name stringlengths 2 347 | module stringlengths 6 90 | type stringlengths 1 5.67M | allowCompletion bool 2
classes |
|---|---|---|---|
_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) | 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) | false |
Finsupp.DegLex.single_antitone | Mathlib.Data.Finsupp.MonomialOrder.DegLex | ∀ {α : Type u_1} [inst : LinearOrder α], Antitone fun a => toDegLex fun₀ | a => 1 | true |
_private.Mathlib.Combinatorics.SimpleGraph.Walks.Decomp.0.SimpleGraph.Walk.takeUntil_eq_take._proof_1_11 | Mathlib.Combinatorics.SimpleGraph.Walks.Decomp | ∀ {V : Type u_1} {G : SimpleGraph V} {a v_1 w_1 : V} (h_1 : G.Adj a v_1) (p : G.Walk v_1 w_1),
a = (SimpleGraph.Walk.cons ⋯ p).getVert 0 | false |
_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 | false |
_private.Batteries.Data.Array.Monadic.0.cond.match_1.splitter | Batteries.Data.Array.Monadic | (motive : Bool → Sort u_1) → (c : Bool) → (Unit → motive true) → (Unit → motive false) → motive c | true |
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 | true |
Lean.Doc.State.openDecls | Lean.Elab.DocString | Lean.Doc.State → List Lean.OpenDecl | 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) | 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) | 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 | true |
chartAt | Mathlib.Geometry.Manifold.ChartedSpace | (H : Type u_5) →
[inst : TopologicalSpace H] →
{M : Type u_6} → [inst_1 : TopologicalSpace M] → [ChartedSpace H M] → M → OpenPartialHomeomorph M H | 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) | 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 | 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 | 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 | false |
Lean.Elab.CheckTactic.elabCheckTactic | Lean.Elab.CheckTactic | Lean.Elab.Command.CommandElab | true |
Subring.toAddSubgroup_strictMono | Mathlib.Algebra.Ring.Subring.Basic | ∀ {R : Type u} [inst : NonAssocRing R], StrictMono Subring.toAddSubgroup | true |
MeasureTheory.SimpleFunc.pow_apply | Mathlib.MeasureTheory.Function.SimpleFunc | ∀ {α : Type u_1} {β : Type u_2} [inst : MeasurableSpace α] [inst_1 : Monoid β] (n : ℕ)
(f : MeasureTheory.SimpleFunc α β) (a : α), (f ^ n) a = f a ^ n | true |
continuousSMul_closedBall_ball | Mathlib.Analysis.Normed.Module.Ball.Action | ∀ {𝕜 : Type u_1} {E : Type u_3} [inst : NormedField 𝕜] [inst_1 : SeminormedAddCommGroup E] [inst_2 : NormedSpace 𝕜 E]
{r : ℝ}, ContinuousSMul ↑(Metric.closedBall 0 1) ↑(Metric.ball 0 r) | true |
Set.sUnion_sub | Mathlib.Algebra.Group.Pointwise.Set.Lattice | ∀ {α : Type u_2} [inst : Sub α] (S : Set (Set α)) (t : Set α), ⋃₀ S - t = ⋃ s ∈ S, s - t | true |
BitVec.getMsbD_rotateLeft | Init.Data.BitVec.Lemmas | ∀ {r n w : ℕ} {x : BitVec w}, (x.rotateLeft r).getMsbD n = (decide (n < w) && x.getMsbD ((r + n) % w)) | true |
CommSemiRingCat.Hom.hom | Mathlib.Algebra.Category.Ring.Basic | {R S : CommSemiRingCat} → R.Hom S → ↑R →+* ↑S | true |
Submodule.Quotient.equiv._proof_1 | Mathlib.LinearAlgebra.Quotient.Basic | ∀ {R : Type u_2} {M : Type u_3} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] {N : Type u_1}
[inst_3 : AddCommGroup N] [inst_4 : Module R N] (P : Submodule R M) (Q : Submodule R N) (f : M ≃ₗ[R] N),
Submodule.map (↑f) P = Q → ∀ x ∈ Q, x ∈ Submodule.comap (↑f.symm) P | false |
CategoryTheory.Limits.createsFiniteLimitsOfCreatesFiniteLimitsOfSize | Mathlib.CategoryTheory.Limits.Preserves.Creates.Finite | {C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
{D : Type u₂} →
[inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
(F : CategoryTheory.Functor C D) →
((J : Type w) →
{x : CategoryTheory.SmallCategory J} →
CategoryTheory.FinCategory J → CategoryTheor... | true |
CategoryTheory.Equivalence.enoughProjectives_iff | Mathlib.CategoryTheory.Preadditive.Projective.Basic | ∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {D : Type u'} [inst_1 : CategoryTheory.Category.{v', u'} D]
(F : C ≌ D), CategoryTheory.EnoughProjectives C ↔ CategoryTheory.EnoughProjectives D | true |
_private.Mathlib.CategoryTheory.Shift.ShiftedHomOpposite.0.CategoryTheory.ShiftedHom.opEquiv_symm_comp._proof_1 | Mathlib.CategoryTheory.Shift.ShiftedHomOpposite | ∀ {a b c : ℤ}, b + a = c → a + b = c | false |
Nat.getElem_toArray_roc | Init.Data.Range.Polymorphic.NatLemmas | ∀ {m n i : ℕ} (_h : i < (m<...=n).toArray.size), (m<...=n).toArray[i] = m + 1 + i | true |
Lean.Compiler.LCNF.instInhabitedSpecEntry | Lean.Compiler.LCNF.SpecInfo | Inhabited Lean.Compiler.LCNF.SpecEntry | true |
_private.Mathlib.GroupTheory.DivisibleHull.0.«term↑ⁿ» | Mathlib.GroupTheory.DivisibleHull | Lean.ParserDescr | true |
Left.one_lt_mul | Mathlib.Algebra.Order.Monoid.Unbundled.Basic | ∀ {α : Type u_1} [inst : MulOneClass α] [inst_1 : Preorder α] [MulLeftStrictMono α] {a b : α}, 1 < a → 1 < b → 1 < a * b | true |
_private.Init.Data.String.Basic.0.String.Slice.Pos.next_eq_nextFast._proof_1_7 | Init.Data.String.Basic | ∀ (s : String.Slice) (pos : s.Pos) (h : pos ≠ s.endPos),
¬pos.offset.byteIdx + (pos.str.get ⋯).utf8Size =
s.startInclusive.offset.byteIdx + pos.offset.byteIdx + (pos.str.get ⋯).utf8Size -
s.startInclusive.offset.byteIdx →
False | false |
NormedField.toNormedSpace._proof_1 | Mathlib.Analysis.Normed.Module.Basic | ∀ {𝕜 : Type u_1} [inst : NormedField 𝕜] (a b : 𝕜), ‖a * b‖ ≤ ‖a‖ * ‖b‖ | false |
USize.ofNatLT_sub | Init.Data.UInt.Lemmas | ∀ {a b : ℕ} (ha : a < 2 ^ System.Platform.numBits) (hab : b ≤ a),
USize.ofNatLT (a - b) ⋯ = USize.ofNatLT a ha - USize.ofNatLT b ⋯ | true |
SimpleGraph.Subgraph.instDecidableRel_deleteVerts_adj._proof_1 | Mathlib.Combinatorics.SimpleGraph.Subgraph | ∀ {V : Type u_1} {G : SimpleGraph V} (u : Set V) (x : ↑(⊤.deleteVerts u).verts), ↑x ∈ ⊤.verts | false |
Lean.Grind.AC.SubseqResult.false.sizeOf_spec | Lean.Meta.Tactic.Grind.AC.Seq | sizeOf Lean.Grind.AC.SubseqResult.false = 1 | true |
Homotopy.compLeft | Mathlib.Algebra.Homology.Homotopy | {ι : Type u_1} →
{V : Type u} →
[inst : CategoryTheory.Category.{v, u} V] →
[inst_1 : CategoryTheory.Preadditive V] →
{c : ComplexShape ι} →
{C D E : HomologicalComplex V c} →
{f g : D ⟶ E} →
Homotopy f g →
(e : C ⟶ D) → Homotopy (CategoryTheory.Ca... | true |
Sym2.inf | Mathlib.Data.Sym.Sym2.Order | {α : Type u_1} → [SemilatticeInf α] → Sym2 α → α | true |
Aesop.RuleTerm.const.elim | Aesop.RuleTac.RuleTerm | {motive : Aesop.RuleTerm → Sort u} →
(t : Aesop.RuleTerm) → t.ctorIdx = 0 → ((decl : Lean.Name) → motive (Aesop.RuleTerm.const decl)) → motive t | false |
Algebra.SubmersivePresentation.jacobianRelationsOfHasCoeffs._proof_1 | Mathlib.RingTheory.Extension.Presentation.Core | ∀ {R : Type u_2} {S : Type u_4} {ι : Type u_1} {σ : Type u_5} [inst : CommRing R] [inst_1 : CommRing S]
[inst_2 : Algebra R S] [inst_3 : Finite σ] (P : Algebra.SubmersivePresentation R S ι σ) (R₀ : Type u_3)
[inst_4 : CommRing R₀] [inst_5 : Algebra R₀ R] [inst_6 : Algebra R₀ S] [inst_7 : IsScalarTower R₀ R S]
[P.... | false |
Std.DHashMap.Internal.Raw₀.getKey?_insert_self | Std.Data.DHashMap.Internal.RawLemmas | ∀ {α : Type u} {β : α → Type v} (m : Std.DHashMap.Internal.Raw₀ α β) [inst : BEq α] [inst_1 : Hashable α] [EquivBEq α]
[LawfulHashable α], (↑m).WF → ∀ {k : α} {v : β k}, (m.insert k v).getKey? k = some k | true |
Lean.Elab.Attribute.stx | Lean.Elab.Attributes | Lean.Elab.Attribute → Lean.Syntax | true |
CategoryTheory.Functor.splitEpiEquiv._proof_6 | Mathlib.CategoryTheory.Functor.EpiMono | ∀ {C : Type u_4} [inst : CategoryTheory.Category.{u_3, u_4} C] {D : Type u_2}
[inst_1 : CategoryTheory.Category.{u_1, u_2} D] (F : CategoryTheory.Functor C D) {X Y : C} (f : X ⟶ Y)
[inst_2 : F.Full] [inst_3 : F.Faithful] (x : CategoryTheory.SplitEpi (F.map f)),
(fun f_1 => f_1.map F) ((fun s => { section_ := F.pr... | false |
_private.Mathlib.MeasureTheory.Measure.Typeclasses.SFinite.0.MeasureTheory.Measure.countable_meas_pos_of_disjoint_iUnion₀._simp_1_4 | Mathlib.MeasureTheory.Measure.Typeclasses.SFinite | ∀ {α : Type u} [inst : AddZeroClass α] [inst_1 : PartialOrder α] [CanonicallyOrderedAdd α] {a : α}, (a ≤ 0) = (a = 0) | false |
_private.Init.TacticsExtra.0.Lean.Parser.Tactic._aux_Init_TacticsExtra___macroRules_Lean_Parser_Tactic_tacticRw_mod_cast____1.match_1 | Init.TacticsExtra | (motive : Option (Lean.TSyntax `Lean.Parser.Tactic.location) → Sort u_1) →
(loc : Option (Lean.TSyntax `Lean.Parser.Tactic.location)) →
((loc : Lean.TSyntax `Lean.Parser.Tactic.location) → motive (some loc)) →
((x : Option (Lean.TSyntax `Lean.Parser.Tactic.location)) → motive x) → motive loc | false |
Cardinal.add_one_inj | Mathlib.SetTheory.Cardinal.Arithmetic | ∀ {α β : Cardinal.{u_1}}, α + 1 = β + 1 ↔ α = β | true |
PowerSeries.IsWeierstrassDivision.unique | Mathlib.RingTheory.PowerSeries.WeierstrassPreparation | ∀ {A : Type u_1} [inst : CommRing A] [inst_1 : IsLocalRing A] {f g : PowerSeries A},
(PowerSeries.map (IsLocalRing.residue A)) g ≠ 0 →
∀ [inst_2 : IsAdicComplete (IsLocalRing.maximalIdeal A) A] {q : PowerSeries A} {r : Polynomial A},
f.IsWeierstrassDivision g q r → q = f /ʷ g ∧ r = f %ʷ g | true |
Ideal.add_eq_sup | Mathlib.RingTheory.Ideal.Operations | ∀ {R : Type u} [inst : Semiring R] {I J : Ideal R}, I + J = I ⊔ J | true |
_private.Mathlib.LinearAlgebra.TensorProduct.Map.0.LinearMap.rTensor_neg._simp_1_1 | Mathlib.LinearAlgebra.TensorProduct.Map | ∀ {R : Type u_1} [inst : CommSemiring R] (M : Type u_7) {N : Type u_8} {P : Type u_9} [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], LinearMap.rTensor M = ⇑(LinearMap.rTensorHom M) | false |
IsRightRegular.mul_right_eq_self_iff | Mathlib.Algebra.Regular.Basic | ∀ {R : Type u_1} [inst : Monoid R] {a b : R}, IsRightRegular a → (b * a = a ↔ b = 1) | true |
StrictAnti.strictAntiOn | Mathlib.Order.Monotone.Defs | ∀ {α : Type u} {β : Type v} [inst : Preorder α] [inst_1 : Preorder β] {f : α → β},
StrictAnti f → ∀ (s : Set α), StrictAntiOn f s | true |
NonUnitalStarRingHom.copy._proof_2 | Mathlib.Algebra.Star.StarRingHom | ∀ {A : Type u_2} {B : Type u_1} [inst : NonUnitalNonAssocSemiring A] [inst_1 : Star A]
[inst_2 : NonUnitalNonAssocSemiring B] [inst_3 : Star B] (f : A →⋆ₙ+* B) (f' : A → B), f' = ⇑f → f' 0 = 0 | false |
Lean.Elab.FixedParams.instToFormatInfo | Lean.Elab.PreDefinition.FixedParams | Std.ToFormat Lean.Elab.FixedParams.Info | true |
BitVec.ushiftRight_eq_extractLsb'_of_lt | Init.Data.BitVec.Lemmas | ∀ {w : ℕ} {x : BitVec w} {n : ℕ} (hn : n < w), x >>> n = BitVec.cast ⋯ (0#n ++ BitVec.extractLsb' n (w - n) x) | true |
HomologicalComplex.leftUnitor'_inv_comm_assoc | Mathlib.Algebra.Homology.Monoidal | ∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.MonoidalCategory C]
[inst_2 : CategoryTheory.Preadditive C] [inst_3 : CategoryTheory.Limits.HasZeroObject C]
[inst_4 : (CategoryTheory.MonoidalCategory.curriedTensor C).Additive]
[inst_5 : ∀ (X₁ : C), ((CategoryTheory.Monoidal... | true |
FirstOrder.Field.FieldAxiom.toProp | Mathlib.ModelTheory.Algebra.Field.Basic | (K : Type u_2) → [Add K] → [Mul K] → [Neg K] → [Zero K] → [One K] → FirstOrder.Field.FieldAxiom → Prop | true |
_private.Mathlib.NumberTheory.Padics.PadicNumbers.0.PadicSeq.equiv_zero_of_val_eq_of_equiv_zero.match_1_1 | Mathlib.NumberTheory.Padics.PadicNumbers | ∀ {p : ℕ} [inst : Fact (Nat.Prime p)] {f : PadicSeq p} (ε : ℚ)
(motive : (∃ i, ∀ j ≥ i, padicNorm p (↑(f - 0) j) < ε) → Prop) (x : ∃ i, ∀ j ≥ i, padicNorm p (↑(f - 0) j) < ε),
(∀ (i : ℕ) (hi : ∀ j ≥ i, padicNorm p (↑(f - 0) j) < ε), motive ⋯) → motive x | false |
ProbabilityTheory.Kernel.isProper_iff_inter_eq_indicator_mul | Mathlib.Probability.Kernel.Proper | ∀ {X : Type u_1} {𝓑 𝓧 : MeasurableSpace X} {π : ProbabilityTheory.Kernel X X},
𝓑 ≤ 𝓧 →
(π.IsProper ↔
∀ ⦃A : Set X⦄,
MeasurableSet A → ∀ ⦃B : Set X⦄, MeasurableSet B → ∀ (x : X), (π x) (A ∩ B) = B.indicator 1 x * (π x) A) | true |
Std.Net.instDecidableEqIPv6Addr.decEq | Std.Net.Addr | (x x_1 : Std.Net.IPv6Addr) → Decidable (x = x_1) | true |
IsCancelSMul.toIsLeftCancelSMul | Mathlib.Algebra.Group.Action.Defs | ∀ {G : Type u_9} {P : Type u_10} {inst : SMul G P} [self : IsCancelSMul G P], IsLeftCancelSMul G P | true |
«_aux_Init_Notation___macroRules_term_∘__1» | Init.Notation | Lean.Macro | false |
DFinsupp.comapDomain'.congr_simp | Mathlib.Data.DFinsupp.Defs | ∀ {ι : Type u} {β : ι → Type v} {κ : Type u_1} [inst : (i : ι) → Zero (β i)] (h : κ → ι) {h' h'_1 : ι → κ}
(e_h' : h' = h'_1) (hh' : Function.LeftInverse h' h) (f f_1 : Π₀ (i : ι), β i),
f = f_1 → DFinsupp.comapDomain' h hh' f = DFinsupp.comapDomain' h ⋯ f_1 | true |
VectorField.mlieBracketWithin_congr_set | Mathlib.Geometry.Manifold.VectorField.LieBracket | ∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {H : Type u_2} [inst_1 : TopologicalSpace H] {E : Type u_3}
[inst_2 : NormedAddCommGroup E] [inst_3 : NormedSpace 𝕜 E] {I : ModelWithCorners 𝕜 E H} {M : Type u_4}
[inst_4 : TopologicalSpace M] [inst_5 : ChartedSpace H M] {s t : Set M} {x : M} {V W : (x : M) → ... | true |
Representation.isTrivial_def | Mathlib.RepresentationTheory.Basic | ∀ {k : Type u_1} {G : Type u_2} {V : Type u_3} [inst : Semiring k] [inst_1 : Monoid G] [inst_2 : AddCommMonoid V]
[inst_3 : Module k V] (ρ : Representation k G V) [ρ.IsTrivial] (g : G), ρ g = LinearMap.id | true |
Lean.Kernel.Environment.addDeclWithoutChecking | Lean.Environment | Lean.Kernel.Environment → Lean.Declaration → Except Lean.Kernel.Exception Lean.Kernel.Environment | true |
CategoryTheory.isNoetherianObject_iff_isEventuallyConstant | Mathlib.CategoryTheory.Subobject.NoetherianObject | ∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (X : C),
CategoryTheory.IsNoetherianObject X ↔
∀ (F : CategoryTheory.Functor ℕ (CategoryTheory.MonoOver X)), CategoryTheory.IsFiltered.IsEventuallyConstant F | true |
_private.Lean.Shell.0.Lean.ShellOptions.process.liftIO | Lean.Shell | {α : Type} → IO α → EIO UInt32 α | true |
MulAction.is_one_preprimitive_iff | Mathlib.GroupTheory.GroupAction.MultiplePrimitivity | ∀ (M : Type u_1) (α : Type u_2) [inst : Group M] [inst_1 : MulAction M α],
MulAction.IsMultiplyPreprimitive M α 1 ↔ MulAction.IsPreprimitive M α | true |
CategoryTheory.Functor.leftKanExtensionIsoFiberwiseColimit._proof_2 | Mathlib.CategoryTheory.Functor.KanExtension.Adjunction | ∀ {C : Type u_2} {D : Type u_6} [inst : CategoryTheory.Category.{u_1, u_2} C]
[inst_1 : CategoryTheory.Category.{u_3, u_6} D] (L : CategoryTheory.Functor C D) {H : Type u_5}
[inst_2 : CategoryTheory.Category.{u_4, u_5} H] (F : CategoryTheory.Functor C H) [L.HasPointwiseLeftKanExtension F]
(X : D),
CategoryTheor... | false |
Lean.Server.Test.Runner.Client.WidgetInstance.mk.injEq | Lean.Server.Test.Runner | ∀ (id : Lean.Name) (javascriptHash : UInt64) (props : Lean.Json) (id_1 : Lean.Name) (javascriptHash_1 : UInt64)
(props_1 : Lean.Json),
({ id := id, javascriptHash := javascriptHash, props := props } =
{ id := id_1, javascriptHash := javascriptHash_1, props := props_1 }) =
(id = id_1 ∧ javascriptHash = jav... | true |
_private.Mathlib.Algebra.Order.GroupWithZero.Unbundled.Defs.0.«_aux_Mathlib_Algebra_Order_GroupWithZero_Unbundled_Defs___macroRules__private_Mathlib_Algebra_Order_GroupWithZero_Unbundled_Defs_0_termα>0_1» | Mathlib.Algebra.Order.GroupWithZero.Unbundled.Defs | Lean.Macro | false |
_private.Mathlib.Data.Nat.Squarefree.0.Nat.minSqFacAux.match_1._arg_pusher | Mathlib.Data.Nat.Squarefree | ∀ (motive : ℕ → ℕ → Sort u_1) (α : Sort u✝) (β : α → Sort v✝) (f : (x : α) → β x) (rel : ℕ → ℕ → α → Prop) (x x_1 : ℕ)
(h_1 : (n k : ℕ) → ((y : α) → rel n k y → β y) → motive n k),
((match (motive := (x x_2 : ℕ) → ((y : α) → rel x x_2 y → β y) → motive x x_2) x, x_1 with
| n, k => fun x => h_1 n k x)
fu... | false |
CochainComplex.augmentTruncate_hom_f_succ | Mathlib.Algebra.Homology.Augment | ∀ {V : Type u} [inst : CategoryTheory.Category.{v, u} V] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms V]
(C : CochainComplex V ℕ) (i : ℕ), C.augmentTruncate.hom.f (i + 1) = CategoryTheory.CategoryStruct.id (C.X (i + 1)) | true |
ArzelaAscoli.compactSpace_of_isClosedEmbedding | Mathlib.Topology.UniformSpace.Ascoli | ∀ {ι : Type u_1} {X : Type u_2} {α : Type u_3} [inst : TopologicalSpace X] [inst_1 : UniformSpace α] {F : ι → X → α}
[inst_2 : TopologicalSpace ι] {𝔖 : Set (Set X)},
(∀ K ∈ 𝔖, IsCompact K) →
Topology.IsClosedEmbedding (⇑(UniformOnFun.ofFun 𝔖) ∘ F) →
(∀ K ∈ 𝔖, EquicontinuousOn F K) → (∀ K ∈ 𝔖, ∀ x ∈ K... | true |
Lean.Level.quote | Lean.Level | Lean.Level → optParam ℕ 0 → optParam Bool true → Lean.Syntax.Level | true |
Lean.Parser.Term.structInstField | Lean.Parser.Term.Basic | Lean.Parser.Parser | true |
ModuleCat.restrictScalarsId | Mathlib.Algebra.Category.ModuleCat.ChangeOfRings | (R : Type u₁) → [inst : Ring R] → ModuleCat.restrictScalars (RingHom.id R) ≅ CategoryTheory.Functor.id (ModuleCat R) | true |
QuadraticModuleCat.toModuleCat_tensor | Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat.Monoidal | ∀ {R : Type u} [inst : CommRing R] [inst_1 : Invertible 2] (X Y : QuadraticModuleCat R),
(CategoryTheory.MonoidalCategoryStruct.tensorObj X Y).toModuleCat =
CategoryTheory.MonoidalCategoryStruct.tensorObj X.toModuleCat Y.toModuleCat | true |
CategoryTheory.AddMon.equivLaxMonoidalFunctorPUnit_counitIso_inv_app_hom | Mathlib.CategoryTheory.Monoidal.Mon_ | ∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.MonoidalCategory C]
(X : CategoryTheory.AddMon C),
(CategoryTheory.AddMon.equivLaxMonoidalFunctorPUnit.counitIso.inv.app X).hom = CategoryTheory.CategoryStruct.id X.X | true |
WithTop.mul_lt_mul | Mathlib.Algebra.Order.Ring.WithTop | ∀ {α : Type u_1} [inst : DecidableEq α] [inst_1 : CommSemiring α] [inst_2 : PartialOrder α] [OrderBot α]
[inst_4 : CanonicallyOrderedAdd α] [PosMulStrictMono α] {a₁ a₂ b₁ b₂ : WithTop α},
a₁ < a₂ → b₁ < b₂ → a₁ * b₁ < a₂ * b₂ | true |
Lean.Elab.Tactic.BVDecide.Frontend.ReifiedBVLogical.of | Lean.Elab.Tactic.BVDecide.Frontend.BVDecide.Reify | Lean.Expr → Lean.Elab.Tactic.BVDecide.Frontend.LemmaM (Option Lean.Elab.Tactic.BVDecide.Frontend.ReifiedBVLogical) | true |
_private.Mathlib.Algebra.Order.Field.Basic.0.sub_self_div_two._proof_1_1 | Mathlib.Algebra.Order.Field.Basic | (1 + 1).AtLeastTwo | false |
SimpleGraph.Subgraph.comap_equiv_top | Mathlib.Combinatorics.SimpleGraph.Subgraph | ∀ {V : Type u} {W : Type v} {G : SimpleGraph V} {H : SimpleGraph W} (f : G →g H), SimpleGraph.Subgraph.comap f ⊤ = ⊤ | true |
exteriorPower.presentation.Rels | Mathlib.LinearAlgebra.ExteriorPower.Basic | Type u → Type u_4 → Type u_5 → Type (max (max u u_4) u_5) | true |
CategoryTheory.Pretriangulated.Triangle.rotate_mor₂ | Mathlib.CategoryTheory.Triangulated.Rotate | ∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Preadditive C]
[inst_2 : CategoryTheory.HasShift C ℤ] (T : CategoryTheory.Pretriangulated.Triangle C), T.rotate.mor₂ = T.mor₃ | true |
ProofWidgets.RpcEncodablePacket.«_@».ProofWidgets.Presentation.Expr.4196812879._hygCtx._hyg.1.recOn | ProofWidgets.Presentation.Expr | {motive : ProofWidgets.RpcEncodablePacket✝ → Sort u} →
(t : ProofWidgets.RpcEncodablePacket✝) → ((expr : Lean.Json) → motive { expr := expr }) → motive t | false |
ULift.algebra | Mathlib.Algebra.Algebra.Basic | {R : Type u_1} →
{A : Type u_2} → [inst : CommSemiring R] → [inst_1 : Semiring A] → [Algebra R A] → Algebra R (ULift.{u_4, u_2} A) | true |
CategoryTheory.Triangulated.Octahedron.mk.noConfusion | Mathlib.CategoryTheory.Triangulated.Triangulated | {C : Type u_1} →
{inst : CategoryTheory.Category.{v_1, u_1} C} →
{inst_1 : CategoryTheory.Preadditive C} →
{inst_2 : CategoryTheory.Limits.HasZeroObject C} →
{inst_3 : CategoryTheory.HasShift C ℤ} →
{inst_4 : ∀ (n : ℤ), (CategoryTheory.shiftFunctor C n).Additive} →
{inst_5 : Ca... | false |
_private.Mathlib.NumberTheory.Padics.Hensel.0.newton_seq_deriv_norm | Mathlib.NumberTheory.Padics.Hensel | ∀ {p : ℕ} [inst : Fact (Nat.Prime p)] {R : Type u_1} [inst_1 : CommSemiring R] [inst_2 : Algebra R ℤ_[p]]
{F : Polynomial R} {a : ℤ_[p]}
(hnorm : ‖(Polynomial.aeval a) F‖ < ‖(Polynomial.aeval a) (Polynomial.derivative F)‖ ^ 2) (n : ℕ),
‖(Polynomial.aeval (newton_seq_gen✝ hnorm n)) (Polynomial.derivative F)‖ =
... | true |
Std.DTreeMap.Const.getD_insertMany_list_of_contains_eq_false | Std.Data.DTreeMap.Lemmas | ∀ {α : Type u} {cmp : α → α → Ordering} {β : Type v} {t : Std.DTreeMap α (fun x => β) cmp} [Std.TransCmp cmp]
[inst : BEq α] [Std.LawfulBEqCmp cmp] {l : List (α × β)} {k : α} {fallback : β},
(List.map Prod.fst l).contains k = false →
Std.DTreeMap.Const.getD (Std.DTreeMap.Const.insertMany t l) k fallback = Std.D... | true |
CategoryTheory.Presieve.Arrows.Compatible.familyOfElements.congr_simp | Mathlib.CategoryTheory.Sites.IsSheafFor | ∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {P : CategoryTheory.Functor Cᵒᵖ (Type w)} {B : C}
{I : Type u_1} {X : I → C} {π π_1 : (i : I) → X i ⟶ B} (e_π : π = π_1) {x x_1 : (i : I) → P.obj (Opposite.op (X i))}
(e_x : x = x_1) (hx : CategoryTheory.Presieve.Arrows.Compatible P π x) ⦃Y : C⦄ (f f_1 : Y... | true |
MeasureTheory.OuterMeasure.mkMetric' | Mathlib.MeasureTheory.Measure.Hausdorff | {X : Type u_2} → [EMetricSpace X] → (Set X → ENNReal) → MeasureTheory.OuterMeasure X | true |
BitVec.instTransOrd | Init.Data.Ord.BitVec | ∀ {n : ℕ}, Std.TransOrd (BitVec n) | true |
Fin.preimage_rev_Ioo | Mathlib.Order.Interval.Set.Fin | ∀ {n : ℕ} (i j : Fin n), Fin.rev ⁻¹' Set.Ioo i j = Set.Ioo j.rev i.rev | true |
Lean.Compiler.LCNF.Simp.State.mk.sizeOf_spec | Lean.Compiler.LCNF.Simp.SimpM | ∀ (subst : Lean.Compiler.LCNF.FVarSubst Lean.Compiler.LCNF.Purity.pure) (used : Lean.Compiler.LCNF.UsedLocalDecls)
(binderRenaming : Lean.Compiler.LCNF.Renaming) (funDeclInfoMap : Lean.Compiler.LCNF.Simp.FunDeclInfoMap)
(simplified : Bool) (visited inline inlineLocal : ℕ),
sizeOf
{ subst := subst, used := u... | true |
Lean.Language.Lean.HeaderProcessedState.casesOn | Lean.Language.Lean.Types | {motive : Lean.Language.Lean.HeaderProcessedState → Sort u} →
(t : Lean.Language.Lean.HeaderProcessedState) →
((cmdState : Lean.Elab.Command.State) →
(firstCmdSnap : Lean.Language.SnapshotTask Lean.Language.Lean.CommandParsedSnapshot) →
motive { cmdState := cmdState, firstCmdSnap := firstCmdSnap... | false |
Nat.map_add_toArray_roc | Init.Data.Range.Polymorphic.NatLemmas | ∀ {m n k : ℕ}, Array.map (fun x => x + k) (m<...=n).toArray = ((m + k)<...=n + k).toArray | true |
Lean.Grind.decide_eq_false | Init.Grind.Lemmas | ∀ {p : Prop} {x : Decidable p}, p = False → decide p = false | true |
CategoryTheory.Bicategory.Pith.pseudofunctorToPithCompInclusionStrongIsoHom._proof_6 | Mathlib.CategoryTheory.Bicategory.LocallyGroupoid | ∀ {B : Type u_6} [inst : CategoryTheory.Bicategory B] {B' : Type u_2} [inst_1 : CategoryTheory.Bicategory B']
[inst_2 : CategoryTheory.Bicategory.IsLocallyGroupoid B'] (F : CategoryTheory.Pseudofunctor B' B) {a b c : B'}
(f : a ⟶ b) (g : b ⟶ c),
CategoryTheory.CategoryStruct.comp
(CategoryTheory.Bicategory.... | false |
CategoryTheory.Functor.isRightAdjoint_comp | Mathlib.CategoryTheory.Adjunction.Basic | ∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
{E : Type u₃} [inst_2 : CategoryTheory.Category.{v₃, u₃} E] {F : CategoryTheory.Functor C D}
{G : CategoryTheory.Functor D E} [F.IsRightAdjoint] [G.IsRightAdjoint], (F.comp G).IsRightAdjoint | true |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.