name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Std.Tactic.BVDecide.BVExpr.bitblast.blastExtractAndExtend.go._unary._proof_5 | Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Impl.Operations.Cpop | [
"HMul.hMul",
"instMulNat",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"instAddNat",
"OfNat.ofNat",
"Eq.symm",
"Eq",
"instHMul"
] | false |
InitialSeg.mem_range_of_rel' | Mathlib.Order.InitialSeg | [
"Membership.mem",
"RelEmbedding",
"InitialSeg.toRelEmbedding",
"InitialSeg",
"Set.range",
"Set.instMembership",
"DFunLike.coe",
"RelEmbedding.instFunLike",
"Set"
] | true |
Std.DHashMap.Internal.List.HashesTo.mk | Std.Data.DHashMap.Internal.Defs | [
"Std.DHashMap.Internal.mkIdx",
"Membership.mem",
"Sigma.fst",
"instOfNatNat",
"List",
"List.instMembership",
"USize.toNat",
"Hashable.hash",
"Nat",
"LT.lt",
"Std.DHashMap.Internal.List.HashesTo.mk",
"Hashable",
"instLTNat",
"OfNat.ofNat",
"Subtype.val",
"BEq",
"Eq",
"Std.DHashMap.I... | true |
MonCat.instConcreteCategoryMonoidHomCarrier._proof_1 | Mathlib.Algebra.Category.MonCat.Basic | [
"MonoidHom",
"Monoid.toMulOneClass",
"_private.Mathlib.Algebra.Category.MonCat.Basic.0.MonCat.Hom.mk",
"id",
"MonCat",
"MonCat.carrier",
"MulOneClass.toMulOne",
"Eq.refl",
"Eq",
"MonCat.str",
"MonCat.Hom.hom'"
] | false |
_private.Mathlib.RingTheory.Polynomial.SmallDegreeVieta.0.Polynomial.eq_quadratic_of_degree_le_two._abel_1_1 | Mathlib.RingTheory.Polynomial.SmallDegreeVieta | [
"Polynomial.C",
"NonAssocSemiring.toAddCommMonoidWithOne",
"HMul.hMul",
"AddMonoid.toAddZeroClass",
"Mathlib.Tactic.Abel.subst_into_add",
"Mathlib.Tactic.Abel.term",
"RingHom",
"AddZeroClass.toAddZero",
"instOfNatNat",
"Polynomial.instAdd",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"zero_add"... | false |
CategoryTheory.PullbackShift.adjunction_counit | Mathlib.CategoryTheory.Shift.Pullback | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"AddMonoid.toAddZeroClass",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.id",
"AddZeroClass.toAddZero",
"CategoryTheory.Adjunction.counit",
"CategoryTheory.NatTrans.Pullba... | true |
CategoryTheory.SmallObject.FunctorObjIndex.comm_assoc | Mathlib.CategoryTheory.SmallObject.Construction | [
"CategoryTheory.Category.assoc",
"CategoryTheory.SmallObject.FunctorObjIndex.i",
"CategoryTheory.Limits.hasColimitOfHasColimitsOfShape",
"CategoryTheory.SmallObject.FunctorObjIndex",
"CategoryTheory.Limits.HasColimitsOfShape",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"Cate... | true |
ContinuousLinearMap.IsIdempotentElem.ext | Mathlib.Topology.Algebra.Module.ContinuousLinearMap.Idempotent | [
"Iff.mpr",
"Submodule",
"RingHomSurjective.ids",
"ContinuousLinearMap.IsIdempotentElem.ext_iff",
"AddCommGroup.toAddCommMonoid",
"LinearMap.ker",
"LinearMap.range",
"AddCommGroup",
"ContinuousLinearMap.toLinearMap",
"ContinuousLinearMap",
"TopologicalSpace",
"And",
"IsIdempotentElem",
"Mod... | true |
_private.Mathlib.RingTheory.MvPowerSeries.Order.0.MvPowerSeries.le_weightedOrder._simp_1_1 | Mathlib.RingTheory.MvPowerSeries.Order | [
"Preorder.toLT",
"AddMonoid.toAddSemigroup",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"AddLeftMono",
"Preorder.toLE",
"AddZeroClass.toAddZero",
"PartialOrder",
"ZeroLEOneClass",
"AddMonoidWithOne.toNatCast",
"Nat.cast",
"CharZero",
"AddMonoidWithOne.toOne",
"AddZero.toZero",
... | false |
Pi.cancelMonoid._proof_1 | Mathlib.Algebra.Group.Pi.Basic | [
"CancelMonoid.toRightCancelMonoid",
"Semigroup.toMul",
"Pi.rightCancelMonoid",
"RightCancelMonoid.toIsRightCancelMul",
"CancelMonoid",
"Monoid.toSemigroup",
"RightCancelMonoid.toMonoid",
"IsRightCancelMul"
] | false |
ULift.forall | Mathlib.Data.ULift | [
"Function.Surjective.forall",
"ULift",
"ULift.up_surjective",
"Iff",
"ULift.up"
] | true |
MonoidHom.smulOneHom | Mathlib.Algebra.Group.Action.Hom | [
"Monoid",
"MulOne.toOne",
"instHSMul",
"instSMulOfMul",
"MonoidHom",
"Monoid.toMulOneClass",
"MonoidHom.smulOneHom._proof_1",
"IsScalarTower",
"OneHom.mk",
"MulOne.toMul",
"MonoidHom.mk",
"MulOneClass.toMulOne",
"MulAction",
"Monoid.toSemigroup",
"One.toOfNat1",
"HSMul.hSMul",
"Semig... | true |
_private.Lean.Meta.Tactic.Grind.Intro.0.Lean.Meta.Grind.Action.hugeNumber | Lean.Meta.Tactic.Grind.Intro | [
"instOfNatNat",
"Nat",
"OfNat.ofNat"
] | true |
Lean.Macro.State | Init.Prelude | [
"_private.Init.Prelude.0.Lean.Macro.State.mk"
] | true |
List.perm_reverse | Mathlib.Data.List.Basic | [
"List.Perm",
"List.Perm.trans",
"List",
"Iff",
"Iff.intro",
"List.reverse",
"List.Perm.symm",
"List.reverse_perm"
] | true |
CategoryTheory.EnrichedCat.bicategory._proof_3 | Mathlib.CategoryTheory.Enriched.EnrichedCat | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.EnrichedFunctor.category",
"CategoryTheory.EnrichedFunctor",
"CategoryTheory.EnrichedCat.str",
"CategoryTheory.EnrichedCat.whisker_exchange",
"CategoryTheory.Bundled.α",
"CategoryTheory.Enriche... | false |
UInt16.toUInt32_and | Init.Data.UInt.Bitwise | [
"UInt16",
"UInt32",
"instAndOpUInt32",
"HAnd.hAnd",
"instAndOpUInt16",
"Eq",
"instHAndOfAndOp",
"rfl",
"UInt16.toUInt32"
] | true |
Lean.Grind.instToIntIntIi._proof_2 | Init.GrindInstances.ToInt | [
"outParam",
"Lean.Grind.IntInterval.instMembershipInt",
"Membership.mem",
"id",
"Int",
"Lean.Grind.IntInterval.ii",
"Lean.Grind.IntInterval.mem_ii._simp_1",
"True",
"of_eq_true",
"implies_true",
"Lean.Grind.IntInterval",
"Eq.trans",
"forall_congr"
] | false |
SimpleGraph.Walk.isHamiltonianCycle_iff_isCycle_and_support_count_tail_eq_one | Mathlib.Combinatorics.SimpleGraph.Hamiltonian | [
"False",
"congrArg",
"SimpleGraph.Walk.IsCycle",
"SimpleGraph.Walk.support",
"SimpleGraph.Walk",
"instOfNatNat",
"_private.Mathlib.Combinatorics.SimpleGraph.Hamiltonian.0.SimpleGraph.Walk.isHamiltonianCycle_iff_isCycle_and_support_count_tail_eq_one._simp_1_1",
"and_congr_right_iff._simp_1",
"instBEq... | true |
Lean.Meta.Grind.Arith.CommRing.PolyDerivation.brecOn | Lean.Meta.Tactic.Grind.Arith.CommRing.Types | [
"Lean.Meta.Grind.Arith.CommRing.PolyDerivation.brecOn.go",
"Lean.Meta.Grind.Arith.CommRing.PolyDerivation",
"Lean.Meta.Grind.Arith.CommRing.PolyDerivation.below"
] | false |
_private.Mathlib.Probability.Kernel.IonescuTulcea.Maps.0.IocProdIoc_preimage._proof_1_10 | Mathlib.Probability.Kernel.IonescuTulcea.Maps | [
"Preorder.toLT",
"_private.Mathlib.Probability.Kernel.IonescuTulcea.Maps.0.IocProdIoc_preimage._proof_1_9",
"Lean.Grind.nestedProof",
"Finset",
"LinearOrder",
"PartialOrder.toPreorder",
"IocProdIoc._proof_1",
"Preorder.toLE",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toL... | false |
_private.Mathlib.Analysis.Convex.Segment.0.insert_endpoints_openSegment._simp_1_1 | Mathlib.Analysis.Convex.Segment | [
"Std.Antisymm",
"HasSubset.Subset",
"Std.Refl",
"And",
"subset_antisymm_iff",
"propext",
"HasSubset",
"Eq"
] | false |
MeasureTheory.AEStronglyMeasurable.add_const | Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable | [
"MeasureTheory.Measure",
"MeasureTheory.aestronglyMeasurable_const",
"MeasureTheory.AEStronglyMeasurable.add",
"MeasurableSpace",
"TopologicalSpace",
"instHAdd",
"HAdd.hAdd",
"ContinuousAdd",
"MeasureTheory.AEStronglyMeasurable",
"Add"
] | true |
Monoid.PushoutI.hom_ext_iff | Mathlib.GroupTheory.PushoutI | [
"Monoid.PushoutI.hom_ext",
"Monoid",
"MonoidHom",
"Monoid.toMulOneClass",
"Monoid.PushoutI.monoid",
"HEq.refl",
"Monoid.PushoutI.base",
"Eq.casesOn",
"MonoidHom.comp",
"And.casesOn",
"Monoid.PushoutI",
"MulOneClass.toMulOne",
"And",
"Iff",
"And.intro",
"Iff.intro",
"Eq.ndrec",
"Mon... | true |
_private.Aesop.Nanos.0.Aesop.instBEqNanos.beq.match_1 | Aesop.Nanos | [
"Aesop.Nanos.mk",
"Aesop.Nanos",
"Nat",
"Aesop.Nanos.casesOn"
] | false |
HXor.mk.noConfusion | Init.Prelude | [
"outParam",
"HXor.noConfusion",
"HXor",
"id",
"heq_of_eq",
"Eq.refl",
"HEq",
"Eq",
"HXor.mk"
] | false |
_private.Init.Data.Nat.Bitwise.Lemmas.0.Nat.testBit_of_two_pow_le_and_two_pow_add_one_gt._proof_1_1 | Init.Data.Nat.Bitwise.Lemmas | [
"instPowNat",
"Nat.lt_of_not_le",
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"Int.natCast_add",
"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",
"Lean.Omeg... | false |
CategoryTheory.MonObj.pow_comp | Mathlib.CategoryTheory.Monoidal.Cartesian.Mon | [
"MulOne.toOne",
"Nat.recAux",
"HMul.hMul",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Monoid.toMulOneClass",
"congrArg",
"pow_succ",
"CategoryTheory.MonObj.mul_comp",
"CategoryTheory.IsMonHom",
"MulOne.toMul",
"instOfNatNat",
"CategoryTheory.SemiCartesianMonoidalCategory.toMono... | true |
_private.Init.Data.List.Sort.Basic.0.List.merge.match_1 | Init.Data.List.Sort.Basic | [
"List.cons",
"List",
"List.casesOn",
"List.nil"
] | false |
Subgroup.descending_central_series_ge_lower | Mathlib.GroupTheory.Nilpotent | [
"Subgroup.descending_central_series_ge_lower._f",
"PartialOrder.toPreorder",
"Group",
"Preorder.toLE",
"Nat.brecOn",
"Subgroup",
"LE.le",
"Subgroup.lowerCentralSeries",
"Nat",
"Subgroup.instPartialOrder",
"Subgroup.IsDescendingCentralSeries"
] | true |
Polynomial.contentIdeal_le_span_content | Mathlib.RingTheory.Polynomial.ContentIdeal | [
"Ideal.span_le",
"Polynomial.contentIdeal",
"Eq.mpr",
"CommRing",
"Dvd.dvd",
"Semiring.toModule",
"Polynomial.contentIdeal_def",
"CommSemiring.toNonUnitalCommSemiring",
"congrArg",
"CommSemiring.toSemiring",
"Finset",
"NormalizedGCDMonoid",
"PartialOrder.toPreorder",
"semigroupDvd",
"Pre... | true |
Mathlib.Tactic.LibraryRewrite.Kind.hypothesis.sizeOf_spec | Mathlib.Tactic.Widget.LibraryRewrite | [
"Mathlib.Tactic.LibraryRewrite.Kind",
"instOfNatNat",
"Mathlib.Tactic.LibraryRewrite.Kind.hypothesis",
"Nat",
"SizeOf.sizeOf",
"Eq.refl",
"OfNat.ofNat",
"Eq",
"Mathlib.Tactic.LibraryRewrite.Kind._sizeOf_inst"
] | true |
exists_ne_mem_inter_of_not_pairwise_disjoint | Mathlib.Data.Set.Pairwise.Basic | [
"Function.onFun",
"congrArg",
"Set.univ",
"Set.pairwise_univ",
"Disjoint",
"Membership.mem",
"Exists",
"SemilatticeInf.toPartialOrder",
"Eq.mp",
"BiheytingAlgebra.toHeytingAlgebra",
"Ne",
"BiheytingAlgebra.toCoheytingAlgebra",
"Set.instInter",
"Set.Pairwise",
"BooleanAlgebra.toBiheytingA... | true |
_private.Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.NormalForms.0.SimplexCategoryGenRel.isAdmissible_iff_isChain_and_le._proof_1_20 | Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.NormalForms | [
"Lean.RArray.leaf",
"False",
"Classical.byContradiction",
"Nat.not_le_eq",
"Preorder.toLE",
"Lean.RArray.branch",
"id",
"False.casesOn",
"instOfNatNat",
"LE.le",
"instLENat",
"Nat.Linear.Expr.num",
"Bool.true",
"instHAdd",
"Nat.Linear.ExprCnstr.eq_false_of_isUnsat",
"HAdd.hAdd",
"Nat... | false |
Std.DTreeMap.Equiv.getEntryGT_eq.match_1 | Std.Data.DTreeMap.Lemmas | [
"Ordering.gt",
"Std.DTreeMap",
"Membership.mem",
"Ordering",
"And.casesOn",
"Std.DTreeMap.instMembership",
"And",
"And.intro",
"Eq"
] | false |
CommGroupWithZero.toGroupWithZero | Mathlib.Algebra.GroupWithZero.Defs | [
"CommMonoidWithZero.toCommMonoid",
"CommGroupWithZero.mul_inv_cancel",
"GroupWithZero",
"CommMonoidWithZero.zero_mul",
"CommGroupWithZero.toInv",
"CommGroupWithZero.zpow_succ'",
"CommMonoid.toMonoid",
"CommMonoidWithZero.toZero",
"CommGroupWithZero.toDiv",
"GroupWithZero.mk",
"CommGroupWithZero.... | true |
Lean.Grind.CommRing.Mon.sharesVar._unary | Lean.Meta.Tactic.Grind.Arith.CommRing.Poly | [
"Lean.Grind.CommRing.Power",
"Lean.Grind.CommRing.Mon.mult",
"invImage",
"Lean.Grind.CommRing.Power.x",
"_private.Lean.Meta.Tactic.Grind.Arith.CommRing.Poly.0.Lean.Grind.CommRing.Mon.sharesVar._unary._proof_3",
"Ordering",
"_private.Lean.Meta.Tactic.Grind.Arith.CommRing.Poly.0.Lean.Grind.CommRing.Mon.sh... | false |
Aesop.NormalizationState.noConfusion | Aesop.Tree.Data | [
"Lean.Meta.SavedState",
"Lean.MVarId",
"Aesop.NormalizationState",
"Aesop.DisplayRuleName",
"Array",
"Aesop.NormalizationState.noConfusionType",
"Eq.ndrec",
"Eq.refl",
"Prod",
"Eq",
"Aesop.NormalizationState.casesOn",
"Aesop.Script.LazyStep",
"Option"
] | false |
CategoryTheory.CopyDiscardCategory.copy_tensor | Mathlib.CategoryTheory.CopyDiscardCategory.Basic | [
"CategoryTheory.ComonObj.comul",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.CopyDiscardCategory.comonObj",
"CategoryTheory.MonoidalCategory.tensorμ",
"CategoryTheory.MonoidalCategoryStruct.tensorObj",
"CategoryTheory.CategoryStruct.comp",... | true |
Lean.Meta.Try.collect | Lean.Meta.Tactic.Try.Collect | [
"Lean.Meta.Try.Info",
"_private.Lean.Meta.Tactic.Try.Collect.0.Lean.Meta.Try.collect.unsafe_impl_2",
"Lean.MVarId",
"Lean.Meta.MetaM",
"Lean.Try.Config"
] | true |
MeasureTheory.SimpleFunc.noConfusionType | Mathlib.MeasureTheory.Function.SimpleFunc | [
"MeasurableSet",
"Set.Finite",
"MeasureTheory.SimpleFunc",
"Set.instSingletonSet",
"MeasureTheory.SimpleFunc.casesOn",
"MeasurableSpace",
"Set.preimage",
"HEq",
"Set.range",
"Singleton.singleton",
"Set"
] | false |
Std.ExtDTreeMap.eq_empty_iff_size_eq_zero | Std.Data.ExtDTreeMap.Lemmas | [
"Eq.mpr",
"Std.ExtDTreeMap.mk",
"Std.DTreeMap",
"congrArg",
"Std.ExtDTreeMap.isEmpty_eq_size_beq_zero",
"Ordering",
"id",
"instDecidableEqBool",
"Std.ExtDTreeMap.instEmptyCollection",
"instOfNatNat",
"Std.TransCmp",
"Std.ExtDTreeMap.isEmpty",
"Bool.true",
"Iff",
"_private.Std.Data.ExtDTr... | true |
Multiset.ssubset_singleton_iff | Mathlib.Data.Multiset.ZeroCons | [
"Eq.mpr",
"False",
"Multiset.singleton_ne_zero._simp_1",
"congrArg",
"False.elim",
"Multiset.instHasSubset",
"Multiset.eq_zero_of_subset_zero",
"HasSSubset.SSubset",
"Membership.mem",
"Multiset",
"id",
"HasSubset.Subset",
"Ne",
"Multiset.instSingleton",
"Multiset.instMembership",
"Iff"... | true |
UpperSet.completeLattice | Mathlib.Order.UpperLower.CompleteLattice | [
"OrderDual.toDual",
"UpperSet.completeLattice._proof_5",
"Preorder.toLT",
"Equiv.instEquivLike",
"UpperSet",
"UpperSet.completeLattice._proof_1",
"UpperSet.completeLattice._proof_4",
"UpperSet.instSetLike",
"PartialOrder.toPreorder",
"UpperSet.completeLattice._proof_2",
"Preorder.toLE",
"Funct... | true |
QuotientGroup.dense_preimage_mk._simp_2 | Mathlib.Topology.Algebra.Group.Quotient | [
"Monoid.toMulOneClass",
"QuotientGroup.mk",
"Group",
"Dense",
"MulOne.toMul",
"QuotientGroup.instHasQuotientSubgroup",
"DivInvMonoid.toMonoid",
"Subgroup",
"QuotientGroup.dense_preimage_mk",
"Group.toDivInvMonoid",
"QuotientGroup.instTopologicalSpace",
"TopologicalSpace",
"HasQuotient.Quotie... | false |
NonarchAddGroupSeminorm.instZero._proof_3 | Mathlib.Analysis.Normed.Group.Seminorm | [
"AddGroup.toSubtractionMonoid",
"NegZeroClass.toNeg",
"Real",
"Real.instZero",
"Pi.instZero",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"AddGroup",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq",
"Neg.neg",
"rfl"
] | false |
Std.Iter.toList_zip_of_finite_right | Std.Data.Iterators.Lemmas.Combinators.Zip | [
"Pure.pure",
"Eq.mpr",
"Std.Iterators.Types.Take.instIterator",
"False",
"instAlternativeOption",
"Std.Iter.atIdxSlow?_take",
"_private.Std.Data.Iterators.Lemmas.Combinators.Zip.0.Std.Iter.toList_zip_of_finite_right._simp_1_4",
"Std.Iter.getElem?_toList_eq_atIdxSlow?",
"Option.ctorIdx",
"congrArg"... | true |
Set.BijOn.surjOn | Mathlib.Data.Set.Function | [
"Set.SurjOn",
"And",
"And.right",
"Set.MapsTo",
"Set.BijOn",
"Set.InjOn",
"Set"
] | true |
MeasureTheory.Measure.FiniteAtFilter | Mathlib.MeasureTheory.Measure.Typeclasses.Finite | [
"Filter.instMembership",
"MeasureTheory.Measure",
"Preorder.toLT",
"PartialOrder.toPreorder",
"Membership.mem",
"Exists",
"MeasurableSpace",
"And",
"LT.lt",
"ENNReal",
"ENNReal.instPartialOrder",
"ENNReal.instTop",
"Top.top",
"DFunLike.coe",
"Filter",
"MeasureTheory.Measure.instFunLike... | true |
_private.Mathlib.GroupTheory.OrderOfElement.0.mem_zpowers_zpow_iff._simp_1_4 | Mathlib.GroupTheory.OrderOfElement | [
"Semigroup",
"Semigroup.toMul",
"Dvd.dvd",
"HMul.hMul",
"dvd_def",
"semigroupDvd",
"Exists",
"propext",
"Eq.symm",
"Eq",
"instHMul"
] | false |
Lean.Parser.nameLitFn | Lean.Parser.Basic | [
"Lean.nameLitKind",
"Lean.Parser.expectTokenFn",
"Lean.Parser.ParserFn"
] | true |
QuaternionAlgebra.instRing._proof_3 | Mathlib.Algebra.Quaternion | [
"AddCommGroupWithOne.toOne",
"CommRing",
"QuaternionAlgebra.imI",
"AddCommGroupWithOne",
"HMul.hMul",
"sub_self",
"AddGroupWithOne.toAddGroup",
"congrArg",
"CommSemiring.toSemiring",
"sub_zero",
"AddMonoid.toAddZeroClass",
"AddGroupWithOne.toAddMonoidWithOne",
"HSub.hSub",
"QuaternionAlgeb... | false |
ConditionallyCompletePartialOrderInf.isGLB_csInf_of_directed | Mathlib.Order.ConditionallyCompletePartialOrder.Defs | [
"PartialOrder.toPreorder",
"Preorder.toLE",
"DirectedOn",
"GE.ge",
"ConditionallyCompletePartialOrderInf.toPartialOrder",
"Set.Nonempty",
"IsGLB",
"BddBelow",
"ConditionallyCompletePartialOrderInf.toInfSet",
"ConditionallyCompletePartialOrderInf",
"InfSet.sInf",
"Set"
] | true |
CategoryTheory.Endofunctor.Algebra.Hom.mk.inj | Mathlib.CategoryTheory.Endofunctor.Algebra | [
"CategoryTheory.Functor",
"CategoryTheory.Endofunctor.Algebra",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Endofunctor.Algebra.Hom.mk.noConfusion",
"CategoryTheory.Endofunctor.Algebra.Hom",
"CategoryTheory.Endofunctor.Algebra.Hom.mk",
"CategoryTheory.Endofunctor.Algebra.st... | true |
CategoryTheory.Limits.PushoutCocone.ofCocone | Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.WalkingSpan",
"CategoryTheory.Limits.Cocone",
"CategoryTheory.Functor.category",
"CategoryTheory.Limits.diagramIsoSpan",
"CategoryTheory.Limits.WalkingSpan.left",
"CategoryTheory.Limits.Cocone.mk",
"CategoryTheory.Limits.WalkingPair",
"CategoryTheory.... | true |
LaurentSeries.coe_range_dense | Mathlib.RingTheory.LaurentSeries | [
"Int.instAddCommGroup",
"RatFunc.instFaithfulSMulPolynomialLaurentSeries",
"Filter.instMembership",
"Multiplicative.group",
"AddGroup.toSubtractionMonoid",
"Set.ext",
"Units.val",
"Eq.mpr",
"Int.instAddCommMonoid",
"GroupWithZero.toMonoidWithZero",
"LinearOrderedCommGroupWithZero.toLinearOrdered... | true |
_private.Mathlib.NumberTheory.Cyclotomic.Basic.0.isCyclotomicExtension_iff_eq_adjoin._simp_1_9 | Mathlib.NumberTheory.Cyclotomic.Basic | [
"and_imp",
"And",
"propext",
"Eq"
] | false |
WeierstrassCurve.Projective.addY_of_X_eq | Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Formula | [
"Eq.mpr",
"mul_div_mul_right",
"GroupWithZero.toMonoidWithZero",
"NegZeroClass.toNeg",
"IsDomain.to_noZeroDivisors",
"instHDiv",
"WeierstrassCurve.Projective.addY_of_X_eq'",
"HMul.hMul",
"WeierstrassCurve.Projective.Equation",
"GroupWithZero.toDivInvMonoid",
"MulZeroClass.toMul",
"WeierstrassC... | true |
MeasureTheory.hittingBtwn.eq_1 | Mathlib.Probability.Process.HittingTime | [
"setOf",
"Classical.propDecidable",
"Membership.mem",
"Exists",
"InfSet",
"MeasureTheory.hittingBtwn",
"Set.instInter",
"Inter.inter",
"And",
"Set.Icc",
"Eq.refl",
"Eq",
"Set.instMembership",
"InfSet.sInf",
"Preorder",
"ite",
"Set"
] | true |
CategoryTheory.Functor.Faithful.mapMon | Mathlib.CategoryTheory.Monoidal.Mon | [
"CategoryTheory.Functor",
"CategoryTheory.Mon.Hom.ext",
"CategoryTheory.Mon.Hom",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Mon.Hom.hom",
"id",
"CategoryTheory.Functor.Faithful.mk",
"CategoryTheory.Functor.map",
"Cate... | true |
Finset.inv_subset_inv | Mathlib.Algebra.Group.Pointwise.Finset.Basic | [
"Inv",
"Finset",
"HasSubset.Subset",
"Inv.inv",
"Finset.image_subset_image",
"Finset.instHasSubset",
"DecidableEq",
"Finset.inv"
] | true |
Algebra.Extension.tensorCotangentInvFun._proof_5 | Mathlib.RingTheory.Etale.Kaehler | [
"Submodule",
"Submodule.module._proof_1",
"CommRing",
"Algebra.Extension.commRing",
"Semiring.toModule",
"instSMulOfMul",
"IsScalarTower.right",
"Algebra.Extension.ker",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"AddMonoid.toAddZeroClass",
"Algebra",
"Al... | false |
groupHomology.coinfNatTrans._proof_1 | Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality | [
"Eq.mpr",
"Rep.V",
"HomologicalComplex.homologyπ",
"CommRing",
"HomologicalComplex.instCategory",
"Nat.instOne",
"CategoryTheory.CategoryStruct.toQuiver",
"_private.Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality.0.groupHomology.functor._simp_4",
"Quiver.Hom",
"ModuleCat",
"... | false |
Nat.odd_mul_odd_div_two | Mathlib.Data.Nat.ModEq | [
"Distrib.leftDistribClass",
"Eq.mpr",
"MulOne.toOne",
"False",
"Nat.instMulZeroClass",
"instHDiv",
"HMul.hMul",
"Nat.instOne",
"congrArg",
"Nat.le_mul_of_pos_right",
"Nat.instIsCancelMulZero",
"False.elim",
"Nat.add_sub_assoc",
"HSub.hSub",
"Nat.instMulOneClass",
"mul_right_injective₀"... | true |
initFn._@.Lean.Elab.Tactic.TreeTacAttr.1721268732._hygCtx._hyg.2 | Lean.Elab.Tactic.TreeTacAttr | [
"IO",
"Lean.Name.mkStr3",
"Lean.Meta.registerSimpAttr",
"Lean.Meta.SimpExtension",
"Lean.Name.mkStr1"
] | false |
Module.AEval.instModuleOrig._proof_4 | Mathlib.Algebra.Polynomial.Module.AEval | [
"Module.AEval.instModuleOrig._proof_3",
"MulOne.toOne",
"instHSMul",
"Module.AEval.instModuleOrig._aux_1",
"Monoid.toMulOneClass",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"AddMonoid.toAddZeroClass",
"Module.AEval",
"Algebra",
"Algebra.toSMul",
"AddZeroCl... | false |
Computability.encodingNatBool | Mathlib.Computability.Encoding | [
"Computability.decodeNat",
"Option.some",
"Computability.Encoding.mk",
"List",
"Computability.encodeNat",
"Computability.encodingNatBool._proof_1",
"Nat",
"Bool",
"Computability.Encoding"
] | true |
Std.Do.Spec.modifyGet_StateT | Std.Do.Triple.SpecLemmas | [
"Std.Do.SPred.entails",
"Std.Do.WP.modifyGet_StateT",
"congrArg",
"Std.Do.PostCond",
"Std.Do.Assertion",
"Std.Do.PostShape.arg",
"Std.Do.WPMonad.toWP",
"Std.Do.PostShape",
"Prod.fst",
"instMonadStateOfStateTOfMonad",
"MonadStateOf.modifyGet",
"Std.Do.SPred.entails.refl._simp_1",
"Std.Do.Pred... | true |
PartOrdEmb.instConcreteCategoryOrderEmbeddingCarrier._proof_1 | Mathlib.Order.Category.PartOrdEmb | [
"PartOrdEmb.str",
"PartialOrder.toPreorder",
"Preorder.toLE",
"id",
"_private.Mathlib.Order.Category.PartOrdEmb.0.PartOrdEmb.Hom.mk",
"PartOrdEmb.carrier",
"PartOrdEmb.Hom.hom'",
"Eq.refl",
"OrderEmbedding",
"PartOrdEmb",
"Eq"
] | false |
_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_56 | Mathlib.Data.List.Induction | [
"List.getLast",
"List.head_append._proof_2",
"Lean.Grind.nestedProof",
"Ne",
"List.dropLast",
"List.cons",
"Bool.true",
"instHAppendOfAppend",
"List",
"List.isEmpty",
"List.cons_ne_nil",
"Bool",
"List.instAppend",
"Eq",
"Not",
"HAppend.hAppend",
"List.nil"
] | false |
Lean.VersoModuleDocs.snippets | Lean.DocString.Extension | [
"Lean.VersoModuleDocs",
"Lean.PersistentArray",
"Lean.VersoModuleDocs.Snippet"
] | true |
Std.Time.instHSubOffsetOffset_22 | Std.Time.Date.Basic | [
"Rat.instOfNat",
"Std.Time.Day.Offset.toMinutes",
"Rat",
"Std.Time.Day.Offset",
"Std.Time.Internal.UnitVal.sub",
"Std.Time.Minute.Offset",
"HSub.mk",
"OfNat.ofNat",
"HSub"
] | true |
instMulPosMonoWithZeroOfMulRightMono | Mathlib.Algebra.Order.GroupWithZero.WithZero | [
"Eq.mpr",
"False",
"WithZero.instIsBotZeroClass",
"HMul.hMul",
"MulZeroClass.toMul",
"instReflLe",
"congrArg",
"zero_le._simp_1",
"False.elim",
"MulZeroClass.zero_mul",
"Preorder.toLE",
"Mul",
"Std.le_refl._simp_1",
"Eq.mp",
"id",
"MulRightMono",
"LE.le",
"MulZeroClass.mul_zero",
... | true |
CFC.nnrpow_two | Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic | [
"cfcₙ",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"NNReal.instCommSemiring",
"IsSelfAdjoint",
"Real.partialOrder",
"Real",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"instStarRingReal",
"instSMulOfMul",
"HMul.hMul",
"pow_two",
"cfcₙ.congr_simp",
"IsTopologicalRing.toIsTopo... | true |
Std.ExtDHashMap.instInsertSigmaOfEquivBEqOfLawfulHashable.match_1 | Std.Data.ExtDHashMap.Basic | [
"Std.ExtDHashMap",
"Hashable",
"Sigma.mk",
"Sigma.casesOn",
"BEq",
"Sigma"
] | false |
CategoryTheory.Oplax.OplaxTrans.vcomp._proof_5 | Mathlib.CategoryTheory.Bicategory.NaturalTransformation.Oplax | [
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Oplax.OplaxTrans.whiskerLeft_naturality_comp_assoc",
"CategoryTheory.OplaxFunctor.mapComp",
"CategoryTheory.OplaxFunctor.toPrelaxFunctor",
"CategoryTheory.Bicategory.whisker... | false |
Antitone.iSup_comp_tendsto_atBot | Mathlib.Order.Filter.AtTopBot.CompleteLattice | [
"iSup",
"Filter.NeBot",
"PartialOrder.toPreorder",
"ConditionallyCompleteLattice",
"Preorder.toLE",
"OrderTop.bddAbove",
"OrderTop",
"Antitone",
"Filter.Tendsto",
"Filter.atBot",
"Antitone.ciSup_comp_tendsto_atBot",
"ConditionallyCompletePartialOrderSup.toPartialOrder",
"ConditionallyComplet... | true |
CategoryTheory.Mat.instAddCommGroupHom | Mathlib.CategoryTheory.Preadditive.Mat | [
"CategoryTheory.Mat.instAddCommGroupHom._proof_19",
"AddGroup.toSubtractionMonoid",
"NegZeroClass.toNeg",
"CategoryTheory.Mat.instAddCommGroupHom._proof_4",
"CategoryTheory.Mat.instAddCommGroupHom._proof_20",
"AddMonoid.toAddSemigroup",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"SubNeg... | true |
RingQuot.ringQuot_ext | Mathlib.Algebra.RingQuot | [
"RingHom.congr_fun",
"RingHom",
"Exists",
"RingQuot.instSemiring",
"RingQuot",
"RingHom.ext",
"RingHom.comp",
"NonAssocSemiring",
"RingHom.instFunLike",
"Exists.casesOn",
"RingQuot.mkRingHom_surjective",
"RingQuot.mkRingHom",
"Eq.ndrec",
"Semiring",
"Semiring.toNonAssocSemiring",
"Eq",... | true |
AlgebraicGeometry.isIso_ΓSpec_adjunction_unit_app_basicOpen | Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated | [
"CommRingCat.forgetReflectIsos",
"Eq.mpr",
"CategoryTheory.Category.assoc",
"AlgebraicGeometry.Spec",
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"AlgebraicGeometry.Scheme",
"Lattice.toSemilatticeSup",
"CommRingCat.Hom.hom",
"CategoryTheory.IsIso",
"Opposite",
"CommRingC... | true |
RingEquiv.toNonUnitalRingHom_trans | Mathlib.Algebra.Ring.Equiv | [
"Distrib.toAdd",
"NonUnitalRingHom.comp",
"RingEquiv.toNonUnitalRingHom",
"Distrib.toMul",
"NonUnitalNonAssocSemiring.toDistrib",
"RingEquiv.trans",
"NonUnitalRingHom",
"RingEquiv",
"NonUnitalNonAssocSemiring",
"Eq",
"rfl"
] | true |
AddSubgroup.single_mem_pi._simp_1 | Mathlib.Algebra.Group.Subgroup.Basic | [
"AddGroup.toSubtractionMonoid",
"Pi.addGroup",
"AddSubgroup.single_mem_pi",
"Membership.mem",
"SubtractionMonoid.toSubNegZeroMonoid",
"Pi.single",
"SubNegZeroMonoid.toNegZeroClass",
"AddSubgroup",
"AddGroup",
"AddSubgroup.instSetLike",
"propext",
"NegZeroClass.toZero",
"Eq",
"Set.instMembe... | false |
Lean.Parser.«_aux_Init_Simproc___macroRules_Lean_Parser_command__Simproc__[_]_(_):=__1» | Init.Simproc | [
"Pure.pure",
"cond",
"Lean.Syntax.TSepArray.mk",
"Lean.Syntax.node",
"Lean.mkNullNode",
"Lean.TSyntax",
"Array.instAppend",
"Unit.unit",
"Lean.MonadRef.mkInfoFromRefPos",
"instMonadExceptOfMonadExceptOf",
"Lean.Syntax.getArgs",
"Lean.SourceInfo",
"MonadExcept.throw",
"Lean.Syntax.isOfKind"... | false |
Nat.exists_subseq_of_forall_mem_union | Mathlib.Order.OrderIsoNat | [
"Iff.mpr",
"congrArg",
"Set.univ",
"Classical.propDecidable",
"_private.Mathlib.Order.OrderIsoNat.0.Nat.exists_subseq_of_forall_mem_union._simp_1_1",
"Membership.mem",
"Exists",
"Set.instUnion",
"Set.Elem",
"_private.Mathlib.Order.OrderIsoNat.0.Nat.exists_subseq_of_forall_mem_union._simp_1_4",
"... | true |
_private.Lean.Elab.StructInst.0.Lean.Elab.Term.StructInst.SavedState.mk.injEq | Lean.Elab.StructInst | [
"Eq.propIntro",
"Lean.injEq_helper",
"_private.Lean.Elab.StructInst.0.Lean.Elab.Term.StructInst.SavedState.mk.inj",
"Lean.Elab.Term.SavedState",
"And",
"_private.Lean.Elab.StructInst.0.Lean.Elab.Term.StructInst.StructInstState",
"Eq.ndrec",
"Eq.refl",
"_private.Lean.Elab.StructInst.0.Lean.Elab.Term.... | true |
CategoryTheory.FreeMonoidalCategory.Hom.l_inv | Mathlib.CategoryTheory.Monoidal.Free.Basic | [
"CategoryTheory.FreeMonoidalCategory",
"CategoryTheory.FreeMonoidalCategory.unit",
"CategoryTheory.FreeMonoidalCategory.Hom.l_inv",
"CategoryTheory.FreeMonoidalCategory.Hom",
"CategoryTheory.FreeMonoidalCategory.tensor"
] | true |
HomotopyGroup.commGroup._proof_3 | Mathlib.Topology.Homotopy.HomotopyGroup | [
"Nontrivial",
"Exists",
"exists_ne",
"Ne",
"Nontrivial.to_nonempty",
"Classical.arbitrary"
] | false |
hasStrictDerivAt_exp_smul_const_of_mem_ball | Mathlib.Analysis.SpecialFunctions.Exponential | [
"NormedCommRing.toNormedRing",
"NormedCommRing.toSeminormedCommRing",
"NormedCommRing.toCommRing",
"Algebra.to_smulCommClass",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CompleteSpace",
"Semiring.toModule",
"NormedRing.toRing",
"NormedSpace.toIsBoundedSMul",
"HMul.hMul",
"R... | true |
CategoryTheory.Functor.ι_biproductComparison'_assoc | Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Functor",
"CategoryTheory.Limits.HasBiproduct",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"Function.comp",
"Eq.mp",
"id",
"Mathlib.Tactic.Reassoc.eq_whisker'",
"CategoryTheory.F... | true |
_private.Lean.Parser.Tactic.Doc.0.Lean.Parser.Tactic.Doc.initFn._@.Lean.Parser.Tactic.Doc.1176478476._hygCtx._hyg.2 | Lean.Parser.Tactic.Doc | [
"Pure.pure",
"Lean.TSyntax",
"Lean.MessageData",
"Lean.MonadError.mk",
"Unit.unit",
"Lean.instMonadExceptOfExceptionCoreM",
"Std.instToFormatString",
"Lean.NameMap",
"Lean.TSyntax.getId",
"Lean.Name.mkNum",
"Lean.PersistentEnvExtensionState",
"Bool.not",
"Lean.MessageData.joinSep",
"Lean.C... | false |
_private.Std.Data.Internal.List.Associative.0.Std.Internal.List.length_le_length_insertEntry._proof_1_2 | Std.Data.Internal.List.Associative | [
"Nat.lt_of_not_le",
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"Int.natCast_add",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int.add_congr",
"Lean.Omega.LinearCombo.eval",
"Option.some",
"id",
"instDec... | false |
String.rawStartPos_eq | Init.Data.String.Defs | [
"String",
"String.Pos.Raw",
"String.rawStartPos",
"String.instOfNatRaw",
"OfNat.ofNat",
"Eq",
"rfl"
] | true |
_private.Mathlib.RingTheory.MvPowerSeries.Substitution.0.MvPowerSeries.le_weightedOrder_subst_of_forall_ne_zero._simp_1_1 | Mathlib.RingTheory.MvPowerSeries.Substitution | [
"iInf",
"PartialOrder.toPreorder",
"Preorder.toLE",
"le_iInf_iff",
"LE.le",
"CompleteLattice.toCompleteSemilatticeInf",
"propext",
"CompleteLattice.toCompleteSemilatticeSup",
"CompleteSemilatticeInf.toInfSet",
"CompleteSemilatticeSup.toPartialOrder",
"CompleteLattice",
"Eq"
] | false |
CategoryTheory.Endofunctor.algebraPreadditive._proof_24 | Mathlib.CategoryTheory.Preadditive.EndoFunctor | [
"CategoryTheory.Functor",
"CategoryTheory.Endofunctor.Algebra",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"AddCommGroup.toAddCommMonoid",
"CategoryTheory.Functor.Additive",
"Add.mk",
"CategoryTheory.Endofunctor.Algebra.Hom",
"CategoryTheory.Endofunctor.Algebra.Hom.mk",
"CategoryTheor... | false |
CategoryTheory.congrArg_cast_hom_left | Mathlib.CategoryTheory.EqToHom | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"HEq.refl",
"CategoryTheory.eqToHom",
"cast",
"Eq.casesOn",
"True",
"eq_self",
"CategoryTheory.CategoryStruct.comp",
"of_eq_true",
"eq_of_heq",
"Eq.ndrec",
"Eq.refl",
"HEq",
"CategoryTheory.Category.toCategoryStruct",
... | true |
Topology.IsInducing.mk | Mathlib.Topology.Defs.Induced | [
"Topology.IsInducing",
"TopologicalSpace",
"TopologicalSpace.induced",
"Topology.IsInducing.mk",
"Eq"
] | true |
SFinKer.instMonoidalCategory._proof_15 | Mathlib.Probability.Kernel.Category.SFinKer | [
"MeasurableEquiv.instEquivLike",
"Eq.mpr",
"SFinKer.hom_ext",
"ProbabilityTheory.IsZeroOrMarkovKernel.isFiniteKernel",
"SFinKer.Hom.hom",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Measurable.comp",
"congrArg",
"ProbabilityTheory.Kernel.comp",
"measurable_id",
"ProbabilityTheory.... | false |
WType.mk.injEq | Mathlib.Data.W.Basic | [
"WType",
"Eq.propIntro",
"Lean.injEq_helper",
"HEq.homo_ndrec",
"WType.mk",
"And",
"Eq.ndrec",
"Eq.refl",
"HEq",
"WType.mk.inj",
"Eq"
] | true |
Lean.Server.Test.Runner.Client.NormalizeState.mk.noConfusion | Lean.Server.Test.Runner | [
"Lean.Server.Test.Runner.Client.NormalizeState",
"USize.instOrd",
"id",
"Ord.compare",
"Lean.Server.Test.Runner.Client.NormalizeState.noConfusion",
"Lean.Server.Test.Runner.Client.NormalizeState.mk",
"Eq",
"Std.TreeMap",
"USize"
] | false |
NormedSpace.inclusionInDoubleDualWeak | Mathlib.Analysis.Normed.Module.DoubleDual | [
"NormedCommRing.toNormedRing",
"NormedCommRing.toSeminormedCommRing",
"Algebra.to_smulCommClass",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"SeminormedAddCommGroup",
"Semiring.toModule",
"NormedRing.toRing",
"NormedSpace",
"ContinuousLinearMap.topologicalSpace",
"CommSemiring.toSemiring",
... | true |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.