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2 classes
CochainComplex.HomComplex.CohomologyClass.toSmallShiftedHom_mk
Mathlib.Algebra.Homology.DerivedCategory.SmallShiftedHom
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C] {K L : CochainComplex C ℤ} {n : ℤ} [inst_2 : CategoryTheory.Localization.HasSmallLocalizedShiftedHom (HomologicalComplex.quasiIso C (ComplexShape.up ℤ)) ℤ K L] (x : CochainComplex.HomComplex.Cocycle K L n), (CochainComplex.HomComplex.CohomologyClass.mk x).toSmallShiftedHom = CategoryTheory.Localization.SmallShiftedHom.mk (HomologicalComplex.quasiIso C (ComplexShape.up ℤ)) (CochainComplex.HomComplex.Cocycle.equivHomShift.symm x)
true
RightPreLieRing.instLeftPreLieRingMulOpposite
Mathlib.Algebra.NonAssoc.PreLie.Basic
{L : Type u_2} → [RightPreLieRing L] → LeftPreLieRing Lᵐᵒᵖ
true
Lean.Meta.Grind.EMatch.Choice.noConfusion
Lean.Meta.Tactic.Grind.EMatch
{P : Sort u} → {t t' : Lean.Meta.Grind.EMatch.Choice} → t = t' → Lean.Meta.Grind.EMatch.Choice.noConfusionType P t t'
false
IsRightUniformAddGroup.rec
Mathlib.Topology.Algebra.IsUniformGroup.Defs
{G : Type u_7} → [inst : UniformSpace G] → [inst_1 : AddGroup G] → {motive : IsRightUniformAddGroup G → Sort u} → ([toIsTopologicalAddGroup : IsTopologicalAddGroup G] → (uniformity_eq : uniformity G = Filter.comap (fun x => x.2 + -x.1) (nhds 0)) → motive ⋯) → (t : IsRightUniformAddGroup G) → motive t
false
_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.rankFinite_iff_cRank_lt_aleph0._simp_1_6
Mathlib.Combinatorics.Matroid.Rank.Cardinal
∀ {α : Type u}, Finite α = (Cardinal.mk α < Cardinal.aleph0)
false
AlgebraicGeometry.ExistsHomHomCompEqCompAux.mk.inj
Mathlib.AlgebraicGeometry.AffineTransitionLimit
∀ {I : Type u} {inst : CategoryTheory.Category.{u, u} I} {S X : AlgebraicGeometry.Scheme} {D : CategoryTheory.Functor I AlgebraicGeometry.Scheme} {t : D ⟶ (CategoryTheory.Functor.const I).obj S} {f : X ⟶ S} {c : CategoryTheory.Limits.Cone D} {hc : CategoryTheory.Limits.IsLimit c} {i : I} {a : D.obj i ⟶ X} {ha : t.app i = CategoryTheory.CategoryStruct.comp a f} {b : D.obj i ⟶ X} {hb : t.app i = CategoryTheory.CategoryStruct.comp b f} {hab : CategoryTheory.CategoryStruct.comp (c.π.app i) a = CategoryTheory.CategoryStruct.comp (c.π.app i) b} {𝒰S : S.OpenCover} {h𝒰S : ∀ (i : 𝒰S.I₀), AlgebraicGeometry.IsAffine (𝒰S.X i)} {𝒰X : (i : (CategoryTheory.Precoverage.ZeroHypercover.pullback₁ f 𝒰S).I₀) → ((CategoryTheory.Precoverage.ZeroHypercover.pullback₁ f 𝒰S).X i).OpenCover} {h𝒰X : ∀ (i : (CategoryTheory.Precoverage.ZeroHypercover.pullback₁ f 𝒰S).I₀) (j : (𝒰X i).I₀), AlgebraicGeometry.IsAffine ((𝒰X i).X j)} {c_1 : CategoryTheory.Limits.Cone D} {hc_1 : CategoryTheory.Limits.IsLimit c_1} {i_1 : I} {a_1 : D.obj i_1 ⟶ X} {ha_1 : t.app i_1 = CategoryTheory.CategoryStruct.comp a_1 f} {b_1 : D.obj i_1 ⟶ X} {hb_1 : t.app i_1 = CategoryTheory.CategoryStruct.comp b_1 f} {hab_1 : CategoryTheory.CategoryStruct.comp (c_1.π.app i_1) a_1 = CategoryTheory.CategoryStruct.comp (c_1.π.app i_1) b_1} {𝒰S_1 : S.OpenCover} {h𝒰S_1 : ∀ (i : 𝒰S_1.I₀), AlgebraicGeometry.IsAffine (𝒰S_1.X i)} {𝒰X_1 : (i : (CategoryTheory.Precoverage.ZeroHypercover.pullback₁ f 𝒰S_1).I₀) → ((CategoryTheory.Precoverage.ZeroHypercover.pullback₁ f 𝒰S_1).X i).OpenCover} {h𝒰X_1 : ∀ (i : (CategoryTheory.Precoverage.ZeroHypercover.pullback₁ f 𝒰S_1).I₀) (j : (𝒰X_1 i).I₀), AlgebraicGeometry.IsAffine ((𝒰X_1 i).X j)}, { c := c, hc := hc, i := i, a := a, ha := ha, b := b, hb := hb, hab := hab, 𝒰S := 𝒰S, h𝒰S := h𝒰S, 𝒰X := 𝒰X, h𝒰X := h𝒰X } = { c := c_1, hc := hc_1, i := i_1, a := a_1, ha := ha_1, b := b_1, hb := hb_1, hab := hab_1, 𝒰S := 𝒰S_1, h𝒰S := h𝒰S_1, 𝒰X := 𝒰X_1, h𝒰X := h𝒰X_1 } → c = c_1 ∧ hc ≍ hc_1 ∧ i = i_1 ∧ a ≍ a_1 ∧ b ≍ b_1 ∧ 𝒰S = 𝒰S_1 ∧ 𝒰X ≍ 𝒰X_1
true
Function.FromTypes.uncurry_apply_cons
Mathlib.Data.Fin.Tuple.Curry
∀ {n : ℕ} {α : Type u} {p : Fin n → Type u} {τ : Type u} (f : Function.FromTypes (Matrix.vecCons α p) τ) (a : α) (args : (i : Fin n) → p i), f.uncurry (Fin.cons a args) = (f a).uncurry args
true
Array.«_aux_Init_Data_Array_Perm___macroRules_Array_term_~__1»
Init.Data.Array.Perm
Lean.Macro
false
QuasispectrumRestricts.nonUnitalStarAlgHom._proof_19
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Restrict
∀ {R : Type u_1} {S : Type u_3} {A : Type u_2} [inst : Semifield R] [inst_1 : TopologicalSpace R] [inst_2 : Field S] [inst_3 : TopologicalSpace S] [inst_4 : NonUnitalRing A] [inst_5 : Algebra R S] [inst_6 : Module R A] [inst_7 : Module S A] [inst_8 : IsScalarTower S A A] [inst_9 : SMulCommClass S A A] [inst_10 : IsScalarTower R S A] {a : A} {f : C(S, R)} (h : QuasispectrumRestricts a ⇑f), { toFun := Subtype.map ⇑f ⋯, continuous_toFun := ⋯ } 0 = 0
false
Monotone.rightLim
Mathlib.Topology.Order.LeftRightLim
∀ {α : Type u_1} {β : Type u_2} [inst : LinearOrder α] [inst_1 : ConditionallyCompleteLinearOrder β] [inst_2 : TopologicalSpace β] [OrderTopology β] {f : α → β}, Monotone f → Monotone (Function.rightLim f)
true
Lean.Meta.Grind.instInhabitedCasesTypes
Lean.Meta.Tactic.Grind.Extension
Inhabited Lean.Meta.Grind.CasesTypes
true
Aesop.RuleTac.tacGen
Aesop.RuleTac.Tactic
Lean.Name → Aesop.RuleTac
true
Polynomial.SplittingField.instGroupWithZero._proof_3
Mathlib.FieldTheory.SplittingField.Construction
∀ {K : Type u_1} [inst : Field K] (f : Polynomial K) (n : ℕ) (a : f.SplittingField), zpowRec npowRec (↑n.succ) a = zpowRec npowRec (↑n) a * a
false
Lean.Omega.Int.mul_congr
Init.Omega.Int
∀ {a b c d : ℤ}, a = b → c = d → a * c = b * d
true
Ord.ext
Init.Data.Ord.Basic
∀ {α : Type u} {x y : Ord α}, compare = compare → x = y
true
SpectrumRestricts.nnreal_add
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Basic
∀ {A : Type u_1} [inst : CStarAlgebra A] {a b : A}, IsSelfAdjoint a → IsSelfAdjoint b → SpectrumRestricts a ⇑ContinuousMap.realToNNReal → SpectrumRestricts b ⇑ContinuousMap.realToNNReal → SpectrumRestricts (a + b) ⇑ContinuousMap.realToNNReal
true
_private.Mathlib.Analysis.Calculus.FDeriv.Measurable.0.FDerivMeasurableAux.isOpen_A_with_param._simp_1_4
Mathlib.Analysis.Calculus.FDeriv.Measurable
∀ {α : Type u} {β : Type v} {s : Set α} {t : Set β} {p : α × β}, (p ∈ s ×ˢ t) = (p.1 ∈ s ∧ p.2 ∈ t)
false
_private.Aesop.Script.StructureStatic.0.Aesop.Script.structureStaticCore.go
Aesop.Script.StructureStatic
Aesop.Script.TacticState → Aesop.Script.StaticStructureM (List Aesop.Script.Step × Aesop.Script.TacticState)
true
_private.Init.Data.List.Find.0.List.lookup_eq_some_iff._simp_1_2
Init.Data.List.Find
∀ {α : Type u_1} [inst : BEq α] [LawfulBEq α] {a b : α}, ((a == b) = true) = (a = b)
false
EReal.nsmul_eq_mul
Mathlib.Data.EReal.Operations
∀ (n : ℕ) (x : EReal), n • x = ↑n * x
true
_private.Init.Prelude.0.Lean.Macro.State.mk._flat_ctor
Init.Prelude
Lean.MacroScope → List (Lean.Name × String) → List Lean.Name → Lean.Macro.State
false
ContinuousOn.cfc_nnreal._auto_1
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Continuity
Lean.Syntax
false
Lean.Lsp.InitializeParams.initializationOptions?._default
Lean.Data.Lsp.InitShutdown
Option Lean.Lsp.InitializationOptions
false
bot_lt_affineSpan._simp_1
Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs
∀ (k : Type u_1) {V : Type u_2} {P : Type u_3} [inst : Ring k] [inst_1 : AddCommGroup V] [inst_2 : Module k V] [inst_3 : AddTorsor V P] {s : Set P}, (⊥ < affineSpan k s) = s.Nonempty
false
Matrix.toBilin._proof_1
Mathlib.LinearAlgebra.Matrix.BilinearForm
∀ {R₁ : Type u_1} {M₁ : Type u_2} [inst : CommSemiring R₁] [inst_1 : AddCommMonoid M₁] [inst_2 : Module R₁ M₁], SMulCommClass R₁ R₁ (M₁ →ₗ[R₁] R₁)
false
IsSelfAdjoint.eq_smul_self_of_isLocalExtrOn
Mathlib.Analysis.InnerProductSpace.Rayleigh
∀ {𝕜 : Type u_1} [inst : RCLike 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E] [inst_3 : CompleteSpace E] {T : E →L[𝕜] E}, IsSelfAdjoint T → ∀ {x₀ : E}, IsLocalExtrOn T.reApplyInnerSelf (Metric.sphere 0 ‖x₀‖) x₀ → T x₀ = ↑(T.rayleighQuotient x₀) • x₀
true
Lean.Parser.Term.prop.parenthesizer
Lean.Parser.Term
Lean.PrettyPrinter.Parenthesizer
true
RelIso.instFunLike._proof_1
Mathlib.Order.RelIso.Basic
∀ {α : Type u_1} {β : Type u_2} {r : α → α → Prop} {s : β → β → Prop}, Function.Injective ((fun e => ⇑e) ∘ RelIso.toEquiv)
false
MulChar.ringHomComp_pow
Mathlib.NumberTheory.MulChar.Basic
∀ {R : Type u_1} [inst : CommMonoid R] {R' : Type u_2} [inst_1 : CommRing R'] {R'' : Type u_3} [inst_2 : CommRing R''] (χ : MulChar R R') (f : R' →+* R'') (n : ℕ), χ.ringHomComp f ^ n = (χ ^ n).ringHomComp f
true
ringChar
Mathlib.Algebra.CharP.Defs
(R : Type u_1) → [NonAssocSemiring R] → ℕ
true
RingCon.unop
Mathlib.RingTheory.Congruence.Opposite
{R : Type u_1} → [inst : Add R] → [inst_1 : Mul R] → RingCon Rᵐᵒᵖ → RingCon R
true
_private.Mathlib.Analysis.Complex.Hadamard.0.Complex.HadamardThreeLines.norm_le_interp_of_mem_verticalClosedStrip₀₁'._simp_1_2
Mathlib.Analysis.Complex.Hadamard
∀ {α : Type u} {β : Type v} {f : α → β} {s : Set β} {a : α}, (a ∈ f ⁻¹' s) = (f a ∈ s)
false
Pi.instAddTorsor._proof_1
Mathlib.Algebra.AddTorsor.Basic
∀ {I : Type u_1} {fg : I → Type u_3} [inst : (i : I) → AddGroup (fg i)] {fp : I → Type u_2} [(i : I) → AddTorsor (fg i) (fp i)], Nonempty ((a : I) → fp a)
false
_private.Init.Data.Range.Polymorphic.Internal.SignedBitVec.0.BitVec.Signed.sle_iff_rotate_le_rotate._simp_1_15
Init.Data.Range.Polymorphic.Internal.SignedBitVec
∀ {a b : ℕ}, (¬a ≤ b) = (b < a)
false
_private.Lean.Util.Recognizers.0.Lean.Expr.eqOrIff?._sparseCasesOn_1
Lean.Util.Recognizers
{α : Type u} → {motive : Option α → Sort u_1} → (t : Option α) → ((val : α) → motive (some val)) → (Nat.hasNotBit 2 t.ctorIdx → motive t) → motive t
false
MeromorphicAt.neg_iff._simp_1
Mathlib.Analysis.Meromorphic.Basic
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_3} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace 𝕜 E] {x : 𝕜} {f : 𝕜 → E}, MeromorphicAt (-f) x = MeromorphicAt f x
false
ProbabilityTheory.uniformOn_singleton
Mathlib.Probability.UniformOn
∀ {Ω : Type u_1} [inst : MeasurableSpace Ω] [MeasurableSingletonClass Ω] (ω : Ω) (t : Set Ω) [inst_2 : Decidable (ω ∈ t)], (ProbabilityTheory.uniformOn {ω}) t = if ω ∈ t then 1 else 0
true
_private.Mathlib.Tactic.FBinop.0.FBinopElab.Tree.recOn
Mathlib.Tactic.FBinop
{motive : FBinopElab.Tree✝ → Sort u} → (t : FBinopElab.Tree✝¹) → ((ref : Lean.Syntax) → (infoTrees : Lean.PersistentArray Lean.Elab.InfoTree) → (val : Lean.Expr) → motive (FBinopElab.Tree.term✝ ref infoTrees val)) → ((ref : Lean.Syntax) → (f : Lean.Expr) → (lhs rhs : FBinopElab.Tree✝²) → motive lhs → motive rhs → motive (FBinopElab.Tree.binop✝ ref f lhs rhs)) → ((macroName : Lean.Name) → (stx stx' : Lean.Syntax) → (nested : FBinopElab.Tree✝³) → motive nested → motive (FBinopElab.Tree.macroExpansion✝ macroName stx stx' nested)) → motive t
false
Lean.mkLevelSuccEx
Lean.Level
Lean.Level → Lean.Level
true
Vector.map_attachWith_eq_pmap
Init.Data.Vector.Attach
∀ {α : Type u_1} {n : ℕ} {β : Type u_2} {xs : Vector α n} {P : α → Prop} {H : ∀ a ∈ xs, P a} {f : { x // P x } → β}, Vector.map f (xs.attachWith P H) = Vector.pmap (fun a h => f ⟨a, ⋯⟩) xs ⋯
true
Lean.Meta.Grind.DelayedTheoremInstance.mk.noConfusion
Lean.Meta.Tactic.Grind.Types
{P : Sort u} → {thm : Lean.Meta.Grind.EMatchTheorem} → {proof prop : Lean.Expr} → {generation : ℕ} → {guards : List Lean.Meta.Grind.TheoremGuard} → {thm' : Lean.Meta.Grind.EMatchTheorem} → {proof' prop' : Lean.Expr} → {generation' : ℕ} → {guards' : List Lean.Meta.Grind.TheoremGuard} → { thm := thm, proof := proof, prop := prop, generation := generation, guards := guards } = { thm := thm', proof := proof', prop := prop', generation := generation', guards := guards' } → (thm = thm' → proof = proof' → prop = prop' → generation = generation' → guards = guards' → P) → P
false
ContinuousAlgHom.prodEquiv._proof_1
Mathlib.Topology.Algebra.Algebra
∀ {R : Type u_4} [inst : CommSemiring R] {A : Type u_1} [inst_1 : Semiring A] [inst_2 : TopologicalSpace A] {B : Type u_2} [inst_3 : Semiring B] [inst_4 : TopologicalSpace B] [inst_5 : Algebra R A] [inst_6 : Algebra R B] {C : Type u_3} [inst_7 : Semiring C] [inst_8 : Algebra R C] [inst_9 : TopologicalSpace C], Function.LeftInverse (fun f => ((ContinuousAlgHom.fst R B C).comp f, (ContinuousAlgHom.snd R B C).comp f)) fun f => f.1.prod f.2
false
BoundedContinuousFunction.extend._proof_1
Mathlib.Topology.ContinuousMap.Bounded.Basic
∀ {α : Type u_2} {β : Type u_1} [inst : TopologicalSpace α] [inst_1 : PseudoMetricSpace β] {δ : Type u_3} [inst_2 : TopologicalSpace δ] (f : α ↪ δ) (g : BoundedContinuousFunction α β) (h : BoundedContinuousFunction δ β), ∃ C, ∀ (x y : δ), dist (Function.extend (⇑f) (⇑g) (⇑h) x) (Function.extend (⇑f) (⇑g) (⇑h) y) ≤ C
false
Equiv.Perm.two_le_length_toList_iff_mem_support
Mathlib.GroupTheory.Perm.Cycle.Concrete
∀ {α : Type u_1} [inst : Fintype α] [inst_1 : DecidableEq α] {p : Equiv.Perm α} {x : α}, 2 ≤ (p.toList x).length ↔ x ∈ p.support
true
ValuationSubring.valuation_le_one_iff
Mathlib.RingTheory.Valuation.ValuationSubring
∀ {K : Type u} [inst : Field K] (A : ValuationSubring K) (x : K), A.valuation x ≤ 1 ↔ x ∈ A
true
WeierstrassCurve.a₃_of_isCharTwoJNeZeroNF
Mathlib.AlgebraicGeometry.EllipticCurve.NormalForms
∀ {R : Type u_1} [inst : CommRing R] (W : WeierstrassCurve R) [W.IsCharTwoJNeZeroNF], W.a₃ = 0
true
Lean.Meta.DiscrTree.Key.lit.injEq
Lean.Meta.DiscrTree.Types
∀ (a a_1 : Lean.Literal), (Lean.Meta.DiscrTree.Key.lit a = Lean.Meta.DiscrTree.Key.lit a_1) = (a = a_1)
true
Int8.instNeg
Init.Data.SInt.Basic
Neg Int8
true
AlgebraicIndependent.aevalEquiv
Mathlib.RingTheory.AlgebraicIndependent.Defs
{ι : Type u_1} → {R : Type u_3} → {A : Type u_5} → {x : ι → A} → [inst : CommRing R] → [inst_1 : CommRing A] → [inst_2 : Algebra R A] → AlgebraicIndependent R x → MvPolynomial ι R ≃ₐ[R] ↥(Algebra.adjoin R (Set.range x))
true
Equiv.sigmaFiberEquiv.match_1
Mathlib.Logic.Equiv.Sum
∀ {α : Type u_2} {β : Type u_1} (f : α → β) (motive : (y : β) × { x // f x = y } → Prop) (x : (y : β) × { x // f x = y }), (∀ (a : α), motive ⟨f a, ⟨a, ⋯⟩⟩) → motive x
false
_private.Lean.Meta.LetToHave.0.Lean.Meta.LetToHave.visitApp.match_1
Lean.Meta.LetToHave
(motive : Lean.Expr → Sort u_1) → (fType : Lean.Expr) → ((binderName : Lean.Name) → (d b : Lean.Expr) → (binderInfo : Lean.BinderInfo) → motive (Lean.Expr.forallE binderName d b binderInfo)) → ((x : Lean.Expr) → motive x) → motive fType
false
FinBddDistLat.instBoundedOrderCarrier
Mathlib.Order.Category.FinBddDistLat
(X : FinBddDistLat) → BoundedOrder ↑X.toDistLat
true
LaurentSeries.powerSeriesPart_eq_zero._simp_1
Mathlib.RingTheory.LaurentSeries
∀ {R : Type u_1} [inst : Semiring R] (x : LaurentSeries R), (x.powerSeriesPart = 0) = (x = 0)
false
Std.Internal.List.self_le_maxKey_insertEntry
Std.Data.Internal.List.Associative
∀ {α : Type u} {β : α → Type v} [inst : Ord α] [Std.TransOrd α] [inst_2 : BEq α] [Std.LawfulBEqOrd α] {l : List ((a : α) × β a)}, Std.Internal.List.DistinctKeys l → ∀ {k : α} {v : β k}, (compare k (Std.Internal.List.maxKey (Std.Internal.List.insertEntry k v l) ⋯)).isLE = true
true
CategoryTheory.Localization.HasProductsOfShapeAux.isLimitMapCone._proof_2
Mathlib.CategoryTheory.Localization.FiniteProducts
∀ {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] (L : CategoryTheory.Functor C D) (W : CategoryTheory.MorphismProperty C) [inst_2 : L.IsLocalization W] (J : Type) [inst_3 : CategoryTheory.Limits.HasProductsOfShape J C] [inst_4 : W.IsStableUnderProductsOfShape J] [inst_5 : W.ContainsIdentities] [inst_6 : Finite J] (F : CategoryTheory.Functor (CategoryTheory.Discrete J) C) (j : CategoryTheory.Discrete J), (CategoryTheory.Limits.coneOfAdj (CategoryTheory.Localization.HasProductsOfShapeAux.adj L W J) (F.comp L)).π.app j = CategoryTheory.CategoryStruct.comp ((CategoryTheory.Localization.HasProductsOfShapeAux.compLimitFunctorIso L W J).app F).hom ((L.mapCone (CategoryTheory.Limits.limit.cone F)).π.app j)
false
MeasurableEquiv.symm_vadd
Mathlib.MeasureTheory.Group.MeasurableEquiv
∀ {G : Type u_1} {α : Type u_3} [inst : MeasurableSpace α] [inst_1 : AddGroup G] [inst_2 : AddAction G α] [inst_3 : MeasurableConstVAdd G α] (c : G), (MeasurableEquiv.vadd c).symm = MeasurableEquiv.vadd (-c)
true
Lean.Server.ServerTask.BaseIO.mapTaskCostly
Lean.Server.ServerTask
{α : Type u_1} → {β : Type} → (α → BaseIO β) → Lean.Server.ServerTask α → BaseIO (Lean.Server.ServerTask β)
true
Lean.Meta.LazyDiscrTree.buildPath._unsafe_rec
Lean.Meta.LazyDiscrTree
(Bool → Array Lean.Expr → Lean.Expr → Lean.MetaM (Lean.Meta.LazyDiscrTree.Key × Array Lean.Expr)) → Bool → Array Lean.Expr → Array Lean.Meta.LazyDiscrTree.Key → Lean.MetaM (Array Lean.Meta.LazyDiscrTree.Key)
false
Lean.Elab.Tactic.RCases.RCasesPatt.brecOn
Lean.Elab.Tactic.RCases
{motive_1 : Lean.Elab.Tactic.RCases.RCasesPatt → Sort u} → {motive_2 : List Lean.Elab.Tactic.RCases.RCasesPatt → Sort u} → (t : Lean.Elab.Tactic.RCases.RCasesPatt) → ((t : Lean.Elab.Tactic.RCases.RCasesPatt) → t.below → motive_1 t) → ((t : List Lean.Elab.Tactic.RCases.RCasesPatt) → Lean.Elab.Tactic.RCases.RCasesPatt.below_1 t → motive_2 t) → motive_1 t
false
_private.Lean.Meta.Sym.Pattern.0.Lean.Meta.Sym.isLevelDefEqS.match_1._arg_pusher
Lean.Meta.Sym.Pattern
∀ (motive : Lean.Level → Lean.Level → Sort u_1) (α : Sort u✝) (β : α → Sort v✝) (f : (x : α) → β x) (rel : Lean.Level → Lean.Level → α → Prop) (u v : Lean.Level) (h_1 : (u v : Lean.Name) → ((y : α) → rel (Lean.Level.param u) (Lean.Level.param v) y → β y) → motive (Lean.Level.param u) (Lean.Level.param v)) (h_2 : Unit → ((y : α) → rel Lean.Level.zero Lean.Level.zero y → β y) → motive Lean.Level.zero Lean.Level.zero) (h_3 : (u v : Lean.Level) → ((y : α) → rel u.succ v.succ y → β y) → motive u.succ v.succ) (h_4 : (a : Lean.Level) → ((y : α) → rel Lean.Level.zero a.succ y → β y) → motive Lean.Level.zero a.succ) (h_5 : (a : Lean.Level) → ((y : α) → rel a.succ Lean.Level.zero y → β y) → motive a.succ Lean.Level.zero) (h_6 : (v₁ v₂ : Lean.Level) → ((y : α) → rel Lean.Level.zero (v₁.max v₂) y → β y) → motive Lean.Level.zero (v₁.max v₂)) (h_7 : (u₁ u₂ : Lean.Level) → ((y : α) → rel (u₁.max u₂) Lean.Level.zero y → β y) → motive (u₁.max u₂) Lean.Level.zero) (h_8 : (a v : Lean.Level) → ((y : α) → rel Lean.Level.zero (a.imax v) y → β y) → motive Lean.Level.zero (a.imax v)) (h_9 : (a u : Lean.Level) → ((y : α) → rel (a.imax u) Lean.Level.zero y → β y) → motive (a.imax u) Lean.Level.zero) (h_10 : (u₁ u₂ v₁ v₂ : Lean.Level) → ((y : α) → rel (u₁.max u₂) (v₁.max v₂) y → β y) → motive (u₁.max u₂) (v₁.max v₂)) (h_11 : (u₁ u₂ v₁ v₂ : Lean.Level) → ((y : α) → rel (u₁.imax u₂) (v₁.imax v₂) y → β y) → motive (u₁.imax u₂) (v₁.imax v₂)) (h_12 : (x x_1 : Lean.Level) → ((y : α) → rel x x_1 y → β y) → motive x x_1), ((match (motive := (u v : Lean.Level) → ((y : α) → rel u v y → β y) → motive u v) u, v with | Lean.Level.param u, Lean.Level.param v => fun x => h_1 u v x | Lean.Level.zero, Lean.Level.zero => fun x => h_2 a x | u.succ, v.succ => fun x => h_3 u v x | Lean.Level.zero, a.succ => fun x => h_4 a x | a.succ, Lean.Level.zero => fun x => h_5 a x | Lean.Level.zero, v₁.max v₂ => fun x => h_6 v₁ v₂ x | u₁.max u₂, Lean.Level.zero => fun x => h_7 u₁ u₂ x | Lean.Level.zero, a.imax v => fun x => h_8 a v x | a.imax u, Lean.Level.zero => fun x => h_9 a u x | u₁.max u₂, v₁.max v₂ => fun x => h_10 u₁ u₂ v₁ v₂ x | u₁.imax u₂, v₁.imax v₂ => fun x => h_11 u₁ u₂ v₁ v₂ x | x, x_1 => fun x_2 => h_12 x x_1 x_2) fun y h => f y) = match u, v with | Lean.Level.param u, Lean.Level.param v => h_1 u v fun y h => f y | Lean.Level.zero, Lean.Level.zero => h_2 a fun y h => f y | u.succ, v.succ => h_3 u v fun y h => f y | Lean.Level.zero, a.succ => h_4 a fun y h => f y | a.succ, Lean.Level.zero => h_5 a fun y h => f y | Lean.Level.zero, v₁.max v₂ => h_6 v₁ v₂ fun y h => f y | u₁.max u₂, Lean.Level.zero => h_7 u₁ u₂ fun y h => f y | Lean.Level.zero, a.imax v => h_8 a v fun y h => f y | a.imax u, Lean.Level.zero => h_9 a u fun y h => f y | u₁.max u₂, v₁.max v₂ => h_10 u₁ u₂ v₁ v₂ fun y h => f y | u₁.imax u₂, v₁.imax v₂ => h_11 u₁ u₂ v₁ v₂ fun y h => f y | x, x_1 => h_12 x x_1 fun y h => f y
false
AdjoinRoot.quotEquivQuotMap_symm_apply_mk
Mathlib.RingTheory.AdjoinRoot
∀ {R : Type u_1} [inst : CommRing R] (f g : Polynomial R) (I : Ideal R), (AdjoinRoot.quotEquivQuotMap f I).symm ((Ideal.Quotient.mk (Ideal.span {Polynomial.map (Ideal.Quotient.mk I) f})) (Polynomial.map (Ideal.Quotient.mk I) g)) = (Ideal.Quotient.mk (Ideal.map (AdjoinRoot.of f) I)) ((AdjoinRoot.mk f) g)
true
StarMonoidHom.mk.noConfusion
Mathlib.Algebra.Star.MonoidHom
{A : Type u_6} → {B : Type u_7} → {inst : Monoid A} → {inst_1 : Star A} → {inst_2 : Monoid B} → {inst_3 : Star B} → {P : Sort u} → {toMonoidHom : A →* B} → {map_star' : ∀ (a : A), (↑toMonoidHom).toFun (star a) = star ((↑toMonoidHom).toFun a)} → {toMonoidHom' : A →* B} → {map_star'' : ∀ (a : A), (↑toMonoidHom').toFun (star a) = star ((↑toMonoidHom').toFun a)} → { toMonoidHom := toMonoidHom, map_star' := map_star' } = { toMonoidHom := toMonoidHom', map_star' := map_star'' } → (toMonoidHom ≍ toMonoidHom' → P) → P
false
AlgebraicGeometry.Scheme.Pullback.gluing_V
Mathlib.AlgebraicGeometry.Pullbacks
∀ {X Y Z : AlgebraicGeometry.Scheme} (𝒰 : X.OpenCover) (f : X ⟶ Z) (g : Y ⟶ Z) [inst : ∀ (i : 𝒰.I₀), CategoryTheory.Limits.HasPullback (CategoryTheory.CategoryStruct.comp (𝒰.f i) f) g] (x : 𝒰.I₀ × 𝒰.I₀), (AlgebraicGeometry.Scheme.Pullback.gluing 𝒰 f g).V x = match x with | (i, j) => AlgebraicGeometry.Scheme.Pullback.v 𝒰 f g i j
true
TensorProduct.exists_finite_submodule_of_setFinite'
Mathlib.LinearAlgebra.TensorProduct.Finiteness
∀ {R : Type u_1} {M : Type u_2} {N : Type u_3} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : AddCommMonoid N] [inst_3 : Module R M] [inst_4 : Module R N] {M₁ : Submodule R M} {N₁ : Submodule R N} (s : Set (TensorProduct R ↥M₁ ↥N₁)), s.Finite → ∃ M' N', ∃ (hM : M' ≤ M₁) (hN : N' ≤ N₁), Module.Finite R ↥M' ∧ Module.Finite R ↥N' ∧ s ⊆ ↑(TensorProduct.map (Submodule.inclusion hM) (Submodule.inclusion hN)).range
true
IntermediateField.one_mem'._inherited_default
Mathlib.FieldTheory.IntermediateField.Basic
∀ {K : Type u_1} {L : Type u_2} {inst : Field K} {inst_1 : Field L} {inst_2 : Algebra K L} (carrier : Set L), (∀ (r : K), (algebraMap K L) r ∈ carrier) → 1 ∈ carrier
false
Lean.Meta.Grind.Order.mkPropagateEqTrueProof
Lean.Meta.Tactic.Grind.Order.Proof
Lean.Expr → Lean.Expr → Lean.Meta.Grind.Order.Weight → Lean.Expr → Lean.Meta.Grind.Order.Weight → Lean.Meta.Grind.Order.OrderM Lean.Expr
true
Lean.Meta.Simp.ConfigCtx.unfoldPartialApp._inherited_default
Init.MetaTypes
Bool
false
_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.comap_monotone._simp_1_2
Mathlib.Combinatorics.SimpleGraph.Subgraph
∀ {a b c : Prop}, (a ∧ b → c) = (a → b → c)
false
Std.DTreeMap.Internal.Impl.Const.entryAtIdx.match_1
Std.Data.DTreeMap.Internal.Queries
{α : Type u_1} → {β : Type u_2} → (motive : (x : Std.DTreeMap.Internal.Impl α fun x => β) → x.Balanced → (x_2 : ℕ) → x_2 < x.size → Sort u_3) → (x : Std.DTreeMap.Internal.Impl α fun x => β) → (x_1 : x.Balanced) → (x_2 : ℕ) → (x_3 : x_2 < x.size) → ((size : ℕ) → (k : α) → (v : β) → (l' r' : Std.DTreeMap.Internal.Impl α fun x => β) → (hl : (Std.DTreeMap.Internal.Impl.inner size k v l' r').Balanced) → (n : ℕ) → (h : n < (Std.DTreeMap.Internal.Impl.inner size k v l' r').size) → motive (Std.DTreeMap.Internal.Impl.inner size k v l' r') hl n h) → motive x x_1 x_2 x_3
false
_private.Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable.0.summable_jacobiTheta₂'_term_iff._simp_1_3
Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
∀ (n : ℤ), ↑n = ↑↑n
false
_private.Mathlib.CategoryTheory.Monoidal.Bimod.0.Bimod.id_whiskerLeft_bimod._proof_1_1
Mathlib.CategoryTheory.Monoidal.Bimod
∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] [inst_1 : CategoryTheory.MonoidalCategory C] [inst_2 : CategoryTheory.Limits.HasCoequalizers C] {X Y : CategoryTheory.Mon C} {N : Bimod X Y}, CategoryTheory.Limits.HasColimit (CategoryTheory.Limits.parallelPair (CategoryTheory.MonoidalCategoryStruct.whiskerRight { X := X.X, actLeft := CategoryTheory.MonObj.mul, one_actLeft := ⋯, left_assoc := ⋯, actRight := CategoryTheory.MonObj.mul, actRight_one := ⋯, right_assoc := ⋯, middle_assoc := ⋯ }.actRight N.X) (CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.associator { X := X.X, actLeft := CategoryTheory.MonObj.mul, one_actLeft := ⋯, left_assoc := ⋯, actRight := CategoryTheory.MonObj.mul, actRight_one := ⋯, right_assoc := ⋯, middle_assoc := ⋯ }.X X.X N.X).hom (CategoryTheory.MonoidalCategoryStruct.whiskerLeft { X := X.X, actLeft := CategoryTheory.MonObj.mul, one_actLeft := ⋯, left_assoc := ⋯, actRight := CategoryTheory.MonObj.mul, actRight_one := ⋯, right_assoc := ⋯, middle_assoc := ⋯ }.X N.actLeft)))
false
Field.toEuclideanDomain.match_1
Mathlib.Algebra.EuclideanDomain.Field
∀ {K : Type u_1} [inst : Field K] (x x_1 : K) (motive : x_1 = 0 ∧ x ≠ 0 → Prop) (x_2 : x_1 = 0 ∧ x ≠ 0), (∀ (left : x_1 = 0) (hnb : x ≠ 0), motive ⋯) → motive x_2
false
Int.Linear.Poly.mul'
Init.Data.Int.Linear
Int.Linear.Poly → ℤ → Int.Linear.Poly
true
_private.Mathlib.Tactic.ComputeDegree.0.Mathlib.Tactic.ComputeDegree.dispatchLemma.match_1
Mathlib.Tactic.ComputeDegree
(motive : Lean.Name → Lean.Name → Sort u_1) → (na1 na2 : Lean.Name) → (Unit → motive `Polynomial.natDegree `LE.le) → (Unit → motive `Polynomial.degree `LE.le) → (Unit → motive `Polynomial.coeff `Eq) → ((x : Lean.Name) → motive x `LE.le) → ((x x_1 : Lean.Name) → motive x x_1) → motive na1 na2
false
Order.Ideal.instLattice
Mathlib.Order.Ideal
{P : Type u_1} → [inst : SemilatticeSup P] → [IsCodirectedOrder P] → Lattice (Order.Ideal P)
true
Submodule.existsUnique_add_of_isCompl
Mathlib.LinearAlgebra.Projection
∀ {R : Type u_1} [inst : Ring R] {E : Type u_2} [inst_1 : AddCommGroup E] [inst_2 : Module R E] {p q : Submodule R E}, IsCompl p q → ∀ (x : E), ∃ u v, ↑u + ↑v = x ∧ ∀ (r : ↥p) (s : ↥q), ↑r + ↑s = x → r = u ∧ s = v
true
MonoidHom.coe_ofClosureMEqTopRight
Mathlib.Algebra.Group.Submonoid.Basic
∀ {M : Type u_1} {N : Type u_2} [inst : Monoid M] [inst_1 : Monoid N] {s : Set M} (f : M → N) (hs : Submonoid.closure s = ⊤) (h1 : f 1 = 1) (hmul : ∀ (x y : M), y ∈ s → f (x * y) = f x * f y), ⇑(MonoidHom.ofClosureMEqTopRight f hs h1 hmul) = f
true
Std.TreeSet.inter_eq
Std.Data.TreeSet.Lemmas
∀ {α : Type u} {cmp : α → α → Ordering} {t₁ t₂ : Std.TreeSet α cmp}, t₁.inter t₂ = t₁ ∩ t₂
true
Std.DHashMap.Internal.Raw.inter_eq
Std.Data.DHashMap.Internal.Raw
∀ {α : Type u} {β : α → Type v} [inst : BEq α] [inst_1 : Hashable α] {m₁ m₂ : Std.DHashMap.Raw α β} (h₁ : m₁.WF) (h₂ : m₂.WF), m₁.inter m₂ = ↑(Std.DHashMap.Internal.Raw₀.inter ⟨m₁, ⋯⟩ ⟨m₂, ⋯⟩)
true
_private.Lean.Meta.InferType.0.Lean.Meta.isArrowProposition'.checkProp._sunfold
Lean.Meta.InferType
Lean.Expr → Lean.Meta.ArrowPropResult✝
false
Pointed.Hom.instInhabited
Mathlib.CategoryTheory.Category.Pointed
(X : Pointed) → Inhabited (X.Hom X)
true
_private.Mathlib.Analysis.Calculus.ContDiff.Operations.0.contDiff_pi._simp_1_2
Mathlib.Analysis.Calculus.ContDiff.Operations
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type uE} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace 𝕜 E] {s : Set E} {n : WithTop ℕ∞} {ι : Type u_3} [inst_3 : Fintype ι] {F' : ι → Type u_5} [inst_4 : (i : ι) → NormedAddCommGroup (F' i)] [inst_5 : (i : ι) → NormedSpace 𝕜 (F' i)] {Φ : E → (i : ι) → F' i}, ContDiffOn 𝕜 n Φ s = ∀ (i : ι), ContDiffOn 𝕜 n (fun x => Φ x i) s
false
Std.HashSet.Raw.get?_of_isEmpty
Std.Data.HashSet.RawLemmas
∀ {α : Type u} {m : Std.HashSet.Raw α} [inst : BEq α] [inst_1 : Hashable α] [EquivBEq α] [LawfulHashable α], m.WF → ∀ {a : α}, m.isEmpty = true → m.get? a = none
true
existsUnique_eq._simp_1
Mathlib.Logic.ExistsUnique
∀ {α : Sort u_1} {a' : α}, (∃! a, a = a') = True
false
ModuleCat.semilinearMapAddEquiv
Mathlib.Algebra.Category.ModuleCat.ChangeOfRings
{R : Type u₁} → {S : Type u₂} → [inst : Ring R] → [inst_1 : Ring S] → (f : R →+* S) → (M : ModuleCat R) → (N : ModuleCat S) → (↑M →ₛₗ[f] ↑N) ≃+ (M ⟶ (ModuleCat.restrictScalars f).obj N)
true
CategoryTheory.IsKernelPair.lift'
Mathlib.CategoryTheory.Limits.Shapes.KernelPair
{C : Type u} → [inst : CategoryTheory.Category.{v, u} C] → {R X Y : C} → {f : X ⟶ Y} → {a b : R ⟶ X} → {S : C} → CategoryTheory.IsKernelPair f a b → (p q : S ⟶ X) → CategoryTheory.CategoryStruct.comp p f = CategoryTheory.CategoryStruct.comp q f → { t // CategoryTheory.CategoryStruct.comp t a = p ∧ CategoryTheory.CategoryStruct.comp t b = q }
true
QuaternionAlgebra.equivTuple._proof_2
Mathlib.Algebra.Quaternion
∀ {R : Type u_1} (c₁ c₂ c₃ : R) (x : Fin 4 → R), (fun a => ![a.re, a.imI, a.imJ, a.imK]) ((fun a => { re := a 0, imI := a 1, imJ := a 2, imK := a 3 }) x) = x
false
MeasureTheory.Measure.toSignedMeasure_toMeasureOfZeroLE
Mathlib.MeasureTheory.VectorMeasure.Basic
∀ {α : Type u_1} {m : MeasurableSpace α} (μ : MeasureTheory.Measure α) [inst : MeasureTheory.IsFiniteMeasure μ], μ.toSignedMeasure.toMeasureOfZeroLE Set.univ ⋯ ⋯ = μ
true
MDifferentiableWithinAt.congr_nhds
Mathlib.Geometry.Manifold.MFDeriv.Basic
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace 𝕜 E] {H : Type u_3} [inst_3 : TopologicalSpace H] {I : ModelWithCorners 𝕜 E H} {M : Type u_4} [inst_4 : TopologicalSpace M] [inst_5 : ChartedSpace H M] {E' : Type u_5} [inst_6 : NormedAddCommGroup E'] [inst_7 : NormedSpace 𝕜 E'] {H' : Type u_6} [inst_8 : TopologicalSpace H'] {I' : ModelWithCorners 𝕜 E' H'} {M' : Type u_7} [inst_9 : TopologicalSpace M'] [inst_10 : ChartedSpace H' M'] {f : M → M'} {x : M} {s : Set M}, MDiffAt[s] f x → ∀ {t : Set M}, nhdsWithin x s = nhdsWithin x t → MDiffAt[t] f x
true
WeakDual.CharacterSpace.continuousMapEval._proof_8
Mathlib.Topology.ContinuousMap.Ideals
∀ (X : Type u_1) (𝕜 : Type u_2) [inst : TopologicalSpace X] [inst_1 : CommRing 𝕜] [inst_2 : TopologicalSpace 𝕜] [inst_3 : IsTopologicalRing 𝕜] (x : X) (x_1 : 𝕜) (x_2 : C(X, 𝕜)), (x_1 • x_2) x = (x_1 • x_2) x
false
List.getLast_append_right._proof_1
Init.Data.List.Lemmas
∀ {α : Type u_1} {l' l : List α}, l' ≠ [] → l ++ l' = [] → False
false
List.Vector.snoc_cons
Mathlib.Data.Vector.Snoc
∀ {α : Type u_1} {n : ℕ} {x : α} (xs : List.Vector α n) {y : α}, (x ::ᵥ xs).snoc y = x ::ᵥ xs.snoc y
true
BitVec.getMsbD_ofBoolListLE
Init.Data.BitVec.Lemmas
∀ {bs : List Bool} {i : ℕ}, (BitVec.ofBoolListLE bs).getMsbD i = (decide (i < bs.length) && bs.getD (bs.length - 1 - i) false)
true
HomologicalComplex₂.toGradedObject.match_1
Mathlib.Algebra.Homology.HomologicalBicomplex
{I₁ : Type u_1} → {I₂ : Type u_2} → (motive : I₁ × I₂ → Sort u_3) → (x : I₁ × I₂) → ((i₁ : I₁) → (i₂ : I₂) → motive (i₁, i₂)) → motive x
false
GroupLike.instGroup._proof_5
Mathlib.RingTheory.HopfAlgebra.GroupLike
∀ {R : Type u_2} {A : Type u_1} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : HopfAlgebra R A] (a : GroupLike R A), a⁻¹ * a = 1
false
ContinuousMultilinearMap.recOn
Mathlib.Topology.Algebra.Module.Multilinear.Basic
{R : Type u} → {ι : Type v} → {M₁ : ι → Type w₁} → {M₂ : Type w₂} → [inst : Semiring R] → [inst_1 : (i : ι) → AddCommMonoid (M₁ i)] → [inst_2 : AddCommMonoid M₂] → [inst_3 : (i : ι) → Module R (M₁ i)] → [inst_4 : Module R M₂] → [inst_5 : (i : ι) → TopologicalSpace (M₁ i)] → [inst_6 : TopologicalSpace M₂] → {motive : ContinuousMultilinearMap R M₁ M₂ → Sort u_1} → (t : ContinuousMultilinearMap R M₁ M₂) → ((toMultilinearMap : MultilinearMap R M₁ M₂) → (cont : Continuous toMultilinearMap.toFun) → motive { toMultilinearMap := toMultilinearMap, cont := cont }) → motive t
false
Nat.multichoose_succ_succ
Mathlib.Data.Nat.Choose.Basic
∀ (n k : ℕ), (n + 1).multichoose (k + 1) = n.multichoose (k + 1) + (n + 1).multichoose k
true
ProbabilityTheory.Kernel.piecewise.congr_simp
Mathlib.Probability.Kernel.Basic
∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {s s_1 : Set α} (e_s : s = s_1) {inst : DecidablePred fun x => x ∈ s} [inst_1 : DecidablePred fun x => x ∈ s_1] (hs : MeasurableSet s) (κ κ_1 : ProbabilityTheory.Kernel α β), κ = κ_1 → ∀ (η η_1 : ProbabilityTheory.Kernel α β), η = η_1 → ProbabilityTheory.Kernel.piecewise hs κ η = ProbabilityTheory.Kernel.piecewise ⋯ κ_1 η_1
true
_private.Lean.Elab.PreDefinition.Structural.FindRecArg.0.Lean.Elab.Structural.argsInGroup.match_5
Lean.Elab.PreDefinition.Structural.FindRecArg
(motive : Option (ℕ × Std.Iter ℕ) → Sort u_1) → (x : Option (ℕ × Std.Iter ℕ)) → (Unit → motive none) → ((indIdx : ℕ) → (s' : Std.Iter ℕ) → motive (some (indIdx, s'))) → motive x
false
instNontrivialFreeRing
Mathlib.RingTheory.FreeRing
∀ (α : Type u_1), Nontrivial (FreeRing α)
true