name stringlengths 2 347 | module stringlengths 6 90 | type stringlengths 1 5.42M | docString stringlengths 0 11k ⌀ | allowCompletion bool 2
classes |
|---|---|---|---|---|
_private.Mathlib.Algebra.Homology.HomotopyCategory.Plus.0.HomotopyCategory.instIsStableUnderShiftIntUpPlus._proof_1 | Mathlib.Algebra.Homology.HomotopyCategory.Plus | ∀ (n q : ℤ), n + (q - n) = q | null | false |
AlgebraicGeometry.Spec.sheafedSpaceMap._proof_1 | Mathlib.AlgebraicGeometry.Spec | ∀ {R S : CommRingCat} (f : R ⟶ S)
{x x_1 : (TopologicalSpace.Opens ↑↑(AlgebraicGeometry.Spec.sheafedSpaceObj R).toPresheafedSpace)ᵒᵖ} (x_2 : x ⟶ x_1),
CategoryTheory.CategoryStruct.comp ((AlgebraicGeometry.Spec.sheafedSpaceObj R).presheaf.map x_2)
(CommRingCat.ofHom
(AlgebraicGeometry.StructureSheaf.c... | null | false |
UInt32.ofFin_rev | Init.Data.UInt.Bitwise | ∀ (a : Fin UInt32.size), UInt32.ofFin a.rev = ~~~UInt32.ofFin a | null | true |
CategoryTheory.SpectralSequence.pageXIsoOfEq._auto_1 | Mathlib.Algebra.Homology.SpectralSequence.Basic | Lean.Syntax | null | false |
Aesop.Check.mk._flat_ctor | Aesop.Check | Lean.Option Bool → Aesop.Check | null | false |
Array.mem_of_getElem? | Init.Data.Array.Lemmas | ∀ {α : Type u_1} {xs : Array α} {i : ℕ} {a : α}, xs[i]? = some a → a ∈ xs | null | true |
_private.Mathlib.Algebra.ContinuedFractions.ConvergentsEquiv.0.GenContFract.succ_nth_conv_eq_squashGCF_nth_conv._proof_1_5 | Mathlib.Algebra.ContinuedFractions.ConvergentsEquiv | ∀ {K : Type u_1} {g : GenContFract K} [inst : Field K] (a b : K),
b ≠ 0 →
∀ (n' : ℕ) (pa pb : K),
((pb + a / b) * (g.contsAux (n' + 1)).a + pa * (g.contsAux n').a) /
((pb + a / b) * (g.contsAux (n' + 1)).b + pa * (g.contsAux n').b) =
(b * (pb * (g.contsAux (n' + 1)).a + pa * (g.contsAux n'... | null | false |
ContinuousOrderHom.instFunLike._proof_1 | Mathlib.Topology.Order.Hom.Basic | ∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : Preorder α] [inst_2 : TopologicalSpace β]
[inst_3 : Preorder β] (f g : α →Co β), (fun f => f.toFun) f = (fun f => f.toFun) g → f = g | null | false |
Rep.FiniteCyclicGroup.coinvariantsTensorResolutionIso._proof_2 | Mathlib.RepresentationTheory.Homological.GroupHomology.FiniteCyclic | ∀ {k G : Type u_1} [inst : CommRing k] [inst_1 : CommGroup G],
CategoryTheory.Limits.HasZeroObject (Rep.{u_1, u_1, u_1} k G) | null | false |
Lean.Grind.CommRing.Expr.toPolyS.match_4.congr_eq_3 | Init.Grind.Ring.CommSemiringAdapter | ∀ (motive : Lean.Grind.CommRing.Expr → Sort u_1) (x : Lean.Grind.CommRing.Expr)
(h_1 : (n : ℤ) → motive (Lean.Grind.CommRing.Expr.num n))
(h_2 : (x : Lean.Grind.CommRing.Var) → motive (Lean.Grind.CommRing.Expr.var x))
(h_3 : (a b : Lean.Grind.CommRing.Expr) → motive (a.add b))
(h_4 : (a b : Lean.Grind.CommRing.... | null | true |
NormedAddGroupHom.ext | Mathlib.Analysis.Normed.Group.Hom | ∀ {V₁ : Type u_2} {V₂ : Type u_3} [inst : SeminormedAddCommGroup V₁] [inst_1 : SeminormedAddCommGroup V₂]
{f g : NormedAddGroupHom V₁ V₂}, (∀ (x : V₁), f x = g x) → f = g | null | true |
Set.Icc_subset_Icc_iff | Mathlib.Order.Interval.Set.Basic | ∀ {α : Type u_1} [inst : Preorder α] {a₁ a₂ b₁ b₂ : α}, a₁ ≤ b₁ → (Set.Icc a₁ b₁ ⊆ Set.Icc a₂ b₂ ↔ a₂ ≤ a₁ ∧ b₁ ≤ b₂) | null | true |
Lean.Literal.natVal.sizeOf_spec | Lean.Expr | ∀ (val : ℕ), sizeOf (Lean.Literal.natVal val) = 1 + sizeOf val | null | true |
AddSubgroup.fintypeOfIndexNeZero.eq_1 | Mathlib.GroupTheory.Index | ∀ {G : Type u_1} [inst : AddGroup G] {H : AddSubgroup G} (hH : H.index ≠ 0),
AddSubgroup.fintypeOfIndexNeZero hH = Fintype.ofFinite (G ⧸ H) | null | true |
Lean.Elab.Tactic.Conv.evalReduce | Lean.Elab.Tactic.Conv.Basic | Lean.Elab.Tactic.Tactic | null | true |
_private.Lean.Meta.Basic.0.Lean.Meta.withExistingLocalDeclsImp | Lean.Meta.Basic | {α : Type} → List Lean.LocalDecl → Lean.MetaM α → Lean.MetaM α | null | true |
AlgebraicGeometry.ExistsHomHomCompEqCompAux.mk | 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) →
CategoryTh... | null | true |
Array.ne_of_not_mem_push | Init.Data.Array.Lemmas | ∀ {α : Type u_1} {a b : α} {xs : Array α}, a ∉ xs.push b → a ≠ b | null | true |
CochainComplex.HomComplex.Cochain.rightShift.congr_simp | Mathlib.Algebra.Homology.HomotopyCategory.HomComplexShift | ∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Preadditive C]
{K L : CochainComplex C ℤ} {n : ℤ} (γ γ_1 : CochainComplex.HomComplex.Cochain K L n),
γ = γ_1 →
∀ (a n' : ℤ) (hn' : n' + a = n) (T : CochainComplex.HomComplex.Triplet n'),
γ.rightShift a n' hn' T = γ_1.rightSh... | null | true |
Lean.Language.SnapshotTask.cancelRec._unsafe_rec | Lean.Language.Basic | {α : Type} → [Lean.Language.ToSnapshotTree α] → Lean.Language.SnapshotTask α → BaseIO Unit | null | false |
CategoryTheory.ShortComplex.RightHomologyData.ofEpiOfIsIsoOfMono'_p | Mathlib.Algebra.Homology.ShortComplex.RightHomology | ∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
{S₁ S₂ : CategoryTheory.ShortComplex C} (φ : S₁ ⟶ S₂) (h : S₂.RightHomologyData) [inst_2 : CategoryTheory.Epi φ.τ₁]
[inst_3 : CategoryTheory.IsIso φ.τ₂] [inst_4 : CategoryTheory.Mono φ.τ₃],
(Category... | null | true |
_private.Mathlib.Order.KrullDimension.0.Order.height_eq_coe_iff_minimal_le_height._simp_1_1 | Mathlib.Order.KrullDimension | ∀ {α : Type u_2} {P : α → Prop} {x : α} [inst : Preorder α], Minimal P x = (P x ∧ ∀ ⦃y : α⦄, y < x → ¬P y) | null | false |
CategoryTheory.Functor.splitMonoBiprodComparison'_retraction | Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts | ∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
[inst_2 : CategoryTheory.Limits.HasZeroMorphisms C] [inst_3 : CategoryTheory.Limits.HasZeroMorphisms D]
(F : CategoryTheory.Functor C D) (X Y : C) [inst_4 : CategoryTheory.Limits.HasBinaryBiproduc... | null | true |
Std.DTreeMap.Const.foldr_eq_foldr_toArray | Std.Data.DTreeMap.Lemmas | ∀ {α : Type u} {cmp : α → α → Ordering} {δ : Type w} {β : Type v} {t : Std.DTreeMap α (fun x => β) cmp}
{f : α → β → δ → δ} {init : δ},
Std.DTreeMap.foldr f init t = Array.foldr (fun a b => f a.1 a.2 b) init (Std.DTreeMap.Const.toArray t) | null | true |
Monoid.CoprodI.Word.cons | Mathlib.GroupTheory.CoprodI | {ι : Type u_1} →
{M : ι → Type u_2} →
[inst : (i : ι) → Monoid (M i)] →
{i : ι} → (m : M i) → (w : Monoid.CoprodI.Word M) → w.fstIdx ≠ some i → m ≠ 1 → Monoid.CoprodI.Word M | Construct a new `Word` without any reduction. The underlying list of
`cons m w _ _` is `⟨_, m⟩::w` | true |
HomologicalComplex.Hom.isoOfComponents._proof_1 | Mathlib.Algebra.Homology.HomologicalComplex | ∀ {ι : Type u_3} {V : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} V]
[inst_1 : CategoryTheory.Limits.HasZeroMorphisms V] {c : ComplexShape ι} {C₁ C₂ : HomologicalComplex V c}
(f : (i : ι) → C₁.X i ≅ C₂.X i) (i j : ι),
CategoryTheory.CategoryStruct.comp (f i).inv (C₁.d i j) =
CategoryTheory.CategorySt... | null | false |
Function.Periodic.sub | Mathlib.Algebra.Ring.Periodic | ∀ {α : Type u_1} {β : Type u_2} {f g : α → β} {c : α} [inst : Add α] [inst_1 : Sub β],
Function.Periodic f c → Function.Periodic g c → Function.Periodic (f - g) c | null | true |
EisensteinSeries.norm_le_tsum_norm | Mathlib.NumberTheory.ModularForms.EisensteinSeries.IsBoundedAtImInfty | ∀ (N : ℕ) (a : Fin 2 → ZMod N) (k : ℤ),
3 ≤ k → ∀ (z : UpperHalfPlane), ‖eisensteinSeries a k z‖ ≤ ∑' (x : Fin 2 → ℤ), ‖EisensteinSeries.eisSummand k x z‖ | The norm of the restricted sum is less than the full sum of the norms. | true |
_private.Mathlib.GroupTheory.FreeGroup.Reduce.0.FreeGroup.idxOf_toWord_mul_of_eq._proof_1_5 | Mathlib.GroupTheory.FreeGroup.Reduce | ∀ {α : Type u_1} [inst : DecidableEq α] {a : α} (x : FreeGroup α) {b : α × Bool},
b ∈ x.toWord → List.idxOf b (x.toWord.concat (a, true)) = List.idxOf b x.toWord | null | false |
ContinuousAlternatingMap.curryLeftLI_apply | Mathlib.Analysis.Normed.Module.Alternating.Curry | ∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {n : ℕ}
(f : E [⋀^Fin (n + 1)]→L[𝕜] F), ContinuousAlternatingMap.curryLeftLI f = f.curryLeft | null | true |
_private.Mathlib.CategoryTheory.Filtered.Small.0.CategoryTheory.IsFiltered.FilteredClosureSmall.InductiveStep._sizeOf_inst | Mathlib.CategoryTheory.Filtered.Small | {C : Type u} →
{inst : CategoryTheory.Category.{v, u} C} →
(n : ℕ) →
(X : (k : ℕ) → k < n → (t : Type (max v w)) × (t → C)) →
[SizeOf C] → SizeOf (CategoryTheory.IsFiltered.FilteredClosureSmall.InductiveStep✝ n X) | null | false |
TensorProduct.LieModule.liftLie._proof_1 | Mathlib.Algebra.Lie.TensorProduct | ∀ (R : Type u_1) [inst : CommRing R] (L : Type u_2) (M : Type u_4) (N : Type u_5) (P : Type u_3) [inst_1 : LieRing L]
[inst_2 : LieAlgebra R L] [inst_3 : AddCommGroup M] [inst_4 : Module R M] [inst_5 : LieRingModule L M]
[inst_6 : LieModule R L M] [inst_7 : AddCommGroup N] [inst_8 : Module R N] [inst_9 : LieRingMod... | null | false |
Vector.tail_eq_of_zero | Batteries.Data.Vector.Lemmas | ∀ {α : Type u_1} {v : Vector α 0}, v.tail = #v[] | null | true |
MeasureTheory.lintegral_withDensity_eq_lintegral_mul_non_measurable | Mathlib.MeasureTheory.Measure.WithDensity | ∀ {α : Type u_1} {m0 : MeasurableSpace α} (μ : MeasureTheory.Measure α) {f : α → ENNReal},
Measurable f →
(∀ᵐ (x : α) ∂μ, f x < ⊤) → ∀ (g : α → ENNReal), ∫⁻ (a : α), g a ∂μ.withDensity f = ∫⁻ (a : α), (f * g) a ∂μ | null | true |
Std.ExtHashMap.getElem_filterMap | Std.Data.ExtHashMap.Lemmas | ∀ {α : Type u} {β : Type v} {γ : Type w} {x : BEq α} {x_1 : Hashable α} {m : Std.ExtHashMap α β} [inst : EquivBEq α]
[inst_1 : LawfulHashable α] {f : α → β → Option γ} {k : α} {h : k ∈ Std.ExtHashMap.filterMap f m},
(Std.ExtHashMap.filterMap f m)[k] = (f (m.getKey k ⋯) m[k]).get ⋯ | null | true |
nonUnitalSubalgebraOfNonUnitalSubring | Mathlib.Algebra.Algebra.NonUnitalSubalgebra | {R : Type u_1} → [inst : NonUnitalNonAssocRing R] → NonUnitalSubring R → NonUnitalSubalgebra ℤ R | A non-unital subring is a non-unital `ℤ`-subalgebra. | true |
_private.Mathlib.Tactic.Linter.TextBased.0.Mathlib.Linter.TextBased.UnicodeLinter.findBadUnicodeAux.match_1.splitter | Mathlib.Tactic.Linter.TextBased | (motive : Option Char → Sort u_1) →
(x : Option Char) → (Unit → motive none) → ((cₙ : Char) → motive (some cₙ)) → motive x | null | true |
ValuativeRel.ValueGroupWithZero.mk_eq_div | Mathlib.RingTheory.Valuation.ValuativeRel.Basic | ∀ {R : Type u_2} [inst : Ring R] [inst_1 : ValuativeRel R] (r : R) (s : ↥(ValuativeRel.posSubmonoid R)),
ValuativeRel.ValueGroupWithZero.mk r s = (ValuativeRel.valuation R) r / (ValuativeRel.valuation R) ↑s | null | true |
_private.Mathlib.NumberTheory.Pell.0.Pell.exists_of_not_isSquare._proof_1_7 | Mathlib.NumberTheory.Pell | (1 + 1).AtLeastTwo | null | false |
Sublattice.isSublattice | Mathlib.Order.Sublattice | ∀ {α : Type u_2} [inst : Lattice α] (L : Sublattice α), IsSublattice ↑L | null | true |
SemigroupAction.mk | Mathlib.Algebra.Group.Action.Defs | {α : Type u_9} →
{β : Type u_10} →
[inst : Semigroup α] → [toSMul : SMul α β] → (∀ (x y : α) (b : β), (x * y) • b = x • y • b) → SemigroupAction α β | null | true |
_private.Mathlib.Analysis.Normed.Operator.NormedSpace.0.ContinuousLinearMap.opNNNorm_linearIsometryEquiv_comp._simp_1_1 | Mathlib.Analysis.Normed.Operator.NormedSpace | ∀ {𝕜 : Type u_1} {𝕜₂ : Type u_2} {E : Type u_4} {F : Type u_5} [inst : NontriviallyNormedField 𝕜]
[inst_1 : NontriviallyNormedField 𝕜₂] [inst_2 : SeminormedAddCommGroup E] [inst_3 : SeminormedAddCommGroup F]
[inst_4 : NormedSpace 𝕜 E] [inst_5 : NormedSpace 𝕜₂ F] {σ₁₂ : 𝕜 →+* 𝕜₂} [inst_6 : RingHomIsometric σ... | null | false |
_private.Mathlib.Algebra.Homology.ShortComplex.Ab.0.CategoryTheory.ShortComplex.ShortExact.ab_finite_iff.match_1_1 | Mathlib.Algebra.Homology.ShortComplex.Ab | ∀ {S : CategoryTheory.ShortComplex Ab} (motive : Finite ↑S.X₁ ∧ Finite ↑S.X₃ → Prop) (x : Finite ↑S.X₁ ∧ Finite ↑S.X₃),
(∀ (left : Finite ↑S.X₁) (right : Finite ↑S.X₃), motive ⋯) → motive x | null | false |
_private.Lean.Meta.WHNF.0.Lean.Meta.smartUnfoldingReduce?.goMatch._sparseCasesOn_1 | Lean.Meta.WHNF | {motive : Lean.Meta.ReduceMatcherResult → Sort u} →
(t : Lean.Meta.ReduceMatcherResult) →
((val : Lean.Expr) → motive (Lean.Meta.ReduceMatcherResult.reduced val)) →
((val : Lean.Expr) → motive (Lean.Meta.ReduceMatcherResult.stuck val)) →
(Nat.hasNotBit 3 t.ctorIdx → motive t) → motive t | null | false |
_private.Mathlib.FieldTheory.LinearDisjoint.0.IntermediateField.LinearDisjoint.adjoin_rank_eq_rank_left_of_isAlgebraic.match_1_5 | Mathlib.FieldTheory.LinearDisjoint | ∀ {F : Type u_2} {E : Type u_1} [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] {L : Type u_3}
[inst_3 : Field L] [inst_4 : Algebra F L] [inst_5 : Algebra L E] [inst_6 : IsScalarTower F L E] (x : E),
let L' := (IsScalarTower.toAlgHom F L E).range;
∀ (motive : (∃ a, ∃ (b : a ∈ L'), (algebraMap (↥L') E) ... | null | false |
Std.DTreeMap.isEmpty_modify | Std.Data.DTreeMap.Lemmas | ∀ {α : Type u} {β : α → Type v} {cmp : α → α → Ordering} {t : Std.DTreeMap α β cmp} [Std.TransCmp cmp]
[inst : Std.LawfulEqCmp cmp] {k : α} {f : β k → β k}, (t.modify k f).isEmpty = t.isEmpty | null | true |
_private.Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Lemmas.Expr.0.Std.Tactic.BVDecide.BVExpr.bitblast.go.match_17.eq_9 | Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Lemmas.Expr | ∀ (motive : (w : ℕ) → Std.Tactic.BVDecide.BVExpr w → Sort u_1) (w n : ℕ) (lhs : Std.Tactic.BVDecide.BVExpr w)
(rhs : Std.Tactic.BVDecide.BVExpr n) (h_1 : (w a : ℕ) → motive w (Std.Tactic.BVDecide.BVExpr.var a))
(h_2 : (w : ℕ) → (val : BitVec w) → motive w (Std.Tactic.BVDecide.BVExpr.const val))
(h_3 :
(w : ℕ)... | null | true |
ContinuousLinearMap.toPseudoMetricSpace._proof_1 | Mathlib.Analysis.Normed.Operator.Basic | ∀ {𝕜₂ : Type u_1} {F : Type u_2} [inst : SeminormedAddCommGroup F] [inst_1 : NontriviallyNormedField 𝕜₂]
[inst_2 : NormedSpace 𝕜₂ F], ContinuousConstSMul 𝕜₂ F | null | false |
Set.biUnion_singleton | Mathlib.Data.Set.Lattice.Bounded | ∀ {α : Type u_1} {β : Type u_2} (a : α) (s : α → Set β), ⋃ x ∈ {a}, s x = s a | null | true |
ULiftable.refl | Mathlib.Control.ULiftable | (f : Type u₀ → Type u₁) → [inst : Functor f] → [LawfulFunctor f] → ULiftable f f | null | true |
GT.gt.lt | Mathlib.Order.Basic | ∀ {α : Type u_2} [inst : LT α] {a b : α}, a > b → b < a | null | true |
MulChar.commGroup._proof_5 | Mathlib.NumberTheory.MulChar.Basic | ∀ {R : Type u_1} [inst : CommMonoid R] {R' : Type u_2} [inst_1 : CommMonoidWithZero R'] (a : MulChar R R'), a ^ 0 = 1 | null | false |
CochainComplex.mappingCone.shiftTriangleIso._proof_2 | Mathlib.Algebra.Homology.HomotopyCategory.Pretriangulated | ∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] [inst_1 : CategoryTheory.Preadditive C]
[inst_2 : CategoryTheory.Limits.HasBinaryBiproducts C] {K L : CochainComplex C ℤ} (φ : K ⟶ L) (n : ℤ),
CategoryTheory.CategoryStruct.comp
((CategoryTheory.Pretriangulated.Triangle.shiftFunctor (CochainComple... | null | false |
Lean.Meta.AuxLemmaKey._sizeOf_inst | Lean.Meta.Tactic.AuxLemma | SizeOf Lean.Meta.AuxLemmaKey | null | false |
Differentiable.sub._simp_2 | Mathlib.Analysis.Calculus.FDeriv.Add | ∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {F : Type u_3} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {f g : E → F},
Differentiable 𝕜 f → Differentiable 𝕜 g → Differentiable 𝕜 (f - g) = True | null | false |
Lean.Elab.Tactic.TacticParsedSnapshot.ctorIdx | Lean.Elab.Term.TermElabM | Lean.Elab.Tactic.TacticParsedSnapshot → ℕ | null | false |
EquicontinuousWithinAt.eq_1 | Mathlib.Topology.UniformSpace.Equicontinuity | ∀ {ι : Type u_1} {X : Type u_3} {α : Type u_6} [tX : TopologicalSpace X] [uα : UniformSpace α] (F : ι → X → α)
(S : Set X) (x₀ : X),
EquicontinuousWithinAt F S x₀ = ∀ U ∈ uniformity α, ∀ᶠ (x : X) in nhdsWithin x₀ S, ∀ (i : ι), (F i x₀, F i x) ∈ U | null | true |
Std.DTreeMap.Internal.Impl.minKey!_insertIfNew_le_minKey! | Std.Data.DTreeMap.Internal.Lemmas | ∀ {α : Type u} {β : α → Type v} {instOrd : Ord α} {t : Std.DTreeMap.Internal.Impl α β} [Std.TransOrd α]
[inst : Inhabited α] (h : t.WF),
t.isEmpty = false →
∀ {k : α} {v : β k}, (compare (Std.DTreeMap.Internal.Impl.insertIfNew k v t ⋯).impl.minKey! t.minKey!).isLE = true | null | true |
Filter.liminf_eq_iSup_iInf | Mathlib.Order.LiminfLimsup | ∀ {α : Type u_1} {β : Type u_2} [inst : CompleteLattice α] {f : Filter β} {u : β → α},
Filter.liminf u f = ⨆ s ∈ f, ⨅ a ∈ s, u a | In a complete lattice, the liminf of a function is the infimum over sets `s` in the filter
of the supremum of the function over `s` | true |
_private.Lean.Environment.0.Lean.Kernel.Environment.Diagnostics.recordUnfold.match_1 | Lean.Environment | (motive : Option ℕ → Sort u_1) → (x : Option ℕ) → ((c : ℕ) → motive (some c)) → ((x : Option ℕ) → motive x) → motive x | null | false |
Tactic.ComputeAsymptotics.MultiseriesExpansion.monomialRpow_seq | Mathlib.Tactic.ComputeAsymptotics.Multiseries.Basic | ∀ {basis_hd : ℝ → ℝ} {basis_tl : Tactic.ComputeAsymptotics.Basis} {n : ℕ} {r : ℝ},
(Tactic.ComputeAsymptotics.MultiseriesExpansion.monomialRpow (basis_hd :: basis_tl) n r).seq =
Tactic.ComputeAsymptotics.MultiseriesExpansion.Multiseries.monomialRpow basis_hd basis_tl n r | null | true |
AlgebraicGeometry.Scheme.Hom.copyBase._proof_1 | Mathlib.AlgebraicGeometry.Scheme | ∀ {X Y : AlgebraicGeometry.Scheme} (f : X.Hom Y) (g : ↥X → ↥Y) (h : ⇑f = g),
f.base = TopCat.ofHom { toFun := g, continuous_toFun := ⋯ } | null | false |
HomotopicalAlgebra.Cylinder.ofFactorizationData_i₀ | Mathlib.AlgebraicTopology.ModelCategory.Cylinder | ∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : HomotopicalAlgebra.ModelCategory C] {A : C}
(h :
(HomotopicalAlgebra.cofibrations C).MapFactorizationData (HomotopicalAlgebra.trivialFibrations C)
(CategoryTheory.Limits.codiag A)),
(HomotopicalAlgebra.Cylinder.ofFactorizationData h).i₀ =
... | null | true |
_private.Init.Data.Range.Polymorphic.Lemmas.0.Std.Rci.succ_mem_succ_succ_iff._simp_1_1 | Init.Data.Range.Polymorphic.Lemmas | ∀ {α : Type u} [inst : LE α] [inst_1 : Std.PRange.UpwardEnumerable α] [Std.PRange.LinearlyUpwardEnumerable α]
[Std.PRange.LawfulUpwardEnumerableLE α] [inst_4 : Std.PRange.InfinitelyUpwardEnumerable α] [Std.Rxi.IsAlwaysFinite α]
[Std.PRange.LawfulUpwardEnumerable α] {lo a : α},
(a ∈ Std.PRange.succ lo...*) = ∃ a',... | null | false |
BitVec.sdivOverflow.eq_1 | Init.Data.BitVec.Lemmas | ∀ {w : ℕ} (x y : BitVec w),
x.sdivOverflow y = (decide (2 ^ (w - 1) ≤ x.toInt / y.toInt) || decide (x.toInt / y.toInt < -2 ^ (w - 1))) | null | true |
Submodule.colon._proof_1 | Mathlib.RingTheory.Ideal.Colon | ∀ {R : Type u_2} {M : Type u_1} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
(N : Submodule R M), ↑N + ↑N = ↑N | null | false |
_private.Batteries.Data.Array.Pairwise.0.Array.pairwise_iff_getElem._simp_1_1 | Batteries.Data.Array.Pairwise | ∀ {α : Type u_1} {R : α → α → Prop} {l : List α},
List.Pairwise R l = ∀ (i j : ℕ) (_hi : i < l.length) (_hj : j < l.length), i < j → R l[i] l[j] | null | false |
SetLike.GradeZero.instSemiring._aux_5 | Mathlib.Algebra.DirectSum.Internal | {ι : Type u_3} →
{σ : Type u_2} →
{R : Type u_1} →
[inst : Semiring R] →
[inst_1 : AddMonoid ι] →
[inst_2 : SetLike σ R] → [AddSubmonoidClass σ R] → (A : ι → σ) → [SetLike.GradedMonoid A] → ℕ → ↥(A 0) | null | false |
_private.Init.Data.ToString.Name.0.Lean.Name.toStringWithToken.maybePseudoSyntax.match_1 | Init.Data.ToString.Name | (motive : Lean.Name → Sort u_1) →
(x : Lean.Name) → ((pre : Lean.Name) → (s : String) → motive (pre.str s)) → ((x : Lean.Name) → motive x) → motive x | null | false |
_private.Mathlib.RingTheory.Polynomial.Nilpotent.0.Polynomial.not_isUnit_of_natDegree_pos_of_isReduced._simp_1_1 | Mathlib.RingTheory.Polynomial.Nilpotent | ∀ {R : Type u_3} {x : R} [inst : MonoidWithZero R] [IsReduced R], IsNilpotent x = (x = 0) | null | false |
Aesop.RuleState.enqueueRawHyp | Aesop.Forward.State | Aesop.RawHyp → Aesop.PremiseIndex → Aesop.RuleState → Aesop.RuleState | Add a hypothesis or pattern substitution to the rule state. The
hypothesis's type does not necessarily need to match the given premise. If it
does not, this is detected by `update` and the hyp is not added. | true |
Lean.Parser.ParserState.keepNewError | Lean.Parser.Basic | Lean.Parser.ParserState → ℕ → Lean.Parser.ParserState | null | true |
SSet.Subcomplex.Pairing.instIsRegularOp | Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.Op | ∀ {X : SSet} {A : X.Subcomplex} (P : A.Pairing) [P.IsRegular], P.op.IsRegular | null | true |
Lean.Grind.Semiring.pow_add_congr | Init.Grind.Ring.Basic | ∀ {α : Type u} [inst : Lean.Grind.Semiring α] (a r : α) (k k₁ k₂ : ℕ), k = k₁ + k₂ → a ^ k₁ * a ^ k₂ = r → a ^ k = r | null | true |
_private.Mathlib.Data.Nat.Nth.0.Nat.le_nth_of_monotoneOn_of_surjOn._proof_1_4 | Mathlib.Data.Nat.Nth | ∀ {p : ℕ → Prop} (f : ℕ → ℕ) (n : ℕ),
((∀ (hf : (Set.ofPred p).Finite), n < hf.toFinset.card) → f n ≤ Nat.nth p n) →
(∀ (hf : (Set.ofPred p).Finite), n + 1 < hf.toFinset.card) → ∀ (m : ℕ), (∀ k < n + 1, Nat.nth p k < f m) → f n < f m | null | false |
CategoryTheory.Presieve.BindStruct.mk.sizeOf_spec | Mathlib.CategoryTheory.Sites.Sieves.Presieve | ∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X : C} {S : CategoryTheory.Presieve X}
{R : ⦃Y : C⦄ → ⦃f : Y ⟶ X⦄ → S f → CategoryTheory.Presieve Y} {Z : C} {h : Z ⟶ X} [inst_1 : SizeOf C]
[inst_2 : ⦃Y : C⦄ → (a : Y ⟶ X) → SizeOf (S a)]
[inst_3 : ⦃Y : C⦄ → ⦃f : Y ⟶ X⦄ → (a : S f) → ⦃Y_1 : C⦄ → (a_1 :... | null | true |
HomologicalComplex.Hom.isoOfComponents | 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} →
{C₁ C₂ : HomologicalComplex V c} →
(f : (i : ι) → C₁.X i ≅ C₂.X i) →
autoParam
(∀ (i j : ι),
... | Construct an isomorphism of chain complexes from isomorphism of the objects
which commute with the differentials. | true |
FirstOrder.Language.BoundedFormula.IsQF.below | Mathlib.ModelTheory.Complexity | {L : FirstOrder.Language} →
{α : Type u'} →
{n : ℕ} → {motive : (a : L.BoundedFormula α n) → a.IsQF → Prop} → {a : L.BoundedFormula α n} → a.IsQF → Prop | null | true |
_private.Mathlib.RingTheory.Valuation.ValuativeRel.Basic.0.ValuativeRel.ValueGroupWithZero.embed._simp_14 | Mathlib.RingTheory.Valuation.ValuativeRel.Basic | ∀ {M₀ : Type u_1} [inst : MonoidWithZero M₀] {a : M₀} [IsReduced M₀] (n : ℕ), a ≠ 0 → (a ^ n = 0) = False | null | false |
Lean.Elab.Term.ToDepElimPattern.Context.userName._default | Lean.Elab.Match | Lean.Name | null | false |
Matrix.transpose_hasOrthogonalCols_iff_hasOrthogonalRows._simp_1 | Mathlib.LinearAlgebra.Matrix.Orthogonal | ∀ {α : Type u_1} {n : Type u_2} {m : Type u_3} [inst : Mul α] [inst_1 : AddCommMonoid α] (A : Matrix m n α)
[inst_2 : Fintype n], A.transpose.HasOrthogonalCols = A.HasOrthogonalRows | null | false |
_private.Mathlib.RingTheory.Extension.Cotangent.BaseChange.0.Algebra.Extension.tensorCotangentOfFlat._proof_2 | Mathlib.RingTheory.Extension.Cotangent.BaseChange | ∀ {R : Type u_3} {S : Type u_4} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S]
(P : Algebra.Extension R S) (T : Type u_2) [inst_3 : CommRing T] [inst_4 : Algebra R T],
LinearMap.CompatibleSMul (Ideal.map Algebra.TensorProduct.includeRight.toRingHom P.ker).Cotangent
P.baseChange.ker.Cotangent T... | null | false |
DirectSum.lie_of_same | Mathlib.Algebra.Lie.DirectSum | ∀ {ι : Type v} (L : ι → Type w) [inst : (i : ι) → LieRing (L i)] [inst_1 : DecidableEq ι] {i : ι} (x y : L i),
⁅(DirectSum.of L i) x, (DirectSum.of L i) y⁆ = (DirectSum.of L i) ⁅x, y⁆ | null | true |
NSMul.mk | Mathlib.Algebra.Group.Monoid | {M : Type u_2} → (ℕ → M → M) → NSMul M | null | true |
WithVal.instField | Mathlib.Topology.Algebra.Valued.WithVal | {R : Type u_1} →
{Γ₀ : Type u_2} →
[inst : LinearOrderedCommGroupWithZero Γ₀] → [inst_1 : Field R] → (v : Valuation R Γ₀) → Field (WithVal v) | null | true |
ContinuousGeneratedByCat.coe_of | Mathlib.Topology.Convenient.Category | ∀ {ι : Type t} {X : ι → Type u} [inst : (i : ι) → TopologicalSpace (X i)] (Y : Type v) [inst_1 : TopologicalSpace Y],
↑↧Y = Y | null | true |
SSet.Truncated.instCategoryHomotopyCategory._proof_8 | Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat | ∀ (V : SSet.Truncated 2),
autoParam
(∀ {X Y : V.HomotopyCategory} (f : X ⟶ Y),
CategoryTheory.CategoryStruct.comp f (CategoryTheory.CategoryStruct.id Y) = f)
CategoryTheory.Category.comp_id._autoParam | null | false |
_private.Mathlib.CategoryTheory.ComposableArrows.Basic.0._auto_282 | Mathlib.CategoryTheory.ComposableArrows.Basic | Lean.Syntax | null | false |
Nat.cast_mem_Ioi_iff | Mathlib.Order.Interval.Finset.Floor | ∀ {α : Type u_1} [inst : Semiring α] [inst_1 : LinearOrder α] [inst_2 : FloorSemiring α] {a : α} {n : ℕ},
0 ≤ a → (↑n ∈ Set.Ioi a ↔ n ∈ Set.Ioi ⌊a⌋₊) | null | true |
Int.Internal.Linear.Poly.append.eq_1 | Init.Data.Int.Linear | ∀ (p₂ : Int.Internal.Linear.Poly) (k : ℤ), (Int.Internal.Linear.Poly.num k).append p₂ = p₂.addConst k | null | true |
_private.Mathlib.Order.CountableSupClosed.0.countableInfClosure._proof_4 | Mathlib.Order.CountableSupClosed | ∀ {α : Type u_1} (A : Set α), ∀ i ∈ A, i ∈ A | null | false |
LinearMap.convIntrinsicStarRing._proof_4 | Mathlib.Algebra.Star.LinearMap | ∀ {R : Type u_3} {A : Type u_1} {C : Type u_2} [inst : CommSemiring R] [inst_1 : StarRing R]
[inst_2 : NonUnitalNonAssocSemiring A] [inst_3 : Module R A] [inst_4 : StarRing A] [inst_5 : StarModule R A]
[inst_6 : AddCommMonoid C] [inst_7 : Module R C] [inst_8 : StarAddMonoid C] [inst_9 : StarModule R C]
(r s : Wit... | null | false |
_private.Batteries.Data.Fin.Lemmas.0.Fin.findSome?_eq_none_iff._simp_1_3 | Batteries.Data.Fin.Lemmas | ∀ {n : ℕ} {P : Fin (n + 1) → Prop}, (∀ (i : Fin (n + 1)), P i) = (P 0 ∧ ∀ (i : Fin n), P i.succ) | null | false |
LinearMap.iterateKer._proof_1 | Mathlib.Algebra.Module.Submodule.Ker | ∀ {R : Type u_2} {M : Type u_1} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (f : M →ₗ[R] M)
(n m : ℕ), n ≤ m → ∀ x ∈ (fun n => (f ^ n).ker) n, x ∈ (fun n => (f ^ n).ker) m | null | false |
_private.Mathlib.Tactic.ClickSuggestions.FindPremises.0.Mathlib.Tactic.ClickSuggestions.blacklist.match_1 | Mathlib.Tactic.ClickSuggestions.FindPremises | (motive : Lean.Name → Sort u_1) →
(declName : Lean.Name) →
((pre : Lean.Name) → (s : String) → motive (pre.str s)) → ((x : Lean.Name) → motive x) → motive declName | null | false |
_private.Lean.Linter.MissingDocs.0.Lean.Linter.MissingDocs.docOptStatus | Lean.Linter.MissingDocs | Lean.Syntax → Lean.Syntax → optParam Bool false → Lean.Elab.Command.CommandElabM (Option Bool) | null | true |
SSet.stdSimplex.objMk₁._proof_6 | Mathlib.AlgebraicTopology.SimplicialSet.StdSimplexOne | NeZero ({ len := 1 }.len + 1) | null | false |
_private.Mathlib.MeasureTheory.Constructions.BorelSpace.Order.0.borel_eq_generateFrom_Ico._simp_1_1 | Mathlib.MeasureTheory.Constructions.BorelSpace.Order | ∀ {b a : Prop}, (∃ (_ : a), b) = (a ∧ b) | null | false |
List.maxIdxOn_lt_length | Init.Data.List.MinMaxIdx | ∀ {β : Type u_1} {α : Type u_2} [inst : LE β] [inst_1 : DecidableLE β] {f : α → β} {xs : List α} (h : xs ≠ []),
List.maxIdxOn f xs h < xs.length | null | true |
Mathlib.Tactic.GCongr.GCongrHyp._sizeOf_1 | Mathlib.Tactic.GCongr.Core | Mathlib.Tactic.GCongr.GCongrHyp → ℕ | null | false |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.