name stringlengths 2 347 | module stringlengths 6 90 | type stringlengths 1 5.67M | allowCompletion bool 2
classes |
|---|---|---|---|
_private.Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs.0.vectorSpan_add_self._proof_1_3 | Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs | ∀ (k : Type u_2) {V : Type u_1} [inst : Ring k] [inst_1 : AddCommGroup V] [inst_2 : Module k V] (s : Set V) (x : V),
(∃ x_1 ∈ vectorSpan k s, ∃ y ∈ s, x_1 + y = x) ↔ ∃ p₁ ∈ s, ∃ v ∈ vectorSpan k s, x = v + p₁ | false |
InfHom.dual._proof_3 | Mathlib.Order.Hom.Lattice | ∀ {α : Type u_1} {β : Type u_2} [inst : Min α] [inst_1 : Min β] (f : SupHom αᵒᵈ βᵒᵈ) (a b : αᵒᵈ),
f.toFun (a ⊔ b) = f.toFun a ⊔ f.toFun b | false |
_private.Mathlib.Data.List.Nodup.0.List.Nodup.ne_singleton_iff._simp_1_2 | Mathlib.Data.List.Nodup | ∀ {a b c : Prop}, (a ∧ (b ∨ c)) = (a ∧ b ∨ a ∧ c) | false |
CochainComplex.shiftEval_inv_app | Mathlib.Algebra.Homology.HomotopyCategory.Shift | ∀ (C : Type u) [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Preadditive C] (n i i' : ℤ)
(hi : n + i = i') (X : CochainComplex C ℤ),
(CochainComplex.shiftEval C n i i' hi).inv.app X = (HomologicalComplex.XIsoOfEq X ⋯).inv | true |
_private.Mathlib.Combinatorics.SimpleGraph.Walks.Decomp.0.SimpleGraph.Walk.getVert_lt_length_takeUntil_ne._proof_1_2 | Mathlib.Combinatorics.SimpleGraph.Walks.Decomp | ∀ {V : Type u_1} {G : SimpleGraph V} {v w : V} [inst : DecidableEq V] {n : ℕ} {p : G.Walk v w}
(h : p.getVert n ∈ p.support),
p.getVert n ∈ (p.takeUntil (p.getVert n) h).support.dropLast →
List.count (p.getVert n) ((p.takeUntil (p.getVert n) h).support.dropLast.concat (p.getVert n)) = 1 → False | false |
NonUnitalStarAlgHom.codRestrict._proof_1 | Mathlib.Algebra.Star.NonUnitalSubalgebra | ∀ {F : Type u_4} {R : Type u_2} {A : Type u_3} {B : Type u_1} [inst : CommSemiring R]
[inst_1 : NonUnitalNonAssocSemiring A] [inst_2 : Module R A] [inst_3 : Star A] [inst_4 : NonUnitalNonAssocSemiring B]
[inst_5 : Module R B] [inst_6 : Star B] [inst_7 : FunLike F A B] [inst_8 : NonUnitalAlgHomClass F R A B]
[Star... | false |
BitVec.ofNat_sub_ofNat_of_le | Init.Data.BitVec.Lemmas | ∀ {w : ℕ} (x y : ℕ), y < 2 ^ w → y ≤ x → BitVec.ofNat w x - BitVec.ofNat w y = BitVec.ofNat w (x - y) | true |
Algebra.mem_adjoin_of_map_mul | Mathlib.Algebra.Algebra.Subalgebra.Lattice | ∀ (R : Type uR) {A : Type uA} {B : Type uB} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Semiring B]
[inst_3 : Algebra R A] [inst_4 : Algebra R B] {s : Set A} {x : A} {f : A →ₗ[R] B},
(∀ (a₁ a₂ : A), f (a₁ * a₂) = f a₁ * f a₂) → x ∈ Algebra.adjoin R s → f x ∈ Algebra.adjoin R (⇑f '' (s ∪ {1})) | true |
Lean.Parser.Term.elabToSyntax.formatter | Lean.Elab.Term.TermElabM | Lean.PrettyPrinter.Formatter | true |
SaturatedSubmonoid.instSetLike | Mathlib.Algebra.Group.Submonoid.Saturation | (M : Type u_1) → [inst : MulOneClass M] → SetLike (SaturatedSubmonoid M) M | true |
ContinuousMap.HomotopyWith.instFunLike | Mathlib.Topology.Homotopy.Basic | {X : Type u} →
{Y : Type v} →
[inst : TopologicalSpace X] →
[inst_1 : TopologicalSpace Y] →
{f₀ f₁ : C(X, Y)} → {P : C(X, Y) → Prop} → FunLike (f₀.HomotopyWith f₁ P) (↑unitInterval × X) Y | true |
Matrix.replicateCol_zero | Mathlib.LinearAlgebra.Matrix.RowCol | ∀ {m : Type u_2} {α : Type v} {ι : Type u_6} [inst : Zero α], Matrix.replicateCol ι 0 = 0 | true |
_private.Mathlib.GroupTheory.FreeGroup.Orbit.0.FreeGroup.startsWith.disjoint_iff_ne._simp_1_6 | Mathlib.GroupTheory.FreeGroup.Orbit | ∀ {a b : Prop}, (¬(a ∧ b)) = (a → ¬b) | false |
FirstOrder.Language.Hom.homClass | Mathlib.ModelTheory.Basic | ∀ {L : FirstOrder.Language} {M : Type w} {N : Type w'} [inst : L.Structure M] [inst_1 : L.Structure N],
L.HomClass (L.Hom M N) M N | true |
MonCat.Colimits.monoidColimitType._proof_1 | Mathlib.Algebra.Category.MonCat.Colimits | ∀ {J : Type u_1} [inst : CategoryTheory.Category.{u_2, u_1} J] (F : CategoryTheory.Functor J MonCat)
(x : MonCat.Colimits.ColimitType F), npowRecAuto 0 x = 1 | false |
Thunk.fn | Init.Core | {α : Type u} → Thunk α → Unit → α | true |
_private.Mathlib.Combinatorics.Derangements.Finite.0.card_derangements_fin_eq_numDerangements._proof_1_1 | Mathlib.Combinatorics.Derangements.Finite | ∀ (n : ℕ), n + 1 < n + 1 + 1 | false |
PFunctor.W | Mathlib.Data.PFunctor.Univariate.Basic | PFunctor.{uA, uB} → Type (max uA uB) | true |
Quaternion.instRing._proof_17 | Mathlib.Algebra.Quaternion | ∀ {R : Type u_1} [inst : CommRing R] (a : Quaternion R), 0 * a = 0 | false |
_private.Mathlib.Topology.Filter.0.Filter.sInter_nhds._simp_1_1 | Mathlib.Topology.Filter | ∀ {α : Type u} {s : Set α} {f : Filter α}, (f ≤ Filter.principal s) = (s ∈ f) | false |
CategoryTheory.LocalizerMorphism.LeftResolution.Hom.ext_iff | Mathlib.CategoryTheory.Localization.Resolution | ∀ {C₁ : Type u_1} {C₂ : Type u_2} {inst : CategoryTheory.Category.{v_1, u_1} C₁}
{inst_1 : CategoryTheory.Category.{v_2, u_2} C₂} {W₁ : CategoryTheory.MorphismProperty C₁}
{W₂ : CategoryTheory.MorphismProperty C₂} {Φ : CategoryTheory.LocalizerMorphism W₁ W₂} {X₂ : C₂}
{L L' : Φ.LeftResolution X₂} {x y : L.Hom L'}... | true |
BooleanRing.mul_one_add_self | Mathlib.Algebra.Ring.BooleanRing | ∀ {α : Type u_1} [inst : BooleanRing α] (a : α), a * (1 + a) = 0 | true |
CategoryTheory.Abelian.SpectralObject.EIsoH_hom_naturality._auto_5 | Mathlib.Algebra.Homology.SpectralObject.Page | Lean.Syntax | false |
CategoryTheory.ComposableArrows.fourδ₃Toδ₂._proof_2 | Mathlib.CategoryTheory.ComposableArrows.Four | ∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] {i₀ i₁ i₂ i₃ i₄ : C} (f₁ : i₀ ⟶ i₁) (f₂ : i₁ ⟶ i₂)
(f₃ : i₂ ⟶ i₃) (f₄ : i₃ ⟶ i₄) (f₂₃ : i₁ ⟶ i₃) (f₃₄ : i₂ ⟶ i₄),
CategoryTheory.CategoryStruct.comp f₂ f₃ = f₂₃ →
CategoryTheory.CategoryStruct.comp f₃ f₄ = f₃₄ →
CategoryTheory.CategoryStruct.c... | false |
SimpleGraph.Walk.head_support._proof_1 | Mathlib.Combinatorics.SimpleGraph.Walks.Basic | ∀ {V : Type u_1} {G : SimpleGraph V} {a b : V} (p : G.Walk a b), p.support ≠ [] | false |
CategoryTheory.Functor.Monoidal.toUnit_ε | Mathlib.CategoryTheory.Monoidal.Cartesian.Basic | ∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
{D : Type u₂} [inst_2 : CategoryTheory.Category.{v₂, u₂} D] [inst_3 : CategoryTheory.CartesianMonoidalCategory D]
(F : CategoryTheory.Functor C D) [inst_4 : F.Monoidal] (X : C),
CategoryTheory.Categor... | true |
Filter.rcomap'_sets | Mathlib.Order.Filter.Partial | ∀ {α : Type u} {β : Type v} (r : SetRel α β) (f : Filter β),
(Filter.rcomap' r f).sets = SetRel.image {(s, t) | r.preimage s ⊆ t} f.sets | true |
Set.image2_iInter_subset_right | Mathlib.Data.Set.Lattice.Image | ∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} {ι : Sort u_5} (f : α → β → γ) (s : Set α) (t : ι → Set β),
Set.image2 f s (⋂ i, t i) ⊆ ⋂ i, Set.image2 f s (t i) | true |
Lean.Compiler.LCNF.Probe.filterByUnreach | Lean.Compiler.LCNF.Probing | (pu : Lean.Compiler.LCNF.Purity) →
(Lean.Expr → Lean.Compiler.LCNF.CompilerM Bool) →
Lean.Compiler.LCNF.Probe (Lean.Compiler.LCNF.Decl pu) (Lean.Compiler.LCNF.Decl pu) | true |
AddMonoidHom.mulRight₃._proof_2 | Mathlib.Algebra.Ring.Associator | ∀ {R : Type u_1} [inst : NonUnitalNonAssocSemiring R] (x y : R),
AddMonoidHom.mul.compr₂ (AddMonoidHom.mulLeft (x + y)) =
AddMonoidHom.mul.compr₂ (AddMonoidHom.mulLeft x) + AddMonoidHom.mul.compr₂ (AddMonoidHom.mulLeft y) | false |
_private.Mathlib.MeasureTheory.Measure.Typeclasses.Finite.0.wrapped._proof_1._@.Mathlib.MeasureTheory.Measure.Typeclasses.Finite.588747923._hygCtx._hyg.2 | Mathlib.MeasureTheory.Measure.Typeclasses.Finite | @definition✝ = @definition✝ | false |
SimpleGraph.Walk.getVert_comp_val_eq_get_support | Mathlib.Combinatorics.SimpleGraph.Walks.Traversal | ∀ {V : Type u} {G : SimpleGraph V} {u v : V} (p : G.Walk u v), p.getVert ∘ Fin.val = p.support.get | true |
UniformSpace.Completion.isDenseInducing_coe | Mathlib.Topology.UniformSpace.Completion | ∀ {α : Type u_1} [inst : UniformSpace α], IsDenseInducing UniformSpace.Completion.coe' | true |
CategoryTheory.Functor.instLaxMonoidalMonMapAddMon._proof_3 | Mathlib.CategoryTheory.Monoidal.Mon_ | ∀ {C : Type u_4} [inst : CategoryTheory.Category.{u_3, u_4} C] [inst_1 : CategoryTheory.MonoidalCategory C]
{D : Type u_2} [inst_2 : CategoryTheory.Category.{u_1, u_2} D] [inst_3 : CategoryTheory.MonoidalCategory D]
(F : CategoryTheory.Functor C D) [inst_4 : CategoryTheory.BraidedCategory C]
[inst_5 : CategoryThe... | false |
instFinitePresentationForall | Mathlib.Algebra.Module.FinitePresentation | ∀ {R : Type u_1} [inst : Ring R] {ι : Type u_2} [Finite ι], Module.FinitePresentation R (ι → R) | true |
AffineIsometry.norm_map | Mathlib.Analysis.Normed.Affine.Isometry | ∀ {𝕜 : Type u_1} {V : Type u_2} {V₂ : Type u_5} {P : Type u_10} {P₂ : Type u_11} [inst : NormedField 𝕜]
[inst_1 : SeminormedAddCommGroup V] [inst_2 : NormedSpace 𝕜 V] [inst_3 : PseudoMetricSpace P]
[inst_4 : NormedAddTorsor V P] [inst_5 : SeminormedAddCommGroup V₂] [inst_6 : NormedSpace 𝕜 V₂]
[inst_7 : Pseudo... | true |
Lean.IR.CollectMaps.collectDecl | Lean.Compiler.IR.EmitUtil | Lean.IR.Decl → Lean.IR.CollectMaps.Collector | true |
Finset.instGradeMinOrder_nat | Mathlib.Data.Finset.Grade | {α : Type u_1} → GradeMinOrder ℕ (Finset α) | true |
ZeroAtInftyContinuousMap.instFunLike | Mathlib.Topology.ContinuousMap.ZeroAtInfty | {α : Type u} →
{β : Type v} →
[inst : TopologicalSpace α] →
[inst_1 : TopologicalSpace β] → [inst_2 : Zero β] → FunLike (ZeroAtInftyContinuousMap α β) α β | true |
Lean.Meta.Grind.Arith.Cutsat.LeCnstrProof.dvdTight.sizeOf_spec | Lean.Meta.Tactic.Grind.Arith.Cutsat.Types | ∀ (c₁ : Lean.Meta.Grind.Arith.Cutsat.DvdCnstr) (c₂ : Lean.Meta.Grind.Arith.Cutsat.LeCnstr),
sizeOf (Lean.Meta.Grind.Arith.Cutsat.LeCnstrProof.dvdTight c₁ c₂) = 1 + sizeOf c₁ + sizeOf c₂ | true |
ValuationRing.commGroupWithZero._proof_9 | Mathlib.RingTheory.Valuation.ValuationRing | ∀ (A : Type u_1) [inst : CommRing A] (K : Type u_2) [inst_1 : Field K] [inst_2 : Algebra A K]
(a b : ValuationRing.ValueGroup A K), a / b = a * b⁻¹ | false |
HOrElse.ctorIdx | Init.Prelude | {α : Type u} → {β : Type v} → {γ : outParam (Type w)} → HOrElse α β γ → ℕ | false |
AddCon.comap_eq | Mathlib.GroupTheory.Congruence.Hom | ∀ {M : Type u_1} {N : Type u_2} [inst : AddZeroClass M] [inst_1 : AddZeroClass N] {c : AddCon M} {f : N →+ M},
AddCon.comap ⇑f ⋯ c = AddCon.ker (c.mk'.comp f) | true |
Finmap.insert | Mathlib.Data.Finmap | {α : Type u} → {β : α → Type v} → [DecidableEq α] → (a : α) → β a → Finmap β → Finmap β | true |
Polynomial.fourierCoeff_toAddCircle | Mathlib.Analysis.Polynomial.Fourier | ∀ (p : Polynomial ℂ) (n : ℤ), fourierCoeff (⇑(Polynomial.toAddCircle p)) n = if 0 ≤ n then p.coeff n.natAbs else 0 | true |
Std.Internal.List.Const.getValueD_filter | Std.Data.Internal.List.Associative | ∀ {α : Type u} {β : Type v} [inst : BEq α] [EquivBEq α] {fallback : β} {f : α → β → Bool} {l : List ((_ : α) × β)},
Std.Internal.List.DistinctKeys l →
∀ {k : α},
Std.Internal.List.getValueD k (List.filter (fun p => f p.fst p.snd) l) fallback =
((Std.Internal.List.getValue? k l).pfilter fun v h => f ... | true |
Matrix.nondegenerate_iff_det_ne_zero | Mathlib.LinearAlgebra.Matrix.ToLinearEquiv | ∀ {n : Type u_1} [inst : Fintype n] {A : Type u_4} [inst_1 : DecidableEq n] [inst_2 : CommRing A] [IsDomain A]
{M : Matrix n n A}, M.Nondegenerate ↔ M.det ≠ 0 | true |
AlgebraicGeometry.StructureSheaf.const_mul | Mathlib.AlgebraicGeometry.StructureSheaf | ∀ {R A : Type u} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A] (f₁ f₂ : A) (g₁ g₂ : R)
(U : TopologicalSpace.Opens ↑(AlgebraicGeometry.PrimeSpectrum.Top R)) (hu₁ : U ≤ PrimeSpectrum.basicOpen g₁)
(hu₂ : U ≤ PrimeSpectrum.basicOpen g₂),
AlgebraicGeometry.StructureSheaf.const f₁ g₁ U hu₁ * Algebr... | true |
IsCoercive.continuousLinearEquivOfBilin | Mathlib.Analysis.InnerProductSpace.LaxMilgram | {V : Type u} →
[inst : NormedAddCommGroup V] →
[inst_1 : InnerProductSpace ℝ V] → [CompleteSpace V] → {B : V →L[ℝ] V →L[ℝ] ℝ} → IsCoercive B → V ≃L[ℝ] V | true |
Bundle.Pretrivialization.linearEquivAt | Mathlib.Topology.VectorBundle.Basic | (R : Type u_1) →
{B : Type u_2} →
{F : Type u_3} →
{E : B → Type u_4} →
[inst : Semiring R] →
[inst_1 : TopologicalSpace F] →
[inst_2 : TopologicalSpace B] →
[inst_3 : AddCommMonoid F] →
[inst_4 : Module R F] →
[inst_5 : (x : B) →... | true |
HasSubset.Subset.trans | Mathlib.Order.RelClasses | ∀ {α : Type u} [inst : HasSubset α] [IsTrans α fun x1 x2 => x1 ⊆ x2] {a b c : α}, a ⊆ b → b ⊆ c → a ⊆ c | true |
Units.mul_right_inj | Mathlib.Algebra.Group.Units.Basic | ∀ {α : Type u} [inst : Monoid α] (a : αˣ) {b c : α}, ↑a * b = ↑a * c ↔ b = c | true |
Derivation.liftOfSurjective.congr_simp | Mathlib.RingTheory.Derivation.Basic | ∀ {R : Type u_1} {A : Type u_2} {M : Type u_3} [inst : CommSemiring R] [inst_1 : CommRing A] [inst_2 : CommRing M]
[inst_3 : Algebra R A] [inst_4 : Algebra R M] {F : Type u_4} [inst_5 : FunLike F A M] [inst_6 : AlgHomClass F R A M]
{f f_1 : F} (e_f : f = f_1) (hf : Function.Surjective ⇑f) ⦃d d_1 : Derivation R A A⦄... | true |
NormedSpace.inclusionInDoubleDualWeak._proof_11 | Mathlib.Analysis.Normed.Module.DoubleDual | ∀ (𝕜 : Type u_2) [inst : NontriviallyNormedField 𝕜] (X : Type u_1) [inst_1 : SeminormedAddCommGroup X]
[inst_2 : NormedSpace 𝕜 X],
Continuous (((toWeakSpace 𝕜 X).arrowCongr StrongDual.toWeakDual) ↑(NormedSpace.inclusionInDoubleDual 𝕜 X)).toFun | false |
RingTheory.LinearMap._aux_Mathlib_Algebra_Algebra_Bilinear___macroRules_RingTheory_LinearMap_termμ_1 | Mathlib.Algebra.Algebra.Bilinear | Lean.Macro | false |
ProbabilityTheory.Kernel.borelMarkovFromReal.congr_simp | Mathlib.Probability.Kernel.Disintegration.StandardBorel | ∀ {α : Type u_1} {mα : MeasurableSpace α} (Ω : Type u_5) [inst : Nonempty Ω] [inst_1 : MeasurableSpace Ω]
[inst_2 : StandardBorelSpace Ω] (η η_1 : ProbabilityTheory.Kernel α ℝ),
η = η_1 → ProbabilityTheory.Kernel.borelMarkovFromReal Ω η = ProbabilityTheory.Kernel.borelMarkovFromReal Ω η_1 | true |
Equiv.pemptyArrowEquivPUnit | Mathlib.Logic.Equiv.Defs | (α : Sort u_1) → (PEmpty.{u_2} → α) ≃ PUnit.{u} | true |
CategoryTheory.Cat.FreeRefl.lift | Mathlib.CategoryTheory.Category.ReflQuiv | {V : Type u_1} →
[inst : CategoryTheory.ReflQuiver V] →
{D : Type u_2} →
[inst_1 : CategoryTheory.Category.{v_1, u_2} D] →
V ⥤rq D → CategoryTheory.Functor (CategoryTheory.Cat.FreeRefl V) D | true |
PerfectClosure.instNeg | Mathlib.FieldTheory.PerfectClosure | (K : Type u) →
[inst : CommRing K] → (p : ℕ) → [inst_1 : Fact (Nat.Prime p)] → [inst_2 : CharP K p] → Neg (PerfectClosure K p) | true |
CategoryTheory.LocalizerMorphism.RightResolution._sizeOf_1 | Mathlib.CategoryTheory.Localization.Resolution | {C₁ : Type u_1} →
{C₂ : Type u_2} →
{inst : CategoryTheory.Category.{v_1, u_1} C₁} →
{inst_1 : CategoryTheory.Category.{v_2, u_2} C₂} →
{W₁ : CategoryTheory.MorphismProperty C₁} →
{W₂ : CategoryTheory.MorphismProperty C₂} →
{Φ : CategoryTheory.LocalizerMorphism W₁ W₂} →
... | false |
AddSubsemigroup.coe_op | Mathlib.Algebra.Group.Subsemigroup.MulOpposite | ∀ {M : Type u_2} [inst : Add M] (x : AddSubsemigroup M), ↑x.op = AddOpposite.unop ⁻¹' ↑x | true |
Polynomial.mapRingHom_comp_C | Mathlib.Algebra.Polynomial.Eval.Defs | ∀ {R : Type u_1} {S : Type u_2} [inst : Semiring R] [inst_1 : Semiring S] (f : R →+* S),
(Polynomial.mapRingHom f).comp Polynomial.C = Polynomial.C.comp f | true |
CategoryTheory.instBicategoryMonoidalSingleObj._proof_6 | Mathlib.CategoryTheory.Bicategory.SingleObj | ∀ (C : Type u_2) [inst : CategoryTheory.Category.{u_1, u_2} C] [inst_1 : CategoryTheory.MonoidalCategory C]
{a b : CategoryTheory.MonoidalSingleObj C} {f g : C} (η : f ⟶ g),
CategoryTheory.MonoidalCategoryStruct.whiskerLeft (CategoryTheory.MonoidalCategoryStruct.tensorUnit C) η =
CategoryTheory.CategoryStruct.c... | false |
_private.Init.Data.List.Basic.0.List.getLastD.match_1.eq_1 | Init.Data.List.Basic | ∀ {α : Type u_1} (motive : List α → α → Sort u_2) (a₀ : α) (h_1 : (a₀ : α) → motive [] a₀)
(h_2 : (a : α) → (as : List α) → (x : α) → motive (a :: as) x),
(match [], a₀ with
| [], a₀ => h_1 a₀
| a :: as, x => h_2 a as x) =
h_1 a₀ | true |
Aesop.Script.Tactic.sTactic? | Aesop.Script.Tactic | Aesop.Script.Tactic → Option Aesop.Script.STactic | true |
_private.Lean.Parser.Term.Doc.0.Lean.Parser.Term.Doc.recommendedSpellingByNameExt.match_1 | Lean.Parser.Term.Doc | (motive : Lean.Parser.Term.Doc.RecommendedSpelling × Array Lean.Name → Sort u_1) →
(x : Lean.Parser.Term.Doc.RecommendedSpelling × Array Lean.Name) →
((rec : Lean.Parser.Term.Doc.RecommendedSpelling) → (xs : Array Lean.Name) → motive (rec, xs)) → motive x | false |
Real.convexOn_log_Gamma | Mathlib.Analysis.SpecialFunctions.Gamma.BohrMollerup | ConvexOn ℝ (Set.Ioi 0) (Real.log ∘ Real.Gamma) | true |
Array.beq_eq_decide | Init.Data.Array.DecidableEq | ∀ {α : Type u_1} [inst : BEq α] (xs ys : Array α),
(xs == ys) = if h : xs.size = ys.size then decide (∀ (i : ℕ) (h' : i < xs.size), (xs[i] == ys[i]) = true) else false | true |
CategoryTheory.Localization.Monoidal.functorCoreMonoidalOfComp | Mathlib.CategoryTheory.Localization.Monoidal.Functor | {C : Type u_1} →
{D : Type u_2} →
{E : Type u_3} →
[inst : CategoryTheory.Category.{v_1, u_1} C] →
[inst_1 : CategoryTheory.Category.{v_2, u_2} D] →
[inst_2 : CategoryTheory.Category.{v_3, u_3} E] →
[inst_3 : CategoryTheory.MonoidalCategory C] →
[inst_4 : Category... | true |
SimpleGraph.le_chromaticNumber_iff_coloring | Mathlib.Combinatorics.SimpleGraph.Coloring | ∀ {V : Type u} {G : SimpleGraph V} {n : ℕ}, ↑n ≤ G.chromaticNumber ↔ ∀ (m : ℕ) (a : G.Coloring (Fin m)), n ≤ m | true |
Subgroup.Commensurable.eq_1 | Mathlib.GroupTheory.Commensurable | ∀ {G : Type u_1} [inst : Group G] (H K : Subgroup G), H.Commensurable K = (H.relIndex K ≠ 0 ∧ K.relIndex H ≠ 0) | true |
Unitization.instNonAssocRing._proof_9 | Mathlib.Algebra.Algebra.Unitization | ∀ {R : Type u_1} {A : Type u_2} [inst : CommRing R] [inst_1 : NonUnitalNonAssocRing A] [inst_2 : Module R A],
autoParam (↑0 = 0) AddMonoidWithOne.natCast_zero._autoParam | false |
Std.Iter.toIter_toIterM | Init.Data.Iterators.Basic | ∀ {α β : Type w} (it : Std.Iter β), it.toIterM.toIter = it | true |
LinearIsometry.strictConvexSpace_range | Mathlib.Analysis.Convex.LinearIsometry | ∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : NormedField 𝕜] [inst_1 : PartialOrder 𝕜]
[inst_2 : NormedAddCommGroup E] [inst_3 : NormedSpace 𝕜 E] [inst_4 : NormedAddCommGroup F] [inst_5 : NormedSpace 𝕜 F]
[StrictConvexSpace 𝕜 E] (e : E →ₗᵢ[𝕜] F), StrictConvexSpace 𝕜 ↥(↑e).range | true |
monotoneOn_of_le_add_one | Mathlib.Algebra.Order.SuccPred | ∀ {α : Type u_2} {β : Type u_3} [inst : PartialOrder α] [inst_1 : Preorder β] [inst_2 : Add α] [inst_3 : One α]
[inst_4 : SuccAddOrder α] [IsSuccArchimedean α] {s : Set α} {f : α → β},
s.OrdConnected → (∀ (a : α), ¬IsMax a → a ∈ s → a + 1 ∈ s → f a ≤ f (a + 1)) → MonotoneOn f s | true |
ContinuousAlternatingMap.ofSubsingleton_toAlternatingMap | Mathlib.Topology.Algebra.Module.Alternating.Basic | ∀ (R : Type u_1) (M : Type u_2) (N : Type u_4) {ι : Type u_6} [inst : Semiring R] [inst_1 : AddCommMonoid M]
[inst_2 : Module R M] [inst_3 : TopologicalSpace M] [inst_4 : AddCommMonoid N] [inst_5 : Module R N]
[inst_6 : TopologicalSpace N] [inst_7 : Subsingleton ι] (i : ι) (f : M →L[R] N),
((ContinuousAlternating... | true |
Filter.bliminf_or_le_inf_aux_right._simp_1 | Mathlib.Order.LiminfLimsup | ∀ {α : Type u_1} {β : Type u_2} [inst : CompleteLattice α] {f : Filter β} {p q : β → Prop} {u : β → α},
((Filter.bliminf u f fun x => p x ∨ q x) ≤ Filter.bliminf u f q) = True | false |
definition._@.Mathlib.Analysis.InnerProductSpace.PiL2.1554134833._hygCtx._hyg.2 | Mathlib.Analysis.InnerProductSpace.PiL2 | {ι : Type u_1} →
{𝕜 : Type u_3} →
[inst : RCLike 𝕜] →
{E : Type u_4} →
[inst_1 : NormedAddCommGroup E] →
[inst_2 : InnerProductSpace 𝕜 E] →
[Fintype ι] →
[FiniteDimensional 𝕜 E] →
{n : ℕ} →
Module.finrank 𝕜 E = n →
... | false |
_private.Lean.Meta.Tactic.Grind.Arith.Cutsat.Proof.0.Lean.Meta.Grind.Arith.Cutsat.EqCnstr.collectDecVars.match_1 | Lean.Meta.Tactic.Grind.Arith.Cutsat.Proof | (motive : Lean.Meta.Grind.Arith.Cutsat.EqCnstrProof → Sort u_1) →
(x : Lean.Meta.Grind.Arith.Cutsat.EqCnstrProof) →
((a zero : Lean.Expr) → motive (Lean.Meta.Grind.Arith.Cutsat.EqCnstrProof.core0 a zero)) →
((a b : Lean.Expr) →
(p₁ p₂ : Int.Linear.Poly) → motive (Lean.Meta.Grind.Arith.Cutsat.EqCns... | false |
ProofWidgets.RpcEncodablePacket.«_@».ProofWidgets.Component.Basic.2277670097._hygCtx._hyg.1.noConfusion | ProofWidgets.Component.Basic | {P : Sort u} →
{t t' : ProofWidgets.RpcEncodablePacket✝} →
t = t' →
ProofWidgets.RpcEncodablePacket.«_@».ProofWidgets.Component.Basic.2277670097._hygCtx._hyg.1.noConfusionType P t t' | false |
Lean.guardMsgsPositions | Init.Notation | Lean.ParserDescr | true |
subset_tangentConeAt_prod_left | Mathlib.Analysis.Calculus.TangentCone.Prod | ∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : Semiring 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
[inst_3 : TopologicalSpace E] [ContinuousAdd E] [ContinuousConstSMul 𝕜 E] [inst_6 : AddCommGroup F]
[inst_7 : Module 𝕜 F] [inst_8 : TopologicalSpace F] [ContinuousAdd F] [ContinuousConstSMul 𝕜 F]... | true |
AlgebraicGeometry.Scheme.kerAdjunction_counit_app | Mathlib.AlgebraicGeometry.IdealSheaf.Subscheme | ∀ (Y : AlgebraicGeometry.Scheme) (f : (CategoryTheory.Over Y)ᵒᵖ),
Y.kerAdjunction.counit.app f =
(CategoryTheory.Over.homMk (AlgebraicGeometry.Scheme.Hom.toImage (Opposite.unop f).hom) ⋯).op | true |
ZFSet.card_empty | Mathlib.SetTheory.ZFC.Cardinal | ∅.card = 0 | true |
SeparatelyContinuousMul.rec | Mathlib.Topology.Algebra.Monoid.Defs | {M : Type u_1} →
[inst : TopologicalSpace M] →
[inst_1 : Mul M] →
{motive : SeparatelyContinuousMul M → Sort u} →
((continuous_const_mul : ∀ {a : M}, Continuous fun x => a * x) →
(continuous_mul_const : ∀ {a : M}, Continuous fun x => x * a) → motive ⋯) →
(t : SeparatelyContinuo... | false |
Subring.mem_toSubsemiring._simp_1 | Mathlib.Algebra.Ring.Subring.Defs | ∀ {R : Type u} [inst : NonAssocRing R] {s : Subring R} {x : R}, (x ∈ s.toSubsemiring) = (x ∈ s) | false |
Lean.Syntax.ident.inj | Init.Core | ∀ {info : Lean.SourceInfo} {rawVal : Substring.Raw} {val : Lean.Name} {preresolved : List Lean.Syntax.Preresolved}
{info_1 : Lean.SourceInfo} {rawVal_1 : Substring.Raw} {val_1 : Lean.Name}
{preresolved_1 : List Lean.Syntax.Preresolved},
Lean.Syntax.ident info rawVal val preresolved = Lean.Syntax.ident info_1 rawV... | true |
CliffordAlgebra.reverse_mem_evenOdd_iff | Mathlib.LinearAlgebra.CliffordAlgebra.Conjugation | ∀ {R : Type u_1} [inst : CommRing R] {M : Type u_2} [inst_1 : AddCommGroup M] [inst_2 : Module R M]
(Q : QuadraticForm R M) {x : CliffordAlgebra Q} {n : ZMod 2},
CliffordAlgebra.reverse x ∈ CliffordAlgebra.evenOdd Q n ↔ x ∈ CliffordAlgebra.evenOdd Q n | true |
_private.Lean.Meta.LetToHave.0.Lean.Meta.LetToHave.State.rec | Lean.Meta.LetToHave | {motive : Lean.Meta.LetToHave.State✝ → Sort u} →
((count : ℕ) →
(results : Std.HashMap Lean.ExprStructEq Lean.Meta.LetToHave.Result✝) →
motive { count := count, results := results }) →
(t : Lean.Meta.LetToHave.State✝¹) → motive t | false |
QuadraticAlgebra.algebraMap_norm_eq_mul_star | Mathlib.Algebra.QuadraticAlgebra.Basic | ∀ {R : Type u_1} {a b : R} [inst : CommRing R] (z : QuadraticAlgebra R a b),
(algebraMap R (QuadraticAlgebra R a b)) (QuadraticAlgebra.norm z) = z * star z | true |
Module.DirectLimit.addCommGroup._proof_12 | Mathlib.Algebra.Colimit.Module | ∀ {R : Type u_1} [inst : Semiring R] {ι : Type u_2} [inst_1 : Preorder ι] [inst_2 : DecidableEq ι] (G : ι → Type u_3)
[inst_3 : (i : ι) → AddCommGroup (G i)] [inst_4 : (i : ι) → Module R (G i)] (f : (i j : ι) → i ≤ j → G i →ₗ[R] G j)
(a b : Module.DirectLimit G f), a + b = b + a | false |
_private.Mathlib.Order.Filter.Bases.Finite.0.Filter.hasBasis_generate._simp_1_1 | Mathlib.Order.Filter.Bases.Finite | ∀ {α : Type u} {s : Set (Set α)} {U : Set α}, (U ∈ Filter.generate s) = ∃ t ⊆ s, t.Finite ∧ ⋂₀ t ⊆ U | false |
HahnSeries.orderTop_embDomain | Mathlib.RingTheory.HahnSeries.Basic | ∀ {Γ' : Type u_2} {R : Type u_3} [inst : Zero R] [inst_1 : PartialOrder Γ'] {Γ : Type u_5} [inst_2 : LinearOrder Γ]
{f : Γ ↪o Γ'} {x : HahnSeries Γ R}, (HahnSeries.embDomain f x).orderTop = WithTop.map (⇑f) x.orderTop | true |
orthogonalFamily_iff_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},
(OrthogonalFamily 𝕜 (fun i => ↥(V i)) fun i => (V i).subtypeₗᵢ) ↔ Pairwise (Function.onFun (fun x1 x2 => x1 ⟂ x2) V) | true |
ProofWidgets.MakeEditLinkProps.ctorIdx | ProofWidgets.Component.MakeEditLink | ProofWidgets.MakeEditLinkProps → ℕ | false |
Int.zsmul_eq_mul | Mathlib.Algebra.Group.Int.Defs | ∀ (n a : ℤ), n • a = n * a | true |
_private.Lean.Elab.PreDefinition.Structural.FindRecArg.0.Lean.Elab.Structural.nonIndicesFirst.match_1 | Lean.Elab.PreDefinition.Structural.FindRecArg | (motive : Array Lean.Elab.Structural.RecArgInfo × Array Lean.Elab.Structural.RecArgInfo → Sort u_1) →
(x : Array Lean.Elab.Structural.RecArgInfo × Array Lean.Elab.Structural.RecArgInfo) →
((indices nonIndices : Array Lean.Elab.Structural.RecArgInfo) → motive (indices, nonIndices)) → motive x | false |
MeromorphicOn.neg | Mathlib.Analysis.Meromorphic.Basic | ∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_3} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {f : 𝕜 → E} {U : Set 𝕜}, MeromorphicOn f U → MeromorphicOn (-f) U | true |
List.nil_lt_cons | Init.Data.List.Lex | ∀ {α : Type u_1} [inst : LT α] (a : α) (l : List α), [] < a :: l | true |
_private.Init.Grind.Ring.CommSolver.0.Lean.Grind.CommRing.instBEqMon.beq.match_1.eq_1 | Init.Grind.Ring.CommSolver | ∀ (motive : Lean.Grind.CommRing.Mon → Lean.Grind.CommRing.Mon → Sort u_1)
(h_1 : Unit → motive Lean.Grind.CommRing.Mon.unit Lean.Grind.CommRing.Mon.unit)
(h_2 :
(a : Lean.Grind.CommRing.Power) →
(a_1 : Lean.Grind.CommRing.Mon) →
(b : Lean.Grind.CommRing.Power) →
(b_1 : Lean.Grind.CommRin... | true |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.