name
stringlengths
2
347
module
stringlengths
6
90
type
stringlengths
1
5.67M
allowCompletion
bool
2 classes
Lean.Parser.patternIgnore.formatter
Lean.Parser.Extra
Lean.PrettyPrinter.Formatter → Lean.PrettyPrinter.Formatter
true
Std.Sat.CNF.emptyWithCapacity.eq_1
Std.Sat.CNF.Basic
∀ {α : Type u_1} (n : ℕ), Std.Sat.CNF.emptyWithCapacity n = { clauses := Array.emptyWithCapacity n }
true
_private.Lean.Meta.Tactic.Simp.BuiltinSimprocs.Char.0._regBuiltin.Char.reduceToLower.declare_18._@.Lean.Meta.Tactic.Simp.BuiltinSimprocs.Char.334306140._hygCtx._hyg.13
Lean.Meta.Tactic.Simp.BuiltinSimprocs.Char
IO Unit
false
AdicCompletion.instSMulQuotientIdealHSMulTopSubmodule
Mathlib.RingTheory.AdicCompletion.Algebra
{R : Type u_1} → [inst : CommRing R] → (I : Ideal R) → {M : Type u_3} → [inst_1 : AddCommGroup M] → [inst_2 : Module R M] → SMul (R ⧸ I • ⊤) (M ⧸ I • ⊤)
true
Equiv.sigmaSumDistrib_symm_apply
Mathlib.Logic.Equiv.Sum
∀ {ι : Type u_11} (α : ι → Type u_9) (β : ι → Type u_10) (a : (i : ι) × α i ⊕ (i : ι) × β i), (Equiv.sigmaSumDistrib α β).symm a = Sum.elim (Sigma.map id fun x => Sum.inl) (Sigma.map id fun x => Sum.inr) a
true
Function.Surjective.mulActionLeft._proof_2
Mathlib.Algebra.Group.Action.Hom
∀ {R : Type u_3} {S : Type u_2} {M : Type u_1} [inst : Monoid R] [inst_1 : MulAction R M] [inst_2 : Monoid S] [inst_3 : SMul S M] (f : R →* S), (∀ (c : R) (x : M), f c • x = c • x) → ∀ (b : M), 1 • b = b
false
_private.Mathlib.Probability.Process.Stopping.0.MeasureTheory.IsStoppingTime.measurableSet_le'._simp_1_1
Mathlib.Probability.Process.Stopping
∀ {α : Type u} (x : α) (a b : Set α), (x ∈ a ∩ b) = (x ∈ a ∧ x ∈ b)
false
SimpleGraph.Iso.boxProdSumDistrib
Mathlib.Combinatorics.SimpleGraph.Prod
{V : Type u_4} → {W₁ : Type u_8} → {W₂ : Type u_9} → (G : SimpleGraph V) → (H₁ : SimpleGraph W₁) → (H₂ : SimpleGraph W₂) → G □ (H₁ ⊕g H₂) ≃g G □ H₁ ⊕g G □ H₂
true
ModuleCat.ExtendScalars.obj'
Mathlib.Algebra.Category.ModuleCat.ChangeOfRings
{R : Type u₁} → {S : Type u₂} → [inst : CommRing R] → [inst_1 : CommRing S] → (R →+* S) → ModuleCat R → ModuleCat S
true
_private.Mathlib.FieldTheory.RatFunc.AsPolynomial.0.Polynomial.valuation_le_one_of_valuation_X_le_one._simp_1_3
Mathlib.FieldTheory.RatFunc.AsPolynomial
∀ {M : Type u_3} [inst : Monoid M] [inst_1 : Preorder M] [MulLeftMono M] {a : M}, a ≤ 1 → ∀ (n : ℕ), (a ^ n ≤ 1) = True
false
Plausible.Testable.orTestable.match_1
Plausible.Testable
{p : Prop} → (motive : Plausible.TestResult p → Sort u_1) → (xp : Plausible.TestResult p) → ((h : Unit) → motive (Plausible.TestResult.success (PSum.inl h))) → ((h : p) → motive (Plausible.TestResult.success (PSum.inr h))) → ((x : Plausible.TestResult p) → motive x) → motive xp
false
Lean.Grind.AC.eq_norm_a_cert.eq_1
Init.Grind.AC
∀ (lhs rhs : Lean.Grind.AC.Expr) (lhs' rhs' : Lean.Grind.AC.Seq), Lean.Grind.AC.eq_norm_a_cert lhs rhs lhs' rhs' = (lhs.toSeq.beq' lhs').and' (rhs.toSeq.beq' rhs')
true
CategoryTheory.NatIso.removeOp._proof_4
Mathlib.CategoryTheory.Opposites
∀ {C : Type u_1} [inst : CategoryTheory.Category.{u_4, u_1} C] {D : Type u_3} [inst_1 : CategoryTheory.Category.{u_2, u_3} D] {F G : CategoryTheory.Functor C D} (α : F.op ≅ G.op), CategoryTheory.CategoryStruct.comp (CategoryTheory.NatTrans.removeOp α.inv) (CategoryTheory.NatTrans.removeOp α.hom) = CategoryTheor...
false
_private.Lean.Elab.MutualInductive.0.Lean.Elab.Command.accLevelAtCtor.match_1
Lean.Elab.MutualInductive
(motive : Except Lean.MessageData Unit → Sort u_1) → (__do_lift : Except Lean.MessageData Unit) → ((a : Unit) → motive (Except.ok a)) → ((msg : Lean.MessageData) → motive (Except.error msg)) → motive __do_lift
false
Batteries.Tactic.TransRelation.ctorElimType
Batteries.Tactic.Trans
{motive : Batteries.Tactic.TransRelation → Sort u} → ℕ → Sort (max 1 u)
false
_private.Mathlib.Algebra.Order.Group.DenselyOrdered.0.exists_nsmul_lt_of_pos.match_1_1
Mathlib.Algebra.Order.Group.DenselyOrdered
∀ (motive : ℕ → Prop) (x : ℕ), (∀ (a : Unit), motive 0) → (∀ (a : Unit), motive 1) → (∀ (n : ℕ), motive n.succ.succ) → motive x
false
deltaGenerated_le
Mathlib.Topology.Compactness.DeltaGeneratedSpace
∀ {X : Type u_1} [tX : TopologicalSpace X], TopologicalSpace.deltaGenerated X ≤ tX
true
CategoryTheory.Limits.ImageFactorisation.ofIsoI
Mathlib.CategoryTheory.Limits.Shapes.Images
{C : Type u} → [inst : CategoryTheory.Category.{v, u} C] → {X Y : C} → {f : X ⟶ Y} → (F : CategoryTheory.Limits.ImageFactorisation f) → {I' : C} → (F.F.I ≅ I') → CategoryTheory.Limits.ImageFactorisation f
true
ProofWidgets.RpcEncodablePacket.«_@».ProofWidgets.Component.HtmlDisplay.3304690324._hygCtx._hyg.1.noConfusion
ProofWidgets.Component.HtmlDisplay
{P : Sort u} → {t t' : ProofWidgets.RpcEncodablePacket✝} → t = t' → ProofWidgets.RpcEncodablePacket.«_@».ProofWidgets.Component.HtmlDisplay.3304690324._hygCtx._hyg.1.noConfusionType P t t'
false
Turing.PointedMap.mk._flat_ctor
Mathlib.Computability.TuringMachine.Tape
{Γ : Type u} → {Γ' : Type v} → [inst : Inhabited Γ] → [inst_1 : Inhabited Γ'] → (f : Γ → Γ') → f default = default → Turing.PointedMap Γ Γ'
false
MonomialOrder.lex
Mathlib.Data.Finsupp.MonomialOrder
{σ : Type u_1} → [inst : LinearOrder σ] → [WellFoundedGT σ] → MonomialOrder σ
true
_private.Mathlib.Analysis.SpecialFunctions.Bernstein.0._aux_Mathlib_Analysis_SpecialFunctions_Bernstein___unexpand_bernstein_z_1
Mathlib.Analysis.SpecialFunctions.Bernstein
Lean.PrettyPrinter.Unexpander
false
CategoryTheory.CostructuredArrow.ext_iff
Mathlib.CategoryTheory.Comma.StructuredArrow.Basic
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D] {T : D} {S : CategoryTheory.Functor C D} {A B : CategoryTheory.CostructuredArrow S T} (f g : A ⟶ B), f = g ↔ f.left = g.left
true
_private.Mathlib.NumberTheory.PellMatiyasevic.0.Pell.matiyasevic.match_1_9
Mathlib.NumberTheory.PellMatiyasevic
∀ {a : ℕ} (y u : ℕ) (motive : { k // k ≡ a [MOD u] ∧ k ≡ 1 [MOD 4 * y] } → Prop) (x : { k // k ≡ a [MOD u] ∧ k ≡ 1 [MOD 4 * y] }), (∀ (b : ℕ) (ba : b ≡ a [MOD u]) (bm1 : b ≡ 1 [MOD 4 * y]), motive ⟨b, ⋯⟩) → motive x
false
EuclideanDomain.gcdB_zero_left
Mathlib.Algebra.EuclideanDomain.Defs
∀ {R : Type u} [inst : EuclideanDomain R] [inst_1 : DecidableEq R] {s : R}, EuclideanDomain.gcdB 0 s = 1
true
Profinite.fintypeDiagram._proof_3
Mathlib.Topology.Category.Profinite.AsLimit
∀ (X : Profinite) {X_1 Y : DiscreteQuotient ↑X.toTop} (f : X_1 ⟶ Y), X_1 ≤ Y
false
IsGδ.setOf_irrational
Mathlib.Topology.Instances.Irrational
IsGδ {x | Irrational x}
true
Ordinal.IsNormal.nfp_le_apply
Mathlib.SetTheory.Ordinal.FixedPoint
∀ {f : Ordinal.{u} → Ordinal.{u}}, Order.IsNormal f → ∀ {a b : Ordinal.{u}}, Ordinal.nfp f a ≤ f b ↔ Ordinal.nfp f a ≤ b
true
LinearIsometry.rTensor
Mathlib.Analysis.InnerProductSpace.TensorProduct
{𝕜 : Type u_1} → {E : Type u_2} → {F : Type u_3} → (G : Type u_4) → [inst : RCLike 𝕜] → [inst_1 : NormedAddCommGroup E] → [inst_2 : InnerProductSpace 𝕜 E] → [inst_3 : NormedAddCommGroup F] → [inst_4 : InnerProductSpace 𝕜 F] → ...
true
UpperHalfPlane.ne_intCast
Mathlib.Analysis.Complex.UpperHalfPlane.Basic
∀ (z : UpperHalfPlane) (n : ℤ), ↑z ≠ ↑n
true
CompactlySupportedContinuousMap.pullback_monoidHom_def
Mathlib.Topology.ContinuousMap.CompactlySupported
∀ {α : Type u_2} {β : Type u_3} {γ : Type u_4} [inst : TopologicalSpace α] [inst_1 : R1Space α] [inst_2 : Group α] [inst_3 : TopologicalSpace β] [inst_4 : R1Space β] [inst_5 : Group β] [inst_6 : ContinuousMul β] [inst_7 : NormedAddCommGroup γ] {φ : α →* β} (hφ : Topology.IsClosedEmbedding ⇑φ) (f : CompactlySuppor...
true
CategoryTheory.Pseudofunctor.mapComp_assoc_left_hom_app
Mathlib.CategoryTheory.Bicategory.Functor.Pseudofunctor
∀ {B : Type u_1} [inst : CategoryTheory.Bicategory B] (F : CategoryTheory.Pseudofunctor B CategoryTheory.Cat) {a b c d : B} (f : a ⟶ b) (g : b ⟶ c) (h : c ⟶ d) (X : ↑(F.obj a)), CategoryTheory.CategoryStruct.comp ((F.mapComp (CategoryTheory.CategoryStruct.comp f g) h).hom.toNatTrans.app X) ((F.map h).toFuncto...
true
Monoid.CoprodI.NeWord.toList._unsafe_rec
Mathlib.GroupTheory.CoprodI
{ι : Type u_1} → {M : ι → Type u_2} → [inst : (i : ι) → Monoid (M i)] → {i j : ι} → Monoid.CoprodI.NeWord M i j → List ((i : ι) × M i)
false
CategoryTheory.ShiftMkCore.recOn
Mathlib.CategoryTheory.Shift.Basic
{C : Type u} → {A : Type u_1} → [inst : CategoryTheory.Category.{v, u} C] → [inst_1 : AddMonoid A] → {motive : CategoryTheory.ShiftMkCore C A → Sort u_2} → (t : CategoryTheory.ShiftMkCore C A) → ((F : A → CategoryTheory.Functor C C) → (zero : F 0 ≅ CategoryTheor...
false
DiscreteQuotient.ofLE_map
Mathlib.Topology.DiscreteQuotient
∀ {X : Type u_2} {Y : Type u_3} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : C(X, Y)} {A : DiscreteQuotient X} {B B' : DiscreteQuotient Y} (cond : DiscreteQuotient.LEComap f A B) (h : B ≤ B') (a : Quotient A.toSetoid), DiscreteQuotient.ofLE h (DiscreteQuotient.map f cond a) = DiscreteQuotient.map ...
true
OrderBot.lift
Mathlib.Order.BoundedOrder.Basic
{α : Type u} → {β : Type v} → [inst : LE α] → [inst_1 : Bot α] → [inst_2 : LE β] → [inst_3 : OrderBot β] → (f : α → β) → (∀ (b a : α), f b ≤ f a → b ≤ a) → f ⊥ = ⊥ → OrderBot α
true
CategoryTheory.CartesianMonoidalCategory.comp_lift_assoc
Mathlib.CategoryTheory.Monoidal.Cartesian.Basic
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C] {V W X Y : C} (f : V ⟶ W) (g : W ⟶ X) (h : W ⟶ Y) {Z : C} (h_1 : CategoryTheory.MonoidalCategoryStruct.tensorObj X Y ⟶ Z), CategoryTheory.CategoryStruct.comp f (CategoryTheory.CategoryStruct.comp (...
true
String.Slice.RevPosIterator.instIteratorSubtypePosNeEndPosOfPure._proof_7
Init.Data.String.Iterate
∀ {m : Type → Type u_1} {s : String.Slice} (currPos : s.Pos) (h : ¬currPos = s.startPos), match Std.IterStep.yield { internalState := { currPos := currPos.prev h } } ⟨currPos.prev h, ⋯⟩ with | Std.IterStep.yield it' out => ∃ (h : { internalState := { currPos := currPos } }.internalState.currPos ≠ s.startPos), ...
false
_private.Mathlib.NumberTheory.Padics.PadicNumbers.0.Int.padicValuation_lt_one_iff._simp_1_3
Mathlib.NumberTheory.Padics.PadicNumbers
∀ (p : ℕ) [inst : Fact (Nat.Prime p)] (x : ℤ), ((Int.padicValuation p) x ≤ 1) = True
false
WithTop.sumHomeomorph._proof_1
Mathlib.Topology.Order.WithTop
∀ (ι : Type u_1) [inst : LinearOrder ι] [OrderTop ι], Nonempty ι
false
CategoryTheory.Limits.HasColimitOfHasCoproductsOfHasCoequalizers.buildColimit._proof_2
Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers
∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] {J : Type u_3} [inst_1 : CategoryTheory.SmallCategory J] {F : CategoryTheory.Functor J C} {c₁ : CategoryTheory.Limits.Cofan fun f => F.obj f.fst.1} {c₂ : CategoryTheory.Limits.Cofan F.obj} (s t : c₁.pt ⟶ c₂.pt), (∀ (f : (p : J × J) × (p.1 ⟶ p.2)), ...
false
Set.center_units_eq
Mathlib.Algebra.GroupWithZero.Center
∀ {G₀ : Type u_2} [inst : GroupWithZero G₀], Set.center G₀ˣ = Units.val ⁻¹' Set.center G₀
true
_private.Mathlib.Probability.Kernel.Disintegration.CDFToKernel.0.ProbabilityTheory.setLIntegral_stieltjesOfMeasurableRat._simp_1_7
Mathlib.Probability.Kernel.Disintegration.CDFToKernel
∀ {α : Type u_1} {m0 : MeasurableSpace α} (μ : MeasureTheory.Measure α) [MeasureTheory.IsFiniteMeasure μ] (s : Set α), (μ s = ⊤) = False
false
UInt64.ofFin_div
Init.Data.UInt.Lemmas
∀ (a b : Fin UInt64.size), UInt64.ofFin (a / b) = UInt64.ofFin a / UInt64.ofFin b
true
String.Slice.Pos._sizeOf_1
Init.Data.String.Defs
{s : String.Slice} → s.Pos → ℕ
false
Lean.Elab.Tactic.Do.ProofMode.parseMGoal?
Lean.Elab.Tactic.Do.ProofMode.MGoal
Lean.Expr → Option Lean.Elab.Tactic.Do.ProofMode.MGoal
true
CategoryTheory.ObjectProperty.instEssentiallySmallMax
Mathlib.CategoryTheory.ObjectProperty.Small
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {P Q : CategoryTheory.ObjectProperty C} [CategoryTheory.ObjectProperty.EssentiallySmall.{w, v, u} P] [CategoryTheory.ObjectProperty.EssentiallySmall.{w, v, u} Q], CategoryTheory.ObjectProperty.EssentiallySmall.{w, v, u} (P ⊔ Q)
true
_private.Mathlib.Data.List.Intervals.0.List.Ico.filter_lt_of_le_bot._simp_1_1
Mathlib.Data.List.Intervals
∀ {α : Type u_1} [inst : LinearOrder α] {a b : α}, (¬a < b) = (b ≤ a)
false
CategoryTheory.Comonad.comonadicOfHasPreservesCoreflexiveEqualizersOfReflectsIsomorphisms
Mathlib.CategoryTheory.Monad.Comonadicity
{C : Type u₁} → {D : Type u₂} → [inst : CategoryTheory.Category.{v₁, u₁} C] → [inst_1 : CategoryTheory.Category.{v₁, u₂} D] → {F : CategoryTheory.Functor C D} → {G : CategoryTheory.Functor D C} → (F ⊣ G) → [CategoryTheory.Limits.HasCoreflexiveEqualizers C] → ...
true
CategoryTheory.MorphismProperty.instHasOfPrecompPropertyUnopOfHasOfPostcompPropertyOpposite
Mathlib.CategoryTheory.MorphismProperty.Composition
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (W₁ W₂ : CategoryTheory.MorphismProperty Cᵒᵖ) [W₁.HasOfPostcompProperty W₂], W₁.unop.HasOfPrecompProperty W₂.unop
true
UpperHalfPlane.IsZeroAtImInfty.petersson_exp_decay_right
Mathlib.NumberTheory.ModularForms.Petersson
∀ {F : Type u_1} {F' : Type u_2} [inst : FunLike F UpperHalfPlane ℂ] [inst_1 : FunLike F' UpperHalfPlane ℂ] (k : ℤ) (Γ : Subgroup (GL (Fin 2) ℝ)) [Fact (IsCusp OnePoint.infty Γ)] [Γ.HasDetPlusMinusOne] [DiscreteTopology ↥Γ] [ModularFormClass F Γ k] [ModularFormClass F' Γ k] (f : F) {f' : F'}, UpperHalfPlane.IsZer...
true
FP.Float.sign'
Mathlib.Data.FP.Basic
[C : FP.FloatCfg] → FP.Float → Semiquot Bool
true
IntermediateField.restrictScalars._proof_5
Mathlib.FieldTheory.IntermediateField.Basic
∀ (K : Type u_2) {L : Type u_1} {L' : Type u_3} [inst : Field K] [inst_1 : Field L] [inst_2 : Field L'] [inst_3 : Algebra K L] [inst_4 : Algebra K L'] [inst_5 : Algebra L' L] [inst_6 : IsScalarTower K L' L] (E : IntermediateField L' L) (r : K), (algebraMap K L) r ∈ (Subalgebra.restrictScalars K E.toSubalgebra).carr...
false
Std.TreeSet.Equiv.max!_eq
Std.Data.TreeSet.Lemmas
∀ {α : Type u} {cmp : α → α → Ordering} {t₁ t₂ : Std.TreeSet α cmp} [Std.TransCmp cmp] [inst : Inhabited α], t₁.Equiv t₂ → t₁.max! = t₂.max!
true
CategoryTheory.MorphismProperty.rlp_isStableUnderBaseChange
Mathlib.CategoryTheory.MorphismProperty.LiftingProperty
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (T : CategoryTheory.MorphismProperty C), T.rlp.IsStableUnderBaseChange
true
WeierstrassCurve.Projective.equation_of_Z_ne_zero
Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Basic
∀ {F : Type u} [inst : Field F] {W : WeierstrassCurve.Projective F} {P : Fin 3 → F}, P 2 ≠ 0 → (W.Equation P ↔ W.toAffine.Equation (P 0 / P 2) (P 1 / P 2))
true
Std.TreeSet.Equiv.toList_eq
Std.Data.TreeSet.Lemmas
∀ {α : Type u} {cmp : α → α → Ordering} {t₁ t₂ : Std.TreeSet α cmp} [Std.TransCmp cmp], t₁.Equiv t₂ → t₁.toList = t₂.toList
true
String.IsSuffix
Mathlib.Data.String.Defs
String → String → Prop
true
_private.Mathlib.RingTheory.MvPolynomial.MonomialOrder.0.MonomialOrder.sPolynomial_decomposition._simp_1_3
Mathlib.RingTheory.MvPolynomial.MonomialOrder
∀ {α : Type u_9} {β : Type u_10} {inst : Semigroup α} [self : SemigroupAction α β] (x y : α) (b : β), x • y • b = (x * y) • b
false
Representation.Coinvariants.instModule._proof_8
Mathlib.RepresentationTheory.Coinvariants
∀ {k : Type u_1} {G : Type u_2} {V : Type u_3} [inst : CommRing k] [inst_1 : Monoid G] [inst_2 : AddCommGroup V] [inst_3 : Module k V] (ρ : Representation k G V) (x : ρ.Coinvariants), 0 • x = 0
false
Std.HashMap.Raw.getD_eq_fallback
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 → ∀ {a : α} {fallback : β}, a ∉ m → m.getD a fallback = fallback
true
_private.Lean.Elab.Deriving.Inhabited.0.Lean.Elab.Deriving.mkInhabitedInstanceUsing
Lean.Elab.Deriving.Inhabited
Lean.Name → Lean.Name → Bool → Lean.Elab.Command.CommandElabM Bool
true
Lean.NamePart.cmp
Lean.Data.NameTrie
Lean.NamePart → Lean.NamePart → Ordering
true
CategoryTheory.Comonad.comonadicOfHasPreservesReflectsFSplitEqualizers
Mathlib.CategoryTheory.Monad.Comonadicity
{C : Type u₁} → {D : Type u₂} → [inst : CategoryTheory.Category.{v₁, u₁} C] → [inst_1 : CategoryTheory.Category.{v₁, u₂} D] → {F : CategoryTheory.Functor C D} → {G : CategoryTheory.Functor D C} → (F ⊣ G) → [CategoryTheory.Comonad.HasEqualizerOfIsCosplitPair F] → ...
true
Lean.registerInitAttrUnsafe
Lean.Compiler.InitAttr
Lean.Name → Bool → Lean.Name → IO (Lean.ParametricAttribute Lean.Name)
true
Lean.Server.locationLinksDefault
Lean.Server.GoTo
Lean.Server.GoToM (Array Lean.Lsp.LeanLocationLink)
true
USize.toBitVec_ofBitVec
Init.Data.UInt.Lemmas
∀ (n : BitVec System.Platform.numBits), { toBitVec := n }.toBitVec = n
true
Fin.pred_mk_succ'
Init.Data.Fin.Lemmas
∀ {n : ℕ} (i : ℕ) (h₁ : i + 1 < n + 1 + 1) (h₂ : ⟨i + 1, h₁⟩ ≠ 0), ⟨i + 1, h₁⟩.pred h₂ = ⟨i, ⋯⟩
true
Batteries.instTransCmpCompareLex
Batteries.Classes.Deprecated
∀ {α : Sort u_1} {cmp₁ cmp₂ : α → α → Ordering} [inst₁ : Batteries.TransCmp cmp₁] [inst₂ : Batteries.TransCmp cmp₂], Batteries.TransCmp (compareLex cmp₁ cmp₂)
true
_private.Mathlib.Geometry.Manifold.IntegralCurve.ExistUnique.0.IsMIntegralCurve.periodic_xor_injective.match_1_1
Mathlib.Geometry.Manifold.IntegralCurve.ExistUnique
∀ {M : Type u_1} {γ : ℝ → M} (motive : (∃ T > 0, Function.Periodic γ T) → Prop) (x : ∃ T > 0, Function.Periodic γ T), (∀ (T : ℝ) (hT : T > 0) (hf : Function.Periodic γ T), motive ⋯) → motive x
false
_private.Lean.Meta.Sym.Pattern.0.Lean.Meta.Sym.mkProofInstInfoMapFor
Lean.Meta.Sym.Pattern
Lean.Expr → Lean.MetaM (Lean.AssocList Lean.Name Lean.Meta.Sym.ProofInstInfo)
true
VSub
Mathlib.Algebra.Notation.Defs
outParam (Type u_1) → Type u_2 → Type (max u_1 u_2)
true
Std.TreeMap.getKeyD_unitOfList_of_mem
Std.Data.TreeMap.Lemmas
∀ {α : Type u} {cmp : α → α → Ordering} [Std.TransCmp cmp] {l : List α} {k k' fallback : α}, cmp k k' = Ordering.eq → List.Pairwise (fun a b => ¬cmp a b = Ordering.eq) l → k ∈ l → (Std.TreeMap.unitOfList l cmp).getKeyD k' fallback = k
true
AddConstMap.mkFract._proof_2
Mathlib.Algebra.AddConstMap.Basic
∀ {R : Type u_1} {G : Type u_2} [inst : Ring R] [inst_1 : LinearOrder R] [inst_2 : IsStrictOrderedRing R] [inst_3 : FloorRing R] [inst_4 : AddGroup G] (a : G) (x : ↑(Set.Ico 0 1) → G), (fun f x => f ↑x) ((fun f => { toFun := fun x => f ⟨Int.fract x, ⋯⟩ + ⌊x⌋ • a, map_add_const' := ⋯ }) x) = x
false
BoundedContinuousFunction.indicator._proof_1
Mathlib.Topology.ContinuousMap.Bounded.Basic
∀ {α : Type u_1} [inst : TopologicalSpace α] (s : Set α), IsClopen s → ∀ a ∈ frontier s, 1 a = 0
false
Ordnode.fold._unsafe_rec
Mathlib.Data.Ordmap.Ordnode
{α : Type u_1} → {β : Sort u_2} → β → (β → α → β → β) → Ordnode α → β
false
List.dvd_prod
Mathlib.Algebra.BigOperators.Group.List.Lemmas
∀ {M : Type u_4} [inst : CommMonoid M] {a : M} {l : List M}, a ∈ l → a ∣ l.prod
true
AddCon.coe_mk'
Mathlib.GroupTheory.Congruence.Hom
∀ {M : Type u_1} [inst : AddZeroClass M] {c : AddCon M}, ⇑c.mk' = AddCon.toQuotient
true
FP.FloatCfg.precPos
Mathlib.Data.FP.Basic
∀ [self : FP.FloatCfg], 0 < FP.FloatCfg.prec
true
_private.Mathlib.RingTheory.ZariskisMainTheorem.0.Algebra.ZariskisMainProperty.of_algHom_polynomial._simp_1_1
Mathlib.RingTheory.ZariskisMainTheorem
∀ {R : Type u} {S : Type v} {F : Type u_1} [inst : Semiring R] [inst_1 : Semiring S] [inst_2 : FunLike F R S] [rcf : RingHomClass F R S] (f : F), Ideal.comap f ⊥ = RingHom.ker f
false
_private.Mathlib.RingTheory.Ideal.Norm.AbsNorm.0.Ideal.mem_prime_of_mul_mem_pow._simp_1_3
Mathlib.RingTheory.Ideal.Norm.AbsNorm
∀ {R : Type u} [inst : Semiring R] (r s : R) [(Ideal.span {r}).IsTwoSided], Ideal.span {r * s} = Ideal.span {r} * Ideal.span {s}
false
CochainComplex.ConnectData.comp_d₀
Mathlib.Algebra.Homology.Embedding.Connect
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] {K : ChainComplex C ℕ} {L : CochainComplex C ℕ} (self : CochainComplex.ConnectData K L), CategoryTheory.CategoryStruct.comp (K.d 1 0) self.d₀ = 0
true
TopCat.Sheaf.instIsLeftAdjointPullback
Mathlib.Topology.Sheaves.Functors
∀ {X Y : TopCat} (f : X ⟶ Y) (A : Type u_1) [inst : CategoryTheory.Category.{w, u_1} A] {FA : A → A → Type u_2} {CA : A → Type w} [inst_1 : (X Y : A) → FunLike (FA X Y) (CA X) (CA Y)] [inst_2 : CategoryTheory.ConcreteCategory A FA] [inst_3 : CategoryTheory.Limits.HasColimits A] [inst_4 : CategoryTheory.Limits.Has...
true
MeasureTheory.VectorMeasure.instModule
Mathlib.MeasureTheory.VectorMeasure.Basic
{α : Type u_1} → {m : MeasurableSpace α} → {M : Type u_3} → [inst : AddCommMonoid M] → [inst_1 : TopologicalSpace M] → {R : Type u_4} → [inst_2 : Semiring R] → [inst_3 : Module R M] → [ContinuousConstSMul R M] → [inst_5 : ContinuousAdd M] → Module ...
true
Std.ExtDTreeMap.get_insertIfNew
Std.Data.ExtDTreeMap.Lemmas
∀ {α : Type u} {β : α → Type v} {cmp : α → α → Ordering} {t : Std.ExtDTreeMap α β cmp} [inst : Std.TransCmp cmp] [inst_1 : Std.LawfulEqCmp cmp] {k a : α} {v : β k} {h₁ : a ∈ t.insertIfNew k v}, (t.insertIfNew k v).get a h₁ = if h₂ : cmp k a = Ordering.eq ∧ k ∉ t then cast ⋯ v else t.get a ⋯
true
Lean.Grind.Linarith.Expr.norm
Init.Grind.Ordered.Linarith
Lean.Grind.Linarith.Expr → Lean.Grind.Linarith.Poly
true
DoubleCentralizer.instStar._proof_2
Mathlib.Analysis.CStarAlgebra.Multiplier
∀ {𝕜 : Type u_2} {A : Type u_1} [inst : NontriviallyNormedField 𝕜] [inst_1 : NonUnitalNormedRing A] [inst_2 : NormedSpace 𝕜 A] [inst_3 : SMulCommClass 𝕜 A A] [inst_4 : IsScalarTower 𝕜 A A] [inst_5 : StarRing 𝕜] [inst_6 : StarRing A] [inst_7 : StarModule 𝕜 A] [inst_8 : NormedStarGroup A] (a : DoubleCentralize...
false
Std.ExtHashMap.insertManyIfNewUnit.congr_simp
Std.Data.ExtHashMap.Lemmas
∀ {α : Type u} {x : BEq α} {x_1 : Hashable α} [inst : EquivBEq α] [inst_1 : LawfulHashable α] {ρ : Type w} [inst_2 : ForIn Id ρ α] (m m_1 : Std.ExtHashMap α Unit), m = m_1 → ∀ (l l_1 : ρ), l = l_1 → m.insertManyIfNewUnit l = m_1.insertManyIfNewUnit l_1
true
AlgebraicGeometry.Scheme.Cover.pullbackHom
Mathlib.AlgebraicGeometry.Cover.MorphismProperty
{P : CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme} → [inst : P.IsStableUnderBaseChange] → [inst_1 : AlgebraicGeometry.Scheme.IsJointlySurjectivePreserving P] → {X W : AlgebraicGeometry.Scheme} → (𝒰 : AlgebraicGeometry.Scheme.Cover (AlgebraicGeometry.Scheme.precoverage P) X) → ...
true
Valuation.HasExtension.instAlgebra_valuationSubring._proof_6
Mathlib.RingTheory.Valuation.Extension
∀ {K : Type u_1} {L : Type u_3} {Γ₀ : Type u_2} {Γ₁ : Type u_4} [inst : Field K] [inst_1 : Field L] [inst_2 : Algebra K L] [inst_3 : LinearOrderedCommGroupWithZero Γ₀] [inst_4 : LinearOrderedCommGroupWithZero Γ₁] (vK : Valuation K Γ₀) (vL : Valuation L Γ₁) [inst_5 : vK.HasExtension vL] (r : ↥vK.valuationSubring) ...
false
Metric.sphere_subset_ball
Mathlib.Topology.MetricSpace.Pseudo.Defs
∀ {α : Type u} [inst : PseudoMetricSpace α] {x : α} {r R : ℝ}, r < R → Metric.sphere x r ⊆ Metric.ball x R
true
Polynomial.separable_X_pow_sub_C'
Mathlib.FieldTheory.Separable
∀ {F : Type u} [inst : Field F] (p n : ℕ) (a : F) [CharP F p], ¬p ∣ n → a ≠ 0 → (Polynomial.X ^ n - Polynomial.C a).Separable
true
CategoryTheory.IsPullback.app
Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D] [CategoryTheory.Limits.HasPullbacks D] {F₁ F₂ F₃ F₄ : CategoryTheory.Functor C D} {f₁ : F₁ ⟶ F₂} {f₂ : F₁ ⟶ F₃} {f₃ : F₂ ⟶ F₄} {f₄ : F₃ ⟶ F₄}, CategoryTheory.IsPullback f₁ f₂ f₃ f₄ → ∀ (X : ...
true
CategoryTheory.Limits.Cocones.cone_iso_of_hom_iso
Mathlib.CategoryTheory.Limits.Cones
∀ {J : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} J] {C : Type u₃} [inst_1 : CategoryTheory.Category.{v₃, u₃} C] {K : CategoryTheory.Functor J C} {c d : CategoryTheory.Limits.Cocone K} (f : d ⟶ c) [i : CategoryTheory.IsIso f.hom], CategoryTheory.IsIso f
true
Booleanisation.liftLatticeHom._proof_1
Mathlib.Order.Booleanisation
∀ {α : Type u_1} [inst : GeneralizedBooleanAlgebra α] (x x_1 : α), Booleanisation.lift (x ⊔ x_1) = Booleanisation.lift (x ⊔ x_1)
false
OrthogonalFamily.of_pairwise
Mathlib.Analysis.InnerProductSpace.Orthogonal
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E] {ι : Type u_4} {V : ι → Submodule 𝕜 E}, Pairwise (Function.onFun (fun x1 x2 => x1 ⟂ x2) V) → OrthogonalFamily 𝕜 (fun i => ↥(V i)) fun i => (V i).subtypeₗᵢ
true
Array.attach_congr._proof_1
Init.Data.Array.Attach
∀ {α : Type u_1} {xs ys : Array α}, xs = ys → ∀ (x : { x // x ∈ ys }), ↑x ∈ xs
false
_private.Mathlib.Topology.Compactness.Compact.0.IsCompact.sigma_exists_finite_sigma_eq._simp_1_3
Mathlib.Topology.Compactness.Compact
∀ {α : Type u} {β : Type v} {f : α → β} {s : Set β} {a : α}, (a ∈ f ⁻¹' s) = (f a ∈ s)
false
lieModule_lcs_map_le
Mathlib.Algebra.Lie.Nilpotent
∀ {R : Type u} {L : Type v} {M : Type w} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L] [inst_3 : AddCommGroup M] [inst_4 : Module R M] [inst_5 : LieRingModule L M] [LieModule R L M] {L₂ : Type u_1} {M₂ : Type u_2} [inst_7 : LieRing L₂] [inst_8 : LieAlgebra R L₂] [inst_9 : AddCommGroup M₂] [inst...
true
_private.Init.Data.SInt.Bitwise.0.Int32.and_not_self._simp_1_1
Init.Data.SInt.Bitwise
∀ {a b : Int32}, (a = b) = (a.toBitVec = b.toBitVec)
false