
NNRat.instIsScalarTowerRight | Mathlib.Algebra.Ring.Action.Rat | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Semigroup.toMul",
"instHSMul",
"instSMulOfMul",
"NNRat.instDistribSMul",
"HMul.hMul",
"congrArg",
"IsScalarTower",
"AddMonoid.toAddZeroClass",
"mul_assoc",
"SemigroupWithZero.toSemigroup",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
... | true |
Id.instLawfulMonadLiftTOfLawfulMonad | Init.Control.Lawful.MonadLift.Instances | [
"Pure.pure",
"LawfulMonadLiftT",
"congrArg",
"Monad.toApplicative",
"MonadLiftT.monadLift",
"LawfulMonadLiftT.mk",
"LawfulMonad.bind_pure_comp",
"LawfulMonad",
"Id.run",
"Id",
"Applicative.toPure",
"True",
"eq_self",
"of_eq_true",
"Applicative.toFunctor",
"Monad.toBind",
"Bind.bind",... | true |
DistribLattice.ctorIdx | Mathlib.Order.Lattice | [
"DistribLattice",
"Nat"
] | false |
RelIso.instGroup._proof_2 | Mathlib.Algebra.Order.Group.End | [
"Mul.mk",
"RelIso.refl",
"One.mk",
"HMul.hMul",
"Semigroup.mk",
"npowRecAuto",
"instOfNatNat",
"RelIso",
"instHAdd",
"HAdd.hAdd",
"Nat",
"instAddNat",
"Eq.refl",
"RelIso.trans",
"OfNat.ofNat",
"Eq",
"rfl",
"instHMul"
] | false |
Std.Tactic.BVDecide.BVExpr.replicate.injEq | Std.Tactic.BVDecide.Bitblast.BVExpr.Basic | [
"HMul.hMul",
"Eq.propIntro",
"Lean.injEq_helper",
"HEq.homo_ndrec",
"instMulNat",
"And",
"Std.Tactic.BVDecide.BVExpr.replicate.inj",
"Nat",
"Std.Tactic.BVDecide.BVExpr.replicate",
"Eq.ndrec",
"Eq.refl",
"HEq",
"Std.Tactic.BVDecide.BVExpr",
"Eq",
"instHMul"
] | true |
Prod.map_iterate | Mathlib.Data.Prod.Basic | [
"Nat.recAux",
"congrArg",
"Function.comp",
"id",
"Prod.map",
"instOfNatNat",
"Nat.iterate",
"instHAdd",
"HAdd.hAdd",
"Nat",
"True",
"eq_self",
"of_eq_true",
"instAddNat",
"congrFun'",
"Prod",
"OfNat.ofNat",
"Eq",
"Eq.trans"
] | true |
WeierstrassCurve.Projective.addXYZ_Z | Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Formula | [
"CommRing",
"Fin.instOfNat",
"instOfNatNat",
"WeierstrassCurve.Projective.addZ",
"WeierstrassCurve.Projective",
"Nat.instNeZeroSucc",
"Nat",
"WeierstrassCurve.Projective.addXYZ",
"OfNat.ofNat",
"Fin",
"Eq",
"rfl"
] | true |
String.Legacy.Iterator.s | Init.Data.String.Iterator | [
"String",
"String.Legacy.Iterator"
] | true |
PseudoMetric.coe_le_coe | Mathlib.Topology.MetricSpace.BundledFun | [
"Iff.rfl",
"PseudoMetric",
"LE.le",
"LE",
"Pi.hasLe",
"Iff",
"PseudoMetric.instFunLikeForall",
"PseudoMetric.instLE",
"DFunLike.coe",
"Add",
"Zero"
] | true |
AlgebraicGeometry.morphismRestrictStalkMap._proof_2 | Mathlib.AlgebraicGeometry.Restrict | [
"AlgebraicGeometry.morphismRestrict_base_coe",
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"AlgebraicGeometry.Scheme",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"TopologicalSpace.Opens.instPartialOrder",
"CategoryTheor... | false |
CategoryTheory.NatTrans.naturality | Mathlib.CategoryTheory.NatTrans | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.map",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.NatTrans",
"Eq",
"CategoryTheory.Functor.obj",
"CategoryTheory.NatTrans.app",
"Categor... | true |
_private.Mathlib.Data.Finset.Union.0.Finset.bind_toFinset._simp_1_2 | Mathlib.Data.Finset.Union | [
"Membership.mem",
"Exists",
"Multiset",
"Multiset.instMembership",
"And",
"propext",
"Multiset.mem_bind",
"Eq",
"Multiset.bind"
] | false |
FreeSimplexQuiver.homRel.recOn | Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.Basic | [
"FreeSimplexQuiver.homRel.δ_comp_σ_of_le",
"FreeSimplexQuiver.homRel",
"CategoryTheory.CategoryStruct.toQuiver",
"FreeSimplexQuiver.σ",
"Quiver.Hom",
"Fin.succ",
"CategoryTheory.Paths.categoryPaths",
"FreeSimplexQuiver.mk",
"CategoryTheory.Paths",
"FreeSimplexQuiver.homRel.δ_comp_δ",
"CategoryTh... | false |
conditionallyCompleteLatticeOfsInf.eq_1 | Mathlib.Order.ConditionallyCompleteLattice.Defs | [
"Lattice.ofIsLUBofIsGLB",
"PartialOrder.toPreorder",
"ConditionallyCompleteLattice",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"PartialOrder",
"conditionallyCompleteLatticeOfsInf",
"InfSet",
"Set.instSingletonSet",
"SupSet.mk",
"Insert.insert",
"upperBounds",
"conditionallyCompleteLa... | true |
GrpCat.toAddGrp._proof_1 | Mathlib.Algebra.Category.Grp.EquivalenceGroupAddGroup | [
"GrpCat",
"Equiv.instEquivLike",
"CategoryTheory.CategoryStruct.toQuiver",
"MonoidHom",
"Quiver.Hom",
"GrpCat.str",
"Monoid.toMulOneClass",
"GrpCat.Hom.hom",
"Additive",
"AddGrpCat.instCategory",
"CategoryTheory.CategoryStruct.id",
"AddZeroClass.toAddZero",
"id",
"Equiv",
"DivInvMonoid.t... | false |
CategoryTheory.Abelian.SpectralObject.coreE₂CohomologicalFin | Mathlib.Algebra.Homology.SpectralObject.HasSpectralSequence | [
"CategoryTheory.Abelian.SpectralObject.coreE₂CohomologicalFin._proof_12",
"CategoryTheory.Abelian.SpectralObject.coreE₂CohomologicalFin._proof_27",
"CategoryTheory.Abelian.SpectralObject.coreE₂CohomologicalFin._proof_1",
"Fin.succ",
"PartialOrder.toPreorder",
"HSub.hSub",
"Fin.mk",
"Fin.clamp",
"Pro... | true |
WithBot.unbot_mono | Mathlib.Order.WithBot | [
"Iff.mpr",
"WithBot",
"Ne",
"Bot.bot",
"LE.le",
"LE",
"WithBot.unbot",
"WithBot.unbot_le_unbot_iff",
"WithBot.instLE",
"WithBot.bot"
] | true |
Algebra.traceMatrix._proof_1 | Mathlib.RingTheory.Trace.Basic | [
"CommRing",
"Semiring.toModule",
"CommSemiring.toSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"CommRing.toCommSemiring",
"CommMonoid.toMonoid",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"CommSemiring.toCommMonoid",
"Monoid.toSemigroup",
"Module.toDistribMulAction",
"SemigroupAct... | false |
Real.strictAntiOn_rpow_Ioi_of_exponent_neg | Mathlib.Analysis.SpecialFunctions.Pow.Real | [
"Real.instPow",
"Real",
"Set.Ioi",
"Preorder.toLT",
"Real.instZero",
"StrictAntiOn",
"Real.rpow_lt_rpow_of_neg",
"Real.instLT",
"Membership.mem",
"HPow.hPow",
"LT.lt",
"Zero.toOfNat0",
"instHPow",
"OfNat.ofNat",
"Set.instMembership",
"Real.instPreorder",
"Set"
] | true |
antisymm_of | Mathlib.Order.Defs.Unbundled | [
"Std.Antisymm",
"antisymm",
"Eq"
] | true |
isPurelyInseparable_iff | Mathlib.FieldTheory.PurelyInseparable.Basic | [
"IsPurelyInseparable.inseparable'",
"CommRing",
"Subring.instSetLike",
"Algebra.algebraMap",
"Ring.toNonAssocRing",
"IsPurelyInseparable.isIntegral'",
"Algebra",
"Membership.mem",
"IsPurelyInseparable.mk",
"CommRing.toNonAssocCommRing",
"And",
"CommRing.toCommSemiring",
"Iff",
"IsIntegral"... | true |
RatFunc.num_inv_dvd | Mathlib.FieldTheory.RatFunc.Basic | [
"Eq.mpr",
"DivInvMonoid.toInv",
"Dvd.dvd",
"instHDiv",
"RatFunc.denom",
"CommRing.toNonUnitalCommRing",
"DivisionCommMonoid.toDivisionMonoid",
"Algebra.algebraMap",
"congrArg",
"CommSemiring.toSemiring",
"semigroupDvd",
"RatFunc.instDiv",
"RingHom",
"Exists",
"SemigroupWithZero.toSemigro... | true |
Cardinal.mk_finsupp_lift_of_infinite' | Mathlib.SetTheory.Cardinal.Finsupp | [
"Iff.mpr",
"Eq.mpr",
"PSum.casesOn",
"Cardinal.lift_le_aleph0",
"Lattice.toSemilatticeSup",
"Cardinal.mk_finsupp_lift_of_infinite",
"Cardinal",
"congrArg",
"CommSemiring.toSemiring",
"Cardinal.commSemiring",
"PartialOrder.toPreorder",
"PSum",
"Cardinal.lift",
"Cardinal.mk",
"PSum.inr",
... | true |
Batteries.PairingHeap.headI | Batteries.Data.PairingHeap | [
"Inhabited.default",
"Option.getD",
"Batteries.PairingHeap.head?",
"Bool",
"Inhabited",
"Batteries.PairingHeap"
] | true |
ContinuousMap.instStar | Mathlib.Topology.ContinuousMap.Star | [
"ContinuousStar",
"ContinuousMap",
"ContinuousMap.comp",
"TopologicalSpace",
"Star.mk",
"Star",
"starContinuousMap"
] | true |
antitoneOn_of_le_sub_one | Mathlib.Algebra.Order.SuccPred | [
"Eq.mpr",
"PredSubOrder.toPredOrder",
"Preorder.toLT",
"One",
"congrArg",
"PartialOrder.toPreorder",
"HSub.hSub",
"Preorder.toLE",
"Membership.mem",
"Exists",
"antitoneOn_of_le_pred",
"PartialOrder",
"Eq.mp",
"id",
"LE.le",
"Order.pred_eq_sub_one",
"not_isMin_iff._simp_2",
"forall_... | true |
CommGroup.toDistribLattice._proof_1 | Mathlib.Algebra.Order.Group.Lattice | [
"IsLeftCancelMul.mulLeftReflectLE_of_mulLeftReflectLT",
"Eq.mpr",
"Lattice",
"Preorder.toLT",
"Lattice.toSemilatticeSup",
"HMul.hMul",
"CommMonoid.toCommSemigroup",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"IsLeftCancelMul.mulLeftStrictMono_of_mulLeftMono",
"congrArg",
"CancelC... | false |
Lean.Elab.Term.ToDepElimPattern.State._sizeOf_inst | Lean.Elab.Match | [
"Lean.Elab.Term.ToDepElimPattern.State._sizeOf_1",
"SizeOf.mk",
"SizeOf",
"Lean.Elab.Term.ToDepElimPattern.State"
] | false |
SimpleGraph.Hom.ofLE_apply | Mathlib.Combinatorics.SimpleGraph.Maps | [
"RelHom.instFunLike",
"SimpleGraph.Adj",
"LE.le",
"SimpleGraph",
"SimpleGraph.Hom.ofLE",
"SimpleGraph.Hom",
"Eq",
"DFunLike.coe",
"rfl",
"SimpleGraph.instLE"
] | true |
AdjoinRoot.instNumberFieldRat | Mathlib.NumberTheory.NumberField.Basic | [
"Eq.mpr",
"AdjoinRoot",
"Algebra.algebraMap",
"Ring.toNonAssocRing",
"CommSemiring.toSemiring",
"Rat",
"Rat.commSemiring",
"Field.toDivisionRing",
"Field.instIsLocalRing",
"Fact",
"Irreducible",
"Algebra.toModule",
"Algebra.id",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"Rat.i... | true |
Int.le_add_of_sub_left_le | Init.Data.Int.Order | [
"congrArg",
"Int.add_le_add_right",
"HSub.hSub",
"Eq.mp",
"Int",
"LE.le",
"Int.add_comm",
"Int.sub_add_cancel",
"instHAdd",
"instHSub",
"HAdd.hAdd",
"Int.instAdd",
"Int.instSub",
"Int.instLEInt"
] | true |
Lean.ResolveName.resolveNamespaceUsingOpenDecls | Lean.ResolveName | [
"List.brecOn",
"List",
"Lean.Name",
"Lean.ResolveName.resolveNamespaceUsingOpenDecls._f",
"Lean.Environment",
"Lean.OpenDecl"
] | true |
HomotopicalAlgebra.PrepathObject.map_p₁ | Mathlib.AlgebraicTopology.ModelCategory.PathObject | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HomotopicalAlgebra.PrepathObject.P",
"HomotopicalAlgebra.PrepathObject.p₁",
"CategoryTheory.Functor.map",
"Eq.refl",
"CategoryTheory.Category.toCategoryStruct",
"Eq",
"HomotopicalAlgebra.PrepathObject.map",
"Categ... | true |
_private.Mathlib.Algebra.DirectSum.Basic.0.DirectSum.map_eq_iff._simp_1_1 | Mathlib.Algebra.DirectSum.Basic | [
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"DFinsupp.instDFunLike",
"AddCommMonoid",
"AddZero.toZero",
"DirectSum.ext_iff",
"propext",
"DFinsupp",
"AddCommMonoid.toAddMonoid",
"Eq",
"DirectSum",
"DFunLike.coe"
] | false |
SkewMonoidAlgebra.algHom_ext | Mathlib.Algebra.SkewMonoidAlgebra.Basic | [
"AlgHom.toLinearMap",
"Monoid",
"SkewMonoidAlgebra.lhom_ext'",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Semiring.toModule",
"instSMulOfMul",
"SkewMonoidAlgebra.instModule",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AlgHom",
"AlgHom.funLike",
"AddMonoid.toAddZeroClass",
... | true |
Mathlib.Meta.FunProp.LambdaTheoremArgs.ctorIdx | Mathlib.Tactic.FunProp.Theorems | [
"Nat",
"Mathlib.Meta.FunProp.LambdaTheoremArgs",
"Mathlib.Meta.FunProp.LambdaTheoremArgs.casesOn"
] | false |
_private.Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex.0.Complex.cos_eq_cos_iff._simp_1_3 | Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex | [
"AddMonoid.toAddZeroClass",
"HSub.hSub",
"AddZeroClass.toAddZero",
"SubNegMonoid.toSub",
"instHAdd",
"AddGroup",
"instHSub",
"AddGroup.toSubNegMonoid",
"sub_eq_iff_eq_add",
"HAdd.hAdd",
"propext",
"AddZero.toAdd",
"SubNegMonoid.toAddMonoid",
"Eq"
] | false |
Algebra.FormallyUnramified.localization_base | Mathlib.RingTheory.Unramified.Basic | [
"CommRing",
"CommSemiring.toSemiring",
"IsScalarTower",
"Algebra",
"Algebra.toSMul",
"Algebra.FormallyUnramified",
"MulZeroOneClass.toMulOneClass",
"instMulZeroOneClassOfSemiring",
"CommRing.toCommSemiring",
"Algebra.FormallyUnramified.of_restrictScalars",
"Submonoid"
] | true |
_private.Batteries.Data.MLList.Basic.0.MLList.specImpl | Batteries.Data.MLList.Basic | [
"_private.Batteries.Data.MLList.Basic.0.MLList.unconsImpl",
"_private.Batteries.Data.MLList.Basic.0.MLList.MLListImpl.cons",
"_private.Batteries.Data.MLList.Basic.0.MLList.Spec.mk",
"_private.Batteries.Data.MLList.Basic.0.MLList.MLListImpl.squash",
"_private.Batteries.Data.MLList.Basic.0.MLList.uncons?Impl"... | true |
Lean.Omega.LinearCombo.sub | Init.Omega.LinearCombo | [
"Lean.Omega.IntList.instSub",
"Lean.Omega.LinearCombo.coeffs",
"HSub.hSub",
"Int",
"Lean.Omega.LinearCombo",
"instHSub",
"Lean.Omega.Coeffs",
"Lean.Omega.LinearCombo.mk",
"Int.instSub",
"Lean.Omega.LinearCombo.const"
] | true |
AddCommMonCat.FilteredColimits.M | Mathlib.Algebra.Category.MonCat.FilteredColimits | [
"CategoryTheory.Functor",
"AddMonCat.FilteredColimits.colimit",
"AddMonCat.instConcreteCategoryAddMonoidHomCarrier",
"AddCommMonCat.instCategory",
"AddMonoid.toAddZeroClass",
"CategoryTheory.Functor.comp",
"AddCommMonCat",
"AddZeroClass.toAddZero",
"AddCommMonCat.instConcreteCategoryAddMonoidHomCarr... | true |
Vector.findFinIdx?_singleton._proof_1 | Init.Data.Vector.Find | [
"congrArg",
"instOfNatNat",
"Nat.lt_add_one._simp_1",
"List.toArray",
"List.cons",
"List.size_toArray",
"Nat",
"LT.lt",
"True",
"of_eq_true",
"instLTNat",
"Nat.zero_add",
"OfNat.ofNat",
"List.length",
"Array.size",
"Eq.trans",
"List.nil"
] | false |
_private.Std.Time.Date.ValidDate.0.Std.Time.ValidDate.ofOrdinal._proof_6 | Std.Time.Date.ValidDate | [
"_private.Std.Time.Date.Unit.Month.0.Std.Time.Month.Ordinal.monthSizesNonLeap",
"Iff.mpr",
"Rat.instOfNat",
"False",
"Subtype.mk.congr_simp",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"Std.Time.Day.instOfNatOffset",
"of_decide_eq_true",
"le_of_le_of_eq",
"Std.Time.Month.Ordinal.days",
"L... | false |
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