name
stringlengths
2
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6
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stringlengths
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allowCompletion
bool
2 classes
trdeg_add_eq
Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis
∀ (R : Type u_1) (S : Type v) [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] [Nontrivial R] {A : Type v} [inst_4 : CommRing A] [NoZeroDivisors A] [inst_6 : Algebra R A] [inst_7 : Algebra S A] [FaithfulSMul R S] [FaithfulSMul S A] [IsScalarTower R S A], Algebra.trdeg R S + Algebra.trdeg S A = Algebra.trdeg R A
true
Std.Internal.List.containsKey_filter_not_contains_iff
Std.Data.Internal.List.Associative
∀ {α : Type u} {β : α → Type v} [inst : BEq α] [EquivBEq α] {l₁ : List ((a : α) × β a)} {l₂ : List α} {hl₁ : Std.Internal.List.DistinctKeys l₁} {k : α}, Std.Internal.List.containsKey k (List.filter (fun p => !l₂.contains p.fst) l₁) = true ↔ Std.Internal.List.containsKey k l₁ = true ∧ ¬l₂.contains k = true
true
Lean.Core.CoreM.asTask'
Lean.Elab.Task
{α : Type} → Lean.CoreM α → Lean.CoreM (Task (Lean.CoreM α))
true
Std.Time.Format.parse
Std.Time.Format.Basic
{f : Type} → {typ : Type → f → Type} → [self : Std.Time.Format f typ] → {α : Type} → (fmt : f) → typ (Option α) fmt → String → Except String α
true
_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.sigma_eq_iff_eq_comp_cast.match_1_1
Mathlib.Data.Fin.Tuple.Basic
∀ {α : Type u_1} {a b : (ii : ℕ) × (Fin ii → α)} (motive : (∃ (h : a.fst = b.fst), a.snd = b.snd ∘ Fin.cast h) → Prop) (x : ∃ (h : a.fst = b.fst), a.snd = b.snd ∘ Fin.cast h), (∀ (w : a.fst = b.fst) (h' : a.snd = b.snd ∘ Fin.cast w), motive ⋯) → motive x
false
Lean.Meta.mkImpCongr
Lean.Meta.AppBuilder
Lean.Expr → Lean.Expr → Lean.MetaM Lean.Expr
true
Polynomial.instNatCast
Mathlib.Algebra.Polynomial.Basic
{R : Type u} → [inst : Semiring R] → NatCast (Polynomial R)
true
Equiv.symm_bijective
Mathlib.Logic.Equiv.Defs
∀ {α : Sort u} {β : Sort v}, Function.Bijective Equiv.symm
true
CategoryTheory.Limits.MonoCoprod.isColimitBinaryCofanSum._proof_2
Mathlib.CategoryTheory.Limits.MonoCoprod
∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] {I₁ : Type u_3} {I₂ : Type u_4} {X : I₁ ⊕ I₂ → C} (c : CategoryTheory.Limits.Cofan X) (c₁ : CategoryTheory.Limits.Cofan (X ∘ Sum.inl)) (c₂ : CategoryTheory.Limits.Cofan (X ∘ Sum.inr)) (hc : CategoryTheory.Limits.IsColimit c) (hc₁ : CategoryTheory.Limits.IsColimit c₁) (hc₂ : CategoryTheory.Limits.IsColimit c₂) {T : C} (f₁ : c₁.pt ⟶ T) (f₂ : c₂.pt ⟶ T), CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.MonoCoprod.binaryCofanSum c c₁ c₂ hc₁ hc₂).inr (CategoryTheory.Limits.Cofan.IsColimit.desc hc fun i => match i with | Sum.inl i₁ => CategoryTheory.CategoryStruct.comp (c₁.inj i₁) f₁ | Sum.inr i₂ => CategoryTheory.CategoryStruct.comp (c₂.inj i₂) f₂) = f₂
false
Nat.toList_roc_eq_if
Init.Data.Range.Polymorphic.NatLemmas
∀ {m n : ℕ}, (m<...=n).toList = if m + 1 ≤ n then (m + 1) :: ((m + 1)<...=n).toList else []
true
PadicInt.instCommRing._aux_37
Mathlib.NumberTheory.Padics.PadicIntegers
{p : ℕ} → [hp : Fact (Nat.Prime p)] → ℤ → ℤ_[p] → ℤ_[p]
false
_private.Mathlib.Combinatorics.SimpleGraph.Walks.Counting.0.SimpleGraph.finsetWalkLength.match_1.eq_2
Mathlib.Combinatorics.SimpleGraph.Walks.Counting
∀ (motive : ℕ → Sort u_1) (n : ℕ) (h_1 : Unit → motive 0) (h_2 : (n : ℕ) → motive n.succ), (match n.succ with | 0 => h_1 () | n.succ => h_2 n) = h_2 n
true
AlgebraicGeometry.AffineTargetMorphismProperty.IsLocal.mk._flat_ctor
Mathlib.AlgebraicGeometry.Morphisms.Basic
∀ {P : AlgebraicGeometry.AffineTargetMorphismProperty}, P.toProperty.RespectsIso → (∀ {X Y : AlgebraicGeometry.Scheme} [inst : AlgebraicGeometry.IsAffine Y] (f : X ⟶ Y) (r : ↑(Y.presheaf.obj (Opposite.op ⊤))), P f → P (f ∣_ Y.basicOpen r)) → (∀ {X Y : AlgebraicGeometry.Scheme} [inst : AlgebraicGeometry.IsAffine Y] (f : X ⟶ Y) (s : Finset ↑(Y.presheaf.obj (Opposite.op ⊤))), Ideal.span ↑s = ⊤ → (∀ (r : ↥s), P (f ∣_ Y.basicOpen ↑r)) → P f) → P.IsLocal
false
FirstOrder.Language.LHom.casesOn
Mathlib.ModelTheory.LanguageMap
{L : FirstOrder.Language} → {L' : FirstOrder.Language} → {motive : (L →ᴸ L') → Sort u_1} → (t : L →ᴸ L') → ((onFunction : ⦃n : ℕ⦄ → L.Functions n → L'.Functions n) → (onRelation : ⦃n : ℕ⦄ → L.Relations n → L'.Relations n) → motive { onFunction := onFunction, onRelation := onRelation }) → motive t
false
hasFPowerSeriesOnBall_pi_iff
Mathlib.Analysis.Analytic.Constructions
∀ {𝕜 : Type u_2} [inst : NontriviallyNormedField 𝕜] {E : Type u_3} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace 𝕜 E] {ι : Type u_9} [inst_3 : Fintype ι] {e : E} {Fm : ι → Type u_10} [inst_4 : (i : ι) → NormedAddCommGroup (Fm i)] [inst_5 : (i : ι) → NormedSpace 𝕜 (Fm i)] {f : (i : ι) → E → Fm i} {r : ENNReal} {p : (i : ι) → FormalMultilinearSeries 𝕜 E (Fm i)}, 0 < r → (HasFPowerSeriesOnBall (fun x x_1 => f x_1 x) (FormalMultilinearSeries.pi p) e r ↔ ∀ (i : ι), HasFPowerSeriesOnBall (f i) (p i) e r)
true
Module.comap_annihilator
Mathlib.RingTheory.Ideal.Maps
∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {R₀ : Type u_4} [inst_3 : CommSemiring R₀] [inst_4 : Module R₀ M] [inst_5 : Algebra R₀ R] [IsScalarTower R₀ R M], Ideal.comap (algebraMap R₀ R) (Module.annihilator R M) = Module.annihilator R₀ M
true
_private.Lean.Compiler.IR.LLVMBindings.0.LLVM.Visibility.mk
Lean.Compiler.IR.LLVMBindings
UInt64 → LLVM.Visibility
true
Lean.Elab.Tactic.Doc.TacticDoc.docString
Lean.Elab.Tactic.Doc
Lean.Elab.Tactic.Doc.TacticDoc → Option String
true
Set.mul_sInter_subset
Mathlib.Algebra.Group.Pointwise.Set.Lattice
∀ {α : Type u_2} [inst : Mul α] (s : Set α) (T : Set (Set α)), s * ⋂₀ T ⊆ ⋂ t ∈ T, s * t
true
Lean.ConstantKind.ctor.elim
Lean.Environment
{motive : Lean.ConstantKind → Sort u} → (t : Lean.ConstantKind) → t.ctorIdx = 6 → motive Lean.ConstantKind.ctor → motive t
false
Subgroup.IsSubnormal.brecOn
Mathlib.GroupTheory.IsSubnormal
∀ {G : Type u_1} [inst : Group G] {motive : (a : Subgroup G) → a.IsSubnormal → Prop} {a : Subgroup G} (t : a.IsSubnormal), (∀ (a : Subgroup G) (t : a.IsSubnormal), Subgroup.IsSubnormal.below t → motive a t) → motive a t
true
IsDedekindDomain.HeightOneSpectrum.intValuation_le_pow_iff_dvd
Mathlib.RingTheory.DedekindDomain.AdicValuation
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsDedekindDomain R] (v : IsDedekindDomain.HeightOneSpectrum R) (r : R) (n : ℕ), v.intValuation r ≤ WithZero.exp (-↑n) ↔ v.asIdeal ^ n ∣ Ideal.span {r}
true
Std.DTreeMap.Internal.Impl.Const.getKey!_insertManyIfNewUnit_list_of_not_mem_of_contains_eq_false
Std.Data.DTreeMap.Internal.Lemmas
∀ {α : Type u} {instOrd : Ord α} {t : Std.DTreeMap.Internal.Impl α fun x => Unit} [inst : BEq α] [Std.LawfulBEqOrd α] [Std.TransOrd α] [inst_3 : Inhabited α] (h : t.WF) {l : List α} {k : α}, k ∉ t → l.contains k = false → (↑(Std.DTreeMap.Internal.Impl.Const.insertManyIfNewUnit t l ⋯)).getKey! k = default
true
MulOpposite.unop_inj
Mathlib.Algebra.Opposites
∀ {α : Type u_1} {x y : αᵐᵒᵖ}, MulOpposite.unop x = MulOpposite.unop y ↔ x = y
true
SimpleGraph.Walk.IsPath.transfer
Mathlib.Combinatorics.SimpleGraph.Paths
∀ {V : Type u} {G : SimpleGraph V} {u v : V} {H : SimpleGraph V} {p : G.Walk u v} (hp : ∀ e ∈ p.edges, e ∈ H.edgeSet), p.IsPath → (p.transfer H hp).IsPath
true
_private.Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic.0.Mathlib.Meta.Positivity.evalRealPi.match_1
Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic
(motive : (u : Lean.Level) → {α : Q(Type u)} → (_zα : Q(Zero «$α»)) → (_pα : Q(PartialOrder «$α»)) → (e : Q(«$α»)) → Lean.MetaM (Mathlib.Meta.Positivity.Strictness _zα _pα e) → Lean.MetaM (Mathlib.Meta.Positivity.Strictness _zα _pα e) → Sort u_1) → (u : Lean.Level) → {α : Q(Type u)} → (_zα : Q(Zero «$α»)) → (_pα : Q(PartialOrder «$α»)) → (e : Q(«$α»)) → (__alt __alt_1 : Lean.MetaM (Mathlib.Meta.Positivity.Strictness _zα _pα e)) → ((α : Q(Type)) → (_zα : Q(Zero «$α»)) → (_pα : Q(PartialOrder «$α»)) → (e : Q(«$α»)) → (__alt __alt_2 : Lean.MetaM (Mathlib.Meta.Positivity.Strictness _zα _pα e)) → motive Lean.Level.zero _zα _pα e __alt __alt_2) → ((x : Lean.Level) → (α : Q(Type x)) → (_zα : Q(Zero «$α»)) → (_pα : Q(PartialOrder «$α»)) → (e : Q(«$α»)) → (__alt __alt_2 : Lean.MetaM (Mathlib.Meta.Positivity.Strictness _zα _pα e)) → motive x _zα _pα e __alt __alt_2) → motive u _zα _pα e __alt __alt_1
false
HahnSeries.instNonUnitalCommSemiring
Mathlib.RingTheory.HahnSeries.Multiplication
{Γ : Type u_1} → {R : Type u_3} → [inst : AddCommMonoid Γ] → [inst_1 : PartialOrder Γ] → [IsOrderedCancelAddMonoid Γ] → [inst : NonUnitalCommSemiring R] → NonUnitalCommSemiring (HahnSeries Γ R)
true
CategoryTheory.leftAdjointMate
Mathlib.CategoryTheory.Monoidal.Rigid.Basic
{C : Type u₁} → [inst : CategoryTheory.Category.{v₁, u₁} C] → [inst_1 : CategoryTheory.MonoidalCategory C] → {X Y : C} → [inst_2 : CategoryTheory.HasLeftDual X] → [inst_3 : CategoryTheory.HasLeftDual Y] → (X ⟶ Y) → (ᘁY ⟶ ᘁX)
true
Lean.Elab.Term.elabValueOf._regBuiltin.Lean.Elab.Term.elabValueOf_1
Lean.Elab.BuiltinTerm
IO Unit
false
BitVec.reduceNe
Lean.Meta.Tactic.Simp.BuiltinSimprocs.BitVec
Lean.Meta.Simp.Simproc
true
LightCondensed.locallyConstantIsoFinYoneda
Mathlib.Condensed.Discrete.Colimit
(F : CategoryTheory.Functor LightProfiniteᵒᵖ (Type u)) → FintypeCat.toLightProfinite.op.comp (LightCondensed.locallyConstantPresheaf (F.obj (FintypeCat.toLightProfinite.op.obj (Opposite.op (FintypeCat.of PUnit.{u + 1}))))) ≅ LightCondensed.finYoneda F
true
_private.Mathlib.Topology.Algebra.InfiniteSum.Defs.0.hasSum_sum_support_of_ne_finset_zero._proof_1_4
Mathlib.Topology.Algebra.InfiniteSum.Defs
∀ {α : Type u_2} {β : Type u_1} {L : SummationFilter β} {f : β → α} {s : Finset β} [inst : DecidablePred fun x => x ∈ L.support] (t : Finset β), ∀ a ∈ t, a ∈ (↑s ∩ L.support).toFinset → f a = f a
false
QuotientGroup.quotientQuotientIsometryEquivQuotient.eq_1
Mathlib.Analysis.Normed.Group.Quotient
∀ {M : Type u_1} [inst : SeminormedCommGroup M] {S T : Subgroup M} (h : S ≤ T), QuotientGroup.quotientQuotientIsometryEquivQuotient h = { toEquiv := (QuotientGroup.quotientQuotientEquivQuotient S T h).toEquiv, isometry_toFun := ⋯ }
true
finAddFlip.eq_1
Mathlib.Logic.Equiv.Fin.Basic
∀ {m n : ℕ}, finAddFlip = (finSumFinEquiv.symm.trans (Equiv.sumComm (Fin m) (Fin n))).trans finSumFinEquiv
true
Lean.Meta.Grind.EMatchTheoremConstraint.sizeLt.injEq
Lean.Meta.Tactic.Grind.Extension
∀ (lhs n lhs_1 n_1 : ℕ), (Lean.Meta.Grind.EMatchTheoremConstraint.sizeLt lhs n = Lean.Meta.Grind.EMatchTheoremConstraint.sizeLt lhs_1 n_1) = (lhs = lhs_1 ∧ n = n_1)
true
LinearEquiv.conj_exact_iff_exact
Mathlib.Algebra.Exact
∀ {R : Type u_1} {M : Type u_2} {N : Type u_4} {N' : Type u_5} {P : Type u_6} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : AddCommMonoid N] [inst_3 : AddCommMonoid N'] [inst_4 : AddCommMonoid P] [inst_5 : Module R M] [inst_6 : Module R N] [inst_7 : Module R N'] [inst_8 : Module R P] (f : M →ₗ[R] N) (g : N →ₗ[R] P) (e : N ≃ₗ[R] N'), Function.Exact ⇑(↑e ∘ₗ f) ⇑(g ∘ₗ ↑e.symm) ↔ Function.Exact ⇑f ⇑g
true
ValuativeRel.srel_iff
Mathlib.RingTheory.Valuation.ValuativeRel.Basic
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : ValuativeRel R] {x y : R}, x <ᵥ y ↔ ¬y ≤ᵥ x
true
AffineMap.lineMap_eq_right_iff
Mathlib.LinearAlgebra.AffineSpace.AffineMap
∀ {k : Type u_1} {V1 : Type u_2} {P1 : Type u_3} [inst : Ring k] [inst_1 : AddCommGroup V1] [inst_2 : Module k V1] [inst_3 : AddTorsor V1 P1] [IsDomain k] [Module.IsTorsionFree k V1] {p₀ p₁ : P1} {c : k}, (AffineMap.lineMap p₀ p₁) c = p₁ ↔ p₀ = p₁ ∨ c = 1
true
_private.Mathlib.Data.List.Basic.0.List.getLast_append_of_right_ne_nil._proof_1_12
Mathlib.Data.List.Basic
∀ {α : Type u_1} (l₂ : List α) (head : α) (tail : List α), (head :: tail ++ l₂).length - 1 + 1 ≤ (head :: tail).length → (head :: tail ++ l₂).length - 1 < (head :: tail).length
false
NumberField.FinitePlace.mk._proof_1
Mathlib.NumberTheory.NumberField.Completion.FinitePlace
∀ {K : Type u_1} [inst : Field K] [inst_1 : NumberField K] (v : IsDedekindDomain.HeightOneSpectrum (NumberField.RingOfIntegers K)), ∃ v_1, NumberField.place (NumberField.FinitePlace.embedding v_1) = NumberField.place (NumberField.FinitePlace.embedding v)
false
Std.ExtDTreeMap.getKeyD_maxKey?
Std.Data.ExtDTreeMap.Lemmas
∀ {α : Type u} {β : α → Type v} {cmp : α → α → Ordering} {t : Std.ExtDTreeMap α β cmp} [inst : Std.TransCmp cmp] {km fallback : α}, t.maxKey? = some km → t.getKeyD km fallback = km
true
interior_inter
Mathlib.Topology.Closure
∀ {X : Type u} [inst : TopologicalSpace X] {s t : Set X}, interior (s ∩ t) = interior s ∩ interior t
true
NumberField.IsCMField.of_forall_isConj
Mathlib.NumberTheory.NumberField.CMField
∀ (K : Type u_2) [inst : Field K] [inst_1 : CharZero K] [Algebra.IsIntegral ℚ K] [NumberField.IsTotallyComplex K] [IsGalois ℚ K] {σ : Gal(K/ℚ)}, (∀ (φ : K →+* ℂ), NumberField.ComplexEmbedding.IsConj φ σ) → NumberField.IsCMField K
true
SymmetricPower.Rel.recOn
Mathlib.LinearAlgebra.TensorPower.Symmetric
∀ {R ι : Type u} [inst : CommSemiring R] {M : Type v} [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {motive : (a a_1 : PiTensorProduct R fun x => M) → SymmetricPower.Rel R ι M a a_1 → Prop} {a a_1 : PiTensorProduct R fun x => M} (t : SymmetricPower.Rel R ι M a a_1), (∀ (e : Equiv.Perm ι) (f : ι → M), motive ((PiTensorProduct.tprod R) fun i => f i) ((PiTensorProduct.tprod R) fun i => f (e i)) ⋯) → motive a a_1 t
false
_private.Lean.Parser.Extension.0.Lean.Parser.isParserAlias.match_1
Lean.Parser.Extension
(motive : Option (Lean.Parser.AliasValue Lean.Parser.Parser) → Sort u_1) → (__do_lift : Option (Lean.Parser.AliasValue Lean.Parser.Parser)) → ((val : Lean.Parser.AliasValue Lean.Parser.Parser) → motive (some val)) → ((x : Option (Lean.Parser.AliasValue Lean.Parser.Parser)) → motive x) → motive __do_lift
false
CategoryTheory.Bicategory.InducedBicategory.Hom₂.rec
Mathlib.CategoryTheory.Bicategory.InducedBicategory
{B : Type u_1} → {C : Type u_2} → [inst : CategoryTheory.Bicategory C] → {F : B → C} → {X Y : CategoryTheory.Bicategory.InducedBicategory C F} → {f g : X ⟶ Y} → {motive : CategoryTheory.Bicategory.InducedBicategory.Hom₂ f g → Sort u} → ((hom : f.hom ⟶ g.hom) → motive { hom := hom }) → (t : CategoryTheory.Bicategory.InducedBicategory.Hom₂ f g) → motive t
false
Std.Packages.LinearOrderOfOrdArgs.max_eq._autoParam
Init.Data.Order.PackageFactories
Lean.Syntax
false
IsLocallyConstant.apply_eq_of_preconnectedSpace
Mathlib.Topology.LocallyConstant.Basic
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [PreconnectedSpace X] {f : X → Y}, IsLocallyConstant f → ∀ (x y : X), f x = f y
true
_private.Mathlib.Data.ENat.Basic.0.ENat.top_ne_one.match_1_1
Mathlib.Data.ENat.Basic
∀ (motive : ⊤ = 1 → Prop) (a : ⊤ = 1), motive a
false
Set.powersetCard.compl.congr_simp
Mathlib.GroupTheory.GroupAction.SubMulAction.Combination
∀ {α : Type u_1} {n : ℕ} [inst : DecidableEq α] [inst_1 : Fintype α] {m : ℕ} (hm : m + n = Fintype.card α), Set.powersetCard.compl hm = Set.powersetCard.compl hm
true
Module.Relations.Solution.ofπ'._proof_1
Mathlib.Algebra.Module.Presentation.Basic
∀ {A : Type u_2} [inst : Ring A] {relations : Module.Relations A} {M : Type u_1} [inst_1 : AddCommGroup M] [inst_2 : Module A M] (π : (relations.G →₀ A) →ₗ[A] M), π ∘ₗ relations.map = 0 → ∀ (r : relations.R), π (relations.relation r) = 0
false
_private.Mathlib.GroupTheory.RegularWreathProduct.0.RegularWreathProduct.instFaithfulSMulProdOfNonempty._simp_5
Mathlib.GroupTheory.RegularWreathProduct
∀ {G : Type u_1} [inst : DivInvMonoid G] (x : G), x⁻¹ = x ^ (-1)
false
_private.Mathlib.Algebra.BigOperators.Expect.0.Finset.expect_ite_mem._simp_1_2
Mathlib.Algebra.BigOperators.Expect
∀ {α : Type u_1} [inst : DivisionCommMonoid α] (a b : α), b / a = a⁻¹ * b
false
CategoryTheory.hoFunctor.isIso_prodComparison
Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction
∀ (X Y : SSet), CategoryTheory.IsIso (CategoryTheory.Limits.prodComparison SSet.hoFunctor X Y)
true
_private.Mathlib.Algebra.Lie.Weights.Basic.0.LieModule.posFittingComp_map_incl_sup_of_codisjoint._simp_1_2
Mathlib.Algebra.Lie.Weights.Basic
∀ (R : Type u_2) (L : Type u_3) (M : Type u_4) [inst : CommRing R] [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 : LieRing.IsNilpotent L] [IsNoetherian R M] [IsArtinian R M], LieModule.posFittingComp R L M = ⨅ k, LieModule.lowerCentralSeries R L M k
false
ValuationSubring.integer_valuation
Mathlib.RingTheory.Valuation.ValuationSubring
∀ {K : Type u} [inst : Field K] (A : ValuationSubring K), A.valuation.integer = A.toSubring
true
ContinuousLinearMap.precompCompactConvergenceCLM._proof_1
Mathlib.Topology.Algebra.Module.StrongTopology
∀ {𝕜₁ : Type u_3} {𝕜₂ : Type u_4} [inst : NormedField 𝕜₁] [inst_1 : NormedField 𝕜₂] {σ : 𝕜₁ →+* 𝕜₂} {E : Type u_1} {F : Type u_2} [inst_2 : AddCommGroup E] [inst_3 : Module 𝕜₁ E] [inst_4 : AddCommGroup F] [inst_5 : Module 𝕜₂ F] [inst_6 : TopologicalSpace E] [inst_7 : TopologicalSpace F] (L : E →SL[σ] F), ∀ x ∈ {S | IsCompact S}, IsCompact (⇑L '' x)
false
CategoryTheory.SimplicialObject.Homotopy.h_comp_σ_succ_of_lt_assoc
Mathlib.AlgebraicTopology.SimplicialObject.Homotopy
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : CategoryTheory.SimplicialObject C} {f g : X ⟶ Y} (self : CategoryTheory.SimplicialObject.Homotopy f g) {n : ℕ} (i j : Fin (n + 1)), j ≤ i → ∀ {Z : C} (h : Y.obj (Opposite.op (SimplexCategory.mk (n + 1 + 1))) ⟶ Z), CategoryTheory.CategoryStruct.comp (self.h j) (CategoryTheory.CategoryStruct.comp (Y.σ i.succ) h) = CategoryTheory.CategoryStruct.comp (X.σ i) (CategoryTheory.CategoryStruct.comp (self.h j.castSucc) h)
true
CircleDeg1Lift.lt_map_of_int_lt_translationNumber
Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber
∀ (f : CircleDeg1Lift) {n : ℤ}, ↑n < f.translationNumber → ∀ (x : ℝ), x + ↑n < f x
true
Lean.Order.PartialOrder.noConfusion
Init.Internal.Order.Basic
{P : Sort u_1} → {α : Sort u} → {t : Lean.Order.PartialOrder α} → {α' : Sort u} → {t' : Lean.Order.PartialOrder α'} → α = α' → t ≍ t' → Lean.Order.PartialOrder.noConfusionType P t t'
false
_private.Mathlib.Algebra.Homology.ShortComplex.Preadditive.0.CategoryTheory.ShortComplex.Homotopy.ext.match_1
Mathlib.Algebra.Homology.ShortComplex.Preadditive
∀ {C : Type u_2} {inst : CategoryTheory.Category.{u_1, u_2} C} {inst_1 : CategoryTheory.Preadditive C} {S₁ S₂ : CategoryTheory.ShortComplex C} {φ₁ φ₂ : S₁ ⟶ S₂} (motive : CategoryTheory.ShortComplex.Homotopy φ₁ φ₂ → Prop) (h : CategoryTheory.ShortComplex.Homotopy φ₁ φ₂), (∀ (h₀ : S₁.X₁ ⟶ S₂.X₁) (h₀_f : autoParam (CategoryTheory.CategoryStruct.comp h₀ S₂.f = 0) CategoryTheory.ShortComplex.Homotopy.h₀_f._autoParam) (h₁ : S₁.X₂ ⟶ S₂.X₁) (h₂ : S₁.X₃ ⟶ S₂.X₂) (h₃ : S₁.X₃ ⟶ S₂.X₃) (g_h₃ : autoParam (CategoryTheory.CategoryStruct.comp S₁.g h₃ = 0) CategoryTheory.ShortComplex.Homotopy.g_h₃._autoParam) (comm₁ : autoParam (φ₁.τ₁ = CategoryTheory.CategoryStruct.comp S₁.f h₁ + h₀ + φ₂.τ₁) CategoryTheory.ShortComplex.Homotopy.comm₁._autoParam) (comm₂ : autoParam (φ₁.τ₂ = CategoryTheory.CategoryStruct.comp S₁.g h₂ + CategoryTheory.CategoryStruct.comp h₁ S₂.f + φ₂.τ₂) CategoryTheory.ShortComplex.Homotopy.comm₂._autoParam) (comm₃ : autoParam (φ₁.τ₃ = h₃ + CategoryTheory.CategoryStruct.comp h₂ S₂.g + φ₂.τ₃) CategoryTheory.ShortComplex.Homotopy.comm₃._autoParam), motive { h₀ := h₀, h₀_f := h₀_f, h₁ := h₁, h₂ := h₂, h₃ := h₃, g_h₃ := g_h₃, comm₁ := comm₁, comm₂ := comm₂, comm₃ := comm₃ }) → motive h
false
measurable_from_top
Mathlib.MeasureTheory.MeasurableSpace.Basic
∀ {α : Type u_1} {β : Type u_2} [inst : MeasurableSpace β] {f : α → β}, Measurable f
true
_private.Mathlib.Lean.MessageData.ForExprs.0.Lean.MessageData.forExprsIn.goFmt
Mathlib.Lean.MessageData.ForExprs
{m : Type → Type u} → [Monad m] → {σ : Type} → (Lean.PPContext × Lean.Expr → σ → m (ForInStep σ)) → Lean.PPContext → Lean.PrettyPrinter.InfoPerPos → σ → Std.Format → m (ForInStep σ)
true
Denumerable.lower.eq_2
Mathlib.Logic.Equiv.Multiset
∀ (x m : ℕ) (l : List ℕ), Denumerable.lower (m :: l) x = (m - x) :: Denumerable.lower l m
true
compl_sSup'
Mathlib.Order.CompleteBooleanAlgebra
∀ {α : Type u} [inst : CompleteBooleanAlgebra α] {s : Set α}, (sSup s)ᶜ = sInf (compl '' s)
true
UniformEquiv.prodPUnit._proof_1
Mathlib.Topology.UniformSpace.Equiv
∀ (α : Type u_1) [inst : UniformSpace α], UniformContinuous fun a => (id a, PUnit.unit)
false
LightCondMod.instReflectsEpimorphismsLightCondSetForget
Mathlib.Condensed.Light.Epi
∀ (R : Type u) [inst : Ring R], (LightCondensed.forget R).ReflectsEpimorphisms
true
groupCohomology.dArrowIso₀₁._proof_1
Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree
IsRightCancelAdd ℕ
false
HomologicalComplex₂.ofGradedObject_d_f
Mathlib.Algebra.Homology.HomologicalBicomplex
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] {I₁ : Type u_2} {I₂ : Type u_3} (c₁ : ComplexShape I₁) (c₂ : ComplexShape I₂) (X : CategoryTheory.GradedObject (I₁ × I₂) C) (d₁ : (i₁ i₁' : I₁) → (i₂ : I₂) → X (i₁, i₂) ⟶ X (i₁', i₂)) (d₂ : (i₁ : I₁) → (i₂ i₂' : I₂) → X (i₁, i₂) ⟶ X (i₁, i₂')) (shape₁ : ∀ (i₁ i₁' : I₁), ¬c₁.Rel i₁ i₁' → ∀ (i₂ : I₂), d₁ i₁ i₁' i₂ = 0) (shape₂ : ∀ (i₁ : I₁) (i₂ i₂' : I₂), ¬c₂.Rel i₂ i₂' → d₂ i₁ i₂ i₂' = 0) (d₁_comp_d₁ : ∀ (i₁ i₁' i₁'' : I₁) (i₂ : I₂), CategoryTheory.CategoryStruct.comp (d₁ i₁ i₁' i₂) (d₁ i₁' i₁'' i₂) = 0) (d₂_comp_d₂ : ∀ (i₁ : I₁) (i₂ i₂' i₂'' : I₂), CategoryTheory.CategoryStruct.comp (d₂ i₁ i₂ i₂') (d₂ i₁ i₂' i₂'') = 0) (comm : ∀ (i₁ i₁' : I₁) (i₂ i₂' : I₂), CategoryTheory.CategoryStruct.comp (d₁ i₁ i₁' i₂) (d₂ i₁' i₂ i₂') = CategoryTheory.CategoryStruct.comp (d₂ i₁ i₂ i₂') (d₁ i₁ i₁' i₂')) (i₁ i₁' : I₁) (i₂ : I₂), ((HomologicalComplex₂.ofGradedObject c₁ c₂ X d₁ d₂ shape₁ shape₂ d₁_comp_d₁ d₂_comp_d₂ comm).d i₁ i₁').f i₂ = d₁ i₁ i₁' i₂
true
ContinuousAddEquiv.mk.inj
Mathlib.Topology.Algebra.ContinuousMonoidHom
∀ {G : Type u} {inst : TopologicalSpace G} {H : Type v} {inst_1 : TopologicalSpace H} {inst_2 : Add G} {inst_3 : Add H} {toAddEquiv : G ≃+ H} {continuous_toFun : autoParam (Continuous toAddEquiv.toFun) Homeomorph.continuous_toFun._autoParam} {continuous_invFun : autoParam (Continuous toAddEquiv.invFun) Homeomorph.continuous_invFun._autoParam} {toAddEquiv_1 : G ≃+ H} {continuous_toFun_1 : autoParam (Continuous toAddEquiv_1.toFun) Homeomorph.continuous_toFun._autoParam} {continuous_invFun_1 : autoParam (Continuous toAddEquiv_1.invFun) Homeomorph.continuous_invFun._autoParam}, { toAddEquiv := toAddEquiv, continuous_toFun := continuous_toFun, continuous_invFun := continuous_invFun } = { toAddEquiv := toAddEquiv_1, continuous_toFun := continuous_toFun_1, continuous_invFun := continuous_invFun_1 } → toAddEquiv = toAddEquiv_1
true
CategoryTheory.Limits.FormalCoproduct.category._proof_6
Mathlib.CategoryTheory.Limits.FormalCoproducts.Basic
∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_3, u_2} C] {W X Y Z : CategoryTheory.Limits.FormalCoproduct C} (f : W.Hom X) (g : X.Hom Y) (h : Y.Hom Z), { f := h.f ∘ { f := g.f ∘ f.f, φ := fun x => CategoryTheory.CategoryStruct.comp (f.φ x) (g.φ (f.f x)) }.f, φ := fun x => CategoryTheory.CategoryStruct.comp ({ f := g.f ∘ f.f, φ := fun x => CategoryTheory.CategoryStruct.comp (f.φ x) (g.φ (f.f x)) }.φ x) (h.φ ({ f := g.f ∘ f.f, φ := fun x => CategoryTheory.CategoryStruct.comp (f.φ x) (g.φ (f.f x)) }.f x)) } = { f := { f := h.f ∘ g.f, φ := fun x => CategoryTheory.CategoryStruct.comp (g.φ x) (h.φ (g.f x)) }.f ∘ f.f, φ := fun x => CategoryTheory.CategoryStruct.comp (f.φ x) ({ f := h.f ∘ g.f, φ := fun x => CategoryTheory.CategoryStruct.comp (g.φ x) (h.φ (g.f x)) }.φ (f.f x)) }
false
Lean.Meta.Sym.getLevel
Lean.Meta.Sym.InferType
Lean.Expr → Lean.Meta.Sym.SymM Lean.Level
true
SheafOfModules.pushforwardNatIso
Mathlib.Algebra.Category.ModuleCat.Sheaf.PushforwardContinuous
{C : Type u₁} → [inst : CategoryTheory.Category.{v₁, u₁} C] → {D : Type u₂} → [inst_1 : CategoryTheory.Category.{v₂, u₂} D] → {J : CategoryTheory.GrothendieckTopology C} → {K : CategoryTheory.GrothendieckTopology D} → {F G : CategoryTheory.Functor C D} → {T : CategoryTheory.Sheaf J RingCat} → {S : CategoryTheory.Sheaf K RingCat} → [inst_2 : F.IsContinuous J K] → [inst_3 : G.IsContinuous J K] → (φ : T ⟶ (G.sheafPushforwardContinuous RingCat J K).obj S) → (α : F ≅ G) → SheafOfModules.pushforward φ ≅ SheafOfModules.pushforward (CategoryTheory.CategoryStruct.comp φ ((CategoryTheory.Functor.sheafPushforwardContinuousNatTrans α.hom RingCat J K).app S))
true
Int8.shiftRight_and
Init.Data.SInt.Bitwise
∀ {a b c : Int8}, (a &&& b) >>> c = a >>> c &&& b >>> c
true
BoxIntegral.unitPartition.mem_box_iff_index
Mathlib.Analysis.BoxIntegral.UnitPartition
∀ {ι : Type u_1} {n : ℕ} [inst : NeZero n] {x : ι → ℝ} {ν : ι → ℤ}, x ∈ BoxIntegral.unitPartition.box n ν ↔ BoxIntegral.unitPartition.index n x = ν
true
CategoryTheory.Limits.preservesColimitsOfSize_shrink
Mathlib.CategoryTheory.Limits.Preserves.Basic
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D] (F : CategoryTheory.Functor C D) [CategoryTheory.Limits.PreservesColimitsOfSize.{max w w₂, max w' w₂', v₁, v₂, u₁, u₂} F], CategoryTheory.Limits.PreservesColimitsOfSize.{w, w', v₁, v₂, u₁, u₂} F
true
_private.Mathlib.Topology.UniformSpace.UniformConvergenceTopology.0.UniformOnFun.instCompleteSpace._simp_2
Mathlib.Topology.UniformSpace.UniformConvergenceTopology
∀ {α : Type u} {s : Set α} {f : Filter α}, (f ≤ Filter.principal s) = (s ∈ f)
false
Std.TreeSet.Raw.max?_eq_some_maxD
Std.Data.TreeSet.Raw.Lemmas
∀ {α : Type u} {cmp : α → α → Ordering} {t : Std.TreeSet.Raw α cmp} [Std.TransCmp cmp], t.WF → t.isEmpty = false → ∀ {fallback : α}, t.max? = some (t.maxD fallback)
true
HomologicalComplex.opFunctor._proof_2
Mathlib.Algebra.Homology.Opposite
∀ {ι : Type u_3} (V : Type u_2) [inst : CategoryTheory.Category.{u_1, u_2} V] (c : ComplexShape ι) [inst_1 : CategoryTheory.Limits.HasZeroMorphisms V] {X Y : (HomologicalComplex V c)ᵒᵖ} (f : X ⟶ Y) (i j : ι), CategoryTheory.CategoryStruct.comp (f.unop.f i).op ((Opposite.unop Y).op.d i j) = CategoryTheory.CategoryStruct.comp ((Opposite.unop X).op.d i j) (f.unop.f j).op
false
ValuativeRel.IsNontrivial.condition
Mathlib.RingTheory.Valuation.ValuativeRel.Basic
∀ {R : Type u_1} {inst : CommRing R} {inst_1 : ValuativeRel R} [self : ValuativeRel.IsNontrivial R], ∃ γ, γ ≠ 0 ∧ γ ≠ 1
true
_private.Lean.Compiler.LCNF.FixedParams.0.Lean.Compiler.LCNF.FixedParams.isEquivalentFunDecl?.match_3
Lean.Compiler.LCNF.FixedParams
(motive : Option Lean.Compiler.LCNF.FixedParams.AbsValue → Sort u_1) → (x : Option Lean.Compiler.LCNF.FixedParams.AbsValue) → ((funIdx : ℕ) → motive (some (Lean.Compiler.LCNF.FixedParams.AbsValue.val funIdx))) → ((x : Option Lean.Compiler.LCNF.FixedParams.AbsValue) → motive x) → motive x
false
LinearMap.IsOrthoᵢ.nondegenerate_of_not_isOrtho_basis_self
Mathlib.LinearAlgebra.SesquilinearForm.Basic
∀ {n : Type u_19} {R : Type u_20} {M : Type u_21} {M₁ : Type u_22} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : AddCommMonoid M₁] [inst_3 : Module R M] [inst_4 : Module R M₁] [IsDomain R] [Module.IsTorsionFree R M₁] {B : M →ₗ[R] M →ₗ[R] M₁} (v : Module.Basis n R M), B.IsOrthoᵢ ⇑v → (∀ (i : n), ¬B.IsOrtho (v i) (v i)) → B.Nondegenerate
true
MonoidHom.transfer._proof_2
Mathlib.GroupTheory.Transfer
∀ {G : Type u_2} [inst : Group G] {H : Subgroup G} {A : Type u_1} [inst_1 : CommGroup A] (ϕ : ↥H →* A) [inst_2 : H.FiniteIndex] (g h : G), Subgroup.leftTransversals.diff ϕ default ((g * h) • default) = Subgroup.leftTransversals.diff ϕ default (g • default) * Subgroup.leftTransversals.diff ϕ default (h • default)
false
_private.Mathlib.Order.Monotone.Basic.0.StrictMono.isMin_of_apply.match_1_1
Mathlib.Order.Monotone.Basic
∀ {α : Type u_1} [inst : Preorder α] {a : α} (motive : (∃ b, b < a) → Prop) (x : ∃ b, b < a), (∀ (w : α) (hb : w < a), motive ⋯) → motive x
false
_private.Std.Sat.AIG.RefVecOperator.Map.0.Std.Sat.AIG.RefVec.map.go_get_aux._proof_1_1
Std.Sat.AIG.RefVecOperator.Map
∀ {α : Type} [inst : Hashable α] [inst_1 : DecidableEq α] {len : ℕ} {aig : Std.Sat.AIG α} (curr : ℕ) (s : aig.RefVec curr) (input : aig.RefVec len) (f : (aig : Std.Sat.AIG α) → aig.Ref → Std.Sat.AIG.Entrypoint α) [inst_2 : Std.Sat.AIG.LawfulOperator α Std.Sat.AIG.Ref f] [Std.Sat.AIG.RefVec.LawfulMapOperator α f], ∀ idx < curr, curr < len → ¬idx < curr + 1 → False
false
MeasureTheory.AEEqFun.coeFn_smul
Mathlib.MeasureTheory.Function.AEEqFun
∀ {α : Type u_1} {γ : Type u_3} [inst : MeasurableSpace α] {μ : MeasureTheory.Measure α} [inst_1 : TopologicalSpace γ] {𝕜 : Type u_5} [inst_2 : SMul 𝕜 γ] [inst_3 : ContinuousConstSMul 𝕜 γ] (c : 𝕜) (f : α →ₘ[μ] γ), ↑(c • f) =ᵐ[μ] c • ↑f
true
UpperHalfPlane.smulFDeriv
Mathlib.Analysis.Complex.UpperHalfPlane.Manifold
GL (Fin 2) ℝ → ℂ → ℂ →L[ℝ] ℂ
true
Orientation.oangle.eq_1
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic
∀ {V : Type u_1} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] [inst_2 : Fact (Module.finrank ℝ V = 2)] (o : Orientation ℝ V (Fin 2)) (x y : V), o.oangle x y = ↑((o.kahler x) y).arg
true
nonempty_commRing_iff
Mathlib.SetTheory.Cardinal.Free
∀ (α : Type u), Nonempty (CommRing α) ↔ Nonempty α
true
Polynomial.eval₂RingHom'._proof_1
Mathlib.Algebra.Polynomial.Eval.Defs
∀ {R : Type u_1} {S : Type u_2} [inst : Semiring R] [inst_1 : Semiring S] (f : R →+* S) (x : S), (∀ (a : R), Commute (f a) x) → ∀ (_p q : Polynomial R), Polynomial.eval₂ f x (_p * q) = Polynomial.eval₂ f x _p * Polynomial.eval₂ f x q
false
Dynamics.netMaxcard_zero
Mathlib.Dynamics.TopologicalEntropy.NetEntropy
∀ {X : Type u_1} {F : Set X} (T : X → X), F.Nonempty → ∀ (U : SetRel X X), Dynamics.netMaxcard T F U 0 = 1
true
DistLat.casesOn
Mathlib.Order.Category.DistLat
{motive : DistLat → Sort u} → (t : DistLat) → ((carrier : Type u_1) → [str : DistribLattice carrier] → motive { carrier := carrier, str := str }) → motive t
false
MeasureTheory.innerRegularWRT_isCompact_isClosed
Mathlib.MeasureTheory.Measure.RegularityCompacts
∀ {α : Type u_1} [inst : MeasurableSpace α] [inst_1 : TopologicalSpace α] [SecondCountableTopology α] [TopologicalSpace.IsCompletelyPseudoMetrizableSpace α] [OpensMeasurableSpace α] (P : MeasureTheory.Measure α) [MeasureTheory.IsFiniteMeasure P], P.InnerRegularWRT (fun s => IsCompact s ∧ IsClosed s) IsClosed
true
Int8.casesOn
Init.Data.SInt.Basic
{motive : Int8 → Sort u} → (t : Int8) → ((toUInt8 : UInt8) → motive { toUInt8 := toUInt8 }) → motive t
false
AffineSubspace.card_pos_of_affineSpan_eq_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] {ι : Type u_5} [inst_3 : Fintype ι] {p : ι → P}, affineSpan k (Set.range p) = ⊤ → 0 < Fintype.card ι
true
CategoryTheory.Functor.Monoidal.whiskerLeft_δ_μ
Mathlib.CategoryTheory.Monoidal.Functor
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.MonoidalCategory C] {D : Type u₂} [inst_2 : CategoryTheory.Category.{v₂, u₂} D] [inst_3 : CategoryTheory.MonoidalCategory D] (F : CategoryTheory.Functor C D) [inst_4 : F.Monoidal] (X Y : C) (T : D), CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.whiskerLeft T (CategoryTheory.Functor.OplaxMonoidal.δ F X Y)) (CategoryTheory.MonoidalCategoryStruct.whiskerLeft T (CategoryTheory.Functor.LaxMonoidal.μ F X Y)) = CategoryTheory.CategoryStruct.id (CategoryTheory.MonoidalCategoryStruct.tensorObj T (F.obj (CategoryTheory.MonoidalCategoryStruct.tensorObj X Y)))
true
LightDiagram.instCategory
Mathlib.Topology.Category.LightProfinite.Basic
CategoryTheory.Category.{u_1, u_1 + 1} LightDiagram
true
Lean.IR.ExpandResetReuse.ProjMap
Lean.Compiler.IR.ExpandResetReuse
Type
true
Lean.Meta.Grind.Order.Cnstr.rec
Lean.Meta.Tactic.Grind.Order.Types
{α : Type} → {motive : Lean.Meta.Grind.Order.Cnstr α → Sort u} → ((kind : Lean.Meta.Grind.Order.CnstrKind) → (u v : α) → (k : ℤ) → (e : Lean.Expr) → (h? : Option Lean.Expr) → motive { kind := kind, u := u, v := v, k := k, e := e, h? := h? }) → (t : Lean.Meta.Grind.Order.Cnstr α) → motive t
false
GroupTopology.instSemilatticeInf._proof_1
Mathlib.Topology.Algebra.Group.GroupTopology
∀ {α : Type u_1} [inst : Group α] {x y : GroupTopology α}, y.toTopologicalSpace ≤ x.toTopologicalSpace ↔ y.toTopologicalSpace ≤ x.toTopologicalSpace
false