name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
CategoryTheory.Limits.diagramIsoCospan | Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan | [
"CategoryTheory.Limits.diagramIsoCospan._proof_2",
"CategoryTheory.Functor",
"CategoryTheory.Limits.WalkingCospan.Hom.inl",
"CategoryTheory.Functor.category",
"CategoryTheory.Limits.WalkingCospan.right",
"CategoryTheory.eqToIso",
"CategoryTheory.Limits.WidePullbackShape.category",
"CategoryTheory.Iso"... | true |
MeasureTheory.SimpleFunc.tendsto_approxOn_range_Lp_eLpNorm | Mathlib.MeasureTheory.Function.SimpleFuncDenseLp | [
"MeasureTheory.ae",
"Eq.mpr",
"MeasureTheory.Measure",
"Preorder.toLT",
"congrArg",
"NormedAddCommGroup.toMetricSpace",
"sub_zero",
"subset_closure",
"PartialOrder.toPreorder",
"Measurable",
"setOf",
"HSub.hSub",
"PseudoMetricSpace.toUniformSpace",
"AddCommGroup.toAddGroup",
"MeasureTheo... | true |
Std.DTreeMap.Equiv.any_eq | Std.Data.DTreeMap.Lemmas | [
"Pure.pure",
"Unit.unit",
"Std.DTreeMap.Internal.Impl.Equiv.forIn_eq",
"Std.DTreeMap.any",
"Std.DTreeMap.Internal.Impl.forIn",
"Std.DTreeMap",
"congrArg",
"Monad.toApplicative",
"Ord.mk",
"Option.some",
"Ordering",
"ForInStep.done",
"instDecidableEqBool",
"Prod.mk",
"LawfulMonad",
"Std... | true |
_private.Mathlib.ModelTheory.Arithmetic.Presburger.Semilinear.Basic.0.Nat.isSemilinearSet_preimage | Mathlib.ModelTheory.Arithmetic.Presburger.Semilinear.Basic | [
"Eq.mpr",
"Pi.addCommMonoid",
"congrArg",
"IsSemilinearSet.biUnion",
"Finite",
"AddMonoid.toAddZeroClass",
"_private.Mathlib.ModelTheory.Arithmetic.Presburger.Semilinear.Basic.0.Nat.isSemilinearSet_preimage_of_isLinearSet",
"Set.sUnion",
"Nat.instAddMonoid",
"Set.Finite",
"Membership.mem",
"Ad... | true |
Quaternion.normSq_nonneg._simp_1 | Mathlib.Algebra.Quaternion | [
"NegZeroClass.toNeg",
"CommRing",
"CommSemiring.toSemiring",
"LinearOrder",
"Quaternion.normSq_nonneg",
"PartialOrder.toPreorder",
"AddGroupWithOne.toAddMonoidWithOne",
"Quaternion.normSq",
"IsStrictOrderedRing",
"MonoidWithZeroHom.funLike",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
... | false |
Array.set_eq_empty_iff | Init.Data.Array.Lemmas | [
"congrArg",
"Array.set",
"Array.casesOn",
"List.set",
"instOfNatNat",
"List.toArray",
"Nat.casesAuxOn",
"Array",
"iff_self",
"List",
"instHAdd",
"Array.mk.injEq",
"Iff",
"HAdd.hAdd",
"Nat",
"congr",
"LT.lt",
"True",
"of_eq_true",
"Eq.ndrec",
"instAddNat",
"Eq.refl",
"inst... | true |
Inv.mk.noConfusion | Init.Prelude | [
"Inv",
"id",
"heq_of_eq",
"Inv.mk",
"Eq.refl",
"HEq",
"Inv.noConfusion",
"Eq"
] | false |
Std.DTreeMap.Internal.Impl.getEntryLT.eq_1 | Std.Data.DTreeMap.Internal.Model | [
"Std.DTreeMap.Internal.Impl.getEntryLT",
"Ord",
"Std.TransOrd",
"False.elim",
"Std.DTreeMap.Internal.Impl.Ordered",
"Membership.mem",
"Exists",
"Ordering",
"Std.DTreeMap.Internal.Impl.getEntryLT._proof_3",
"Ord.compare",
"And",
"Std.DTreeMap.Internal.Impl.leaf",
"Ordering.lt",
"Eq.refl",
... | true |
AlgHom.toLieHom | Mathlib.Algebra.Lie.OfAssociative | [
"LieHom",
"AlgHom.toLinearMap",
"CommRing",
"CommSemiring.toSemiring",
"AlgHom",
"Algebra",
"Algebra.toModule",
"LinearMap",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"CommRing.toCommSemiring",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"LieRing.ofAssociativeRing",
"RingHom.id",
"A... | true |
CategoryTheory.Limits.WidePullbackShape.fintypeObj | Mathlib.CategoryTheory.Limits.Shapes.FiniteLimits | [
"CategoryTheory.Limits.WidePullbackShape",
"CategoryTheory.Limits.WidePullbackShape.fintypeObj._proof_3",
"Fintype",
"Fintype.mk",
"CategoryTheory.Limits.WidePullbackShape.fintypeObj._aux_1"
] | true |
Lean.Meta.Grind.Arith.Cutsat.DiseqCnstrProof.core0.noConfusion | Lean.Meta.Tactic.Grind.Arith.Cutsat.Types | [
"Lean.Expr",
"id",
"Lean.Meta.Grind.Arith.Cutsat.DiseqCnstrProof.noConfusion",
"Eq",
"Lean.Meta.Grind.Arith.Cutsat.DiseqCnstrProof",
"Lean.Meta.Grind.Arith.Cutsat.DiseqCnstrProof.core0"
] | false |
OmegaCompletePartialOrder.ContinuousHom.ofFun._auto_1 | Mathlib.Order.OmegaCompletePartialOrder | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
_private.Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Basic.0.WeierstrassCurve.Projective.nonsingular_zero._simp_1_4 | Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Basic | [
"Fin.instOfNat",
"instOfNatNat",
"WeierstrassCurve.Projective.fin3_def_ext",
"Nat.instNeZeroSucc",
"Nat",
"Matrix.vecEmpty",
"OfNat.ofNat",
"Fin",
"Nat.succ",
"Eq",
"Matrix.vecCons"
] | false |
Lean.Elab.DefKind.rec | Lean.Elab.DefView | [
"Lean.Elab.DefKind.def",
"Lean.Elab.DefKind.instance",
"Lean.Elab.DefKind.opaque",
"Lean.Elab.DefKind.abbrev",
"Lean.Elab.DefKind.example",
"Lean.Elab.DefKind",
"Lean.Elab.DefKind.theorem"
] | false |
IsMin.not_isMax | Mathlib.Order.Directed | [
"Nontrivial",
"False",
"IsCodirectedOrder",
"Preorder.toLT",
"LE.le.antisymm'",
"IsMin.isBot",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Exists",
"PartialOrder",
"LE.le",
"Exists.casesOn",
"LT.lt",
"Eq.ndrec",
"exists_lt_of_directed_ge",
"Not",
"IsMin",
"IsMax.not_lt",
"IsMax"... | true |
WithBot.map_comp_map | Mathlib.Order.WithBot | [
"WithBot",
"Function.comp",
"Option.map_comp_map",
"WithBot.map",
"Eq"
] | true |
ContinuousLinearMap.const._proof_1 | Mathlib.Topology.ContinuousMap.Algebra | [
"Continuous",
"ContinuousMap",
"ContinuousMap.continuous_const'",
"TopologicalSpace",
"ContinuousMap.const",
"ContinuousMap.compactOpen"
] | false |
Std.DTreeMap.foldrM | Std.Data.DTreeMap.Basic | [
"Std.DTreeMap",
"Ordering",
"Std.DTreeMap.inner",
"Std.DTreeMap.Internal.Impl.foldrM",
"Monad"
] | true |
HomotopicalAlgebra.Cylinder.IsVeryGood.rec | Mathlib.AlgebraicTopology.ModelCategory.Cylinder | [
"CategoryTheory.Limits.HasBinaryCoproduct",
"HomotopicalAlgebra.Cylinder.IsVeryGood.mk",
"HomotopicalAlgebra.Cylinder.IsVeryGood",
"HomotopicalAlgebra.Precylinder.I",
"HomotopicalAlgebra.Precylinder.π",
"HomotopicalAlgebra.Cylinder",
"HomotopicalAlgebra.Cylinder.toPrecylinder",
"HomotopicalAlgebra.Cat... | false |
String.Slice.Pos.le_trans | Init.Data.String.Basic | [
"Eq.mpr",
"String.instLEPos_1",
"_private.Init.Data.String.Basic.0.String.Slice.Pos.le_trans._simp_1_1",
"String.Slice.Pos.offset",
"String.Slice",
"id",
"LE.le",
"instLENat",
"String.Pos.Raw",
"Nat.le_trans",
"implies_congr",
"Nat",
"String.instLERaw",
"String.Slice.Pos",
"_private.Init... | true |
Prop.instHeytingAlgebra._proof_1 | Mathlib.Order.Heyting.Basic | [
"and_imp",
"And",
"Iff",
"Iff.symm"
] | false |
Topology.IsInducing.isCompact_preimage_iff | Mathlib.Topology.Compactness.Compact | [
"Eq.mpr",
"congrArg",
"Iff.rfl",
"id",
"HasSubset.Subset",
"Topology.IsInducing",
"TopologicalSpace",
"Iff",
"Set.preimage",
"Set.image_preimage_eq_of_subset",
"propext",
"Set.image",
"Set.range",
"Topology.IsInducing.isCompact_iff",
"Eq",
"IsCompact",
"Set.instHasSubset",
"Set"
] | true |
Lean.AssocList.ctorIdx | Lean.Data.AssocList | [
"Lean.AssocList.casesOn",
"Nat",
"Lean.AssocList"
] | false |
Std.IterM.zip | Std.Data.Iterators.Combinators.Monadic.Zip | [
"Std.IterM.IsPlausibleOutput",
"Std.Iterators.Types.Zip.mk",
"Exists",
"Subtype",
"Std.IterM.mk",
"Std.Iterator",
"Option.none",
"Std.IterM",
"Std.Iterators.Types.Zip",
"Prod"
] | true |
_private.Mathlib.Analysis.Convex.Gauge.0.gauge_empty._simp_1_1 | Mathlib.Analysis.Convex.Gauge | [
"False",
"Membership.mem",
"propext",
"Set.instEmptyCollection",
"Set.mem_empty_iff_false",
"EmptyCollection.emptyCollection",
"Eq",
"Set.instMembership",
"Set"
] | false |
MeasureTheory.Submartingale.sub_martingale | Mathlib.Probability.Martingale.Basic | [
"Real",
"MeasureTheory.Measure",
"CompleteSpace",
"NormedSpace",
"AddCommGroup.toAddCommMonoid",
"MeasureTheory.Martingale",
"HSub.hSub",
"PseudoMetricSpace.toUniformSpace",
"AddLeftMono",
"Preorder.toLE",
"AddCommGroup.toAddGroup",
"MeasureTheory.Submartingale",
"MeasureTheory.Submartingale... | true |
Std.DTreeMap.Internal.Impl.keysArray | Std.Data.DTreeMap.Internal.Queries | [
"Std.DTreeMap.Internal.Impl.foldl",
"Array.push",
"Std.DTreeMap.Internal.Impl.size",
"Array",
"Std.DTreeMap.Internal.Impl",
"Array.emptyWithCapacity"
] | true |
Subarray.mergeSort.induct_unfolding | Init.Data.Array.Sort.Lemmas | [
"Std.Rci.mk",
"Subarray",
"instHDiv",
"Subarray.mergeSort._unary.induct_unfolding",
"Std.Slice.toArray",
"Std.Rio.mk",
"instSliceableSubarrayNat_2",
"id",
"HDiv.hDiv",
"instOfNatNat",
"SubarrayIterator",
"instSliceableSubarrayNat_7",
"Array",
"Subarray.mergeSort",
"instHAdd",
"_private... | true |
Std.Http.Status.noContent.sizeOf_spec | Std.Internal.Http.Data.Status | [
"instOfNatNat",
"Std.Http.Status",
"Std.Http.Status.noContent",
"Nat",
"SizeOf.sizeOf",
"Eq.refl",
"OfNat.ofNat",
"Eq",
"Std.Http.Status._sizeOf_inst"
] | true |
Ordinal.mulRightMono | Mathlib.SetTheory.Ordinal.Arithmetic | [
"CovariantClass.mk",
"Iff.mpr",
"Ordinal.monoid._proof_1",
"Quotient.inductionOn₃",
"HMul.hMul",
"Prod.trichotomous",
"Prod.Lex.casesOn",
"Ordinal.partialOrder",
"MulZeroClass.toMul",
"instAsymmOfIsWellFounded",
"_private.Mathlib.SetTheory.Ordinal.Arithmetic.0.Ordinal.leftDistribClass.match_1",
... | true |
HeytAlg.ext | Mathlib.Order.Category.HeytAlg | [
"HeytAlg",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ConcreteCategory.hom",
"HeytAlg.instConcreteCategoryHeytingHomCarrier",
"HeytAlg.carrier",
"HeytingHom",
"HeytAlg.instCategory",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.ConcreteCategory.hom_ext",... | true |
HasFDerivWithinAt.pow'._f | Mathlib.Analysis.Calculus.FDeriv.Pow | [
"_private.Mathlib.Analysis.Calculus.FDeriv.Pow.0.HasFDerivWithinAt.pow'.match_1_1",
"Monoid",
"Eq.mpr",
"hasFDerivWithinAt_const",
"Nat.instCanonicallyOrderedAdd",
"_private.Mathlib.Analysis.Calculus.FDeriv.Pow.0.aux",
"MulOne.toOne",
"Nat.instOrderedSub",
"Algebra.to_smulCommClass",
"instHSMul",
... | false |
_private.Mathlib.Probability.Process.HittingTime.0.MeasureTheory.hittingBtwn_mono_left.match_1_4 | Mathlib.Probability.Process.HittingTime | [
"PartialOrder.toPreorder",
"Membership.mem",
"Exists",
"ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice",
"And",
"Set.Icc",
"Exists.casesOn",
"Exists.intro",
"ConditionallyCompletePartialOrderSup.toPartialOrder",
"ConditionallyCompleteLattice.toConditionallyCompletePartialOrder",
... | false |
_private.Mathlib.Analysis.CStarAlgebra.Extreme.0.isStarProjection_iff_mem_extremePoints_setOf_nonneg_inter_unitClosedBall._simp_1_15 | Mathlib.Analysis.CStarAlgebra.Extreme | [
"Unitization.instSMul",
"instHSMul",
"SMulZeroClass",
"SMul",
"Unitization.inr",
"Unitization.inr_smul",
"HSMul.hSMul",
"SMulZeroClass.toSMul",
"Unitization",
"Eq.symm",
"Eq",
"Zero"
] | false |
Std.DTreeMap.Raw.WF.getThenInsertIfNew? | Std.Data.DTreeMap.Raw.WF | [
"Ord.mk",
"Ordering",
"Std.TransCmp",
"Std.DTreeMap.Raw.WF.out",
"Std.LawfulEqCmp",
"Std.DTreeMap.Raw.inner",
"Std.DTreeMap.Raw.WF.mk",
"Std.DTreeMap.Raw.getThenInsertIfNew?",
"Prod.snd",
"Std.DTreeMap.Raw.WF",
"Std.DTreeMap.Internal.Impl.WF.getThenInsertIfNew?!",
"Option",
"Std.DTreeMap.Raw... | true |
SimplexCategory.Truncated.δ₂_two_comp_σ₂_zero_assoc | Mathlib.AlgebraicTopology.SimplexCategory.Truncated | [
"CategoryTheory.Category.assoc",
"CategoryTheory.ObjectProperty.FullSubcategory.mk",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"SimplexCategory.Truncated.δ₂_zero_comp_σ₂_one._proof_3",
"SimplexCategory.Truncated.δ₂",
"SimplexCategory.Truncated.δ₂_zero_comp_σ₂_one._proof_4",
... | true |
CategoryTheory.MonoidalCategory.MonoidalRightActionStruct.actionHom | Mathlib.CategoryTheory.Monoidal.Action.Basic | [
"CategoryTheory.MonoidalCategoryStruct",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory.MonoidalRightActionStruct.actionObj",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.MonoidalCategory.MonoidalRightActionStruct",
"CategoryTheory.Category"
] | true |
MeasureTheory.tendsto_of_forall_isOpen_le_liminf_nat | Mathlib.MeasureTheory.Measure.Portmanteau | [
"NNReal.instTopologicalSpace",
"Eq.mpr",
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"ENNReal.ofNNReal",
"MeasureTheory.Measure",
"Monotone.map_liminf_of_continuousAt",
"LinearOrderedCommMonoidWithZero.toIsBotZeroClass",
"Filter.liminf",
"congrArg",
"zero_le._simp_1",
"Fi... | true |
_private.Mathlib.Analysis.Real.Pi.Irrational.0.I_one | Mathlib.Analysis.Real.Pi.Irrational | [
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"add_mul",
"Mathlib.Tactic.Ring.Common.neg_zero",
"Eq.mpr",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Mathlib.Tactic.Ring.Common.neg_mul",
"Semigroup.toMul",
"Real",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Mathlib.Tactic... | true |
eq_lim_at_left_extendFrom_Ioo | Mathlib.Topology.Order.ExtendFrom | [
"Eq.mpr",
"OrderTopology",
"Set.Ioi",
"Preorder.toLT",
"Lattice.toSemilatticeSup",
"congrArg",
"LinearOrder",
"nhdsWithin",
"PartialOrder.toPreorder",
"instClosedIciTopology",
"le_of_lt",
"Preorder.toLE",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"nhds",
"DistribLattice.toLatt... | true |
CategoryTheory.GrothendieckTopology.Subcanonical | Mathlib.CategoryTheory.Sites.Canonical | [
"CategoryTheory.GrothendieckTopology.Subcanonical.mk",
"CategoryTheory.GrothendieckTopology",
"CategoryTheory.Category"
] | true |
_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.lt_base_pow_length_digits._simp_1_1 | Mathlib.Data.Nat.Digits.Defs | [
"Nat.instMonoid",
"instOfNatNat",
"Nat.lt_base_pow_length_digits'",
"Monoid.toPow",
"instHAdd",
"HPow.hPow",
"HAdd.hAdd",
"Nat",
"LT.lt",
"True",
"eq_true",
"instAddNat",
"Nat.digits",
"instHPow",
"instLTNat",
"OfNat.ofNat",
"Eq",
"List.length"
] | false |
Std.TreeSet.max!_eq_iff_mem_and_forall | Std.Data.TreeSet.Lemmas | [
"Std.TreeSet",
"Std.TreeSet.max!",
"Std.TreeSet.isEmpty",
"Membership.mem",
"Ordering",
"Std.TreeSet.inner",
"Std.TreeMap.maxKey!_eq_iff_mem_and_forall",
"Std.TransCmp",
"Bool.true",
"And",
"Unit",
"Iff",
"Std.LawfulEqCmp",
"Bool",
"Inhabited",
"Ordering.isLE",
"Bool.false",
"Eq",
... | true |
Set.mulIndicator_apply_eq_self._simp_2 | Mathlib.Algebra.Notation.Indicator | [
"One",
"Set.mulIndicator",
"Membership.mem",
"Set.mulIndicator_apply_eq_self",
"propext",
"One.toOfNat1",
"OfNat.ofNat",
"Eq",
"Set.instMembership",
"Not",
"Set"
] | false |
MonotoneOn.Iic | Mathlib.Order.Interval.Set.Monotone | [
"PartialOrder.toPreorder",
"CompleteLattice.toConditionallyCompleteLattice",
"monotone_Iic",
"MonotoneOn",
"CompleteBooleanAlgebra.toCompleteLattice",
"ConditionallyCompletePartialOrderSup.toPartialOrder",
"Set.Iic",
"ConditionallyCompleteLattice.toConditionallyCompletePartialOrder",
"ConditionallyC... | true |
HomologicalComplex.unopEquivalence_inverse | Mathlib.Algebra.Homology.Opposite | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Functor",
"HomologicalComplex.instCategory",
"Opposite",
"HomologicalComplex.unopInverse",
"HomologicalComplex",
"HomologicalComplex.unopEquivalence",
"ComplexShape",
"CategoryTheory.Category.opposite",
"Eq.refl",
"ComplexShape.symm",
"... | true |
UnivLE_iff_essSurj | Mathlib.CategoryTheory.UnivLE | [
"UnivLE",
"inferInstance",
"CategoryTheory.uliftFunctor",
"Iff",
"Iff.intro",
"CategoryTheory.Functor.EssSurj",
"EssSurj.ofUnivLE",
"CategoryTheory.types",
"UnivLE.ofEssSurj"
] | true |
CategoryTheory.Triangulated.TStructure.ω₁._proof_4 | Mathlib.CategoryTheory.Triangulated.TStructure.SpectralObject | [
"WithBot.instPreorder",
"Eq.mpr",
"CategoryTheory.Category.assoc",
"instNeZeroNatHAdd_1",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.NatTrans.ext'",
"Quiver.Hom",
"WithTop.instPreorder",
"congrArg",
"CategoryTheory.Functor.Additive",
"PartialOrder.toPre... | false |
Unitary.mulLeft._proof_1 | Mathlib.Analysis.CStarAlgebra.Unitary.Maps | [
"RingHomInvPair",
"RingHomInvPair.ids",
"RingHom.id",
"Semiring.toNonAssocSemiring",
"Ring.toSemiring",
"Ring"
] | false |
RingQuot.definition._@.Mathlib.Algebra.RingQuot.1093876312._hygCtx._hyg.2 | Mathlib.Algebra.RingQuot | [
"MulOne.toOne",
"RingQuot.definition._proof_5._@.Mathlib.Algebra.RingQuot.1093876312._hygCtx._hyg.2",
"RingHom.mk",
"RingQuot.toQuot",
"OneHom.mk",
"RingHom",
"RingQuot.instSemiring",
"Quot.lift",
"RingQuot.definition._proof_1._@.Mathlib.Algebra.RingQuot.1093876312._hygCtx._hyg.2",
"RingQuot.Rel",... | false |
_private.Mathlib.Topology.Algebra.Valued.ValuedField.0.Valued.valuation_isClosedMap._simp_1_3 | Mathlib.Topology.Algebra.Valued.ValuedField | [
"Compl.compl",
"Membership.mem",
"Set.instCompl",
"propext",
"Eq",
"Set.instMembership",
"Not",
"Set.mem_compl_iff",
"Set"
] | false |
_private.Mathlib.Algebra.Homology.ExactSequence.0.CategoryTheory.ComposableArrows.isComplex₂_iff._proof_1_5 | Mathlib.Algebra.Homology.ExactSequence | [
"_private.Mathlib.Algebra.Homology.ExactSequence.0.CategoryTheory.ComposableArrows.isComplex₂_iff._proof_1_4",
"PartialOrder.toPreorder",
"Preorder.toLE",
"_private.Mathlib.Algebra.Homology.ExactSequence.0.CategoryTheory.ComposableArrows.isComplex₂_iff._proof_1_3",
"CategoryTheory.ComposableArrows.isComplex... | false |
BEq.rec | Init.Prelude | [
"BEq.mk",
"Bool",
"BEq"
] | false |
Turing.PartrecToTM2.splitAtPred | Mathlib.Computability.TuringMachine.ToPartrec | [
"List.brecOn",
"Turing.PartrecToTM2.splitAtPred._f",
"List",
"Bool",
"Prod",
"Option"
] | true |
Lean.Elab.Term.StructInst.ExplicitSourceView.ctorIdx | Lean.Elab.StructInst | [
"Nat",
"Lean.Elab.Term.StructInst.ExplicitSourceView"
] | false |
CategoryTheory.Functor.RightExtension.isUniversalEquivOfIso₂._proof_1 | Mathlib.CategoryTheory.Functor.KanExtension.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.PreservesLimit",
"CategoryTheory.Functor.rightExtensionEquivalenceOfIso₂",
"CategoryTheory.Limits.PreservesLimitsOfShape.preservesLimit",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.instPreservesLimitsOfShapeOfIsRightAdjoint",
"CategoryTheo... | false |
groupHomology.functor._proof_5 | Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality | [
"Eq.mpr",
"Rep.V",
"CommRing",
"HomologicalComplex.instCategory",
"Nat.instOne",
"CategoryTheory.CategoryStruct.toQuiver",
"_private.Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality.0.groupHomology.functor._simp_4",
"Quiver.Hom",
"ModuleCat",
"Monoid.toMulOneClass",
"congrArg... | false |
Std.DHashMap.Internal.Raw₀.contains_of_contains_union_of_contains_eq_false_left | Std.Data.DHashMap.Internal.RawLemmas | [
"Std.DHashMap.Raw.WF",
"Eq.mpr",
"Std.Internal.List.containsKey_of_perm",
"Std.Internal.List.insertList",
"Std.DHashMap.Internal.Raw₀.contains",
"Std.DHashMap.Internal.Raw.WF.out",
"congrArg",
"Std.DHashMap.Raw",
"Std.DHashMap.Internal.Raw₀.contains_eq_containsKey",
"id",
"instOfNatNat",
"Std.... | true |
Ordnode.diff.match_1 | Mathlib.Data.Ordmap.Ordnode | [
"Ordnode",
"namedPattern",
"Ordnode.node",
"Ordnode.casesOn",
"Nat",
"Ordnode.nil",
"Eq.refl",
"Eq"
] | false |
Set.SurjOn.surjective | Mathlib.Data.Set.Function | [
"Set.SurjOn.mono",
"Set.subset_univ",
"Set.univ",
"Set.SurjOn",
"Set.surjOn_univ",
"Set.Subset.rfl",
"Iff.mp",
"Function.Surjective",
"Set"
] | true |
AddSubsemigroup.centerToAddOpposite_symm_apply_coe | Mathlib.GroupTheory.Submonoid.Center | [
"AddSubsemigroup.instSetLike",
"Membership.mem",
"AddOpposite",
"AddOpposite.instAdd",
"Subtype",
"AddSubsemigroup.center",
"AddSubsemigroup.centerToAddOpposite",
"AddSubsemigroup",
"AddEquiv",
"Eq.refl",
"AddOpposite.unop",
"AddSubsemigroup.center.addCommSemigroup",
"AddCommSemigroup.toAddC... | true |
SimpleGraph.walkLengthTwoEquivCommonNeighbors._proof_7 | Mathlib.Combinatorics.SimpleGraph.Walk.Counting | [
"SimpleGraph.Adj.symm",
"SimpleGraph.Walk.length",
"SimpleGraph.Adj",
"SimpleGraph.Walk",
"Membership.mem",
"SimpleGraph.neighborSet",
"SimpleGraph.commonNeighbors",
"Subtype",
"instOfNatNat",
"SimpleGraph.walkLengthTwoEquivCommonNeighbors._proof_1",
"Subtype.mk",
"SimpleGraph",
"SimpleGraph... | false |
IsTopologicalSemiring.casesOn | Mathlib.Topology.Algebra.Ring.Basic | [
"IsTopologicalSemiring",
"Distrib.toAdd",
"TopologicalSpace",
"ContinuousMul",
"IsTopologicalSemiring.rec",
"Distrib.toMul",
"NonUnitalNonAssocSemiring.toDistrib",
"ContinuousAdd",
"NonUnitalNonAssocSemiring",
"IsTopologicalSemiring.mk"
] | false |
_private.Mathlib.CategoryTheory.ComposableArrows.Basic.0.CategoryTheory.ComposableArrows.homMkSucc._proof_1 | Mathlib.CategoryTheory.ComposableArrows.Basic | [
"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.Omega.LinearCombo.ev... | false |
Multiset.dedup_nsmul | Mathlib.Algebra.Order.Group.Multiset | [
"False",
"instHSMul",
"eq_false",
"Multiset.Nodup",
"congrArg",
"and_self",
"Multiset.dedup",
"AddMonoid.toNSMul",
"Multiset.instAddCancelCommMonoid",
"Membership.mem",
"Multiset.count",
"Multiset",
"Ne",
"Multiset.mem_nsmul._simp_1",
"instOfNatNat",
"dite",
"Multiset.count_eq_one_of... | true |
CategoryTheory.Lax.LaxTrans.id_naturality | Mathlib.CategoryTheory.Bicategory.NaturalTransformation.Lax | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Bicategory.rightUnitor",
"CategoryTheory.Lax.LaxTrans.naturality",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Bicategory.toCategoryStruct",
"CategoryTheory.PrelaxFunctor.toPrelaxFunctorStruct",
"CategoryTheory.Bicategory.... | true |
Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula.ratUnits_insertRupUnits | Std.Tactic.BVDecide.LRAT.Internal.Formula.RupAddResult | [
"Eq.mpr",
"Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula.insertUnit",
"congrArg",
"Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula.assignments",
"id",
"Prod.mk",
"List.foldl",
"Prod.fst",
"Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula",
"Array",
"Std.Tactic.BVDecide.LRAT.Internal.DefaultF... | true |
Std.DTreeMap.mk.congr_simp | Std.Data.DTreeMap.Lemmas | [
"Std.DTreeMap",
"Ord.mk",
"Ordering",
"Eq.rec",
"Std.DTreeMap.Internal.Impl.WF",
"Std.DTreeMap.mk",
"Eq.ndrec",
"Eq.refl",
"Eq",
"Std.DTreeMap.Internal.Impl"
] | true |
CategoryTheory.Adjunction.commShift_of_leftAdjoint | Mathlib.CategoryTheory.Shift.Adjunction | [
"Eq.mpr",
"CategoryTheory.Adjunction.CommShift.mk'",
"CategoryTheory.Functor",
"CategoryTheory.Functor.commShiftIso_comp_hom_app",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.NatTrans.ext'",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.CommShift.id",
"CategoryTheory.Functor.cate... | true |
Multiset.toEnumFinset_subset_iff | Mathlib.Data.Multiset.Fintype | [
"Multiset.map",
"congrArg",
"Finset",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Multiset.map_fst_le_of_subset_toEnumFinset",
"Multiset",
"Eq.mp",
"HasSubset.Subset",
"Multiset.toEnumFinset_mono",
"LE.le",
"Multiset.toEnumFinset",
"Finset.val",
"Prod.fst",
"Multiset.map_toEnumFinset_fs... | true |
_private.Lean.Meta.Sym.AbstractS.0.Lean.Meta.Sym.abstractFVarsRange.go._unsafe_rec | Lean.Meta.Sym.AbstractS | [
"Lean.instBEqFVarId",
"Lean.Expr.fvarId!",
"HSub.hSub",
"Option.some",
"Lean.Expr",
"Lean.FVarId",
"instDecidableEqBool",
"instSubNat",
"instOfNatNat",
"Array",
"GetElem.getElem",
"Bool.true",
"GT.gt",
"Option.none",
"instHAdd",
"BEq.beq",
"instHSub",
"Array.instGetElemNatLtSize",
... | false |
_private.Lean.Elab.Match.0.Lean.Elab.Term.isPatternVar.match_7 | Lean.Elab.Match | [
"Unit.unit",
"Option.casesOn",
"Option.some",
"Lean.Expr",
"Option.none",
"Unit",
"Option"
] | false |
Lean.Meta.Grind.Arith.Linear.inSameNatStruct? | Lean.Meta.Tactic.Grind.Arith.Linear.OfNatModule | [
"Pure.pure",
"Lean.Meta.Grind.GrindM",
"Lean.Meta.Grind.Goal",
"StateRefT'.instAlternativeOfMonad",
"Lean.Meta.Grind.State",
"ReaderT",
"_private.Lean.Meta.Tactic.Grind.Arith.Linear.OfNatModule.0.Lean.Meta.Grind.Arith.Linear.inSameNatStruct?.match_1",
"Lean.Meta.Grind.Arith.Linear.getTermNatStructId?"... | true |
Std.instLawfulIteratorLoopDefaultImplementation | Init.Data.Iterators.Consumers.Monadic.Loop | [
"Std.IteratorLoop.forIn",
"Std.LawfulIteratorLoop.mk",
"Std.IteratorLoop.WellFounded",
"Std.Iterators.Finite",
"Subtype",
"Std.IterM.IsPlausibleIndirectOutput",
"ForInStep",
"Std.Iterator",
"implies_congr",
"Std.Internal.LawfulMonadLiftBindFunction",
"True",
"Std.LawfulIteratorLoop",
"eq_sel... | true |
Height.logHeight₁_zpow | Mathlib.NumberTheory.Height.Basic | [
"Real",
"HMul.hMul",
"congrArg",
"Height.mulHeight₁_zpow",
"DivInvMonoid.toZPow",
"Height.logHeight₁",
"Field.toDivisionRing",
"DivisionRing.toDivInvMonoid",
"Height.AdmissibleAbsValues",
"Int",
"Nat.cast",
"Real.log",
"Monoid.toPow",
"Real.instMonoid",
"HPow.hPow",
"Nat",
"Real.inst... | true |
Std.DTreeMap.Raw.Const.ofList | Std.Data.DTreeMap.Raw.Basic | [
"Ord.mk",
"Ordering",
"Std.DTreeMap.Raw.Const.ofList._auto_1",
"autoParam",
"Std.DTreeMap.Raw.mk",
"Std.DTreeMap.Internal.Impl.Const.ofList",
"List",
"Prod",
"Std.DTreeMap.Raw"
] | true |
LieAlgebra.LieEquiv.ofCoboundary | Mathlib.Algebra.Lie.Extension | [
"LieAlgebra.toModule",
"Submodule",
"CommRing",
"Equiv.instEquivLike",
"LieAlgebra.ofProd._proof_4",
"LieAlgebra.LieEquiv.ofCoboundary._proof_1",
"LieRing.toAddCommGroup",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"LieModule.Cohomology.d₁₂",
"... | true |
SSet.relativeCellComplexOfMono | Mathlib.AlgebraicTopology.SimplicialSet.Skeleton | [
"SSet.relativeCellComplexOfMono.sigmaBoundary._proof_1",
"CategoryTheory.Limits.ColimitCocone.cocone",
"SSet.Subcomplex.toSSet",
"SSet.Subcomplex.range",
"Unit.unit",
"CategoryTheory.Functor",
"CategoryTheory.Functor.mapCocone",
"SSet.relativeCellComplexOfMono.b",
"Lattice.toSemilatticeSup",
"Oppo... | true |
CategoryTheory.Pseudofunctor.IsPrestack.casesOn | Mathlib.CategoryTheory.Sites.Descent.IsPrestack | [
"CategoryTheory.Over",
"CategoryTheory.Pseudofunctor.IsPrestack.rec",
"Opposite",
"CategoryTheory.LocallyDiscrete.mk",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Pseudofunctor.IsPrestack.mk",
"CategoryTheory.locallyDiscreteBicategory",
"CategoryTheory.Pseudofunctor.toPre... | false |
Subrepresentation.mem_ofSubmodule'_iff | Mathlib.RepresentationTheory.Subrepresentation | [
"MonoidAlgebra.semiring",
"Monoid",
"Submodule",
"Subrepresentation.ofSubmodule'",
"Representation",
"Representation.instModuleMonoidAlgebraAsModule",
"CommSemiring.toSemiring",
"Iff.rfl",
"Membership.mem",
"Subrepresentation",
"AddCommMonoid",
"Representation.asModule",
"CommSemiring",
"R... | true |
ProbabilityTheory.avgRisk_const_right' | Mathlib.Probability.Decision.Risk.Basic | [
"instHSMul",
"MeasureTheory.Measure",
"instSMulOfMul",
"MeasureTheory.lintegral_smul_measure",
"HMul.hMul",
"IsScalarTower.right",
"congrArg",
"CommSemiring.toSemiring",
"ProbabilityTheory.Kernel.comp",
"Set.univ",
"ProbabilityTheory.Kernel.instFunLike",
"Algebra.id",
"ProbabilityTheory.avgR... | true |
TypeVec._aux_Mathlib_Data_TypeVec___unexpand_TypeVec_appendFun_1 | Mathlib.Data.TypeVec | [
"Pure.pure",
"cond",
"Lean.TSyntax",
"Unit.unit",
"Lean.MonadRef.mkInfoFromRefPos",
"instMonadExceptOfMonadExceptOf",
"Lean.SourceInfo",
"Lean.PrettyPrinter.UnexpandM",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Syntax.atom",
"Lean.TSyntax.mk",
"Lean.Syntax",
... | false |
CategoryTheory.Pseudofunctor.DescentData'.pullHom'₁₃_eq_pullHom_of_chosenPullback₃._proof_5 | Mathlib.CategoryTheory.Sites.Descent.DescentDataPrime | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.ChosenPullback₃.p₁₃",
"CategoryTheory.Limits.ChosenPullback₃.pullback",
"congrArg",
"CategoryTheory.Limits.ChosenPullback.p₂",
"CategoryTheory.Limits.ChosenPullback₃",
"CategoryTheory.Limits.ChosenPullback.p₁",
"CategoryT... | false |
WithBotTop.coe_strictMono._simp_1 | Mathlib.Order.WithBotTop | [
"WithBotTop.coe",
"WithBotTop.coe_strictMono",
"WithBot.instPreorder",
"StrictMono",
"WithTop.instPreorder",
"True",
"eq_true",
"Eq",
"WithBotTop",
"Preorder",
"WithTop"
] | false |
coplanar_singleton | Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional | [
"collinear_singleton",
"AddCommGroup.toAddCommMonoid",
"AddCommGroup.toAddGroup",
"DivisionRing.toDivisionSemiring",
"AddCommGroup",
"Set.instSingletonSet",
"AddTorsor",
"DivisionSemiring.toSemiring",
"DivisionRing",
"Collinear.coplanar",
"Module",
"Singleton.singleton",
"Coplanar",
"Set"
... | true |
Std.Roo.forIn'_eq_forIn'_toArray | Init.Data.Range.Polymorphic.Lemmas | [
"Std.Iter.forIn'_eq_forIn'_toArray",
"Std.Iter.instForIn'",
"Std.Roo.Internal.isPlausibleIndirectOutput_iter_iff",
"Std.PRange.UpwardEnumerable",
"Array.forIn'_congr",
"congrArg",
"Std.PRange.LawfulUpwardEnumerableLT",
"Std.Roo.instForIn'InferInstanceMembershipOfLawfulUpwardEnumerableOfLawfulUpwardEnu... | true |
_private.Lean.Util.CollectAxioms.0.Lean.CollectAxioms.State.seen | Lean.Util.CollectAxioms | [
"Lean.NameMap",
"Array",
"Lean.Name",
"_private.Lean.Util.CollectAxioms.0.Lean.CollectAxioms.State"
] | true |
CategoryTheory.Idempotents.FunctorExtension₁.obj_obj_X | Mathlib.CategoryTheory.Idempotents.FunctorExtension | [
"CategoryTheory.Functor",
"CategoryTheory.Idempotents.Karoubi",
"CategoryTheory.Idempotents.Karoubi.X",
"CategoryTheory.Idempotents.Karoubi.instCategory",
"Eq.refl",
"CategoryTheory.Idempotents.FunctorExtension₁.obj",
"Eq",
"CategoryTheory.Functor.obj",
"CategoryTheory.Category"
] | true |
Odd.zpow_neg | Mathlib.Algebra.Order.Field.Power | [
"Iff.mpr",
"Preorder.toLT",
"LinearOrder",
"PartialOrder.toPreorder",
"Odd",
"IsStrictOrderedRing",
"DivInvMonoid.toZPow",
"Field.toDivisionRing",
"SemilatticeInf.toPartialOrder",
"DivisionRing.toDivInvMonoid",
"DistribLattice.toLattice",
"Int",
"Field.toSemifield",
"Semifield.toDivisionSe... | true |
AlgebraicGeometry.Scheme.IdealSheafData.inclusion._proof_1 | Mathlib.AlgebraicGeometry.IdealSheaf.Subscheme | [
"Eq.mpr",
"AlgebraicGeometry.Scheme.IdealSheafData.glueDataObjHom_ι_assoc",
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.pullback",
"AlgebraicGeometry.Spec",
"AlgebraicGeometry.Scheme.IdealSheafData.glueDataObjHom",
"AlgebraicGeometry.Scheme.IdealSheafData.instIsPreimmersionSubschemeι",
"Al... | false |
_private.Init.Data.String.Basic.0.String.Pos.Raw.substrEq.loop.eq_def | Init.Data.String.Basic | [
"String",
"_private.Init.Data.String.Basic.0.String.Pos.Raw.substrEq.loop",
"id",
"Bool.and",
"instBEqOfDecidableEq",
"String.Pos.Raw",
"dite",
"Bool.true",
"BEq.beq",
"HAdd.hAdd",
"Nat",
"LT.lt",
"PSigma.mk",
"String.Pos.Raw.get",
"Bool",
"Nat.decLt",
"Char",
"instLTNat",
"_priv... | true |
CommCStarAlgebra.nnnorm_sub_eq_max | Mathlib.Analysis.CStarAlgebra.GelfandDuality | [
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"HMul.hMul",
"NonUnitalCommCStarAlgebra",
"SeminormedAddGroup.toNNNorm",
"NNNorm.nnnorm",
"NonUnitalNonAssocRing.toAddCommGroup",
"HSub.hSub",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"AddCommGroup.toAddGroup",
"SemilatticeSup.toMax",
"NNReal.i... | true |
ModuleCat.limitπLinearMap._proof_1 | Mathlib.Algebra.Category.ModuleCat.Limits | [
"Eq.mpr",
"CategoryTheory.Limits.Cone.π",
"Submodule",
"CategoryTheory.Functor",
"Pi.addCommMonoid",
"Equiv.instEquivLike",
"CategoryTheory.Limits.Types.Small.limitCone",
"ModuleCat",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"AddCommGroup.toAddCommMonoid",
"Submodule.addCommMonoid",
... | false |
Lean.Syntax.setAtomVal | Lean.Syntax | [
"String",
"Lean.SourceInfo",
"Lean.Syntax.atom",
"Lean.Syntax",
"_private.Lean.Syntax.0.Lean.Syntax.setAtomVal.match_1"
] | true |
SimpleGraph.instMeasurableSpace | Mathlib.MeasureTheory.Constructions.SimpleGraph | [
"MeasurableSpace.comap",
"SimpleGraph.Adj",
"inferInstance",
"SimpleGraph",
"MeasurableSpace",
"MeasurableSpace.pi",
"Prop.instMeasurableSpace"
] | true |
TopCat.LocalPredicate.cocone._proof_2 | Mathlib.Topology.Sheaves.LocalPredicate | [
"Opposite",
"TopologicalSpace.Opens",
"Membership.mem",
"TopologicalSpace.Opens.instSetLike",
"TopCat.str",
"TopCat.carrier",
"TopologicalSpace.OpenNhds",
"TopCat",
"Subtype.val",
"Opposite.unop",
"SetLike.instMembership",
"Subtype.property"
] | false |
CategoryTheory.Limits.evaluationJointlyReflectsColimits | Mathlib.CategoryTheory.Limits.FunctorCategory.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"CategoryTheory.Functor.mapCocone",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Limits.evaluationJointlyReflectsColimits._proof_4",
"CategoryTheory.Limits.evaluationJointlyReflectsC... | true |
Lean.Parser.registerAliasCore | Lean.Parser.Extension | [
"instMonadExceptOfMonadExceptOf",
"IO.instMonadLiftSTRealWorldBaseIO",
"String",
"ST.Ref.modify",
"MonadExcept.throw",
"instMonadLiftT",
"IO",
"instMonadExceptOfEIO",
"ST.Ref.get",
"Lean.initializing",
"IO.RealWorld",
"instDecidableEqBool",
"instMonadEIO",
"ToString.toString",
"IO.userEr... | true |
Rat.num_ne_zero | Mathlib.Data.Rat.Defs | [
"Rat.instOfNat",
"Rat.num",
"Rat",
"Iff.not",
"Ne",
"Int",
"Rat.num_eq_zero",
"Iff",
"instOfNat",
"OfNat.ofNat",
"Eq"
] | true |
_private.Mathlib.Analysis.Calculus.AbsolutelyMonotone.0.AbsolutelyMonotoneOn._proof_2 | Mathlib.Analysis.Calculus.AbsolutelyMonotone | [
"Real",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"instSMulOfMul",
"IsSemitopologicalRing.toIsSemitopologicalSemiring",
"SeparatelyContinuousMul.to_continuousSMul",
"PseudoMetricSpace.toUniformSpace",
"instIsTopologicalRingReal",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"Continuou... | false |
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