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2 classes
Matroid.IsBasis.isBase_of_spanning
Mathlib.Combinatorics.Matroid.Closure
∀ {α : Type u_2} {M : Matroid α} {X I : Set α}, M.IsBasis I X → M.Spanning X → M.IsBase I
true
Prod.instCoalgebra._proof_7
Mathlib.RingTheory.Coalgebra.Basic
∀ (R : Type u_1) (A : Type u_2) (B : Type u_3) [inst : CommSemiring R] [inst_1 : AddCommMonoid A] [inst_2 : AddCommMonoid B] [inst_3 : Module R A] [inst_4 : Module R B] [inst_5 : Coalgebra R A] [inst_6 : Coalgebra R B], LinearMap.rTensor (A × B) CoalgebraStruct.counit ∘ₗ CoalgebraStruct.comul = (TensorProduct.mk R R (A × B)) 1
false
LocallyConstant.coe_inj._simp_1
Mathlib.Topology.LocallyConstant.Basic
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] {f g : LocallyConstant X Y}, (⇑f = ⇑g) = (f = g)
false
_private.Init.Data.Int.DivMod.Lemmas.0.Int.ediv_mul_of_nonneg._proof_1_1
Init.Data.Int.DivMod.Lemmas
∀ {x y z : ℤ}, x / y / z = x / (y * z) → ¬x / (y * z) = x / y / z → False
false
AlgebraicGeometry.IsAffineOpen.arrowStalkMapIso._proof_8
Mathlib.AlgebraicGeometry.AffineScheme
∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) {x : ↥X} (U : Y.Opens) (hU : AlgebraicGeometry.IsAffineOpen U) (V : X.Opens) (hV : AlgebraicGeometry.IsAffineOpen V) (hVU : V ≤ (TopologicalSpace.Opens.map f.base).obj U) (hx : x ∈ V) (this : IsLocalization.AtPrime (↑(Y.presheaf.stalk ↑⟨f x, ⋯⟩)) (hU.primeIdealOf ⟨f x, ⋯⟩).asIdeal) (this_1 : IsLocalization.AtPrime (↑(X.presheaf.stalk ↑⟨x, hx⟩)) (hV.primeIdealOf ⟨x, hx⟩).asIdeal), CategoryTheory.CategoryStruct.comp (IsLocalization.algEquiv (hU.primeIdealOf ⟨f x, ⋯⟩).asIdeal.primeCompl (↑(Y.presheaf.stalk (f x))) (Localization.AtPrime (hU.primeIdealOf ⟨f x, ⋯⟩).asIdeal)).toRingEquiv.toCommRingCatIso.hom (CommRingCat.ofHom (Localization.localRingHom (hU.primeIdealOf ⟨f x, ⋯⟩).asIdeal (hV.primeIdealOf ⟨x, hx⟩).asIdeal (CommRingCat.Hom.hom (AlgebraicGeometry.Scheme.Hom.appLE f U V hVU)) ⋯)) = CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Scheme.Hom.stalkMap f x) (IsLocalization.algEquiv (hV.primeIdealOf ⟨x, hx⟩).asIdeal.primeCompl (↑(X.presheaf.stalk x)) (Localization.AtPrime (hV.primeIdealOf ⟨x, hx⟩).asIdeal)).toRingEquiv.toCommRingCatIso.hom
false
Lean.Lsp.CodeActionClientCapabilities.dataSupport?._default
Lean.Data.Lsp.CodeActions
Option Bool
false
_private.Mathlib.Algebra.Homology.BifunctorAssociator.0.HomologicalComplex.instHasMapProdObjGradedObjectFunctorMapBifunctorMapBifunctorMapObjπX._proof_1
Mathlib.Algebra.Homology.BifunctorAssociator
∀ {C₁ : Type u_11} {C₂ : Type u_13} {C₁₂ : Type u_9} {C₃ : Type u_7} {C₄ : Type u_5} [inst : CategoryTheory.Category.{u_10, u_11} C₁] [inst_1 : CategoryTheory.Category.{u_12, u_13} C₂] [inst_2 : CategoryTheory.Category.{u_6, u_7} C₃] [inst_3 : CategoryTheory.Category.{u_4, u_5} C₄] [inst_4 : CategoryTheory.Category.{u_8, u_9} C₁₂] [inst_5 : CategoryTheory.Limits.HasZeroMorphisms C₁] [inst_6 : CategoryTheory.Limits.HasZeroMorphisms C₂] [inst_7 : CategoryTheory.Limits.HasZeroMorphisms C₃] [inst_8 : CategoryTheory.Preadditive C₁₂] [inst_9 : CategoryTheory.Preadditive C₄] {F₁₂ : CategoryTheory.Functor C₁ (CategoryTheory.Functor C₂ C₁₂)} {G : CategoryTheory.Functor C₁₂ (CategoryTheory.Functor C₃ C₄)} [inst_10 : F₁₂.PreservesZeroMorphisms] [inst_11 : ∀ (X₁ : C₁), (F₁₂.obj X₁).PreservesZeroMorphisms] [inst_12 : G.Additive] [inst_13 : ∀ (X₁₂ : C₁₂), (G.obj X₁₂).PreservesZeroMorphisms] {ι₁ : Type u_14} {ι₂ : Type u_15} {ι₃ : Type u_2} {ι₁₂ : Type u_1} {ι₄ : Type u_3} {c₁ : ComplexShape ι₁} {c₂ : ComplexShape ι₂} {c₃ : ComplexShape ι₃} (K₁ : HomologicalComplex C₁ c₁) (K₂ : HomologicalComplex C₂ c₂) (K₃ : HomologicalComplex C₃ c₃) (c₁₂ : ComplexShape ι₁₂) (c₄ : ComplexShape ι₄) [inst_14 : TotalComplexShape c₁ c₂ c₁₂] [inst_15 : TotalComplexShape c₁₂ c₃ c₄] [inst_16 : K₁.HasMapBifunctor K₂ F₁₂ c₁₂] [inst_17 : DecidableEq ι₁₂] [(K₁.mapBifunctor K₂ F₁₂ c₁₂).HasMapBifunctor K₃ G c₄], (((CategoryTheory.GradedObject.mapBifunctor G ι₁₂ ι₃).obj (CategoryTheory.GradedObject.mapBifunctorMapObj F₁₂ (c₁.π c₂ c₁₂) K₁.X K₂.X)).obj K₃.X).HasMap (c₁₂.π c₃ c₄)
false
SimpleGraph.Subgraph.sup_adj
Mathlib.Combinatorics.SimpleGraph.Subgraph
∀ {V : Type u} {G : SimpleGraph V} {G₁ G₂ : G.Subgraph} {a b : V}, (G₁ ⊔ G₂).Adj a b ↔ G₁.Adj a b ∨ G₂.Adj a b
true
_private.Mathlib.Analysis.LocallyConvex.WeakDual.0.LinearMap.mem_span_iff_continuous._simp_1_1
Mathlib.Analysis.LocallyConvex.WeakDual
∀ {ι : Type u_4} {𝕜 : Type u_5} {E : Type u_6} [Finite ι] [inst : Field 𝕜] [t𝕜 : TopologicalSpace 𝕜] [IsTopologicalRing 𝕜] [inst_2 : AddCommGroup E] [inst_3 : Module 𝕜 E] [T0Space 𝕜] {f : ι → E →ₗ[𝕜] 𝕜} (φ : E →ₗ[𝕜] 𝕜), Continuous ⇑φ = (φ ∈ Submodule.span 𝕜 (Set.range f))
false
CategoryTheory.ObjectProperty.LimitOfShape.ofIso
Mathlib.CategoryTheory.ObjectProperty.LimitsOfShape
{C : Type u_1} → [inst : CategoryTheory.Category.{v_1, u_1} C] → {P : CategoryTheory.ObjectProperty C} → {J : Type u'} → [inst_1 : CategoryTheory.Category.{v', u'} J] → {X : C} → P.LimitOfShape J X → {Y : C} → (X ≅ Y) → P.LimitOfShape J Y
true
Std.TreeMap.Equiv.getEntryGED_eq
Std.Data.TreeMap.Lemmas
∀ {α : Type u} {β : Type v} {cmp : α → α → Ordering} {t₁ t₂ : Std.TreeMap α β cmp} [Std.TransCmp cmp] {k : α} {fallback : α × β}, t₁.Equiv t₂ → t₁.getEntryGED k fallback = t₂.getEntryGED k fallback
true
CategoryTheory.Comma.mapLeftComp
Mathlib.CategoryTheory.Comma.Basic
{A : Type u₁} → [inst : CategoryTheory.Category.{v₁, u₁} A] → {B : Type u₂} → [inst_1 : CategoryTheory.Category.{v₂, u₂} B] → {T : Type u₃} → [inst_2 : CategoryTheory.Category.{v₃, u₃} T] → (R : CategoryTheory.Functor B T) → {L₁ L₂ L₃ : CategoryTheory.Functor A T} → (l : L₁ ⟶ L₂) → (l' : L₂ ⟶ L₃) → CategoryTheory.Comma.mapLeft R (CategoryTheory.CategoryStruct.comp l l') ≅ (CategoryTheory.Comma.mapLeft R l').comp (CategoryTheory.Comma.mapLeft R l)
true
CategoryTheory.GrothendieckTopology.pullbackComp
Mathlib.CategoryTheory.Sites.Grothendieck
{C : Type u} → [inst : CategoryTheory.Category.{v, u} C] → (J : CategoryTheory.GrothendieckTopology C) → {X Y Z : C} → (f : X ⟶ Y) → (g : Y ⟶ Z) → J.pullback (CategoryTheory.CategoryStruct.comp f g) ≅ (J.pullback g).comp (J.pullback f)
true
Multiset.Rel.trans
Mathlib.Data.Multiset.ZeroCons
∀ {α : Type u_1} (r : α → α → Prop) [IsTrans α r] {s t u : Multiset α}, Multiset.Rel r s t → Multiset.Rel r t u → Multiset.Rel r s u
true
Equiv.Perm.cycleFactorsFinset_eq_singleton_self_iff._simp_1
Mathlib.GroupTheory.Perm.Cycle.Factors
∀ {α : Type u_2} [inst : DecidableEq α] [inst_1 : Fintype α] {f : Equiv.Perm α}, (f.cycleFactorsFinset = {f}) = f.IsCycle
false
_private.Lean.Meta.Tactic.FunInd.0.Lean.Tactic.FunInd.deriveInductionStructural.match_9
Lean.Meta.Tactic.FunInd
(motive : Option (Lean.Elab.Structural.RecArgInfo × Subarray Lean.Elab.Structural.RecArgInfo) → Sort u_1) → (x : Option (Lean.Elab.Structural.RecArgInfo × Subarray Lean.Elab.Structural.RecArgInfo)) → (Unit → motive none) → ((recArgInfo : Lean.Elab.Structural.RecArgInfo) → (s' : Subarray Lean.Elab.Structural.RecArgInfo) → motive (some (recArgInfo, s'))) → motive x
false
List.replicate_sublist_replicate._simp_1
Init.Data.List.Sublist
∀ {α : Type u_1} {m n : ℕ} (a : α), (List.replicate m a).Sublist (List.replicate n a) = (m ≤ n)
false
_private.Mathlib.Data.Multiset.Fintype.0.Multiset.map_fst_le_of_subset_toEnumFinset._simp_1_4
Mathlib.Data.Multiset.Fintype
∀ {α : Type u_1} [inst : LinearOrder α] {a b : α}, (¬a ≤ b) = (b < a)
false
CategoryTheory.Limits.WalkingParallelFamily.Hom.ctorElimType
Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers
{J : Type w} → {motive : (a a_1 : CategoryTheory.Limits.WalkingParallelFamily J) → CategoryTheory.Limits.WalkingParallelFamily.Hom J a a_1 → Sort u} → ℕ → Sort (max 1 (imax (w + 1) u))
false
Lean.Doc.DocHighlight.option.noConfusion
Lean.Elab.DocString.Builtin
{P : Sort u} → {name declName name' declName' : Lean.Name} → Lean.Doc.DocHighlight.option name declName = Lean.Doc.DocHighlight.option name' declName' → (name = name' → declName = declName' → P) → P
false
Std.Tactic.BVDecide.BVExpr.bitblast.TwoPowShiftTarget.mk
Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Impl.Operations.ShiftRight
{α : Type} → [inst : Hashable α] → [inst_1 : DecidableEq α] → {aig : Std.Sat.AIG α} → {w : ℕ} → (n : ℕ) → aig.RefVec w → aig.RefVec n → ℕ → Std.Tactic.BVDecide.BVExpr.bitblast.TwoPowShiftTarget aig w
true
MeasureTheory.FiniteMeasure.eq_of_forall_apply_eq
Mathlib.MeasureTheory.Measure.FiniteMeasure
∀ {Ω : Type u_1} [inst : MeasurableSpace Ω] (μ ν : MeasureTheory.FiniteMeasure Ω), (∀ (s : Set Ω), MeasurableSet s → μ s = ν s) → μ = ν
true
NumberField.InfinitePlace.orbitRelEquiv._proof_2
Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification
∀ {k : Type u_2} [inst : Field k] {K : Type u_1} [inst_1 : Field K] [inst_2 : Algebra k K] [inst_3 : IsGalois k K], Function.Injective (Quotient.lift (fun x => x.comap (algebraMap k K)) ⋯) ∧ Function.Surjective (Quotient.lift (fun x => x.comap (algebraMap k K)) ⋯)
false
Fin.castLE.eq_1
Mathlib.Data.Fin.Tuple.Take
∀ {n m : ℕ} (h : n ≤ m) (i : Fin n), Fin.castLE h i = ⟨↑i, ⋯⟩
true
Dilation.edist_eq'
Mathlib.Topology.MetricSpace.Dilation
∀ {α : Type u_1} {β : Type u_2} [inst : PseudoEMetricSpace α] [inst_1 : PseudoEMetricSpace β] (self : α →ᵈ β), ∃ r, r ≠ 0 ∧ ∀ (x y : α), edist (self.toFun x) (self.toFun y) = ↑r * edist x y
true
instHashableFin
Init.Data.Hashable
{n : ℕ} → Hashable (Fin n)
true
ArithmeticFunction.one_smul'
Mathlib.NumberTheory.ArithmeticFunction.Defs
∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (b : ArithmeticFunction M), 1 • b = b
true
DFinsupp.addZeroClass._proof_1
Mathlib.Data.DFinsupp.Defs
∀ {ι : Type u_1} {β : ι → Type u_2} [inst : (i : ι) → AddZeroClass (β i)], Function.Injective fun f => ⇑f
false
_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trStmts₁_trans._simp_1_10
Mathlib.Computability.TuringMachine.ToPartrec
∀ {α : Type u_1} [inst : DecidableEq α] {s : Finset α} {a b : α}, (a ∈ insert b s) = (a = b ∨ a ∈ s)
false
Option.getD_eq_iff
Init.Data.Option.Lemmas
∀ {α : Type u_1} {o : Option α} {a b : α}, o.getD a = b ↔ o = some b ∨ o = none ∧ a = b
true
_private.Init.Data.Vector.OfFn.0.Vector.ofFnM_go_succ._proof_7
Init.Data.Vector.OfFn
∀ {α : Type u_1} {i : ℕ} {xs : Array α} {n : ℕ}, autoParam (i ≤ n) Vector.ofFnM_go_succ._auto_5✝ → ∀ {h : xs.size = i}, ¬i ≤ n + 1 → False
false
Matrix.specialUnitaryGroup.coe_star
Mathlib.LinearAlgebra.UnitaryGroup
∀ {n : Type u} [inst : DecidableEq n] [inst_1 : Fintype n] {α : Type v} [inst_2 : CommRing α] [inst_3 : StarRing α] (A : ↥(Matrix.specialUnitaryGroup n α)), ↑(star A) = star ↑A
true
Algebra.isAlgebraic_adjoin_iff
Mathlib.RingTheory.Algebraic.Integral
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] [IsDomain R] {s : Set S}, (Algebra.adjoin R s).IsAlgebraic ↔ ∀ x ∈ s, IsAlgebraic R x
true
_private.Mathlib.GroupTheory.QuotientGroup.Defs.0.QuotientGroup.mk'_eq_mk'._simp_1_1
Mathlib.GroupTheory.QuotientGroup.Defs
∀ {G : Type u_3} [inst : Group G] {a b c : G}, (b * a = c) = (a = b⁻¹ * c)
false
PartitionOfUnity.mem_finsupport
Mathlib.Topology.PartitionOfUnity
∀ {ι : Type u} {X : Type v} [inst : TopologicalSpace X] {s : Set X} (ρ : PartitionOfUnity ι X s) (x₀ : X) {i : ι}, i ∈ ρ.finsupport x₀ ↔ i ∈ Function.support fun i => (ρ i) x₀
true
WittVector.IsocrystalHom._sizeOf_inst
Mathlib.RingTheory.WittVector.Isocrystal
(p : ℕ) → {inst : Fact (Nat.Prime p)} → (k : Type u_1) → {inst_1 : CommRing k} → {inst_2 : CharP k p} → {inst_3 : PerfectRing k p} → (V : Type u_2) → {inst_4 : AddCommGroup V} → {inst_5 : WittVector.Isocrystal p k V} → (V₂ : Type u_3) → {inst_6 : AddCommGroup V₂} → {inst_7 : WittVector.Isocrystal p k V₂} → [SizeOf k] → [SizeOf V] → [SizeOf V₂] → SizeOf (WittVector.IsocrystalHom p k V V₂)
false
UInt64.ofFin_bitVecToFin
Init.Data.UInt.Lemmas
∀ (n : BitVec 64), UInt64.ofFin n.toFin = { toBitVec := n }
true
_private.Init.Grind.Ordered.Ring.0.Lean.Grind.OrderedRing.pos_intCast_of_pos._proof_1_1
Init.Grind.Ordered.Ring
∀ (a : ℕ), 0 < Int.negSucc a → False
false
AlgebraicGeometry.IsAffineOpen.isLocalization_stalk
Mathlib.AlgebraicGeometry.AffineScheme
∀ {X : AlgebraicGeometry.Scheme} {U : X.Opens} (hU : AlgebraicGeometry.IsAffineOpen U) (x : ↥U), IsLocalization.AtPrime (↑(X.presheaf.stalk ↑x)) (hU.primeIdealOf x).asIdeal
true
List.lookmap_congr
Mathlib.Data.List.Lookmap
∀ {α : Type u_1} {f g : α → Option α} {l : List α}, (∀ a ∈ l, f a = g a) → List.lookmap f l = List.lookmap g l
true
_aux_Mathlib_Analysis_Normed_Affine_Isometry___unexpand_AffineIsometryEquiv_1
Mathlib.Analysis.Normed.Affine.Isometry
Lean.PrettyPrinter.Unexpander
false
_private.Mathlib.RingTheory.Polynomial.Basic.0.Polynomial.coeff_prod_mem_ideal_pow_tsub._proof_1_3
Mathlib.RingTheory.Polynomial.Basic
∀ {R : Type u_1} [inst : CommSemiring R] {ι : Type u_2} (f : ι → Polynomial R) (I : Ideal R) (n : ι → ℕ) (a : ι) (s : Finset ι), ((∀ i ∈ s, ∀ (k : ℕ), (f i).coeff k ∈ I ^ (n i - k)) → ∀ (k : ℕ), (s.prod f).coeff k ∈ I ^ (s.sum n - k)) → (∀ i ∈ insert a s, ∀ (k : ℕ), (f i).coeff k ∈ I ^ (n i - k)) → ∀ (i j : ℕ), (∏ x ∈ s, f x).coeff (i, j).2 ∈ I ^ (∑ x ∈ s, n x - j)
false
List.mem_eraseDups._simp_1
Init.Data.List.Lemmas
∀ {α : Type u_1} [inst : BEq α] [LawfulBEq α] {a : α} {l : List α}, (a ∈ l.eraseDups) = (a ∈ l)
false
Lean.Grind.Linarith.Poly.denoteN.match_1
Init.Grind.Module.NatModuleNorm
(motive : Lean.Grind.Linarith.Poly → Sort u_1) → (p : Lean.Grind.Linarith.Poly) → (Unit → motive Lean.Grind.Linarith.Poly.nil) → ((k : ℤ) → (v : Lean.Grind.Linarith.Var) → (p : Lean.Grind.Linarith.Poly) → motive (Lean.Grind.Linarith.Poly.add k v p)) → motive p
false
CategoryTheory.Mon.mkIso_inv_hom
Mathlib.CategoryTheory.Monoidal.Mon_
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.MonoidalCategory C] {M N : CategoryTheory.Mon C} (e : M.X ≅ N.X) (one_f : autoParam (CategoryTheory.CategoryStruct.comp CategoryTheory.MonObj.one e.hom = CategoryTheory.MonObj.one) CategoryTheory.Mon.mkIso._auto_1) (mul_f : autoParam (CategoryTheory.CategoryStruct.comp CategoryTheory.MonObj.mul e.hom = CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.tensorHom e.hom e.hom) CategoryTheory.MonObj.mul) CategoryTheory.Mon.mkIso._auto_3), (CategoryTheory.Mon.mkIso e one_f mul_f).inv.hom = e.inv
true
Module.End.smulLeft._proof_1
Mathlib.Algebra.Module.LinearMap.End
∀ {R : Type u_2} {M : Type u_1} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M], ∀ α ∈ Set.center R, ∀ (β : R) (x : M), α • β • x = (RingHom.id R) β • α • x
false
_private.Init.Data.BitVec.Lemmas.0.BitVec.clzAuxRec_eq_iff_of_getLsbD_false._proof_1_5
Init.Data.BitVec.Lemmas
∀ (w : ℕ), (1 < 2 → w + 1 < 2 ^ (w + 1)) → ∀ (n : ℕ), ¬w - (n + 1) < 2 ^ (w + 1) → False
false
_private.Lean.Meta.Tactic.Grind.EMatch.0.Lean.Meta.Grind.EMatch.processOffset.match_1
Lean.Meta.Tactic.Grind.EMatch
(motive : Option ℕ → Sort u_1) → (__do_lift : Option ℕ) → ((k' : ℕ) → motive (some k')) → ((x : Option ℕ) → motive x) → motive __do_lift
false
IsCoveringMap.liftPath_const
Mathlib.Topology.Homotopy.Lifting
∀ {E : Type u_1} {X : Type u_2} [inst : TopologicalSpace E] [inst_1 : TopologicalSpace X] {p : E → X} (cov : IsCoveringMap p) {e : E} {x : X} (hpe : x = p e), cov.liftPath (ContinuousMap.const (↑unitInterval) x) e hpe = ContinuousMap.const (↑unitInterval) e
true
CategoryTheory.leftAdjointOfStructuredArrowInitials._proof_1
Mathlib.CategoryTheory.Adjunction.Comma
∀ {C : Type u_4} {D : Type u_2} [inst : CategoryTheory.Category.{u_3, u_4} C] [inst_1 : CategoryTheory.Category.{u_1, u_2} D] (G : CategoryTheory.Functor D C) [inst_2 : ∀ (A : C), CategoryTheory.Limits.HasInitial (CategoryTheory.StructuredArrow A G)] (x : C) (x_1 Y' : D) (g : x_1 ⟶ Y') (h : (⊥_ CategoryTheory.StructuredArrow x G).right ⟶ x_1), (CategoryTheory.leftAdjointOfStructuredArrowInitialsAux G x Y') (CategoryTheory.CategoryStruct.comp h g) = CategoryTheory.CategoryStruct.comp ((CategoryTheory.leftAdjointOfStructuredArrowInitialsAux G x x_1) h) (G.map g)
false
String.Slice.PosIterator.recOn
Init.Data.String.Iterate
{s : String.Slice} → {motive : s.PosIterator → Sort u} → (t : s.PosIterator) → ((currPos : s.Pos) → motive { currPos := currPos }) → motive t
false
GradedRing.projZeroRingHom'
Mathlib.RingTheory.GradedAlgebra.Basic
{ι : Type u_1} → {A : Type u_3} → {σ : Type u_4} → [inst : Semiring A] → [inst_1 : DecidableEq ι] → [inst_2 : AddCommMonoid ι] → [inst_3 : PartialOrder ι] → [CanonicallyOrderedAdd ι] → [inst_5 : SetLike σ A] → [inst_6 : AddSubmonoidClass σ A] → (𝒜 : ι → σ) → [inst_7 : GradedRing 𝒜] → A →+* ↥(𝒜 0)
true
_private.Mathlib.Algebra.Polynomial.RuleOfSigns.0.Polynomial.exists_cons_of_leadingCoeff_pos._proof_1_5
Mathlib.Algebra.Polynomial.RuleOfSigns
∀ {R : Type u_1} [inst : Ring R] {P : Polynomial R} (η : R), P.eraseLead.natDegree + 1 = P.natDegree → ∀ (d : ℕ), P.natDegree = 0 + d + 1 → ((Polynomial.X - Polynomial.C η) * P).natDegree = P.natDegree + 1 → ((Polynomial.X - Polynomial.C η) * P).nextCoeff = 0 → Polynomial.C η * (Polynomial.monomial P.natDegree) P.leadingCoeff = (Polynomial.monomial P.natDegree) P.nextCoeff
false
SeminormedGroup.ofMulDist._proof_2
Mathlib.Analysis.Normed.Group.Defs
∀ {E : Type u_1} [inst : Norm E] [inst_1 : Group E] [inst_2 : PseudoMetricSpace E], (∀ (x : E), ‖x‖ = dist 1 x) → (∀ (x y z : E), dist x y ≤ dist (z * x) (z * y)) → ∀ (x y : E), dist x y = ‖x⁻¹ * y‖
false
Mathlib.Tactic.Superscript.scriptFnNoAntiquot
Mathlib.Util.Superscript
Mathlib.Tactic.Superscript.Mapping → String → Lean.Parser.ParserFn → optParam Bool true → Lean.Parser.ParserFn
true
PreTilt.valAux_one
Mathlib.RingTheory.Perfection
∀ {K : Type u₁} [inst : Field K] {v : Valuation K NNReal} {O : Type u₂} [inst_1 : CommRing O] [inst_2 : Algebra O K], v.Integers O → ∀ {p : ℕ} [inst_3 : Fact (Nat.Prime p)] [inst_4 : Fact ¬IsUnit ↑p], PreTilt.valAux K v O p 1 = 1
true
Fintype.decidableForallFintype._proof_1
Mathlib.Data.Fintype.Defs
∀ {α : Type u_1} {p : α → Prop} [inst : Fintype α], (∀ a ∈ Finset.univ, p a) ↔ ∀ (a : α), p a
false
Set.coe_singletonAddMonoidHom
Mathlib.Algebra.Group.Pointwise.Set.Basic
∀ {α : Type u_2} [inst : AddZeroClass α], ⇑Set.singletonAddMonoidHom = singleton
true
CategoryTheory.IsRegularMono.fac_assoc
Mathlib.CategoryTheory.Limits.Shapes.RegularMono
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X Y W : C} (f : X ⟶ Y) [inst_1 : CategoryTheory.IsRegularMono f] (k : W ⟶ Y) (h : CategoryTheory.CategoryStruct.comp k (CategoryTheory.IsRegularMono.left f) = CategoryTheory.CategoryStruct.comp k (CategoryTheory.IsRegularMono.right f)) {Z : C} (h_1 : Y ⟶ Z), CategoryTheory.CategoryStruct.comp (CategoryTheory.IsRegularMono.lift f k h) (CategoryTheory.CategoryStruct.comp f h_1) = CategoryTheory.CategoryStruct.comp k h_1
true
_private.Init.Data.List.Lemmas.0.List.flatMap_eq_nil_iff._simp_1_2
Init.Data.List.Lemmas
∀ {a b c : Prop}, (a ∧ b → c) = (a → b → c)
false
AlgEquiv.lift_trdeg_eq
Mathlib.RingTheory.AlgebraicIndependent.Basic
∀ {R : Type u_2} {A : Type v} {A' : Type v'} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : CommRing A'] [inst_3 : Algebra R A] [inst_4 : Algebra R A'] (e : A ≃ₐ[R] A'), Cardinal.lift.{v', v} (Algebra.trdeg R A) = Cardinal.lift.{v, v'} (Algebra.trdeg R A')
true
_private.Mathlib.GroupTheory.Perm.Support.0.Equiv.Perm.support_inv._simp_1_2
Mathlib.GroupTheory.Perm.Support
∀ {a b : Prop}, (¬a ↔ ¬b) = (a ↔ b)
false
instDecidableEqSum.decEq
Init.Core
{α : Type u_1} → {β : Type u_2} → [DecidableEq α] → [DecidableEq β] → (x x_1 : α ⊕ β) → Decidable (x = x_1)
true
_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.mk'._simp_4
Mathlib.Combinatorics.SimpleGraph.Basic
∀ {a b : Bool}, (a = true ↔ b = true) = (a = b)
false
Vector.map_inj_left
Init.Data.Vector.Lemmas
∀ {α : Type u_1} {β : Type u_2} {n : ℕ} {xs : Vector α n} {f g : α → β}, Vector.map f xs = Vector.map g xs ↔ ∀ a ∈ xs, f a = g a
true
commMonTypeEquivalenceCommMon._proof_1
Mathlib.CategoryTheory.Monoidal.Internal.Types.Basic
∀ {X Y : CommMonCat} (f : X ⟶ Y), CategoryTheory.CategoryStruct.comp ((CommMonTypeEquivalenceCommMon.inverse.comp CommMonTypeEquivalenceCommMon.functor).map f) ((fun A => (let __src := Equiv.refl (CommMonTypeEquivalenceCommMon.inverse.obj A).X; { toEquiv := __src, map_mul' := ⋯ }).toCommMonCatIso) Y).hom = CategoryTheory.CategoryStruct.comp ((fun A => (let __src := Equiv.refl (CommMonTypeEquivalenceCommMon.inverse.obj A).X; { toEquiv := __src, map_mul' := ⋯ }).toCommMonCatIso) X).hom ((CategoryTheory.Functor.id CommMonCat).map f)
false
_private.Init.Data.Array.BasicAux.0.Array.mapM'.go._unary.eq_def
Init.Data.Array.BasicAux
∀ {m : Type u_1 → Type u_2} {α : Type u_3} {β : Type u_1} [inst : Monad m] (f : α → m β) (as : Array α) (_x : (i : ℕ) ×' (_ : { bs // bs.size = i }) ×' i ≤ as.size), Array.mapM'.go._unary✝ f as _x = PSigma.casesOn _x fun i acc => PSigma.casesOn acc fun acc hle => if h : i = as.size then pure (h ▸ acc) else have hlt := ⋯; do let b ← f as[i] Array.mapM'.go._unary✝¹ f as ⟨i + 1, ⟨⟨(↑acc).push b, ⋯⟩, hlt⟩⟩
false
AddAction.vadd_zsmul_movedBy_eq_of_addCommute
Mathlib.GroupTheory.GroupAction.FixedPoints
∀ {α : Type u_1} {G : Type u_2} [inst : AddGroup G] [inst_1 : AddAction G α] {g h : G}, AddCommute g h → ∀ (j : ℤ), j • h +ᵥ (AddAction.fixedBy α g)ᶜ = (AddAction.fixedBy α g)ᶜ
true
IsLocalMax.add
Mathlib.Topology.Order.LocalExtr
∀ {α : Type u} {β : Type v} [inst : TopologicalSpace α] [inst_1 : AddCommMonoid β] [inst_2 : PartialOrder β] [IsOrderedAddMonoid β] {f g : α → β} {a : α}, IsLocalMax f a → IsLocalMax g a → IsLocalMax (fun x => f x + g x) a
true
_private.Mathlib.Algebra.Order.SuccPred.WithBot.0.WithBot.one_le_iff_pos._simp_1_1
Mathlib.Algebra.Order.SuccPred.WithBot
∀ {α : Type u_1} {x : α} [inst : PartialOrder α] [inst_1 : AddMonoidWithOne α] [ZeroLEOneClass α] [NeZero 1] [SuccAddOrder α], (1 ≤ x) = (0 < x)
false
List.filterMap_append
Init.Data.List.Lemmas
∀ {α : Type u_1} {β : Type u_2} {l l' : List α} {f : α → Option β}, List.filterMap f (l ++ l') = List.filterMap f l ++ List.filterMap f l'
true
Std.HashMap.Raw.getKeyD_insert_self
Std.Data.HashMap.RawLemmas
∀ {α : Type u} {β : Type v} {m : Std.HashMap.Raw α β} [inst : BEq α] [inst_1 : Hashable α] [EquivBEq α] [LawfulHashable α], m.WF → ∀ {k fallback : α} {v : β}, (m.insert k v).getKeyD k fallback = k
true
basisOfPiSpaceOfLinearIndependent
Mathlib.LinearAlgebra.FiniteDimensional.Lemmas
{K : Type u} → [inst : DivisionRing K] → {ι : Type u_1} → [Fintype ι] → [Decidable (Nonempty ι)] → {b : ι → ι → K} → LinearIndependent K b → Module.Basis ι K (ι → K)
true
_private.Mathlib.Algebra.Module.Injective.0.Module.Baer.extension_property_addMonoidHom.match_1_1
Mathlib.Algebra.Module.Injective
∀ {Q : Type u_1} [inst : AddCommGroup Q] {M : Type u_3} {N : Type u_2} [inst_1 : AddCommGroup M] [inst_2 : AddCommGroup N] (f : M →+ N) (g : M →+ Q) (motive : (∃ h, h ∘ₗ f.toIntLinearMap = g.toIntLinearMap) → Prop) (x : ∃ h, h ∘ₗ f.toIntLinearMap = g.toIntLinearMap), (∀ (g' : N →ₗ[ℤ] Q) (hg' : g' ∘ₗ f.toIntLinearMap = g.toIntLinearMap), motive ⋯) → motive x
false
CommRingCat.prodFanIsLimit._proof_3
Mathlib.Algebra.Category.Ring.Constructions
∀ (A B : CommRingCat) (s : CategoryTheory.Limits.Cone (CategoryTheory.Limits.pair A B)) (m : s.pt ⟶ (A.prodFan B).pt), (∀ (j : CategoryTheory.Discrete CategoryTheory.Limits.WalkingPair), CategoryTheory.CategoryStruct.comp m ((A.prodFan B).π.app j) = s.π.app j) → m = CommRingCat.ofHom ((CommRingCat.Hom.hom (s.π.app { as := CategoryTheory.Limits.WalkingPair.left })).prod (CommRingCat.Hom.hom (s.π.app { as := CategoryTheory.Limits.WalkingPair.right })))
false
Nat.Primes.coe_pnat_inj
Mathlib.Data.PNat.Prime
∀ (p q : Nat.Primes), ↑p = ↑q ↔ p = q
true
_private.Mathlib.MeasureTheory.Integral.IntervalIntegral.Slope.0.MonotoneOn.intervalIntegral_slope_le._simp_1_24
Mathlib.MeasureTheory.Integral.IntervalIntegral.Slope
∀ {R : Type u_1} [inst : AddMonoidWithOne R] [CharZero R] (n : ℕ), (↑n + 1 = 0) = False
false
Lean.Meta.Grind.Arith.CommRing.State.ncSemirings
Lean.Meta.Tactic.Grind.Arith.CommRing.Types
Lean.Meta.Grind.Arith.CommRing.State → Array Lean.Meta.Grind.Arith.CommRing.Semiring
true
Lists.Equiv.symm
Mathlib.SetTheory.Lists
∀ {α : Type u_1} {l₁ l₂ : Lists α}, l₁.Equiv l₂ → l₂.Equiv l₁
true
fderivWithin_fun_sub
Mathlib.Analysis.Calculus.FDeriv.Add
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace 𝕜 E] {F : Type u_3} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {f g : E → F} {x : E} {s : Set E}, UniqueDiffWithinAt 𝕜 s x → DifferentiableWithinAt 𝕜 f s x → DifferentiableWithinAt 𝕜 g s x → fderivWithin 𝕜 (fun y => f y - g y) s x = fderivWithin 𝕜 f s x - fderivWithin 𝕜 g s x
true
ContinuousMulEquiv.coe_trans
Mathlib.Topology.Algebra.ContinuousMonoidHom
∀ {M : Type u_1} {N : Type u_2} [inst : TopologicalSpace M] [inst_1 : TopologicalSpace N] [inst_2 : Mul M] [inst_3 : Mul N] {L : Type u_3} [inst_4 : Mul L] [inst_5 : TopologicalSpace L] (e₁ : M ≃ₜ* N) (e₂ : N ≃ₜ* L), ⇑(e₁.trans e₂) = ⇑e₂ ∘ ⇑e₁
true
PiTensorProduct.lift_reindex
Mathlib.LinearAlgebra.PiTensorProduct
∀ {ι : Type u_1} {ι₂ : Type u_2} {R : Type u_4} [inst : CommSemiring R] {s : ι → Type u_7} [inst_1 : (i : ι) → AddCommMonoid (s i)] [inst_2 : (i : ι) → Module R (s i)] {E : Type u_9} [inst_3 : AddCommMonoid E] [inst_4 : Module R E] (e : ι ≃ ι₂) (φ : MultilinearMap R (fun i => s (e.symm i)) E) (x : PiTensorProduct R fun i => s i), (PiTensorProduct.lift φ) ((PiTensorProduct.reindex R s e) x) = (PiTensorProduct.lift ((MultilinearMap.domDomCongrLinearEquiv' R R s E e).symm φ)) x
true
Lean.Compiler.LCNF.CodeDecl.casesOn
Lean.Compiler.LCNF.Basic
{pu : Lean.Compiler.LCNF.Purity} → {motive : Lean.Compiler.LCNF.CodeDecl pu → Sort u} → (t : Lean.Compiler.LCNF.CodeDecl pu) → ((decl : Lean.Compiler.LCNF.LetDecl pu) → motive (Lean.Compiler.LCNF.CodeDecl.let decl)) → ((decl : Lean.Compiler.LCNF.FunDecl pu) → (h : pu = Lean.Compiler.LCNF.Purity.pure) → motive (Lean.Compiler.LCNF.CodeDecl.fun decl h)) → ((decl : Lean.Compiler.LCNF.FunDecl pu) → motive (Lean.Compiler.LCNF.CodeDecl.jp decl)) → ((fvarId : Lean.FVarId) → (i : ℕ) → (y : Lean.FVarId) → (h : pu = Lean.Compiler.LCNF.Purity.impure) → motive (Lean.Compiler.LCNF.CodeDecl.uset fvarId i y h)) → ((fvarId : Lean.FVarId) → (i offset : ℕ) → (y : Lean.FVarId) → (ty : Lean.Expr) → (h : pu = Lean.Compiler.LCNF.Purity.impure) → motive (Lean.Compiler.LCNF.CodeDecl.sset fvarId i offset y ty h)) → ((fvarId : Lean.FVarId) → (n : ℕ) → (check persistent : Bool) → (h : pu = Lean.Compiler.LCNF.Purity.impure) → motive (Lean.Compiler.LCNF.CodeDecl.inc fvarId n check persistent h)) → ((fvarId : Lean.FVarId) → (n : ℕ) → (check persistent : Bool) → (h : pu = Lean.Compiler.LCNF.Purity.impure) → motive (Lean.Compiler.LCNF.CodeDecl.dec fvarId n check persistent h)) → motive t
false
Lean.Meta.Grind.Filter.and
Lean.Meta.Tactic.Grind.Filter
Lean.Meta.Grind.Filter → Lean.Meta.Grind.Filter → Lean.Meta.Grind.Filter
true
Tactic.ComputeAsymptotics.WellFormedBasis.tendsto_atTop
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Basis
∀ {basis : Tactic.ComputeAsymptotics.Basis}, Tactic.ComputeAsymptotics.WellFormedBasis basis → ∀ {f : ℝ → ℝ}, f ∈ basis → Filter.Tendsto f Filter.atTop Filter.atTop
true
CategoryTheory.Functor.representableByUliftFunctorEquiv._proof_3
Mathlib.CategoryTheory.Yoneda
∀ {C : Type u_1} [inst : CategoryTheory.Category.{u_3, u_1} C] {F : CategoryTheory.Functor Cᵒᵖ (Type u_2)} {X : C}, Function.RightInverse (fun R => { homEquiv := fun {Y} => R.homEquiv.trans Equiv.ulift.symm, homEquiv_comp := ⋯ }) fun R => { homEquiv := fun {Y} => R.homEquiv.trans Equiv.ulift, homEquiv_comp := ⋯ }
false
Std.Internal.List.insertListIfNew._unsafe_rec
Std.Data.Internal.List.Associative
{α : Type u} → {β : α → Type v} → [BEq α] → List ((a : α) × β a) → List ((a : α) × β a) → List ((a : α) × β a)
false
_private.Mathlib.MeasureTheory.Measure.LevyProkhorovMetric.0.MeasureTheory.levyProkhorovEDist_le_of_forall._simp_1_2
Mathlib.MeasureTheory.Measure.LevyProkhorovMetric
∀ {G : Type u_1} [inst : AddSemigroup G] (a b c : G), a + (b + c) = a + b + c
false
Std.DTreeMap.Internal.Unit.RocSliceData.ctorIdx
Std.Data.DTreeMap.Internal.Zipper
{α : Type u} → {inst : Ord α} → Std.DTreeMap.Internal.Unit.RocSliceData α → ℕ
false
Bornology.isVonNBounded_add_self
Mathlib.Analysis.LocallyConvex.Bounded
∀ {𝕜 : Type u_1} {E : Type u_3} [inst : NormedField 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E] [inst_3 : TopologicalSpace E] [ContinuousSMul 𝕜 E] [ContinuousAdd E] {s : Set E}, Bornology.IsVonNBounded 𝕜 (s + s) ↔ Bornology.IsVonNBounded 𝕜 s
true
_private.Lean.Elab.PreDefinition.Structural.SmartUnfolding.0.Lean.Elab.Structural.addSmartUnfoldingDefAux.visit.match_8
Lean.Elab.PreDefinition.Structural.SmartUnfolding
(motive : Lean.Expr → Sort u_1) → (e : Lean.Expr) → ((binderName : Lean.Name) → (binderType body : Lean.Expr) → (binderInfo : Lean.BinderInfo) → motive (Lean.Expr.lam binderName binderType body binderInfo)) → ((binderName : Lean.Name) → (binderType body : Lean.Expr) → (binderInfo : Lean.BinderInfo) → motive (Lean.Expr.forallE binderName binderType body binderInfo)) → ((n : Lean.Name) → (type val body : Lean.Expr) → (nondep : Bool) → motive (Lean.Expr.letE n type val body nondep)) → ((d : Lean.MData) → (b : Lean.Expr) → motive (Lean.Expr.mdata d b)) → ((n : Lean.Name) → (i : ℕ) → (s : Lean.Expr) → motive (Lean.Expr.proj n i s)) → ((fn arg : Lean.Expr) → motive (fn.app arg)) → ((x : Lean.Expr) → motive x) → motive e
false
LE.opposite_def
Init.Data.Order.Opposite
∀ {α : Type u_1} {le : LE α}, le.opposite = { le := fun a b => b ≤ a }
true
AddMonoidAlgebra.prod_single
Mathlib.Algebra.MonoidAlgebra.Defs
∀ {R : Type u_1} {M : Type u_4} {ι : Type u_7} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] (s : Finset ι) (m : ι → M) (r : ι → R), ∏ i ∈ s, AddMonoidAlgebra.single (m i) (r i) = AddMonoidAlgebra.single (∑ i ∈ s, m i) (∏ i ∈ s, r i)
true
Lean.Elab.Tactic.evalSeq1._regBuiltin.Lean.Elab.Tactic.evalSeq1_1
Lean.Elab.Tactic.BuiltinTactic
IO Unit
false
Polynomial.IsUnitTrinomial.irreducible_of_coprime'
Mathlib.Analysis.Complex.Polynomial.UnitTrinomial
∀ {p : Polynomial ℤ}, p.IsUnitTrinomial → (∀ (z : ℂ), ¬((Polynomial.aeval z) p = 0 ∧ (Polynomial.aeval z) p.mirror = 0)) → Irreducible p
true
CategoryTheory.Arrow.mapCechNerve._proof_1
Mathlib.AlgebraicTopology.CechNerve
∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] {f g : CategoryTheory.Arrow C} [inst_1 : ∀ (n : ℕ), CategoryTheory.Limits.HasWidePullback f.right (fun x => f.left) fun x => f.hom] (F : f ⟶ g) (n : SimplexCategoryᵒᵖ) (j : Fin ((Opposite.unop n).len + 1)), CategoryTheory.CategoryStruct.comp ((fun i => CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.WidePullback.π (fun x => f.hom) i) F.left) j) g.hom = CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.WidePullback.base fun x => f.hom) F.right
false
Submodule.sndEquiv_apply
Mathlib.LinearAlgebra.Prod
∀ (R : Type u) (M : Type v) (M₂ : Type w) [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : AddCommMonoid M₂] [inst_3 : Module R M] [inst_4 : Module R M₂] (x : ↥(Submodule.snd R M M₂)), (Submodule.sndEquiv R M M₂) x = (↑x).2
true
Polynomial.aevalAevalEquiv_symm_apply_snd
Mathlib.Algebra.Polynomial.Bivariate
∀ (R : Type u_1) (A : Type u_2) [inst : CommSemiring R] [inst_1 : CommSemiring A] [inst_2 : Algebra R A] (f : Polynomial (Polynomial R) →ₐ[R] A), ((Polynomial.aevalAevalEquiv R A).symm f).2 = f Polynomial.X
true
ProbabilityTheory.centralMoment_two_eq_variance
Mathlib.Probability.Moments.Basic
∀ {Ω : Type u_1} {m : MeasurableSpace Ω} {X : Ω → ℝ} {μ : MeasureTheory.Measure Ω}, AEMeasurable X μ → ProbabilityTheory.centralMoment X 2 μ = ProbabilityTheory.variance X μ
true
MeasureTheory.IntegrableOn.congr_set_ae
Mathlib.MeasureTheory.Integral.IntegrableOn
∀ {α : Type u_1} {ε : Type u_3} {mα : MeasurableSpace α} {f : α → ε} {s t : Set α} {μ : MeasureTheory.Measure α} [inst : TopologicalSpace ε] [inst_1 : ContinuousENorm ε], MeasureTheory.IntegrableOn f t μ → s =ᵐ[μ] t → MeasureTheory.IntegrableOn f s μ
true