name stringlengths 2 347 | module stringlengths 6 90 | type stringlengths 1 5.42M | docString stringlengths 0 11k ⌀ | allowCompletion bool 2
classes |
|---|---|---|---|---|
_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... | null | 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.under R J).height = J.height | **Alias** of `IsLocalization.height_under`. | true |
Int.instIsCancelMulZero | Mathlib.Algebra.Ring.Int.Defs | IsCancelMulZero ℤ | null | true |
_private.Mathlib.CategoryTheory.PathCategory.MorphismProperty.0.CategoryTheory.MorphismProperty.instIsMultiplicativeStrictMapPathsPathsPathComposition.match_1 | Mathlib.CategoryTheory.PathCategory.MorphismProperty | ∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] (W : CategoryTheory.MorphismProperty C) {X Y Z : C}
(f : X ⟶ Y) (motive : (x : Y ⟶ Z) → W.paths.strictMap (CategoryTheory.pathComposition C) x → Prop) (x : Y ⟶ Z)
(x_1 : W.paths.strictMap (CategoryTheory.pathComposition C) x),
(∀ (f : Y ⟶ Z) (hq : W.p... | null | false |
_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} | null | 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) | null | 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) | null | 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 | The inclusion map of the homology of a homological complex into its opcycles. | true |
QuaternionAlgebra.instNeg | Mathlib.Algebra.Quaternion | {R : Type u_3} → {c₁ c₂ c₃ : R} → [Neg R] → Neg (QuaternionAlgebra R c₁ c₂ c₃) | null | true |
CompleteSublattice.subtype_apply | Mathlib.Order.CompleteSublattice | ∀ {α : Type u_1} [inst : CompleteLattice α] (L : CompleteSublattice α) (a : ↥L), L.subtype a = ↑a | null | true |
_private.Init.Data.Int.Linear.0.Int.Internal.Linear.norm_le_coeff' | Init.Data.Int.Linear | ∀ (ctx : Int.Internal.Linear.Context) (p p' : Int.Internal.Linear.Poly) (k : ℤ),
p = p'.mul k → k > 0 → (Int.Internal.Linear.Poly.denote ctx p ≤ 0 ↔ Int.Internal.Linear.Poly.denote ctx p' ≤ 0) | null | 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)) | null | 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 | null | true |
strictConvexOn_rpow | Mathlib.Analysis.Convex.SpecificFunctions.Basic | ∀ {p : ℝ}, 1 < p → StrictConvexOn ℝ (Set.Ici 0) fun x => x ^ p | For `p : ℝ` with `1 < p`, `fun x ↦ x ^ p` is strictly convex on $[0, +∞)$. | true |
BitVec.extractLsb'_eq_zero | Init.Data.BitVec.Lemmas | ∀ {w : ℕ} {x : BitVec w} {start : ℕ}, BitVec.extractLsb' start 0 x = 0#0 | null | true |
RightCancelMonoid | Mathlib.Algebra.Group.Monoid | Type u_2 → Type u_2 | A monoid in which multiplication is right-cancellative. | 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 instMulZeroClassOfSemiring.toZero | null | 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 | null | true |
_private.Lean.Meta.Tactic.Simp.BuiltinSimprocs.SInt.0.Int8.reduceMod._regBuiltin.Int8.reduceMod.declare_1._@.Lean.Meta.Tactic.Simp.BuiltinSimprocs.SInt.2990342300._hygCtx._hyg.158 | Lean.Meta.Tactic.Simp.BuiltinSimprocs.SInt | IO Unit | null | false |
_private.Batteries.Tactic.Trans.0.Batteries.Tactic.getRel.match_1 | Batteries.Tactic.Trans | (motive : Lean.Expr × Lean.Expr → Sort u_1) →
(x : Lean.Expr × Lean.Expr) → ((rel x : Lean.Expr) → motive (rel, x)) → motive x | null | false |
Lean.Meta.LazyDiscrTree.PartialMatch.score | Lean.Meta.LazyDiscrTree | Lean.Meta.LazyDiscrTree.PartialMatch → ℕ | null | 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... | null | true |
Cardinal.mk_Iio_lt._simp_1 | Mathlib.SetTheory.Ordinal.Basic | ∀ {α : Type u} [inst : LinearOrder α] [inst_1 : WellFoundedLT α] (i : α),
((Cardinal.mk α).ord = Ordinal.type fun x1 x2 => x1 < x2) → (Cardinal.mk ↑(Set.Iio i) < Cardinal.mk α) = True | null | false |
ContinuousENorm.toENorm | Mathlib.Analysis.Normed.Group.Defs | {E : Type u_4} → {inst : TopologicalSpace E} → [self : ContinuousENorm E] → ENorm E | null | true |
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 ⊓... | null | true |
IO.Error.mkInterrupted | Init.System.IOError | String → UInt32 → String → IO.Error | null | 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)) | null | 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... | null | 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) | null | false |
Lean.ReducibilityHints.isAbbrev | Lean.Declaration | Lean.ReducibilityHints → Bool | null | true |
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) (... | null | 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 = ⊤ | The direction of `⊤` is the whole module as a submodule. | 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) | null | 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... | null | 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 | null | false |
CategoryTheory.Discrete.discreteCases | Mathlib.CategoryTheory.Discrete.Basic | Lean.Elab.Tactic.TacticM Unit | Use:
```
attribute [local aesop safe tactic (rule_sets := [CategoryTheory])]
CategoryTheory.Discrete.discreteCases
```
to locally give `cat_disch` the ability to call `cases` on
`Discrete` and `(_ : Discrete _) ⟶ (_ : Discrete _)` hypotheses.
| 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] →
... | A `2`-square consists of a natural transformation `T ⋙ R ⟶ L ⋙ B`
involving fours functors `T`, `L`, `R`, `B` that are on the
top/left/right/bottom sides of a square of categories. | true |
_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 | This is an auxiliary lemma dominated by `linearIndependent_algebraMap_comp_iff`. | true |
Real.rpow_two | Mathlib.Analysis.SpecialFunctions.Pow.Real | ∀ (x : ℝ), x ^ 2 = x ^ 2 | null | 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 | null | 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 | null | true |
mul_lt_mul_of_pos_right | Mathlib.Algebra.Order.GroupWithZero.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 | null | 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... | Given a local frame `s i` on a neighbourhood `u` of `x`, if a section `t` has differentiable
coefficients at `x` w.r.t. `s i`, then `t` is differentiable at `x`. | 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 | null | false |
CategoryTheory.LaxFunctor.map₂_rightUnitor._autoParam | Mathlib.CategoryTheory.Bicategory.Functor.Lax | Lean.Syntax | null | 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 | null | 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 | right whiskering for morphisms | 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) | null | 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 | null | 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 | null | 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)
(... | null | 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 | null | 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 | Tries different modifiers, logs info messages with modifiers that worked, but stores just the first one that worked.
Remark: if `backward.grind.inferPattern` is `true`, then `.default false` is used.
The parameter `showInfo` is only taken into account when `backward.grind.inferPattern` is `true`.
| true |
SimpleGraph.Copy.mapNeighborSet._proof_2 | Mathlib.Combinatorics.SimpleGraph.Copy | ∀ {V : Type u_1} {W : Type u_2} {G : SimpleGraph V} {H : SimpleGraph W} (f : H.Copy G) (a : W) (v : ↑(H.neighborSet a)),
f.toHom ↑v ∈ G.neighborSet (f.toHom a) | null | 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 | null | true |
ArchimedeanOrder.instLE | Mathlib.Algebra.Order.Archimedean.Class | {M : Type u_1} → [AddGroup M] → [Lattice M] → LE (ArchimedeanOrder M) | null | 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 | null | false |
CategoryTheory.ComposableArrows.sc'._auto_5 | Mathlib.Algebra.Homology.ExactSequence | Lean.Syntax | null | false |
Lean.Meta.StructProjDecl.projName | Lean.Meta.Structure | Lean.Meta.StructProjDecl → Lean.Name | null | 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... | null | 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 | null | true |
_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 | null | false |
Real.Lp.fourierTransformInv._proof_1 | Mathlib.Analysis.Fourier.FourierTransform | ∀ {V : Type u_1} [inst : NormedAddCommGroup V], ContinuousNeg V | null | 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 | null | 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 | null | true |
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 | null | 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 | null | 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 | null | 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... | null | 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... | null | true |
RBTree.RBNode.Path.RootOrdered.eq_1 | Batteries.Recycling.RBTree.Alter | ∀ {α : Type u_1} (cmp : α → α → Ordering) (x : α), RBTree.RBNode.Path.RootOrdered cmp RBTree.RBNode.Path.root x = True | null | 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... | null | 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... | null | 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 } | null | 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 | null | true |
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) | null | 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 | null | true |
Plausible.Shrinkable.shrink | Plausible.Shrinkable | {α : Type u} → [self : Plausible.Shrinkable α] → α → List α | null | true |
AddSubgroup.comap_map_eq | Mathlib.Algebra.Group.Subgroup.Ker | ∀ {G : Type u_1} [inst : AddGroup G] {N : Type u_4} [inst_1 : AddGroup N] (f : G →+ N) (H : AddSubgroup G),
AddSubgroup.comap f (AddSubgroup.map f H) = H ⊔ f.ker | null | 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) | null | false |
_aux_Mathlib_Algebra_Group_Hom_Defs___unexpand_MonoidHom_1 | Mathlib.Algebra.Group.Hom.Defs | Lean.PrettyPrinter.Unexpander | null | false |
WithBot.bot_mul_bot | Mathlib.Algebra.Order.Ring.WithTop | ∀ {α : Type u_1} [inst : DecidableEq α] [inst_1 : MulZeroClass α], ⊥ * ⊥ = ⊥ | null | true |
_private.Mathlib.FieldTheory.IntermediateField.Adjoin.Basic.0.IntermediateField.adjoin_simple_isCompactElement._simp_1_2 | Mathlib.FieldTheory.IntermediateField.Adjoin.Basic | ∀ {F : Type u_1} [inst : Field F] {E : Type u_2} [inst_1 : Field E] [inst_2 : Algebra F E] {α : E}
{K : IntermediateField F E}, (F⟮α⟯ ≤ K) = (α ∈ K) | null | false |
_private.Mathlib.Data.Multiset.Filter.0.Multiset.filter_attach'._simp_1_2 | Mathlib.Data.Multiset.Filter | ∀ {α : Sort u_1} {p : α → Prop} {b : Prop}, (∃ x, p x ∧ b) = ((∃ x, p x) ∧ b) | null | false |
_private.Lean.Meta.Tactic.Simp.Arith.Int.Basic.0.Int.Internal.Linear.Poly.toExpr.go._f | Lean.Meta.Tactic.Simp.Arith.Int.Basic | (a : Int.Internal.Linear.Poly) →
Int.Internal.Linear.Poly.below (motive := fun a => Option Int.Internal.Linear.Expr → Int.Internal.Linear.Expr) a →
Option Int.Internal.Linear.Expr → Int.Internal.Linear.Expr | null | false |
Finsupp.DegLex.single_antitone | Mathlib.Data.Finsupp.MonomialOrder.DegLex | ∀ {α : Type u_1} [inst : LinearOrder α], Antitone fun a => toDegLex fun₀ | a => 1 | null | true |
_private.Mathlib.CategoryTheory.Monoidal.Preadditive.0.CategoryTheory.instPreservesFiniteBiproductsTensorLeft._simp_3 | Mathlib.CategoryTheory.Monoidal.Preadditive | ∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.MonoidalCategory C] (X : C)
{Y₁ Y₂ : C} (f : Y₁ ⟶ Y₂),
CategoryTheory.MonoidalCategoryStruct.whiskerLeft X f =
CategoryTheory.MonoidalCategoryStruct.tensorHom (CategoryTheory.CategoryStruct.id X) f | null | false |
compl_unique._to_dual_1 | Mathlib.Order.Heyting.Basic | ∀ {α : Type u_2} [inst : CoheytingAlgebra α] {a b : α}, a ⊔ b = ⊤ → a ⊓ b = ⊥ → ￢a = b | null | false |
Module.FaithfullyFlat.subsingleton_tensorProduct_iff_right | Mathlib.RingTheory.Flat.FaithfullyFlat.Basic | ∀ (R : Type u) (M : Type v) [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] {N : Type u_1}
[inst_3 : AddCommGroup N] [inst_4 : Module R N] [Module.FaithfullyFlat R M],
Subsingleton (TensorProduct R M N) ↔ Subsingleton N | null | true |
_private.Batteries.Data.Array.Merge.0.Array.mergeDedupWith.go._unary | Batteries.Data.Array.Merge | {α : Type u_1} → [ord : Ord α] → Array α → Array α → (α → α → α) → (_ : Array α) ×' (_ : ℕ) ×' ℕ → Array α | Auxiliary definition for `mergeDedupWith`. | false |
Lean.Doc.State.openDecls | Lean.Elab.DocString | Lean.Doc.State → List Lean.OpenDecl | The set of open declarations presently in force.
The `MonadLift TermElabM DocM` instance runs the lifted action in a context where these open
declarations are used, so elaboration commands that mutate this state cause it to take effect in
subsequent commands.
| true |
aeSeq.measurable | Mathlib.MeasureTheory.Function.AEMeasurableSequence | ∀ {ι : Sort u_1} {α : Type u_2} {β : Type u_3} [inst : MeasurableSpace α] [inst_1 : MeasurableSpace β] {f : ι → α → β}
{μ : MeasureTheory.Measure α} (hf : ∀ (i : ι), AEMeasurable (f i) μ) (p : α → (ι → β) → Prop) (i : ι),
Measurable (aeSeq hf p i) | null | true |
Function.argmin._proof_1 | Mathlib.Order.WellFounded | ∀ {α : Type u_1} {β : Type u_2} (f : α → β) [inst : LT β] [WellFoundedLT β],
WellFounded (InvImage (fun x1 x2 => x1 < x2) f) | null | false |
Finset.le_card_mul_mul_mulEnergy | Mathlib.Combinatorics.Additive.Energy | ∀ {α : Type u_1} [inst : DecidableEq α] [inst_1 : Mul α] (s t : Finset α),
s.card ^ 2 * t.card ^ 2 ≤ (s * t).card * s.mulEnergy t | null | true |
chartAt | Mathlib.Geometry.Manifold.ChartedSpace | (H : Type u_4) →
[inst : TopologicalSpace H] →
{M : Type u_5} → [inst_1 : TopologicalSpace M] → [ChartedSpace H M] → M → OpenPartialHomeomorph M H | The preferred chart at a point `x` in a charted space `M`. | true |
RestrictedProduct.instMonoidCoeOfSubmonoidClass._proof_1 | Mathlib.Topology.Algebra.RestrictedProduct.Basic | ∀ {ι : Type u_3} (R : ι → Type u_2) {S : ι → Type u_1} [inst : (i : ι) → SetLike (S i) (R i)]
[inst_1 : (i : ι) → Monoid (R i)] [∀ (i : ι), SubmonoidClass (S i) (R i)] (i : ι), MulMemClass (S i) (R i) | null | false |
_private.Mathlib.MeasureTheory.Measure.Portmanteau.0.MeasureTheory.FiniteMeasure.limsup_measure_closed_le_of_tendsto._simp_1_1 | Mathlib.MeasureTheory.Measure.Portmanteau | ∀ {α : Type u} [inst : LE α] [inst_1 : OrderBot α] {a : α}, (⊥ ≤ a) = True | null | false |
AddUnits.continuousVAdd | Mathlib.Topology.Algebra.MulAction | ∀ {M : Type u_1} {X : Type u_2} [inst : TopologicalSpace M] [inst_1 : TopologicalSpace X] [inst_2 : AddMonoid M]
[inst_3 : AddAction M X] [ContinuousVAdd M X], ContinuousVAdd (AddUnits M) X | null | true |
FixedDetMatrices.instMulActionSpecialLinearGroupFixedDetMatrix._proof_3 | Mathlib.LinearAlgebra.Matrix.FixedDetMatrices | ∀ (n : Type u_1) [inst : DecidableEq n] [inst_1 : Fintype n] (R : Type u_2) [inst_2 : CommRing R] (m : R)
(b : FixedDetMatrix n R m), 1 • b = b | null | false |
Subring.toAddSubgroup_strictMono | Mathlib.Algebra.Ring.Subring.Basic | ∀ {R : Type u} [inst : NonAssocRing R], StrictMono Subring.toAddSubgroup | null | true |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.