name stringlengths 2 347 | module stringlengths 6 90 | type stringlengths 1 5.67M | allowCompletion bool 2
classes |
|---|---|---|---|
List.get_length_sub_one._proof_1 | Mathlib.Data.List.Basic | ∀ {α : Type u_1} {l : List α}, l.length - 1 < l.length → l ≠ [] | false |
OrderIso.sumLexIicIoi | Mathlib.Order.Hom.Lex | {α : Type u_1} → [inst : LinearOrder α] → (x : α) → Lex (↑(Set.Iic x) ⊕ ↑(Set.Ioi x)) ≃o α | true |
Std.DHashMap.Internal.Raw₀.insertListₘ | Std.Data.DHashMap.Internal.Model | {α : Type u} →
{β : α → Type v} →
[BEq α] → [Hashable α] → Std.DHashMap.Internal.Raw₀ α β → List ((a : α) × β a) → Std.DHashMap.Internal.Raw₀ α β | true |
fderiv_fun_smul | Mathlib.Analysis.Calculus.FDeriv.Mul | ∀ {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 : E → F}
{x : E} {𝕜' : Type u_5} [inst_5 : NormedRing 𝕜'] [inst_6 : NormedAlgebra 𝕜 𝕜'] [inst_7 : Module ... | true |
CategoryTheory.ComposableArrows.IsComplex.opcyclesToCycles_fac | Mathlib.Algebra.Homology.ExactSequenceFour | ∀ {C : Type u_1} [inst : CategoryTheory.Category.{u_2, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
{n : ℕ} {S : CategoryTheory.ComposableArrows C (n + 3)} (hS : S.IsComplex) (k : ℕ)
(hk : autoParam (k ≤ n) CategoryTheory.ComposableArrows.IsComplex.opcyclesToCycles_fac._auto_1)
[inst_2 : (S.sc hS k... | true |
CategoryTheory.StructuredArrow.eta_hom_right | Mathlib.CategoryTheory.Comma.StructuredArrow.Basic | ∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
{S : D} {T : CategoryTheory.Functor C D} (f : CategoryTheory.StructuredArrow S T),
f.eta.hom.right = CategoryTheory.CategoryStruct.id f.right | true |
Real.cos_sub_nat_mul_pi | Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic | ∀ (x : ℝ) (n : ℕ), Real.cos (x - ↑n * Real.pi) = (-1) ^ n * Real.cos x | true |
DFinsupp.addCommGroup._proof_7 | Mathlib.Data.DFinsupp.Defs | ∀ {ι : Type u_1} {β : ι → Type u_2} [inst : (i : ι) → AddCommGroup (β i)] (x : Π₀ (i : ι), β i) (x_1 : ℤ),
⇑(x_1 • x) = x_1 • ⇑x | false |
ProofWidgets.CheckRequestResponse.done | ProofWidgets.Cancellable | ProofWidgets.LazyEncodable Lean.Json → ProofWidgets.CheckRequestResponse | true |
Set.card_image_of_inj_on | Mathlib.Data.Set.Finite.Basic | ∀ {α : Type u} {β : Type v} {s : Set α} [inst : Fintype ↑s] {f : α → β} [inst_1 : Fintype ↑(f '' s)],
(∀ x ∈ s, ∀ y ∈ s, f x = f y → x = y) → Fintype.card ↑(f '' s) = Fintype.card ↑s | true |
Lean.Environment.Replay.Context.casesOn | Lean.Replay | {motive : Lean.Environment.Replay.Context → Sort u} →
(t : Lean.Environment.Replay.Context) →
((newConstants : Std.HashMap Lean.Name Lean.ConstantInfo) → motive { newConstants := newConstants }) → motive t | false |
HasStrictFDerivAt.snd | Mathlib.Analysis.Calculus.FDeriv.Prod | ∀ {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] {G : Type u_4}
[inst_5 : NormedAddCommGroup G] [inst_6 : NormedSpace 𝕜 G] {x : E} {f₂ : E → F × G} {f₂' : E →L[... | true |
Vector.set_eraseIdx._proof_2 | Init.Data.Vector.Erase | ∀ {n i : ℕ} {w : i < n} {j : ℕ}, ¬i ≤ j → j < n | false |
Rack.PreEnvelGroupRel'._sizeOf_inst | Mathlib.Algebra.Quandle | (R : Type u) → {inst : Rack R} → (a a_1 : Rack.PreEnvelGroup R) → [SizeOf R] → SizeOf (Rack.PreEnvelGroupRel' R a a_1) | false |
_private.Batteries.Tactic.Alias.0.Batteries.Tactic.Alias.AliasInfo.name.match_1 | Batteries.Tactic.Alias | (motive : Batteries.Tactic.Alias.AliasInfo → Sort u_1) →
(x : Batteries.Tactic.Alias.AliasInfo) →
((n : Lean.Name) → motive (Batteries.Tactic.Alias.AliasInfo.plain n)) →
((n : Lean.Name) → motive (Batteries.Tactic.Alias.AliasInfo.forward n)) →
((n : Lean.Name) → motive (Batteries.Tactic.Alias.AliasI... | false |
IsLocalization.height_comap | Mathlib.RingTheory.Ideal.Height | ∀ {R : Type u_1} [inst : CommRing R] (S : Submonoid R) {A : Type u_2} [inst_1 : CommRing A] [inst_2 : Algebra R A]
[IsLocalization S A] (J : Ideal A), (Ideal.comap (algebraMap R A) J).height = J.height | true |
Int.instIsCancelMulZero | Mathlib.Algebra.Ring.Int.Defs | IsCancelMulZero ℤ | true |
_private.Mathlib.Data.Set.Image.0.Set.image_singleton._proof_1_1 | Mathlib.Data.Set.Image | ∀ {α : Type u_2} {β : Type u_1} {f : α → β} {a : α}, f '' {a} = {f a} | false |
_private.Mathlib.NumberTheory.Padics.ProperSpace.0.PadicInt.totallyBounded_univ._simp_1_3 | Mathlib.NumberTheory.Padics.ProperSpace | ∀ {α : Type u} [inst : PseudoMetricSpace α] {x y : α} {ε : ℝ}, (y ∈ Metric.ball x ε) = (dist y x < ε) | false |
_private.Mathlib.Combinatorics.Matroid.Dual.0.Matroid.IsBase.compl_inter_isBasis_of_inter_isBasis._simp_1_2 | Mathlib.Combinatorics.Matroid.Dual | ∀ {a b : Prop}, (¬(a ∧ b)) = (a → ¬b) | false |
HomologicalComplex.homologyι | Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex | {C : Type u_1} →
[inst : CategoryTheory.Category.{v_1, u_1} C] →
[inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
{ι : Type u_2} →
{c : ComplexShape ι} →
(K : HomologicalComplex C c) → (i : ι) → [inst_2 : K.HasHomology i] → K.homology i ⟶ K.opcycles i | true |
QuaternionAlgebra.instNeg | Mathlib.Algebra.Quaternion | {R : Type u_3} → {c₁ c₂ c₃ : R} → [Neg R] → Neg (QuaternionAlgebra R c₁ c₂ c₃) | true |
CompleteSublattice.subtype_apply | Mathlib.Order.CompleteSublattice | ∀ {α : Type u_1} [inst : CompleteLattice α] (L : Sublattice α) (a : ↥L), L.subtype a = ↑a | true |
NonarchAddGroupSeminorm.add_bddBelow_range_add | Mathlib.Analysis.Normed.Group.Seminorm | ∀ {E : Type u_3} [inst : AddCommGroup E] {p q : NonarchAddGroupSeminorm E} {x : E},
BddBelow (Set.range fun y => p y + q (x - y)) | true |
ProbabilityTheory.Kernel.ext_fun_iff | Mathlib.Probability.Kernel.Defs | ∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {κ η : ProbabilityTheory.Kernel α β},
κ = η ↔ ∀ (a : α) (f : β → ENNReal), Measurable f → ∫⁻ (b : β), f b ∂κ a = ∫⁻ (b : β), f b ∂η a | true |
strictConvexOn_rpow | Mathlib.Analysis.Convex.SpecificFunctions.Basic | ∀ {p : ℝ}, 1 < p → StrictConvexOn ℝ (Set.Ici 0) fun x => x ^ p | true |
BitVec.extractLsb'_eq_zero | Init.Data.BitVec.Lemmas | ∀ {w : ℕ} {x : BitVec w} {start : ℕ}, BitVec.extractLsb' start 0 x = 0#0 | true |
RightCancelMonoid | Mathlib.Algebra.Group.Defs | Type u → Type u | true |
_private.Mathlib.Tactic.Positivity.Core.0.Mathlib.Meta.Positivity.normNumPositivity._proof_1 | Mathlib.Tactic.Positivity.Core | ∀ {u : Lean.Level} {α : Q(Type u)} (zα : Q(Zero «$α»)) (_a : Q(Semiring «$α»)),
«$zα» =Q «$_a».toNonAssocSemiring.toMulZeroClass.toZero | false |
CategoryTheory.ShortComplex.SnakeInput.φ₁_L₂_f_assoc | Mathlib.Algebra.Homology.ShortComplex.SnakeLemma | ∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Abelian C]
(S : CategoryTheory.ShortComplex.SnakeInput C) {Z : C} (h : S.L₂.X₂ ⟶ Z),
CategoryTheory.CategoryStruct.comp S.φ₁ (CategoryTheory.CategoryStruct.comp S.L₂.f h) =
CategoryTheory.CategoryStruct.comp S.φ₂ h | true |
_private.Batteries.Tactic.Trans.0.Batteries.Tactic.getRel.match_1 | Batteries.Tactic.Trans | (motive : Lean.Expr × Lean.Expr → Sort u_1) →
(__discr : Lean.Expr × Lean.Expr) → ((rel x : Lean.Expr) → motive (rel, x)) → motive __discr | false |
Lean.Meta.LazyDiscrTree.PartialMatch.score | Lean.Meta.LazyDiscrTree | Lean.Meta.LazyDiscrTree.PartialMatch → ℕ | true |
ContinuousAt.comp₂_of_eq | Mathlib.Topology.Constructions.SumProd | ∀ {X : Type u} {Y : Type v} {W : Type u_1} {Z : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y]
[inst_2 : TopologicalSpace Z] [inst_3 : TopologicalSpace W] {f : Y × Z → W} {g : X → Y} {h : X → Z} {x : X}
{y : Y × Z},
ContinuousAt f y → ContinuousAt g x → ContinuousAt h x → (g x, h x) = y → Con... | true |
_private.Mathlib.Tactic.Positivity.Basic.0.Mathlib.Meta.Positivity.evalIte._proof_1 | Mathlib.Tactic.Positivity.Basic | ∀ {u : Lean.Level} {α : Q(Type u)} (pα : Q(PartialOrder «$α»)) (_b : Q(Preorder «$α»)), «$_b» =Q «$pα».toPreorder | false |
_private.Mathlib.Algebra.Lie.Basis.0.LieAlgebra.Basis.coroot_eq_h'.match_1_2 | Mathlib.Algebra.Lie.Basis | ∀ {ι : Type u_3} {K : Type u_2} {L : Type u_1} [inst : Fintype ι] [inst_1 : Field K] [inst_2 : LieRing L]
[inst_3 : LieAlgebra K L] (b : LieAlgebra.Basis ι K L) (motive : ↥b.cartan → Prop) (x : ↥b.cartan),
(∀ (z : L) (hz : z ∈ b.cartan), motive ⟨z, hz⟩) → motive x | false |
ContinuousENorm.toENorm | Mathlib.Analysis.Normed.Group.Defs | {E : Type u_8} → {inst : TopologicalSpace E} → [self : ContinuousENorm E] → ENorm E | true |
NNReal.instSemifield._proof_12 | Mathlib.Data.NNReal.Defs | ∀ (x x_1 : NNReal), ↑(x * x_1) = ↑(x * x_1) | false |
Submonoid.instCompleteLattice.eq_1 | Mathlib.Algebra.Group.Submonoid.Basic | ∀ {M : Type u_1} [inst : MulOneClass M],
Submonoid.instCompleteLattice =
{ le := fun x1 x2 => x1 ≤ x2, lt := fun x1 x2 => x1 < x2, le_refl := ⋯, le_trans := ⋯, lt_iff_le_not_ge := ⋯,
le_antisymm := ⋯, sup := SemilatticeSup.sup, le_sup_left := ⋯, le_sup_right := ⋯, sup_le := ⋯,
inf := fun x1 x2 => x1 ⊓... | true |
IO.Error.mkInterrupted | Init.System.IOError | String → UInt32 → String → IO.Error | true |
TensorProduct.assoc._proof_3 | Mathlib.LinearAlgebra.TensorProduct.Associator | ∀ (R : Type u_1) [inst : CommSemiring R] (M : Type u_2) (N : Type u_3) (P : Type u_4) [inst_1 : AddCommMonoid M]
[inst_2 : AddCommMonoid N] [inst_3 : AddCommMonoid P] [inst_4 : Module R M] [inst_5 : Module R N]
[inst_6 : Module R P], SMulCommClass R R (TensorProduct R M (TensorProduct R N P)) | false |
CategoryTheory.monoidalCategoryMop._proof_9 | Mathlib.CategoryTheory.Monoidal.Opposite | ∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] [inst_1 : CategoryTheory.MonoidalCategory C] {X Y : Cᴹᵒᵖ}
(f : X ⟶ Y),
(CategoryTheory.CategoryStruct.comp
(CategoryTheory.MonoidalCategoryStruct.whiskerRight f.unmop
{ unmop := CategoryTheory.MonoidalCategoryStruct.tensorUnit C }.un... | false |
_private.Mathlib.Analysis.SpecialFunctions.Complex.Arg.0.Complex.arg_mul_coe_angle._simp_1_1 | Mathlib.Analysis.SpecialFunctions.Complex.Arg | ∀ (x y : ℝ), ↑x + ↑y = ↑(x + y) | false |
Lean.ReducibilityHints.isAbbrev | Lean.Declaration | Lean.ReducibilityHints → Bool | true |
_private.Lean.Elab.DocString.Builtin.0.Lean.Doc.checkNameExists._sparseCasesOn_1 | Lean.Elab.DocString.Builtin | {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 |
CategoryTheory.compCreatesLimit._proof_1 | Mathlib.CategoryTheory.Limits.Creates | ∀ {C : Type u_5} [inst : CategoryTheory.Category.{u_3, u_5} C] {D : Type u_8}
[inst_1 : CategoryTheory.Category.{u_7, u_8} D] {J : Type u_2} [inst_2 : CategoryTheory.Category.{u_1, u_2} J]
{K : CategoryTheory.Functor J C} {E : Type u_6} [ℰ : CategoryTheory.Category.{u_4, u_6} E]
(F : CategoryTheory.Functor C D) (... | false |
AffineSubspace.direction_top | 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]
[S : AddTorsor V P], ⊤.direction = ⊤ | true |
Filter.disjoint_pure_pure._simp_1 | Mathlib.Order.Filter.Bases.Basic | ∀ {α : Type u_1} {x y : α}, Disjoint (pure x) (pure y) = (x ≠ y) | false |
CategoryTheory.PreZeroHypercover.refineOneHypercover_p₁ | Mathlib.CategoryTheory.Sites.Hypercover.One | ∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X : C} (E : CategoryTheory.PreZeroHypercover X)
[inst_1 : E.HasPullbacks]
(F : (i j : E.I₀) → CategoryTheory.PreZeroHypercover (CategoryTheory.Limits.pullback (E.f i) (E.f j))) (i j : E.I₀)
(k : (F i j).I₀),
(E.refineOneHypercover F).p₁ k =
CategoryT... | true |
NumberField.InfinitePlace.instMulActionAlgEquiv._proof_1 | 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], RingHomClass Gal(K/k) K K | false |
CategoryTheory.Discrete.discreteCases | Mathlib.CategoryTheory.Discrete.Basic | Lean.Elab.Tactic.TacticM Unit | true |
CategoryTheory.TwoSquare | Mathlib.CategoryTheory.Functor.TwoSquare | {C₁ : Type u₁} →
{C₂ : Type u₂} →
{C₃ : Type u₃} →
{C₄ : Type u₄} →
[inst : CategoryTheory.Category.{v₁, u₁} C₁] →
[inst_1 : CategoryTheory.Category.{v₂, u₂} C₂] →
[inst_2 : CategoryTheory.Category.{v₃, u₃} C₃] →
[inst_3 : CategoryTheory.Category.{v₄, u₄} C₄] →
... | true |
_private.Lean.Elab.MutualDef.0.Lean.Elab.Term.elabMutualDef._sparseCasesOn_13 | Lean.Elab.MutualDef | {motive : Lean.ReducibilityStatus → Sort u} →
(t : Lean.ReducibilityStatus) →
motive Lean.ReducibilityStatus.reducible →
motive Lean.ReducibilityStatus.implicitReducible →
motive Lean.ReducibilityStatus.irreducible → (Nat.hasNotBit 13 t.ctorIdx → motive t) → motive t | false |
_private.Mathlib.LinearAlgebra.LinearIndependent.BaseChange.0.LinearIndependent.linearIndependent_algebraMap_comp_aux | Mathlib.LinearAlgebra.LinearIndependent.BaseChange | ∀ {ι : Type u_1} {ι' : Type u_2} [Finite ι'] {K : Type u_3} (L : Type u_4) [inst : Field K] [inst_1 : Field L]
[inst_2 : Algebra K L] {v : ι → ι' → K}, LinearIndependent K v → LinearIndependent L fun i => ⇑(algebraMap K L) ∘ v i | true |
Real.rpow_two | Mathlib.Analysis.SpecialFunctions.Pow.Real | ∀ (x : ℝ), x ^ 2 = x ^ 2 | true |
CategoryTheory.ShortComplex.SnakeInput.exact_C₁_up._proof_1 | Mathlib.Algebra.Homology.ShortComplex.SnakeLemma | ∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] [inst_1 : CategoryTheory.Abelian C]
(S : CategoryTheory.ShortComplex.SnakeInput C), CategoryTheory.CategoryStruct.comp S.v₀₁.τ₁ S.v₁₂.τ₁ = 0 | false |
_private.Std.Data.HashMap.IteratorLemmas.0.Std.HashMap.Raw.keysIter.eq_1 | Std.Data.HashMap.IteratorLemmas | ∀ {α β : Type u} (m : Std.HashMap.Raw α β), m.keysIter = m.inner.keysIter | true |
mul_lt_mul_of_pos_right | Mathlib.Algebra.Order.GroupWithZero.Unbundled.Defs | ∀ {α : Type u_1} [inst : Mul α] [inst_1 : Zero α] [inst_2 : Preorder α] {a b c : α} [MulPosStrictMono α],
b < c → 0 < a → b * a < c * a | true |
IsLocalFrameOn.mdifferentiableAt_of_coeff | Mathlib.Geometry.Manifold.VectorBundle.LocalFrame | ∀ {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] {F : Type u_5} [inst_6 : NormedAddCommG... | true |
_private.Batteries.Data.Array.Monadic.0.cond.match_1.eq_1 | Batteries.Data.Array.Monadic | ∀ (motive : Bool → Sort u_1) (h_1 : Unit → motive true) (h_2 : Unit → motive false),
(match true with
| true => h_1 ()
| false => h_2 ()) =
h_1 () | true |
Units.cfcRpow._proof_3 | Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic | ∀ {A : Type u_1} [inst : PartialOrder A] [inst_1 : Ring A] [inst_2 : StarRing A] [inst_3 : TopologicalSpace A]
[inst_4 : StarOrderedRing A] [inst_5 : Algebra ℝ A] [inst_6 : ContinuousFunctionalCalculus ℝ A IsSelfAdjoint]
[inst_7 : NonnegSpectrumClass ℝ A] (a : Aˣ) (x : ℝ), 0 ≤ ↑a → ↑a ^ (-x) * ↑a ^ x = 1 | false |
CategoryTheory.LaxFunctor.map₂_rightUnitor._autoParam | Mathlib.CategoryTheory.Bicategory.Functor.Lax | Lean.Syntax | false |
CompactlyGenerated.isoEquivHomeo_symm_apply | Mathlib.Topology.Category.CompactlyGenerated | ∀ {X Y : CompactlyGenerated} (f : ↑X.toTop ≃ₜ ↑Y.toTop),
CompactlyGenerated.isoEquivHomeo.symm f = CompactlyGenerated.isoOfHomeo f | true |
CategoryTheory.MonoidalCategoryStruct.whiskerRight | Mathlib.CategoryTheory.Monoidal.Category | {C : Type u} →
{𝒞 : CategoryTheory.Category.{v, u} C} →
[self : CategoryTheory.MonoidalCategoryStruct C] →
{X₁ X₂ : C} →
(X₁ ⟶ X₂) →
(Y : C) →
CategoryTheory.MonoidalCategoryStruct.tensorObj X₁ Y ⟶ CategoryTheory.MonoidalCategoryStruct.tensorObj X₂ Y | true |
ContinuousMap.mk | Mathlib.Topology.ContinuousMap.Defs | {X : Type u_1} →
{Y : Type u_2} →
[inst : TopologicalSpace X] →
[inst_1 : TopologicalSpace Y] →
(toFun : X → Y) → autoParam (Continuous toFun) ContinuousMap.continuous_toFun._autoParam → C(X, Y) | true |
OrderIso.Icc._proof_5 | Mathlib.Order.Hom.Set | ∀ {α : Type u_1} {β : Type u_2} [inst : Lattice α] [inst_1 : Lattice β] (e : α ≃o β) (x y : α) (y_1 : ↑(Set.Icc x y)),
(fun z => ⟨e.symm ↑z, ⋯⟩) ((fun z => ⟨e ↑z, ⋯⟩) y_1) = y_1 | false |
Equiv.Perm.equivUnitsEnd._proof_6 | Mathlib.Algebra.Group.End | ∀ {α : Type u_1} (x x_1 : Equiv.Perm α), ⇑(Equiv.symm (x * x_1)) ∘ ⇑(x * x_1) = id | false |
CategoryTheory.Abelian.SpectralObject.mapFourδ₁Toδ₀'_mapFourδ₃Toδ₃' | Mathlib.Algebra.Homology.SpectralObject.EpiMono | ∀ {C : Type u_1} {ι' : Type u_3} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Abelian C]
[inst_2 : Preorder ι'] (X' : CategoryTheory.Abelian.SpectralObject C ι') (i₀ i₁ i₂ i₃ i₄ i₅ : ι') (hi₀₁ : i₀ ≤ i₁)
(hi₁₂ : i₁ ≤ i₂) (hi₂₃ : i₂ ≤ i₃) (hi₃₄ : i₃ ≤ i₄) (hi₄₅ : i₄ ≤ i₅) (n₀ n₁ n₂ : ℤ)
(... | true |
_private.Mathlib.Data.Int.Bitwise.0.Int.shiftLeft_eq_mul_pow.match_1_1 | Mathlib.Data.Int.Bitwise | ∀ (motive : ℤ → ℕ → Prop) (x : ℤ) (x_1 : ℕ),
(∀ (m x : ℕ), motive (Int.ofNat m) x) → (∀ (a x : ℕ), motive (Int.negSucc a) x) → motive x x_1 | false |
Lean.Meta.Grind.Extension.addEMatchAttrAndSuggest | Lean.Meta.Tactic.Grind.EMatchTheorem | Lean.Meta.Grind.Extension →
Lean.Syntax →
Lean.Name →
Lean.AttributeKind → Lean.Meta.Grind.SymbolPriorities → Bool → Bool → optParam Bool false → Lean.MetaM Unit | true |
SimpleGraph.Copy.mapNeighborSet._proof_2 | Mathlib.Combinatorics.SimpleGraph.Copy | ∀ {α : Type u_2} {β : Type u_1} {A : SimpleGraph α} {B : SimpleGraph β} (f : A.Copy B) (a : α) (v : ↑(A.neighborSet a)),
f.toHom ↑v ∈ B.neighborSet (f.toHom a) | false |
IsReduced.mk | Mathlib.Algebra.GroupWithZero.Basic | ∀ {R : Type u_5} [inst : Zero R] [inst_1 : Pow R ℕ], (∀ (x : R), IsNilpotent x → x = 0) → IsReduced R | true |
ArchimedeanOrder.instLE | Mathlib.Algebra.Order.Archimedean.Class | {M : Type u_1} → [AddGroup M] → [Lattice M] → LE (ArchimedeanOrder M) | true |
Plausible.TestResult.ctorElim | Plausible.Testable | {p : Prop} →
{motive : Plausible.TestResult p → Sort u} →
(ctorIdx : ℕ) →
(t : Plausible.TestResult p) → ctorIdx = t.ctorIdx → Plausible.TestResult.ctorElimType ctorIdx → motive t | false |
CategoryTheory.ComposableArrows.sc'._auto_5 | Mathlib.Algebra.Homology.ExactSequence | Lean.Syntax | false |
Lean.Meta.StructProjDecl.projName | Lean.Meta.Structure | Lean.Meta.StructProjDecl → Lean.Name | true |
HomologicalComplex.evalCompCoyonedaCorepresentableBySingle._proof_3 | Mathlib.Algebra.Homology.Double | ∀ {C : Type u_3} [inst : CategoryTheory.Category.{u_1, u_3} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
[inst_2 : CategoryTheory.Limits.HasZeroObject C] {ι : Type u_2} (c : ComplexShape ι) (i : ι) [inst_3 : DecidableEq ι]
(hi : ∀ (j : ι), ¬c.Rel i j) (X : C) {K : HomologicalComplex C c}
(f : ((Homologi... | false |
WithBot.ofDual_lt_ofDual_iff | Mathlib.Order.WithBot | ∀ {α : Type u_1} [inst : LT α] {x y : WithBot αᵒᵈ}, WithBot.ofDual x < WithBot.ofDual y ↔ y < x | true |
Valuation.instLinearOrderedCommGroupWithZeroMrange._aux_7 | Mathlib.RingTheory.Valuation.Archimedean | {F : Type u_2} →
{Γ₀ : Type u_1} →
[inst : Field F] →
[inst_1 : LinearOrderedCommGroupWithZero Γ₀] →
{v : Valuation F Γ₀} → ℤ → ↥(MonoidHom.mrange v) → ↥(MonoidHom.mrange v) | false |
_private.Mathlib.RingTheory.Perfectoid.BDeRham.0.«_aux_Mathlib_RingTheory_Perfectoid_BDeRham___macroRules__private_Mathlib_RingTheory_Perfectoid_BDeRham_0_term𝔹_dR^+(_)_1» | Mathlib.RingTheory.Perfectoid.BDeRham | Lean.Macro | false |
Matrix.det_isEmpty | Mathlib.LinearAlgebra.Matrix.Determinant.Basic | ∀ {n : Type u_2} [inst : DecidableEq n] [inst_1 : Fintype n] {R : Type v} [inst_2 : CommRing R] [IsEmpty n]
{A : Matrix n n R}, A.det = 1 | true |
Lean.JsonRpc.RequestID.num.inj | Lean.Data.JsonRpc | ∀ {n n_1 : Lean.JsonNumber}, Lean.JsonRpc.RequestID.num n = Lean.JsonRpc.RequestID.num n_1 → n = n_1 | true |
_private.Lean.Compiler.LCNF.ExplicitBoxing.0.Lean.Compiler.LCNF.castArgsIfNeededAux.match_3 | Lean.Compiler.LCNF.ExplicitBoxing | (motive :
MProd (Array (Lean.Compiler.LCNF.CodeDecl Lean.Compiler.LCNF.Purity.impure))
(Array (Lean.Compiler.LCNF.Arg Lean.Compiler.LCNF.Purity.impure)) →
Sort u_1) →
(r :
MProd (Array (Lean.Compiler.LCNF.CodeDecl Lean.Compiler.LCNF.Purity.impure))
(Array (Lean.Compiler.LCNF.Arg Lean.C... | false |
Vector.rec | Init.Data.Vector.Basic | {α : Type u} →
{n : ℕ} →
{motive : Vector α n → Sort u_1} →
((toArray : Array α) → (size_toArray : toArray.size = n) → motive (Vector.mk toArray size_toArray)) →
(t : Vector α n) → motive t | false |
Std.TreeMap.mem_of_mem_union_of_not_mem_right | 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},
k ∈ t₁ ∪ t₂ → k ∉ t₂ → k ∈ t₁ | true |
_private.Init.Data.Int.DivMod.Lemmas.0.Int.tdiv_one.match_1_1 | Init.Data.Int.DivMod.Lemmas | ∀ (motive : ℤ → Prop) (x : ℤ), (∀ (n : ℕ), motive (Int.ofNat n)) → (∀ (n : ℕ), motive (Int.negSucc n)) → motive x | false |
_private.Lean.Meta.GeneralizeTelescope.0.Lean.Meta.GeneralizeTelescope.generalizeTelescopeAux.match_1 | Lean.Meta.GeneralizeTelescope | (motive : Lean.LocalDecl → Sort u_1) →
(localDecl : Lean.LocalDecl) →
((index : ℕ) →
(fvarId : Lean.FVarId) →
(userName : Lean.Name) →
(type : Lean.Expr) →
(bi : Lean.BinderInfo) →
(kind : Lean.LocalDeclKind) → motive (Lean.LocalDecl.cdecl index fvarId u... | false |
TensorProduct.finsuppLeft_symm_apply_single | Mathlib.LinearAlgebra.DirectSum.Finsupp | ∀ {R : Type u_1} {S : Type u_2} [inst : CommSemiring R] [inst_1 : Semiring S] [inst_2 : Algebra R S] {M : Type u_3}
[inst_3 : AddCommMonoid M] [inst_4 : Module R M] [inst_5 : Module S M] [inst_6 : IsScalarTower R S M] {N : Type u_4}
[inst_7 : AddCommMonoid N] [inst_8 : Module R N] {ι : Type u_5} [inst_9 : Decidable... | true |
CategoryTheory.SpectralSequence.Hom.mk.injEq | Mathlib.Algebra.Homology.SpectralSequence.Basic | ∀ {C : Type u_1} [inst : CategoryTheory.Category.{u_3, u_1} C] [inst_1 : CategoryTheory.Abelian C] {κ : Type u_2}
{c : ℤ → ComplexShape κ} {r₀ : ℤ} {E E' : CategoryTheory.SpectralSequence C c r₀}
(hom : (r : ℤ) → (hr : autoParam (r₀ ≤ r) CategoryTheory.SpectralSequence.Hom._auto_1) → E.page r ⋯ ⟶ E'.page r ⋯)
(co... | true |
CategoryTheory.EnrichedCat.bicategory._proof_6 | Mathlib.CategoryTheory.Enriched.EnrichedCat | ∀ {V : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} V] [inst_1 : CategoryTheory.MonoidalCategory V]
{a b : CategoryTheory.EnrichedCat V} {f g : CategoryTheory.EnrichedFunctor V ↑a ↑b} (η : f ⟶ g),
CategoryTheory.EnrichedCat.whiskerLeft (CategoryTheory.EnrichedFunctor.id V ↑a) η =
CategoryTheory.Category... | false |
OpenSubgroup.hasCoeSubgroup.eq_1 | Mathlib.Topology.Algebra.OpenSubgroup | ∀ {G : Type u_1} [inst : Group G] [inst_1 : TopologicalSpace G],
OpenSubgroup.hasCoeSubgroup = { coe := OpenSubgroup.toSubgroup } | true |
UniqueAdd.mt | Mathlib.Algebra.Group.UniqueProds.Basic | ∀ {G : Type u_1} [inst : Add G] {A B : Finset G} {a0 b0 : G},
UniqueAdd A B a0 b0 → ∀ ⦃a b : G⦄, a ∈ A → b ∈ B → a ≠ a0 ∨ b ≠ b0 → a + b ≠ a0 + b0 | true |
Batteries.RBColor.black.elim | Batteries.Data.RBMap.Basic | {motive : Batteries.RBColor → Sort u} →
(t : Batteries.RBColor) → t.ctorIdx = 1 → motive Batteries.RBColor.black → motive t | false |
HomologicalComplex.Hom.comm | Mathlib.Algebra.Homology.HomologicalComplex | ∀ {ι : Type u_1} {V : Type u} [inst : CategoryTheory.Category.{v, u} V]
[inst_1 : CategoryTheory.Limits.HasZeroMorphisms V] {c : ComplexShape ι} {A B : HomologicalComplex V c} (f : A.Hom B)
(i j : ι), CategoryTheory.CategoryStruct.comp (f.f i) (B.d i j) = CategoryTheory.CategoryStruct.comp (A.d i j) (f.f j) | true |
PiTensorProduct.constantBaseRingEquiv_symm | Mathlib.RingTheory.PiTensorProduct | ∀ {ι : Type u_1} {R : Type u_3} [inst : CommSemiring R] [inst_1 : Fintype ι] (r : R),
(PiTensorProduct.constantBaseRingEquiv ι R).symm r = (algebraMap R (PiTensorProduct R fun x => R)) r | true |
Plausible.Shrinkable.shrink | Plausible.Sampleable | {α : Type u} → [self : Plausible.Shrinkable α] → α → List α | true |
instAddCommMonoidPrimeMultiset._proof_3 | Mathlib.Data.PNat.Factors | ∀ (a b c : PrimeMultiset), a + b + c = a + (b + c) | false |
AddSubgroup.comap_map_eq | Mathlib.Algebra.Group.Subgroup.Ker | ∀ {G : Type u_1} [inst : AddGroup G] {N : Type u_5} [inst_1 : AddGroup N] (f : G →+ N) (H : AddSubgroup G),
AddSubgroup.comap f (AddSubgroup.map f H) = H ⊔ f.ker | true |
instNonUnitalCStarAlgebraForall._proof_1 | Mathlib.Analysis.CStarAlgebra.Classes | ∀ {ι : Type u_2} {A : ι → Type u_1} [inst : (i : ι) → NonUnitalCStarAlgebra (A i)], CompleteSpace ((i : ι) → A i) | false |
_aux_Mathlib_Algebra_Group_Hom_Defs___unexpand_MonoidHom_1 | Mathlib.Algebra.Group.Hom.Defs | Lean.PrettyPrinter.Unexpander | false |
WithBot.bot_mul_bot | Mathlib.Algebra.Order.Ring.WithTop | ∀ {α : Type u_1} [inst : DecidableEq α] [inst_1 : MulZeroClass α], ⊥ * ⊥ = ⊥ | true |
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