module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.CategoryTheory.Sites.Coherent.RegularSheaves | {
"line": 154,
"column": 4
} | {
"line": 154,
"column": 32
} | {
"line": 154,
"column": 33
} | [
{
"pp": "case refine_2\nC : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\nP : Cᵒᵖ ⥤ Type u_4\nX B : C\nπ : X ⟶ B\ninst✝ : EffectiveEpi π\nc : PullbackCone π π\nhc : IsLimit c\nthis : HasPullback π π\nhP :\n ∀\n (b :\n (fun X ↦ X)\n ↑{x |\n (ConcreteCategory.hom (P.map (pullback.fst π π).o... | [
"case refine_2\nC : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\nP : Cᵒᵖ ⥤ Type u_4\nX B : C\nπ : X ⟶ B\ninst✝ : EffectiveEpi π\nc : PullbackCone π π\nhc : IsLimit c\nthis : HasPullback π π\nhP :\n ∀\n (b :\n (fun X ↦ X)\n ↑{x |\n (ConcreteCategory.hom (P.map (pullback.fst π π).op)) x =\n ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.Coherent.RegularSheaves | {
"line": 204,
"column": 2
} | {
"line": 204,
"column": 38
} | {
"line": 205,
"column": 2
} | [
{
"pp": "C : Type u_1\ninst✝ : Category.{v_1, u_1} C\nX B : C\nπ : X ⟶ B\nc : PullbackCone π π\nhc : IsLimit c\n⊢ (parallelPair (ObjectProperty.homMk (Over.homMk c.fst ⋯)).op (ObjectProperty.homMk (Over.homMk c.snd ⋯)).op).Initial",
"ppTerm": "?m.142",
"assigned": true,
"usedConstants": [
"Uni... | [
"case h₁\nC : Type u_1\ninst✝ : Category.{v_1, u_1} C\nX B : C\nπ : X ⟶ B\nc : PullbackCone π π\nhc : IsLimit c\n⊢ ∀ (Z : (Sieve.ofArrows (fun x ↦ X) fun x ↦ π).arrows.categoryᵒᵖ),\n Nonempty (op ((Sieve.ofArrows (fun x ↦ X) fun x ↦ π).arrows.categoryMk π ⋯) ⟶ Z)",
"case h₂\nC : Type u_1\ninst✝ : Category.{v_1... | apply Limits.parallelPair_initial_mk | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.CategoryTheory.Sites.Coherent.SheafComparison | {
"line": 81,
"column": 6
} | {
"line": 81,
"column": 17
} | {
"line": 81,
"column": 18
} | [
{
"pp": "case refine_2.refine_1\nC : Type u_1\nD : Type u_2\ninst✝⁷ : Category.{v_1, u_1} C\ninst✝⁶ : Category.{v_2, u_2} D\nF : C ⥤ D\ninst✝⁵ : F.PreservesFiniteEffectiveEpiFamilies\ninst✝⁴ : F.ReflectsFiniteEffectiveEpiFamilies\ninst✝³ : F.Full\ninst✝² : F.Faithful\ninst✝¹ : F.EffectivelyEnough\ninst✝ : Preco... | [
"case refine_2.refine_1\nC : Type u_1\nD : Type u_2\ninst✝⁷ : Category.{v_1, u_1} C\ninst✝⁶ : Category.{v_2, u_2} D\nF : C ⥤ D\ninst✝⁵ : F.PreservesFiniteEffectiveEpiFamilies\ninst✝⁴ : F.ReflectsFiniteEffectiveEpiFamilies\ninst✝³ : F.Full\ninst✝² : F.Faithful\ninst✝¹ : F.EffectivelyEnough\ninst✝ : Precoherent D\nX ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.EpiMono | {
"line": 127,
"column": 2
} | {
"line": 128,
"column": 18
} | {
"line": 129,
"column": 2
} | [
{
"pp": "case mp\nC : Type u\ninst✝⁸ : Category.{v, u} C\nJ : GrothendieckTopology C\nA : Type u'\ninst✝⁷ : Category.{v', u'} A\nFA : A → A → Type u_1\nCA : A → Type w\ninst✝⁶ : (X Y : A) → FunLike (FA X Y) (CA X) (CA Y)\ninst✝⁵ : ConcreteCategory A FA\ninst✝⁴ : HasFunctorialSurjectiveInjectiveFactorization A\n... | [
"case mpr\nC : Type u\ninst✝⁸ : Category.{v, u} C\nJ : GrothendieckTopology C\nA : Type u'\ninst✝⁷ : Category.{v', u'} A\nFA : A → A → Type u_1\nCA : A → Type w\ninst✝⁶ : (X Y : A) → FunLike (FA X Y) (CA X) (CA Y)\ninst✝⁵ : ConcreteCategory A FA\ninst✝⁴ : HasFunctorialSurjectiveInjectiveFactorization A\ninst✝³ : J.... | · intro
infer_instance | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.CategoryTheory.Sites.Coherent.RegularSheaves | {
"line": 241,
"column": 2
} | {
"line": 241,
"column": 17
} | {
"line": 243,
"column": 0
} | [
{
"pp": "case zero\nC : Type u_1\nD : Type u_2\nE : Type u_3\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Category.{v_2, u_2} D\ninst✝ : Category.{v_3, u_3} E\nP : Cᵒᵖ ⥤ D\nX B : C\nπ : X ⟶ B\nc : PullbackCone π π\nhc : IsLimit c\nS : Presieve B := (Sieve.ofArrows (fun x ↦ X) fun x ↦ π).arrows\nX' : S.category := ... | [] | all_goals aesop | Lean.Elab.Tactic.evalAllGoals | Lean.Parser.Tactic.allGoals |
Mathlib.CategoryTheory.Sites.Coherent.SheafComparison | {
"line": 295,
"column": 2
} | {
"line": 295,
"column": 75
} | {
"line": 296,
"column": 2
} | [
{
"pp": "C : Type u_1\ninst✝⁵ : Category.{v_1, u_1} C\nA : Type u₃\ninst✝⁴ : Category.{v₃, u₃} A\nF : Cᵒᵖ ⥤ A\nB : Type u₄\ninst✝³ : Category.{v₄, u₄} B\ns : A ⥤ B\ninst✝² : Preregular C\ninst✝¹ : FinitaryExtensive C\nh : ∀ {Y X : C} (f : Y ⟶ X) [EffectiveEpi f], HasPullback f f\ninst✝ : ReflectsFiniteLimits s\... | [
"case refine_1\nC : Type u_1\ninst✝⁵ : Category.{v_1, u_1} C\nA : Type u₃\ninst✝⁴ : Category.{v₃, u₃} A\nF : Cᵒᵖ ⥤ A\nB : Type u₄\ninst✝³ : Category.{v₄, u₄} B\ns : A ⥤ B\ninst✝² : Preregular C\ninst✝¹ : FinitaryExtensive C\nh : ∀ {Y X : C} (f : Y ⟶ X) [EffectiveEpi f], HasPullback f f\ninst✝ : ReflectsFiniteLimits... | refine ⟨⟨fun n ↦ ⟨fun {K} ↦ ⟨fun {c} hc ↦ ?_⟩⟩⟩, fun _ _ π _ c hc ↦ ⟨?_⟩⟩ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.CategoryTheory.Sites.Coherent.RegularSheaves | {
"line": 269,
"column": 4
} | {
"line": 269,
"column": 15
} | {
"line": 269,
"column": 16
} | [
{
"pp": "case refine_1\nC : Type u_1\ninst✝² : Category.{v_1, u_1} C\nX : C\ninst✝¹ : Projective X\nF : Cᵒᵖ ⥤ Type u_4\nY : C\nf : Y ⟶ X\nhf : EffectiveEpi f\ninst✝ : (ofArrows (fun x ↦ Y) fun x ↦ f).regular\nx : Unit → F.obj (op Y)\nhx : Arrows.Compatible F (fun x ↦ f) x\nx✝ : Unit\n⊢ (ConcreteCategory.hom (F.... | [
"case refine_1\nC : Type u_1\ninst✝² : Category.{v_1, u_1} C\nX : C\ninst✝¹ : Projective X\nF : Cᵒᵖ ⥤ Type u_4\nY : C\nf : Y ⟶ X\nhf : EffectiveEpi f\ninst✝ : (ofArrows (fun x ↦ Y) fun x ↦ f).regular\nx : Unit → F.obj (op Y)\nhx : Arrows.Compatible F (fun x ↦ f) x\nx✝ : Unit\n⊢ (ConcreteCategory.hom (F.map f.op)) (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.Coherent.SequentialLimit | {
"line": 103,
"column": 19
} | {
"line": 103,
"column": 48
} | {
"line": 103,
"column": 49
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : Preregular C\ninst✝¹ : FinitaryExtensive C\nF : ℕᵒᵖ ⥤ Sheaf (coherentTopology C) (Type v)\nc : Cone F\nhc : IsLimit c\nhF : ∀ (n : ℕ), Sheaf.IsLocallySurjective (F.map (homOfLE ⋯).op)\ninst✝ : HasLimitsOfShape ℕᵒᵖ C\nh : ∀ (G : ℕᵒᵖ ⥤ C), (∀ (n : ℕ), Effe... | [
"C : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : Preregular C\ninst✝¹ : FinitaryExtensive C\nF : ℕᵒᵖ ⥤ Sheaf (coherentTopology C) (Type v)\nc : Cone F\nhc : IsLimit c\nhF : ∀ (n : ℕ), Sheaf.IsLocallySurjective (F.map (homOfLE ⋯).op)\ninst✝ : HasLimitsOfShape ℕᵒᵖ C\nh : ∀ (G : ℕᵒᵖ ⥤ C), (∀ (n : ℕ), EffectiveEpi (G.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.Descent.IsStack | {
"line": 68,
"column": 2
} | {
"line": 68,
"column": 13
} | {
"line": 68,
"column": 14
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nF : LocallyDiscrete Cᵒᵖ ⥤ᵖ Cat\nJ : GrothendieckTopology C\ninst✝ : F.IsStack J\nS : C\nR : Presieve S\nhR : Sieve.generate R ∈ J S\n⊢ F.IsStackFor R",
"ppTerm": "?m.18",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\nF : LocallyDiscrete Cᵒᵖ ⥤ᵖ Cat\nJ : GrothendieckTopology C\ninst✝ : F.IsStack J\nS : C\nR : Presieve S\nhR : Sieve.generate R ∈ J S\n⊢ F.IsStackFor R"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.Descent.DescentDataAsCoalgebra | {
"line": 161,
"column": 10
} | {
"line": 161,
"column": 52
} | {
"line": 162,
"column": 10
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nF : LocallyDiscrete Cᵒᵖ ⥤ᵖ Adj Cat\nι : Type u_1\ninst✝ : Unique ι\nX S : C\nf : X ⟶ S\nD : F.DescentDataAsCoalgebra fun x ↦ f\ni₁ i₂ : ι\n⊢ ((𝟭 (F.DescentDataAsCoalgebra fun x ↦ f)).obj D).hom i₁ i₂ ≫\n (F.map f.op.toLoc).l.toFunctor.map ((F.map f.op.toLoc... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\nF : LocallyDiscrete Cᵒᵖ ⥤ᵖ Adj Cat\nι : Type u_1\ninst✝ : Unique ι\nX S : C\nf : X ⟶ S\nD : F.DescentDataAsCoalgebra fun x ↦ f\ni₂ : ι\n⊢ ((𝟭 (F.DescentDataAsCoalgebra fun x ↦ f)).obj D).hom default i₂ ≫\n (F.map f.op.toLoc).l.toFunctor.map ((F.map f.op.toLoc).r.toFunc... | obtain rfl := Subsingleton.elim i₁ default | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.CategoryTheory.Sites.Descent.DescentDataAsCoalgebra | {
"line": 164,
"column": 6
} | {
"line": 166,
"column": 10
} | {
"line": 166,
"column": 10
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nF : LocallyDiscrete Cᵒᵖ ⥤ᵖ Adj Cat\nι : Type u_1\ninst✝ : Unique ι\nX S : C\nf : X ⟶ S\nD₁ D₂ : F.DescentDataAsCoalgebra fun x ↦ f\nα : D₁ ⟶ D₂\n⊢ (𝟭 (F.DescentDataAsCoalgebra fun x ↦ f)).map α ≫ (isoMk (fun i ↦ eqToIso ⋯) ⋯).hom =\n (isoMk (fun i ↦ eqToIso ⋯... | [] | ext i
obtain rfl := Subsingleton.elim i default
simp | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Sites.Descent.DescentDataAsCoalgebra | {
"line": 164,
"column": 6
} | {
"line": 166,
"column": 10
} | {
"line": 166,
"column": 10
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nF : LocallyDiscrete Cᵒᵖ ⥤ᵖ Adj Cat\nι : Type u_1\ninst✝ : Unique ι\nX S : C\nf : X ⟶ S\nD₁ D₂ : F.DescentDataAsCoalgebra fun x ↦ f\nα : D₁ ⟶ D₂\n⊢ (𝟭 (F.DescentDataAsCoalgebra fun x ↦ f)).map α ≫ (isoMk (fun i ↦ eqToIso ⋯) ⋯).hom =\n (isoMk (fun i ↦ eqToIso ⋯... | [] | ext i
obtain rfl := Subsingleton.elim i default
simp | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Sites.Finite | {
"line": 44,
"column": 2
} | {
"line": 44,
"column": 13
} | {
"line": 44,
"column": 14
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nX : C\nι : Type u_1\ninst✝ : Finite ι\nY : ι → C\nf : (i : ι) → Y i ⟶ X\n⊢ ofArrows Y f ∈ (finite C).coverings X",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Ho... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\nX : C\nι : Type u_1\ninst✝ : Finite ι\nY : ι → C\nf : (i : ι) → Y i ⟶ X\n⊢ (Set.range fun i ↦ ⟨Y i, f i⟩).Finite"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.Finite | {
"line": 61,
"column": 29
} | {
"line": 61,
"column": 40
} | {
"line": 61,
"column": 41
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : HasPullbacks C\nX Y : C\nu : Y ⟶ X\ns : Presieve X\nhs : s ∈ (Precoverage.finite C).coverings X\n⊢ pullbackArrows u s ∈ (Precoverage.finite C).coverings Y",
"ppTerm": "?m.35",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Categor... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : HasPullbacks C\nX Y : C\nu : Y ⟶ X\ns : Presieve X\nhs : s ∈ (Precoverage.finite C).coverings X\n⊢ ((fun f ↦ ⟨Limits.pullback f.snd u, pullback.snd f.snd u⟩) '' s.uncurry).Finite"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.Finite | {
"line": 62,
"column": 31
} | {
"line": 62,
"column": 42
} | {
"line": 62,
"column": 43
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : HasPullbacks C\nX : C\ns : Presieve X\nt : ⦃Y : C⦄ → (f : Y ⟶ X) → s f → Presieve Y\nhs : s ∈ (Precoverage.finite C).coverings X\nht : ∀ ⦃Y : C⦄ (f : Y ⟶ X) (H : s f), t f H ∈ (Precoverage.finite C).coverings Y\n⊢ s.bind t ∈ (Precoverage.finite C).coverin... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : HasPullbacks C\nX : C\ns : Presieve X\nt : ⦃Y : C⦄ → (f : Y ⟶ X) → s f → Presieve Y\nhs : s ∈ (Precoverage.finite C).coverings X\nht : ∀ ⦃Y : C⦄ (f : Y ⟶ X) (H : s f), t f H ∈ (Precoverage.finite C).coverings Y\n⊢ (⋃ i, ⋃ (h : i ∈ s.uncurry), (Sigma.map id fun Z g ↦ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.GlobalSections | {
"line": 151,
"column": 4
} | {
"line": 151,
"column": 78
} | {
"line": 151,
"column": 79
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\nJ : GrothendieckTopology C\nA : Type u₂\ninst✝² : Category.{v₂, u₂} A\ninst✝¹ : HasWeakSheafify J A\ninst✝ : HasGlobalSectionsFunctor J A\nF : Sheaf J A\nc : Cone F.obj\nf : c.pt ⟶ F.coneΓ.pt\nhf : (Functor.const Cᵒᵖ).map f ≫ F.coneΓ.π = c.π\n⊢ f = ΓHomEquiv c.π"... | [
"C : Type u\ninst✝³ : Category.{v, u} C\nJ : GrothendieckTopology C\nA : Type u₂\ninst✝² : Category.{v₂, u₂} A\ninst✝¹ : HasWeakSheafify J A\ninst✝ : HasGlobalSectionsFunctor J A\nF : Sheaf J A\nc : Cone F.obj\nf : c.pt ⟶ F.coneΓ.pt\nhf : (Functor.const Cᵒᵖ).map f ≫ F.coneΓ.π = c.π\n⊢ f = ΓHomEquiv c.π"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.Descent.Precoverage | {
"line": 213,
"column": 6
} | {
"line": 213,
"column": 17
} | {
"line": 213,
"column": 18
} | [
{
"pp": "case e'_6\nC : Type u\ninst✝¹ : Category.{v, u} C\nF : LocallyDiscrete Cᵒᵖ ⥤ᵖ Cat\nJ : GrothendieckTopology C\ninst✝ : F.IsPrestack J\nι : Type t\nS : C\nX : ι → C\nf : (i : ι) → X i ⟶ S\nι' : Type t'\nX' : ι' → C\nf' : (j : ι') → X' j ⟶ S\nα : ι' → ι\np' : (j : ι') → X' j ⟶ X (α j)\nw : ∀ (j : ι'), p'... | [
"case e'_6\nC : Type u\ninst✝¹ : Category.{v, u} C\nF : LocallyDiscrete Cᵒᵖ ⥤ᵖ Cat\nJ : GrothendieckTopology C\ninst✝ : F.IsPrestack J\nι : Type t\nS : C\nX : ι → C\nf : (i : ι) → X i ⟶ S\nι' : Type t'\nX' : ι' → C\nf' : (j : ι') → X' j ⟶ S\nα : ι' → ι\np' : (j : ι') → X' j ⟶ X (α j)\nw : ∀ (j : ι'), p' j ≫ f (α j)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.Descent.Precoverage | {
"line": 218,
"column": 44
} | {
"line": 218,
"column": 55
} | {
"line": 218,
"column": 56
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nF : LocallyDiscrete Cᵒᵖ ⥤ᵖ Cat\nJ : GrothendieckTopology C\ninst✝ : F.IsPrestack J\nι : Type t\nS : C\nX : ι → C\nf : (i : ι) → X i ⟶ S\nι' : Type t'\nX' : ι' → C\nf' : (j : ι') → X' j ⟶ S\nα : ι' → ι\np' : (j : ι') → X' j ⟶ X (α j)\nw : ∀ (j : ι'), p' j ≫ f (α j... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\nF : LocallyDiscrete Cᵒᵖ ⥤ᵖ Cat\nJ : GrothendieckTopology C\ninst✝ : F.IsPrestack J\nι : Type t\nS : C\nX : ι → C\nf : (i : ι) → X i ⟶ S\nι' : Type t'\nX' : ι' → C\nf' : (j : ι') → X' j ⟶ S\nα : ι' → ι\np' : (j : ι') → X' j ⟶ X (α j)\nw : ∀ (j : ι'), p' j ≫ f (α j) = f' j\nhf... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.Hypercover.Homotopy | {
"line": 203,
"column": 4
} | {
"line": 203,
"column": 85
} | {
"line": 204,
"column": 4
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nS : C\nE : PreOneHypercover S\nF : PreOneHypercover S\ninst✝ : HasPullbacks C\nf g : E.Hom F\ni✝ j✝ : (cylinder f g).I₀\nk : (cylinder f g).I₁ i✝ j✝\n⊢ pullback.snd\n (pullback.map (cylinderf f g i✝.snd) (cylinderf f g j✝.snd) (E.f i✝.fst) (E.f j✝.fst)\n ... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\nS : C\nE : PreOneHypercover S\nF : PreOneHypercover S\ninst✝ : HasPullbacks C\nf g : E.Hom F\ni✝ j✝ : (cylinder f g).I₀\nk : (cylinder f g).I₁ i✝ j✝\nthis : E.p₁ k.down = pullback.lift (E.p₁ k.down) (E.p₂ k.down) ⋯ ≫ pullback.fst (E.f i✝.fst) (E.f j✝.fst)\n⊢ pullback.snd\n ... | have : E.p₁ k.down = pullback.lift _ _ (E.w k.down) ≫ pullback.fst _ _ := by simp | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.CategoryTheory.Sites.Descent.Precoverage | {
"line": 226,
"column": 49
} | {
"line": 226,
"column": 60
} | {
"line": 226,
"column": 61
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF : LocallyDiscrete Cᵒᵖ ⥤ᵖ Cat\nι : Type t\nS : C\nX : ι → C\nf : (i : ι) → X i ⟶ S\nι' : Type t'\nX' : ι' → C\nf' : (j : ι') → X' j ⟶ S\nα : ι' → ι\np' : (j : ι') → X' j ⟶ X (α j)\nw : ∀ (j : ι'), p' j ≫ f (α j) = f' j\nD₁ D₂ : F.DescentData f\nφ : (pullFunctor F... | [
"C : Type u\ninst✝ : Category.{v, u} C\nF : LocallyDiscrete Cᵒᵖ ⥤ᵖ Cat\nι : Type t\nS : C\nX : ι → C\nf : (i : ι) → X i ⟶ S\nι' : Type t'\nX' : ι' → C\nf' : (j : ι') → X' j ⟶ S\nα : ι' → ι\np' : (j : ι') → X' j ⟶ X (α j)\nw : ∀ (j : ι'), p' j ≫ f (α j) = f' j\nD₁ D₂ : F.DescentData f\nφ : (pullFunctor F ⋯).obj D₁ ⟶... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.Descent.Precoverage | {
"line": 227,
"column": 49
} | {
"line": 227,
"column": 60
} | {
"line": 227,
"column": 61
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF : LocallyDiscrete Cᵒᵖ ⥤ᵖ Cat\nι : Type t\nS : C\nX : ι → C\nf : (i : ι) → X i ⟶ S\nι' : Type t'\nX' : ι' → C\nf' : (j : ι') → X' j ⟶ S\nα : ι' → ι\np' : (j : ι') → X' j ⟶ X (α j)\nw : ∀ (j : ι'), p' j ≫ f (α j) = f' j\nD₁ D₂ : F.DescentData f\nφ : (pullFunctor F... | [
"C : Type u\ninst✝ : Category.{v, u} C\nF : LocallyDiscrete Cᵒᵖ ⥤ᵖ Cat\nι : Type t\nS : C\nX : ι → C\nf : (i : ι) → X i ⟶ S\nι' : Type t'\nX' : ι' → C\nf' : (j : ι') → X' j ⟶ S\nα : ι' → ι\np' : (j : ι') → X' j ⟶ X (α j)\nw : ∀ (j : ι'), p' j ≫ f (α j) = f' j\nD₁ D₂ : F.DescentData f\nφ : (pullFunctor F ⋯).obj D₁ ⟶... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.Descent.Precoverage | {
"line": 248,
"column": 12
} | {
"line": 248,
"column": 23
} | {
"line": 248,
"column": 24
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nF : LocallyDiscrete Cᵒᵖ ⥤ᵖ Cat\nJ : GrothendieckTopology C\ninst✝ : F.IsPrestack J\nι : Type t\nS : C\nX : ι → C\nf : (i : ι) → X i ⟶ S\nι' : Type t'\nX' : ι' → C\nf' : (j : ι') → X' j ⟶ S\nα : ι' → ι\np' : (j : ι') → X' j ⟶ X (α j)\nw : ∀ (j : ι'), p' j ≫ f (α j... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\nF : LocallyDiscrete Cᵒᵖ ⥤ᵖ Cat\nJ : GrothendieckTopology C\ninst✝ : F.IsPrestack J\nι : Type t\nS : C\nX : ι → C\nf : (i : ι) → X i ⟶ S\nι' : Type t'\nX' : ι' → C\nf' : (j : ι') → X' j ⟶ S\nα : ι' → ι\np' : (j : ι') → X' j ⟶ X (α j)\nw : ∀ (j : ι'), p' j ≫ f (α j) = f' j\nhf... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.Descent.Precoverage | {
"line": 257,
"column": 10
} | {
"line": 257,
"column": 21
} | {
"line": 257,
"column": 22
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nF : LocallyDiscrete Cᵒᵖ ⥤ᵖ Cat\nJ : GrothendieckTopology C\ninst✝ : F.IsPrestack J\nι : Type t\nS : C\nX : ι → C\nf : (i : ι) → X i ⟶ S\nι' : Type t'\nX' : ι' → C\nf' : (j : ι') → X' j ⟶ S\nα : ι' → ι\np' : (j : ι') → X' j ⟶ X (α j)\nw : ∀ (j : ι'), p' j ≫ f (α j... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\nF : LocallyDiscrete Cᵒᵖ ⥤ᵖ Cat\nJ : GrothendieckTopology C\ninst✝ : F.IsPrestack J\nι : Type t\nS : C\nX : ι → C\nf : (i : ι) → X i ⟶ S\nι' : Type t'\nX' : ι' → C\nf' : (j : ι') → X' j ⟶ S\nα : ι' → ι\np' : (j : ι') → X' j ⟶ X (α j)\nw : ∀ (j : ι'), p' j ≫ f (α j) = f' j\nhf... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.Descent.Precoverage | {
"line": 262,
"column": 12
} | {
"line": 262,
"column": 23
} | {
"line": 262,
"column": 24
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nF : LocallyDiscrete Cᵒᵖ ⥤ᵖ Cat\nJ : GrothendieckTopology C\ninst✝ : F.IsPrestack J\nι : Type t\nS : C\nX : ι → C\nf : (i : ι) → X i ⟶ S\nι' : Type t'\nX' : ι' → C\nf' : (j : ι') → X' j ⟶ S\nα : ι' → ι\np' : (j : ι') → X' j ⟶ X (α j)\nw : ∀ (j : ι'), p' j ≫ f (α j... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\nF : LocallyDiscrete Cᵒᵖ ⥤ᵖ Cat\nJ : GrothendieckTopology C\ninst✝ : F.IsPrestack J\nι : Type t\nS : C\nX : ι → C\nf : (i : ι) → X i ⟶ S\nι' : Type t'\nX' : ι' → C\nf' : (j : ι') → X' j ⟶ S\nα : ι' → ι\np' : (j : ι') → X' j ⟶ X (α j)\nw : ∀ (j : ι'), p' j ≫ f (α j) = f' j\nhf... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.Descent.Precoverage | {
"line": 263,
"column": 2
} | {
"line": 265,
"column": 35
} | {
"line": 265,
"column": 36
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nF : LocallyDiscrete Cᵒᵖ ⥤ᵖ Cat\nJ : GrothendieckTopology C\ninst✝ : F.IsPrestack J\nι : Type t\nS : C\nX : ι → C\nf : (i : ι) → X i ⟶ S\nι' : Type t'\nX' : ι' → C\nf' : (j : ι') → X' j ⟶ S\nα : ι' → ι\np' : (j : ι') → X' j ⟶ X (α j)\nw : ∀ (j : ι'), p' j ≫ f (α j... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\nF : LocallyDiscrete Cᵒᵖ ⥤ᵖ Cat\nJ : GrothendieckTopology C\ninst✝ : F.IsPrestack J\nι : Type t\nS : C\nX : ι → C\nf : (i : ι) → X i ⟶ S\nι' : Type t'\nX' : ι' → C\nf' : (j : ι') → X' j ⟶ S\nα : ι' → ι\np' : (j : ι') → X' j ⟶ X (α j)\nw : ∀ (j : ι'), p' j ≫ f (α j) = f' j\nhf... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.Hypercover.Subcanonical | {
"line": 119,
"column": 4
} | {
"line": 119,
"column": 42
} | {
"line": 119,
"column": 43
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\nJ : Precoverage C\ninst✝² : J.toGrothendieck.Subcanonical\ninst✝¹ : Limits.HasPullbacks C\ninst✝ : J.IsStableUnderBaseChange\nP X Y Z : C\nfst : P ⟶ X\nsnd : P ⟶ Y\nf : X ⟶ Z\ng : Y ⟶ Z\n𝒰 : J.ZeroHypercover X\nH : ∀ (i : 𝒰.I₀), IsPullback (pullback.snd fst (𝒰... | [
"C : Type u\ninst✝³ : Category.{v, u} C\nJ : Precoverage C\ninst✝² : J.toGrothendieck.Subcanonical\ninst✝¹ : Limits.HasPullbacks C\ninst✝ : J.IsStableUnderBaseChange\nP X Y Z : C\nfst : P ⟶ X\nsnd : P ⟶ Y\nf : X ⟶ Z\ng : Y ⟶ Z\n𝒰 : J.ZeroHypercover X\nH : ∀ (i : 𝒰.I₀), IsPullback (pullback.snd fst (𝒰.f i)) (pull... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.Descent.DescentDataPrime | {
"line": 203,
"column": 2
} | {
"line": 203,
"column": 13
} | {
"line": 203,
"column": 14
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF : Pseudofunctor (LocallyDiscrete Cᵒᵖ) Cat\nι : Type t\nS : C\nX : ι → C\nf : (i : ι) → X i ⟶ S\nsq : (i j : ι) → ChosenPullback (f i) (f j)\nsq₃ : (i₁ i₂ i₃ : ι) → ChosenPullback₃ (sq i₁ i₂) (sq i₂ i₃) (sq i₁ i₃)\nD : F.DescentData' sq sq₃\ni₁ i₂ : ι\n⊢ IsIso (D... | [
"C : Type u\ninst✝ : Category.{v, u} C\nF : Pseudofunctor (LocallyDiscrete Cᵒᵖ) Cat\nι : Type t\nS : C\nX : ι → C\nf : (i : ι) → X i ⟶ S\nsq : (i j : ι) → ChosenPullback (f i) (f j)\nsq₃ : (i₁ i₂ i₃ : ι) → ChosenPullback₃ (sq i₁ i₂) (sq i₂ i₃) (sq i₁ i₃)\nD : F.DescentData' sq sq₃\ni₁ i₂ : ι\n⊢ IsIso (D.hom i₁ i₂)"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.Hypercover.Subcanonical | {
"line": 127,
"column": 4
} | {
"line": 127,
"column": 70
} | {
"line": 127,
"column": 71
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\nJ : Precoverage C\ninst✝² : J.toGrothendieck.Subcanonical\ninst✝¹ : Limits.HasPullbacks C\ninst✝ : J.IsStableUnderBaseChange\nP X Y Z : C\nfst : P ⟶ X\nsnd : P ⟶ Y\nf : X ⟶ Z\ng : Y ⟶ Z\n𝒰 : J.ZeroHypercover X\nH : ∀ (i : 𝒰.I₀), IsPullback (pullback.snd fst (𝒰... | [
"C : Type u\ninst✝³ : Category.{v, u} C\nJ : Precoverage C\ninst✝² : J.toGrothendieck.Subcanonical\ninst✝¹ : Limits.HasPullbacks C\ninst✝ : J.IsStableUnderBaseChange\nP X Y Z : C\nfst : P ⟶ X\nsnd : P ⟶ Y\nf : X ⟶ Z\ng : Y ⟶ Z\n𝒰 : J.ZeroHypercover X\nH : ∀ (i : 𝒰.I₀), IsPullback (pullback.snd fst (𝒰.f i)) (pull... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.Hypercover.Subcanonical | {
"line": 133,
"column": 4
} | {
"line": 133,
"column": 15
} | {
"line": 133,
"column": 16
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\nJ : Precoverage C\ninst✝² : J.toGrothendieck.Subcanonical\ninst✝¹ : Limits.HasPullbacks C\ninst✝ : J.IsStableUnderBaseChange\nP X Y Z : C\nfst : P ⟶ X\nsnd : P ⟶ Y\nf : X ⟶ Z\ng : Y ⟶ Z\n𝒰 : J.ZeroHypercover X\nH : ∀ (i : 𝒰.I₀), IsPullback (pullback.snd fst (𝒰... | [
"C : Type u\ninst✝³ : Category.{v, u} C\nJ : Precoverage C\ninst✝² : J.toGrothendieck.Subcanonical\ninst✝¹ : Limits.HasPullbacks C\ninst✝ : J.IsStableUnderBaseChange\nP X Y Z : C\nfst : P ⟶ X\nsnd : P ⟶ Y\nf : X ⟶ Z\ng : Y ⟶ Z\n𝒰 : J.ZeroHypercover X\nH : ∀ (i : 𝒰.I₀), IsPullback (pullback.snd fst (𝒰.f i)) (pull... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.Descent.Precoverage | {
"line": 400,
"column": 4
} | {
"line": 401,
"column": 11
} | {
"line": 401,
"column": 12
} | [
{
"pp": "C : Type u\ninst✝⁴ : Category.{v, u} C\nF : LocallyDiscrete Cᵒᵖ ⥤ᵖ Cat\ninst✝³ : HasPullbacks C\nJ : Precoverage C\ninst✝² : J.HasIsos\ninst✝¹ : J.IsStableUnderBaseChange\ninst✝ : J.IsStableUnderComposition\nhF : ∀ (S : C), ∀ R ∈ J.coverings S, F.IsPrestackFor R\nS : C\nM N : ↑(F.obj { as := op S })\nX... | [
"C : Type u\ninst✝⁴ : Category.{v, u} C\nF : LocallyDiscrete Cᵒᵖ ⥤ᵖ Cat\ninst✝³ : HasPullbacks C\nJ : Precoverage C\ninst✝² : J.HasIsos\ninst✝¹ : J.IsStableUnderBaseChange\ninst✝ : J.IsStableUnderComposition\nhF : ∀ (S : C), ∀ R ∈ J.coverings S, F.IsPrestackFor R\nS : C\nM N : ↑(F.obj { as := op S })\nX : Over S\nR... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.SheafHom | {
"line": 53,
"column": 4
} | {
"line": 53,
"column": 28
} | {
"line": 53,
"column": 29
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nJ : GrothendieckTopology C\nA : Type u'\ninst✝ : Category.{v', u'} A\nF G : Cᵒᵖ ⥤ A\nX : C\nφ : (Over.forget (unop (op X))).op ⋙ F ⟶ (Over.forget (unop (op X))).op ⋙ G\nY : Over (unop (op X))\n⊢ ((ConcreteCategory.hom (↾(Over.map (𝟙 (op X)).unop).op.whiskerLeft)... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\nJ : GrothendieckTopology C\nA : Type u'\ninst✝ : Category.{v', u'} A\nF G : Cᵒᵖ ⥤ A\nX : C\nφ : (Over.forget (unop (op X))).op ⋙ F ⟶ (Over.forget (unop (op X))).op ⋙ G\nY : Over (unop (op X))\n⊢ φ.app (op ((Over.map (𝟙 X)).obj Y)) = φ.app (op Y)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.SheafHom | {
"line": 57,
"column": 4
} | {
"line": 57,
"column": 30
} | {
"line": 57,
"column": 31
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nJ : GrothendieckTopology C\nA : Type u'\ninst✝ : Category.{v', u'} A\nF G : Cᵒᵖ ⥤ A\nX Y Z : C\nf : Y ⟶ X\ng : Z ⟶ Y\nφ : (Over.forget (unop (op X))).op ⋙ F ⟶ (Over.forget (unop (op X))).op ⋙ G\nW : Over (unop (op Z))\n⊢ ((ConcreteCategory.hom (↾(Over.map (op f ≫... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\nJ : GrothendieckTopology C\nA : Type u'\ninst✝ : Category.{v', u'} A\nF G : Cᵒᵖ ⥤ A\nX Y Z : C\nf : Y ⟶ X\ng : Z ⟶ Y\nφ : (Over.forget (unop (op X))).op ⋙ F ⟶ (Over.forget (unop (op X))).op ⋙ G\nW : Over (unop (op Z))\n⊢ φ.app (op ((Over.map (g ≫ f)).obj W)) = φ.app (op ((Ov... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.MayerVietorisSquare | {
"line": 132,
"column": 37
} | {
"line": 132,
"column": 76
} | {
"line": 132,
"column": 77
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\nJ : GrothendieckTopology C\ninst✝² : HasWeakSheafify J (Type v)\nsq : Square C\ninst✝¹ : Mono sq.f₂₄\ninst✝ : Mono sq.f₃₄\nh₁ : sq.IsPullback\nh₂ : Sieve.ofTwoArrows sq.f₂₄ sq.f₃₄ ∈ J sq.X₄\nthis : Mono sq.f₁₃\nF : Sheaf J (Type v)\ns : PullbackCone (sq.op.map F.... | [
"C : Type u\ninst✝³ : Category.{v, u} C\nJ : GrothendieckTopology C\ninst✝² : HasWeakSheafify J (Type v)\nsq : Square C\ninst✝¹ : Mono sq.f₂₄\ninst✝ : Mono sq.f₃₄\nh₁ : sq.IsPullback\nh₂ : Sieve.ofTwoArrows sq.f₂₄ sq.f₃₄ ∈ J sq.X₄\nthis : Mono sq.f₁₃\nF : Sheaf J (Type v)\ns : PullbackCone (sq.op.map F.obj).f₂₄ (sq... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.MayerVietorisSquare | {
"line": 135,
"column": 12
} | {
"line": 135,
"column": 23
} | {
"line": 135,
"column": 24
} | [
{
"pp": "case left.right\nC : Type u\ninst✝³ : Category.{v, u} C\nJ : GrothendieckTopology C\ninst✝² : HasWeakSheafify J (Type v)\nsq : Square C\ninst✝¹ : Mono sq.f₂₄\ninst✝ : Mono sq.f₃₄\nh₁ : sq.IsPullback\nh₂ : Sieve.ofTwoArrows sq.f₂₄ sq.f₃₄ ∈ J sq.X₄\nthis : Mono sq.f₁₃\nF : Sheaf J (Type v)\ns : PullbackC... | [
"case left.right\nC : Type u\ninst✝³ : Category.{v, u} C\nJ : GrothendieckTopology C\ninst✝² : HasWeakSheafify J (Type v)\nsq : Square C\ninst✝¹ : Mono sq.f₂₄\ninst✝ : Mono sq.f₃₄\nh₁ : sq.IsPullback\nh₂ : Sieve.ofTwoArrows sq.f₂₄ sq.f₃₄ ∈ J sq.X₄\nthis : Mono sq.f₁₃\nF : Sheaf J (Type v)\ns : PullbackCone (sq.op.m... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.MayerVietorisSquare | {
"line": 137,
"column": 12
} | {
"line": 137,
"column": 23
} | {
"line": 137,
"column": 24
} | [
{
"pp": "case right.left\nC : Type u\ninst✝³ : Category.{v, u} C\nJ : GrothendieckTopology C\ninst✝² : HasWeakSheafify J (Type v)\nsq : Square C\ninst✝¹ : Mono sq.f₂₄\ninst✝ : Mono sq.f₃₄\nh₁ : sq.IsPullback\nh₂ : Sieve.ofTwoArrows sq.f₂₄ sq.f₃₄ ∈ J sq.X₄\nthis : Mono sq.f₁₃\nF : Sheaf J (Type v)\ns : PullbackC... | [
"case right.left\nC : Type u\ninst✝³ : Category.{v, u} C\nJ : GrothendieckTopology C\ninst✝² : HasWeakSheafify J (Type v)\nsq : Square C\ninst✝¹ : Mono sq.f₂₄\ninst✝ : Mono sq.f₃₄\nh₁ : sq.IsPullback\nh₂ : Sieve.ofTwoArrows sq.f₂₄ sq.f₃₄ ∈ J sq.X₄\nthis : Mono sq.f₁₃\nF : Sheaf J (Type v)\ns : PullbackCone (sq.op.m... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.MayerVietorisSquare | {
"line": 138,
"column": 37
} | {
"line": 138,
"column": 76
} | {
"line": 138,
"column": 77
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\nJ : GrothendieckTopology C\ninst✝² : HasWeakSheafify J (Type v)\nsq : Square C\ninst✝¹ : Mono sq.f₂₄\ninst✝ : Mono sq.f₃₄\nh₁ : sq.IsPullback\nh₂ : Sieve.ofTwoArrows sq.f₂₄ sq.f₃₄ ∈ J sq.X₄\nthis : Mono sq.f₁₃\nF : Sheaf J (Type v)\ns : PullbackCone (sq.op.map F.... | [
"C : Type u\ninst✝³ : Category.{v, u} C\nJ : GrothendieckTopology C\ninst✝² : HasWeakSheafify J (Type v)\nsq : Square C\ninst✝¹ : Mono sq.f₂₄\ninst✝ : Mono sq.f₃₄\nh₁ : sq.IsPullback\nh₂ : Sieve.ofTwoArrows sq.f₂₄ sq.f₃₄ ∈ J sq.X₄\nthis : Mono sq.f₁₃\nF : Sheaf J (Type v)\ns : PullbackCone (sq.op.map F.obj).f₂₄ (sq... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.NonabelianCohomology.H1 | {
"line": 138,
"column": 2
} | {
"line": 138,
"column": 13
} | {
"line": 138,
"column": 14
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nG : Cᵒᵖ ⥤ GrpCat\nI : Type w'\nU : I → C\nγ : OneCocycle G U\ni : I\nT : C\na : T ⟶ U i\n⊢ γ.ev i i a a = 1",
"ppTerm": "?m.17",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"C : Type u\ninst✝ : Category.{v, u} C\nG : Cᵒᵖ ⥤ GrpCat\nI : Type w'\nU : I → C\nγ : OneCocycle G U\ni : I\nT : C\na : T ⟶ U i\n⊢ γ.ev i i a a = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.SheafHom | {
"line": 188,
"column": 59
} | {
"line": 188,
"column": 70
} | {
"line": 188,
"column": 71
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nA : Type u'\ninst✝ : Category.{v', u'} A\nF G : Cᵒᵖ ⥤ A\nX : C\nS : Sieve X\nhG : ⦃Y : C⦄ → (f : Y ⟶ X) → IsLimit (G.mapCone (Sieve.pullback f S).arrows.cocone.op)\nx : Presieve.FamilyOfElements (presheafHom F G) S.arrows\nhx : x.Compatible\nY₁ Y₂ : Over X\nφ : Y... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\nA : Type u'\ninst✝ : Category.{v', u'} A\nF G : Cᵒᵖ ⥤ A\nX : C\nS : Sieve X\nhG : ⦃Y : C⦄ → (f : Y ⟶ X) → IsLimit (G.mapCone (Sieve.pullback f S).arrows.cocone.op)\nx : Presieve.FamilyOfElements (presheafHom F G) S.arrows\nhx : x.Compatible\nY₁ Y₂ : Over X\nφ : Y₂ ⟶ Y₁\nZ : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.SheafHom | {
"line": 195,
"column": 43
} | {
"line": 195,
"column": 54
} | {
"line": 195,
"column": 55
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nA : Type u'\ninst✝ : Category.{v', u'} A\nF G : Cᵒᵖ ⥤ A\nX : C\nS : Sieve X\nhG : ⦃Y : C⦄ → (f : Y ⟶ X) → IsLimit (G.mapCone (Sieve.pullback f S).arrows.cocone.op)\nx : Presieve.FamilyOfElements (presheafHom F G) S.arrows\nhx : x.Compatible\nY : C\ng : Y ⟶ X\nhg ... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\nA : Type u'\ninst✝ : Category.{v', u'} A\nF G : Cᵒᵖ ⥤ A\nX : C\nS : Sieve X\nhG : ⦃Y : C⦄ → (f : Y ⟶ X) → IsLimit (G.mapCone (Sieve.pullback f S).arrows.cocone.op)\nx : Presieve.FamilyOfElements (presheafHom F G) S.arrows\nhx : x.Compatible\nY : C\ng : Y ⟶ X\nhg : S.arrows g... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.Point.Map | {
"line": 124,
"column": 2
} | {
"line": 124,
"column": 62
} | {
"line": 125,
"column": 4
} | [
{
"pp": "C : Type u\ninst✝⁵ : Category.{v, u} C\nD : Type u'\ninst✝⁴ : Category.{v', u'} D\nJ : GrothendieckTopology C\nΦ : J.Point\nF : C ⥤ D\nK : GrothendieckTopology D\ninst✝³ : F.IsCocontinuous J K\ninst✝² : LocallySmall.{w, v', u'} D\nA : Type u''\ninst✝¹ : Category.{v'', u''} A\ninst✝ : HasColimitsOfSize.... | [
"C : Type u\ninst✝⁵ : Category.{v, u} C\nD : Type u'\ninst✝⁴ : Category.{v', u'} D\nJ : GrothendieckTopology C\nΦ : J.Point\nF : C ⥤ D\nK : GrothendieckTopology D\ninst✝³ : F.IsCocontinuous J K\ninst✝² : LocallySmall.{w, v', u'} D\nA : Type u''\ninst✝¹ : Category.{v'', u''} A\ninst✝ : HasColimitsOfSize.{w, w, v'', ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.Point.OfIsCofiltered | {
"line": 77,
"column": 2
} | {
"line": 77,
"column": 69
} | {
"line": 77,
"column": 70
} | [
{
"pp": "C : Type u\ninst✝⁴ : Category.{v, u} C\ninst✝³ : LocallySmall.{w, v, u} C\nN : Type u'\ninst✝² : Category.{v', u'} N\np : N ⥤ C\ninst✝¹ : InitiallySmall N\ninst✝ : IsCofiltered N\nU : N\nX : C\nf₁ f₂ : p.obj U ⟶ X\nhf : fiberMk f₁ = fiberMk f₂\nV : Nᵒᵖ\ng : op U ⟶ V\nhg :\n (hom ((p.op ⋙ shrinkYoneda.... | [
"C : Type u\ninst✝⁴ : Category.{v, u} C\ninst✝³ : LocallySmall.{w, v, u} C\nN : Type u'\ninst✝² : Category.{v', u'} N\np : N ⥤ C\ninst✝¹ : InitiallySmall N\ninst✝ : IsCofiltered N\nU : N\nX : C\nf₁ f₂ : p.obj U ⟶ X\nhf : fiberMk f₁ = fiberMk f₂\nV : Nᵒᵖ\ng : op U ⟶ V\nhg :\n (hom ((p.op ⋙ shrinkYoneda.{w, v, u}.ob... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.Point.Presheaf | {
"line": 42,
"column": 29
} | {
"line": 42,
"column": 40
} | {
"line": 42,
"column": 41
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : LocallySmall.{w, v, u} C\nX U : C\nR : Sieve U\nhR : R ∈ ⊥ U\nx : (shrinkYoneda.{w, v, u}.flip.obj (op X)).obj U\n⊢ R = ⊤",
"ppTerm": "?m.43",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : LocallySmall.{w, v, u} C\nX U : C\nR : Sieve U\nhR : R ∈ ⊥ U\nx : (shrinkYoneda.{w, v, u}.flip.obj (op X)).obj U\n⊢ R = ⊤"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.Point.OfIsCofiltered | {
"line": 91,
"column": 2
} | {
"line": 91,
"column": 13
} | {
"line": 91,
"column": 14
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : LocallySmall.{w, v, u} C\nN : Type u'\ninst✝¹ : Category.{v', u'} N\np : N ⥤ C\ninst✝ : InitiallySmall N\nU V : N\ng : V ⟶ U\n⊢ fiberMk (p.map g) = fiberMk (𝟙 (p.obj U))",
"ppTerm": "?m.39",
"assigned": false,
"usedConstants": [],
"usedF... | [
"C : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : LocallySmall.{w, v, u} C\nN : Type u'\ninst✝¹ : Category.{v', u'} N\np : N ⥤ C\ninst✝ : InitiallySmall N\nU V : N\ng : V ⟶ U\n⊢ fiberMk (p.map g) = fiberMk (𝟙 (p.obj U))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.Point.Presheaf | {
"line": 99,
"column": 4
} | {
"line": 100,
"column": 11
} | {
"line": 100,
"column": 12
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : LocallySmall.{w, v, u} C\nX : C\nS : Sieve X\nhS :\n ∀ (Φ : (pointsBot C).FullSubcategory) (x : Φ.obj.fiber.obj X),\n ∃ Y g, ∃ (_ : S.arrows g), ∃ y, (ConcreteCategory.hom (Φ.obj.fiber.map g)) y = x\nY : C\na : Y ⟶ X\nha : S.arrows a\nb : X ⟶ Y\nhb :\... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : LocallySmall.{w, v, u} C\nX : C\nS : Sieve X\nhS :\n ∀ (Φ : (pointsBot C).FullSubcategory) (x : Φ.obj.fiber.obj X),\n ∃ Y g, ∃ (_ : S.arrows g), ∃ y, (ConcreteCategory.hom (Φ.obj.fiber.map g)) y = x\nY : C\na : Y ⟶ X\nha : S.arrows a\nb : X ⟶ Y\nhb :\n (Concrete... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.Point.OfIsCofiltered | {
"line": 118,
"column": 47
} | {
"line": 118,
"column": 58
} | {
"line": 118,
"column": 59
} | [
{
"pp": "C : Type u\ninst✝⁴ : Category.{v, u} C\ninst✝³ : LocallySmall.{w, v, u} C\nN : Type u'\ninst✝² : Category.{v', u'} N\np : N ⥤ C\ninst✝¹ : InitiallySmall N\nJ : GrothendieckTopology C\ninst✝ : IsCofiltered N\nX : C\nV U : N\nf : p.obj U ⟶ X\nφ₁ : ((functor p).obj V).fst ⟶ ⟨X, fiberMk f⟩.fst\nhφ₁ : (hom ... | [
"C : Type u\ninst✝⁴ : Category.{v, u} C\ninst✝³ : LocallySmall.{w, v, u} C\nN : Type u'\ninst✝² : Category.{v', u'} N\np : N ⥤ C\ninst✝¹ : InitiallySmall N\nJ : GrothendieckTopology C\ninst✝ : IsCofiltered N\nX : C\nV U : N\nf : p.obj U ⟶ X\nφ₁ : ((functor p).obj V).fst ⟶ ⟨X, fiberMk f⟩.fst\nhφ₁ : (hom ((fiber p).m... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.RegularEpi | {
"line": 62,
"column": 8
} | {
"line": 62,
"column": 38
} | {
"line": 62,
"column": 39
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝⁶ : Category.{u_3, u_1} C\ninst✝⁵ : Category.{u_4, u_2} D\nJ : GrothendieckTopology C\ninst✝⁴ : HasPullbacks D\ninst✝³ : HasPushouts D\ninst✝² : IsRegularEpiCategory D\nh : ∀ {F G : Sheaf J D} (f : F ⟶ G) [Epi f], ∃ I p i, Epi p ∧ Mono i ∧ p ≫ i = f.hom\ninst✝¹ : HasShe... | [
"C : Type u_1\nD : Type u_2\ninst✝⁶ : Category.{u_3, u_1} C\ninst✝⁵ : Category.{u_4, u_2} D\nJ : GrothendieckTopology C\ninst✝⁴ : HasPullbacks D\ninst✝³ : HasPushouts D\ninst✝² : IsRegularEpiCategory D\nh : ∀ {F G : Sheaf J D} (f : F ⟶ G) [Epi f], ∃ I p i, Epi p ∧ Mono i ∧ p ≫ i = f.hom\ninst✝¹ : HasSheafify J D\ni... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Subfunctor.Finite | {
"line": 154,
"column": 2
} | {
"line": 154,
"column": 43
} | {
"line": 154,
"column": 44
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF : Cᵒᵖ ⥤ Type w\nι : Type w'\nX : ι → Cᵒᵖ\nx : (i : ι) → F.obj (X i)\nh : PresheafIsGeneratedBy F x\nF' : Cᵒᵖ ⥤ Type w\nf : F ⟶ F'\n⊢ (Subfunctor.range f).IsGeneratedBy fun i ↦ (ConcreteCategory.hom (f.app (X i))) (x i)",
"ppTerm": "?m.33",
"assigned": tr... | [
"C : Type u\ninst✝ : Category.{v, u} C\nF : Cᵒᵖ ⥤ Type w\nι : Type w'\nX : ι → Cᵒᵖ\nx : (i : ι) → F.obj (X i)\nh : PresheafIsGeneratedBy F x\nF' : Cᵒᵖ ⥤ Type w\nf : F ⟶ F'\n⊢ (⊤.image f).IsGeneratedBy fun i ↦ (ConcreteCategory.hom (f.app (X i))) (x i)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Subfunctor.Finite | {
"line": 157,
"column": 2
} | {
"line": 157,
"column": 46
} | {
"line": 157,
"column": 47
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nF : Cᵒᵖ ⥤ Type w\nι : Type w'\nX : ι → Cᵒᵖ\nx : (i : ι) → F.obj (X i)\nh : PresheafIsGeneratedBy F x\nF' : Cᵒᵖ ⥤ Type w\nf : F ⟶ F'\ninst✝ : Epi f\n⊢ PresheafIsGeneratedBy F' fun i ↦ (ConcreteCategory.hom (f.app (X i))) (x i)",
"ppTerm": "?m.32",
"assigne... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\nF : Cᵒᵖ ⥤ Type w\nι : Type w'\nX : ι → Cᵒᵖ\nx : (i : ι) → F.obj (X i)\nh : PresheafIsGeneratedBy F x\nF' : Cᵒᵖ ⥤ Type w\nf : F ⟶ F'\ninst✝ : Epi f\n⊢ PresheafIsGeneratedBy F' fun i ↦ (ConcreteCategory.hom (f.app (X i))) (x i)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Subfunctor.Subobject | {
"line": 73,
"column": 6
} | {
"line": 73,
"column": 17
} | {
"line": 73,
"column": 18
} | [
{
"pp": "case mp\nC : Type u\ninst✝ : Category.{v, u} C\nF : C ⥤ Type w\nA B : Subfunctor F\nh :\n { toFun := fun A ↦ Subobject.mk A.ι, invFun := fun X ↦ range X.arrow, left_inv := ⋯, right_inv := ⋯ } A ≤\n { toFun := fun A ↦ Subobject.mk A.ι, invFun := fun X ↦ range X.arrow, left_inv := ⋯, right_inv := ⋯ }... | [
"case mp\nC : Type u\ninst✝ : Category.{v, u} C\nF : C ⥤ Type w\nA B : Subfunctor F\nh :\n { toFun := fun A ↦ Subobject.mk A.ι, invFun := fun X ↦ range X.arrow, left_inv := ⋯, right_inv := ⋯ } A ≤\n { toFun := fun A ↦ Subobject.mk A.ι, invFun := fun X ↦ range X.arrow, left_inv := ⋯, right_inv := ⋯ } B\nthis : r... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Subobject.Classifier.Defs | {
"line": 542,
"column": 29
} | {
"line": 542,
"column": 40
} | {
"line": 542,
"column": 41
} | [
{
"pp": "C✝ : Type u\ninst✝² : Category.{v, u} C✝\nC : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : HasPullbacks C\nΩ : C\nh : SubobjectRepresentableBy Ω\nX : C\nπ' : X ⟶ underlying.obj h.Ω₀\ns : PullbackCone (π' ≫ h.Ω₀.arrow) h.Ω₀.arrow\nm : s.pt ⟶ X\nhm : m ≫ 𝟙 X = s.fst\nx✝ : m ≫ π' = s.snd\n⊢ m = s.fst",
... | [
"C✝ : Type u\ninst✝² : Category.{v, u} C✝\nC : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : HasPullbacks C\nΩ : C\nh : SubobjectRepresentableBy Ω\nX : C\nπ' : X ⟶ underlying.obj h.Ω₀\ns : PullbackCone (π' ≫ h.Ω₀.arrow) h.Ω₀.arrow\nm : s.pt ⟶ X\nhm : m ≫ 𝟙 X = s.fst\nx✝ : m ≫ π' = s.snd\n⊢ m = s.fst"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Subobject.Classifier.Defs | {
"line": 695,
"column": 4
} | {
"line": 695,
"column": 15
} | {
"line": 695,
"column": 16
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\n𝒞 : Classifier C\nΩ₀ Ω : C\neΩ : 𝒞.Ω ≅ Ω\neΩ₀ : 𝒞.Ω₀ ≅ Ω₀\nfrom' : (C_1 : C) → C_1 ⟶ Ω₀\nt : Ω₀ ⟶ Ω\nht : t = eΩ₀.inv ≫ 𝒞.truth ≫ eΩ.hom\nF G : C\nm : F ⟶ G\nx✝ : Mono m\nχ₀' : F ⟶ Ω₀\nχ' : G ⟶ Ω\nhχ' : IsPullback m χ₀' χ' t\nthis : χ' ≫ eΩ.inv = 𝒞.χ m\n⊢ χ' ... | [
"C : Type u\ninst✝ : Category.{v, u} C\n𝒞 : Classifier C\nΩ₀ Ω : C\neΩ : 𝒞.Ω ≅ Ω\neΩ₀ : 𝒞.Ω₀ ≅ Ω₀\nfrom' : (C_1 : C) → C_1 ⟶ Ω₀\nt : Ω₀ ⟶ Ω\nht : t = eΩ₀.inv ≫ 𝒞.truth ≫ eΩ.hom\nF G : C\nm : F ⟶ G\nx✝ : Mono m\nχ₀' : F ⟶ Ω₀\nχ' : G ⟶ Ω\nhχ' : IsPullback m χ₀' χ' t\nthis : χ' ≫ eΩ.inv = 𝒞.χ m\n⊢ χ' = 𝒞.χ m ≫ e... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Subobject.Classifier.Defs | {
"line": 725,
"column": 4
} | {
"line": 725,
"column": 15
} | {
"line": 725,
"column": 16
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nD : Type u_1\ninst✝ : Category.{v_1, u_1} D\n𝒞₁ : Classifier C\ne : C ≌ D\nF G : D\nm : F ⟶ G\nx✝ : Mono m\nχ₀' : F ⟶ e.functor.obj 𝒞₁.Ω₀\nχ' : G ⟶ e.functor.obj 𝒞₁.Ω\nhχ' : IsPullback m χ₀' χ' (e.functor.map 𝒞₁.truth)\nthis : e.inverse.map χ' ≫ e.unitInv.app... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\nD : Type u_1\ninst✝ : Category.{v_1, u_1} D\n𝒞₁ : Classifier C\ne : C ≌ D\nF G : D\nm : F ⟶ G\nx✝ : Mono m\nχ₀' : F ⟶ e.functor.obj 𝒞₁.Ω₀\nχ' : G ⟶ e.functor.obj 𝒞₁.Ω\nhχ' : IsPullback m χ₀' χ' (e.functor.map 𝒞₁.truth)\nthis : e.inverse.map χ' ≫ e.unitInv.app 𝒞₁.Ω = 𝒞₁... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.Descent.DescentData | {
"line": 456,
"column": 8
} | {
"line": 458,
"column": 40
} | {
"line": 458,
"column": 41
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF : Pseudofunctor (LocallyDiscrete Cᵒᵖ) Cat\nι : Type t\nS : C\nX : ι → C\nf : (i : ι) → X i ⟶ S\nM N : ↑(F.obj { as := op S })\ng : (F.toDescentData f).obj M ⟶ (F.toDescentData f).obj N\ni₁ i₂ : ι\nZ : Over S\nf₁ : Z ⟶ (fun i ↦ Over.mk (f i)) i₁\nf₂ : Z ⟶ (fun i ... | [
"C : Type u\ninst✝ : Category.{v, u} C\nF : Pseudofunctor (LocallyDiscrete Cᵒᵖ) Cat\nι : Type t\nS : C\nX : ι → C\nf : (i : ι) → X i ⟶ S\nM N : ↑(F.obj { as := op S })\ng : (F.toDescentData f).obj M ⟶ (F.toDescentData f).obj N\ni₁ i₂ : ι\nZ : Over S\nf₁ : Z ⟶ (fun i ↦ Over.mk (f i)) i₁\nf₂ : Z ⟶ (fun i ↦ Over.mk (f... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.Descent.DescentData | {
"line": 571,
"column": 45
} | {
"line": 571,
"column": 56
} | {
"line": 571,
"column": 57
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF : Pseudofunctor (LocallyDiscrete Cᵒᵖ) Cat\nS : C\nR : Sieve S\nM N : ↑(F.obj { as := op S })\nX : C\ng : X ⟶ S\nf : Over.mk g ⟶ Over.mk (𝟙 S)\nhf : R.arrows (Over.Hom.left f)\n⊢ Over.Hom.left f = Over.Hom.left (Over.homMk g ⋯)",
"ppTerm": "?m.302",
"ass... | [
"C : Type u\ninst✝ : Category.{v, u} C\nF : Pseudofunctor (LocallyDiscrete Cᵒᵖ) Cat\nS : C\nR : Sieve S\nM N : ↑(F.obj { as := op S })\nX : C\ng : X ⟶ S\nf : Over.mk g ⟶ Over.mk (𝟙 S)\nhf : R.arrows (Over.Hom.left f)\n⊢ Over.Hom.left f = g"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.Descent.DescentData | {
"line": 588,
"column": 67
} | {
"line": 588,
"column": 78
} | {
"line": 588,
"column": 79
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF : Pseudofunctor (LocallyDiscrete Cᵒᵖ) Cat\nS : C\nR : Sieve S\nS₀ : C\nM N : ↑(F.obj { as := op S₀ })\na : S ⟶ S₀\nh :\n Presieve.IsSheafFor (F.presheafHom M N)\n (Sieve.pullback (Over.isoMk (Iso.refl ((Over.map a).obj (Over.mk (𝟙 S))).left) ⋯).inv\n ... | [
"C : Type u\ninst✝ : Category.{v, u} C\nF : Pseudofunctor (LocallyDiscrete Cᵒᵖ) Cat\nS : C\nR : Sieve S\nS₀ : C\nM N : ↑(F.obj { as := op S₀ })\na : S ⟶ S₀\nh :\n Presieve.IsSheafFor (F.presheafHom M N)\n (Sieve.pullback (Over.isoMk (Iso.refl ((Over.map a).obj (Over.mk (𝟙 S))).left) ⋯).inv\n (Sieve.func... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.Descent.DescentData | {
"line": 595,
"column": 4
} | {
"line": 595,
"column": 21
} | {
"line": 595,
"column": 22
} | [
{
"pp": "case refine_2\nC : Type u\ninst✝ : Category.{v, u} C\nF : Pseudofunctor (LocallyDiscrete Cᵒᵖ) Cat\nS : C\nR : Sieve S\nS₀ : C\nM N : ↑(F.obj { as := op S₀ })\na : S ⟶ S₀\nh✝ :\n Presieve.IsSheafFor (F.presheafHom M N)\n (Sieve.pullback (Over.isoMk (Iso.refl ((Over.map a).obj (Over.mk (𝟙 S))).left)... | [
"case refine_2\nC : Type u\ninst✝ : Category.{v, u} C\nF : Pseudofunctor (LocallyDiscrete Cᵒᵖ) Cat\nS : C\nR : Sieve S\nS₀ : C\nM N : ↑(F.obj { as := op S₀ })\na : S ⟶ S₀\nh✝ :\n Presieve.IsSheafFor (F.presheafHom M N)\n (Sieve.pullback (Over.isoMk (Iso.refl ((Over.map a).obj (Over.mk (𝟙 S))).left) ⋯).inv\n ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.Descent.DescentData | {
"line": 605,
"column": 2
} | {
"line": 605,
"column": 13
} | {
"line": 605,
"column": 14
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF : Pseudofunctor (LocallyDiscrete Cᵒᵖ) Cat\nS₀ : C\nM N : ↑(F.obj { as := op S₀ })\nS : C\na : S ⟶ S₀\nR : Sieve (Over.mk a)\nhF :\n ∀ ⦃S₀_1 : C⦄ (M N : ↑(F.obj { as := op S₀_1 })) (a_1 : (Over.mk a).left ⟶ S₀_1),\n Presieve.IsSheafFor (F.presheafHom M N)\n ... | [
"C : Type u\ninst✝ : Category.{v, u} C\nF : Pseudofunctor (LocallyDiscrete Cᵒᵖ) Cat\nS₀ : C\nM N : ↑(F.obj { as := op S₀ })\nS : C\na : S ⟶ S₀\nR : Sieve (Over.mk a)\nhF :\n ∀ ⦃S₀_1 : C⦄ (M N : ↑(F.obj { as := op S₀_1 })) (a_1 : (Over.mk a).left ⟶ S₀_1),\n Presieve.IsSheafFor (F.presheafHom M N)\n ((Sieve.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Topos.Sheaf | {
"line": 119,
"column": 4
} | {
"line": 119,
"column": 15
} | {
"line": 119,
"column": 16
} | [
{
"pp": "case mpr\nC : Type u\ninst✝ : Category.{v, u} C\nF G : Cᵒᵖ ⥤ Type (max u v)\nm : F ⟶ G\nχ' : G ⟶ Functor.sieves C\nX : Cᵒᵖ\nx : G.obj X\nh₁ : ∀ (x : Cᵒᵖ), m.app x ≫ χ'.app x = Types.isTerminalPUnit.from (F.obj x) ≫ ↾fun x_1 ↦ ⊤\nh₂ : ∀ (x : Cᵒᵖ) (x₁ y₁ : F.obj x), (ConcreteCategory.hom (m.app x)) x₁ = ... | [
"case mpr\nC : Type u\ninst✝ : Category.{v, u} C\nF G : Cᵒᵖ ⥤ Type (max u v)\nm : F ⟶ G\nχ' : G ⟶ Functor.sieves C\nX : Cᵒᵖ\nx : G.obj X\nh₁ : ∀ (x : Cᵒᵖ), m.app x ≫ χ'.app x = Types.isTerminalPUnit.from (F.obj x) ≫ ↾fun x_1 ↦ ⊤\nh₂ : ∀ (x : Cᵒᵖ) (x₁ y₁ : F.obj x), (ConcreteCategory.hom (m.app x)) x₁ = (ConcreteCat... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.Adjunction | {
"line": 68,
"column": 6
} | {
"line": 68,
"column": 34
} | {
"line": 68,
"column": 35
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝¹⁵ : Category.{v_1, u_1} C\ninst✝¹⁴ : Category.{v_2, u_2} D\ninst✝¹³ : HasZeroObject C\ninst✝¹² : HasZeroObject D\ninst✝¹¹ : Preadditive C\ninst✝¹⁰ : Preadditive D\ninst✝⁹ : HasShift C ℤ\ninst✝⁸ : HasShift D ℤ\ninst✝⁷ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝⁶ : ∀... | [
"C : Type u_1\nD : Type u_2\ninst✝¹⁵ : Category.{v_1, u_1} C\ninst✝¹⁴ : Category.{v_2, u_2} D\ninst✝¹³ : HasZeroObject C\ninst✝¹² : HasZeroObject D\ninst✝¹¹ : Preadditive C\ninst✝¹⁰ : Preadditive D\ninst✝⁹ : HasShift C ℤ\ninst✝⁸ : HasShift D ℤ\ninst✝⁷ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝⁶ : ∀ (n : ℤ), (s... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.Generators | {
"line": 155,
"column": 4
} | {
"line": 155,
"column": 40
} | {
"line": 156,
"column": 4
} | [
{
"pp": "C : Type u_1\ninst✝⁵ : Category.{v_1, u_1} C\ninst✝⁴ : HasZeroObject C\ninst✝³ : HasShift C ℤ\ninst✝² : Preadditive C\ninst✝¹ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝ : Pretriangulated C\nP : ObjectProperty C\nX Y : C\nr : Retract X Y\nhY : P.triangEnvelope Y\n⊢ P.triangEnvelope X",
"ppTerm"... | [
"C : Type u_1\ninst✝⁵ : Category.{v_1, u_1} C\ninst✝⁴ : HasZeroObject C\ninst✝³ : HasShift C ℤ\ninst✝² : Preadditive C\ninst✝¹ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝ : Pretriangulated C\nP : ObjectProperty C\nX Y : C\nr : Retract X Y\nhY : ∃ n, P.triangEnvelopeIter n Y\n⊢ ∃ n, P.triangEnvelopeIter n X"
] | rw [prop_triangEnvelope_iff] at hY ⊢ | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.CategoryTheory.Topos.Sheaf | {
"line": 143,
"column": 2
} | {
"line": 153,
"column": 38
} | {
"line": 155,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nJ : GrothendieckTopology C\nF G : Cᵒᵖ ⥤ Type (max u v)\nm : F ⟶ G\ninst✝ : Mono m\nhF : Presieve.IsSheaf J F\nhG : Presieve.IsSeparated J G\nX : Cᵒᵖ\nx : G.obj X\n⊢ J.IsClosed ((ConcreteCategory.hom ((χ m).app X)) x)",
"ppTerm": "?m.34",
"assigned": true,... | [] | intro Y f hf
simp only [Presheaf.χ_app, Opposite.op_unop] at hf ⊢
choose a ha using fun Z (g : Z ⟶ Y) (hg : (Sieve.pullback f ((χ m).app X x)).arrows g) => hg
refine ⟨(hF _ hf).amalgamate a ?_, ?_⟩
· introv Y₁ h
apply (mono_iff_injective (m.app (.op Z))).mp inferInstance
simp_rw [NatTrans.naturality_app... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Topos.Sheaf | {
"line": 143,
"column": 2
} | {
"line": 153,
"column": 38
} | {
"line": 155,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nJ : GrothendieckTopology C\nF G : Cᵒᵖ ⥤ Type (max u v)\nm : F ⟶ G\ninst✝ : Mono m\nhF : Presieve.IsSheaf J F\nhG : Presieve.IsSeparated J G\nX : Cᵒᵖ\nx : G.obj X\n⊢ J.IsClosed ((ConcreteCategory.hom ((χ m).app X)) x)",
"ppTerm": "?m.34",
"assigned": true,... | [] | intro Y f hf
simp only [Presheaf.χ_app, Opposite.op_unop] at hf ⊢
choose a ha using fun Z (g : Z ⟶ Y) (hg : (Sieve.pullback f ((χ m).app X x)).arrows g) => hg
refine ⟨(hF _ hf).amalgamate a ?_, ?_⟩
· introv Y₁ h
apply (mono_iff_injective (m.app (.op Z))).mp inferInstance
simp_rw [NatTrans.naturality_app... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Topos.Sheaf | {
"line": 197,
"column": 49
} | {
"line": 197,
"column": 60
} | {
"line": 197,
"column": 61
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nJ : GrothendieckTopology C\nF G : Sheaf J (Type (max u v))\nm : F ⟶ G\ninst✝ : Mono m\n⊢ (m.hom ≫ Subfunctor.lift (Presheaf.χ m.hom) ⋯) ≫ (closedSieves J).ι =\n (((isTerminalTerminal J Types.isTerminalPUnit).from F).hom ≫ Subfunctor.lift (Presheaf.truth C) ⋯) ... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\nJ : GrothendieckTopology C\nF G : Sheaf J (Type (max u v))\nm : F ⟶ G\ninst✝ : Mono m\n⊢ m.hom ≫ Presheaf.χ m.hom = (isTerminalConst Cᵒᵖ Types.isTerminalPUnit).from F.obj ≫ Presheaf.truth C"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Topos.Sheaf | {
"line": 213,
"column": 4
} | {
"line": 213,
"column": 15
} | {
"line": 213,
"column": 16
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nJ : GrothendieckTopology C\nF G : Sheaf J (Type (max u v))\nm : F ⟶ G\ninst✝ : Mono m\nχ' : G ⟶ Ω J\nhχ' : IsPullback m ((isTerminalTerminal J Types.isTerminalPUnit).from F) χ' (truth J)\npb : IsPullback (𝟙 G.obj) χ'.hom (χ'.hom ≫ (closedSieves J).ι) (closedSiev... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\nJ : GrothendieckTopology C\nF G : Sheaf J (Type (max u v))\nm : F ⟶ G\ninst✝ : Mono m\nχ' : G ⟶ Ω J\nhχ' : IsPullback m ((isTerminalTerminal J Types.isTerminalPUnit).from F) χ' (truth J)\npb : IsPullback (𝟙 G.obj) χ'.hom (χ'.hom ≫ (closedSieves J).ι) (closedSieves J).ι\n⊢ I... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.Opposite.Functor | {
"line": 136,
"column": 42
} | {
"line": 141,
"column": 6
} | {
"line": 143,
"column": 0
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝⁴ : Category.{v_1, u_1} C\ninst✝³ : Category.{v_2, u_2} D\ninst✝² : HasShift C ℤ\ninst✝¹ : HasShift D ℤ\nF : C ⥤ D\ninst✝ : F.CommShift ℤ\nX : Cᵒᵖ\nn : ℤ\n⊢ F.map ((opShiftFunctorEquivalence C n).unitIso.inv.app X).unop =\n ((opShiftFunctorEquivalence D n).unitIso.in... | [] | by
rw [← cancel_mono (F.map ((opShiftFunctorEquivalence C n).unitIso.hom.app X).unop),
← F.map_comp, ← unop_comp, Iso.hom_inv_id_app,
map_opShiftFunctorEquivalence_unitIso_hom_app_unop, assoc, assoc,
Iso.inv_hom_id_app_assoc, ← Functor.map_comp_assoc, ← unop_comp]
simp | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Topos.Sheaf | {
"line": 214,
"column": 2
} | {
"line": 214,
"column": 13
} | {
"line": 214,
"column": 14
} | [
{
"pp": "case refine_2\nC : Type u\ninst✝¹ : Category.{v, u} C\nJ : GrothendieckTopology C\nF G : Sheaf J (Type (max u v))\nm : F ⟶ G\ninst✝ : Mono m\nχ' : G ⟶ Ω J\nhχ' : IsPullback m ((isTerminalTerminal J Types.isTerminalPUnit).from F) χ' (truth J)\npb : IsPullback (𝟙 G.obj) χ'.hom (χ'.hom ≫ (closedSieves J)... | [
"case refine_2\nC : Type u\ninst✝¹ : Category.{v, u} C\nJ : GrothendieckTopology C\nF G : Sheaf J (Type (max u v))\nm : F ⟶ G\ninst✝ : Mono m\nχ' : G ⟶ Ω J\nhχ' : IsPullback m ((isTerminalTerminal J Types.isTerminalPUnit).from F) χ' (truth J)\npb : IsPullback (𝟙 G.obj) χ'.hom (χ'.hom ≫ (closedSieves J).ι) (closedS... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.Adjunction | {
"line": 86,
"column": 42
} | {
"line": 86,
"column": 93
} | {
"line": 86,
"column": 94
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝¹⁵ : Category.{v_1, u_1} C\ninst✝¹⁴ : Category.{v_2, u_2} D\ninst✝¹³ : HasZeroObject C\ninst✝¹² : HasZeroObject D\ninst✝¹¹ : Preadditive C\ninst✝¹⁰ : Preadditive D\ninst✝⁹ : HasShift C ℤ\ninst✝⁸ : HasShift D ℤ\ninst✝⁷ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝⁶ : ∀... | [
"C : Type u_1\nD : Type u_2\ninst✝¹⁵ : Category.{v_1, u_1} C\ninst✝¹⁴ : Category.{v_2, u_2} D\ninst✝¹³ : HasZeroObject C\ninst✝¹² : HasZeroObject D\ninst✝¹¹ : Preadditive C\ninst✝¹⁰ : Preadditive D\ninst✝⁹ : HasShift C ℤ\ninst✝⁸ : HasShift D ℤ\ninst✝⁷ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝⁶ : ∀ (n : ℤ), (s... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.TStructure.AbelianSubcategory | {
"line": 121,
"column": 24
} | {
"line": 123,
"column": 48
} | {
"line": 124,
"column": 2
} | [
{
"pp": "C : Type u_1\nA : Type u_2\ninst✝⁹ : Category.{v_1, u_1} C\ninst✝⁸ : HasZeroObject C\ninst✝⁷ : Preadditive C\ninst✝⁶ : HasShift C ℤ\ninst✝⁵ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝⁴ : Pretriangulated C\ninst✝³ : Category.{v_2, u_2} A\nι : A ⥤ C\nhι : ∀ ⦃X Y : A⦄ ⦃n : ℤ⦄ (f : ι.obj X ⟶ (shiftFunc... | [] | by
rw [← cancel_epi ((shiftFunctorAdd' C (1 : ℤ) 1 2 (by lia)).hom.app _), comp_zero]
exact eq_zero_of_hom_shift_pos hι _ (by lia) | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Triangulated.Adjunction | {
"line": 117,
"column": 44
} | {
"line": 117,
"column": 88
} | {
"line": 117,
"column": 89
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝¹⁵ : Category.{v_1, u_1} C\ninst✝¹⁴ : Category.{v_2, u_2} D\ninst✝¹³ : HasZeroObject C\ninst✝¹² : HasZeroObject D\ninst✝¹¹ : Preadditive C\ninst✝¹⁰ : Preadditive D\ninst✝⁹ : HasShift C ℤ\ninst✝⁸ : HasShift D ℤ\ninst✝⁷ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝⁶ : ∀... | [
"C : Type u_1\nD : Type u_2\ninst✝¹⁵ : Category.{v_1, u_1} C\ninst✝¹⁴ : Category.{v_2, u_2} D\ninst✝¹³ : HasZeroObject C\ninst✝¹² : HasZeroObject D\ninst✝¹¹ : Preadditive C\ninst✝¹⁰ : Preadditive D\ninst✝⁹ : HasShift C ℤ\ninst✝⁸ : HasShift D ℤ\ninst✝⁷ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝⁶ : ∀ (n : ℤ), (s... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.Adjunction | {
"line": 119,
"column": 8
} | {
"line": 119,
"column": 40
} | {
"line": 119,
"column": 41
} | [
{
"pp": "case right\nC : Type u_1\nD : Type u_2\ninst✝¹⁵ : Category.{v_1, u_1} C\ninst✝¹⁴ : Category.{v_2, u_2} D\ninst✝¹³ : HasZeroObject C\ninst✝¹² : HasZeroObject D\ninst✝¹¹ : Preadditive C\ninst✝¹⁰ : Preadditive D\ninst✝⁹ : HasShift C ℤ\ninst✝⁸ : HasShift D ℤ\ninst✝⁷ : ∀ (n : ℤ), (shiftFunctor C n).Additive... | [
"case right\nC : Type u_1\nD : Type u_2\ninst✝¹⁵ : Category.{v_1, u_1} C\ninst✝¹⁴ : Category.{v_2, u_2} D\ninst✝¹³ : HasZeroObject C\ninst✝¹² : HasZeroObject D\ninst✝¹¹ : Preadditive C\ninst✝¹⁰ : Preadditive D\ninst✝⁹ : HasShift C ℤ\ninst✝⁸ : HasShift D ℤ\ninst✝⁷ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝⁶ : ∀... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.TStructure.AbelianSubcategory | {
"line": 136,
"column": 24
} | {
"line": 138,
"column": 48
} | {
"line": 139,
"column": 2
} | [
{
"pp": "C : Type u_1\nA : Type u_2\ninst✝⁹ : Category.{v_1, u_1} C\ninst✝⁸ : HasZeroObject C\ninst✝⁷ : Preadditive C\ninst✝⁶ : HasShift C ℤ\ninst✝⁵ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝⁴ : Pretriangulated C\ninst✝³ : Category.{v_2, u_2} A\nι : A ⥤ C\nhι : ∀ ⦃X Y : A⦄ ⦃n : ℤ⦄ (f : ι.obj X ⟶ (shiftFunc... | [] | by
rw [← cancel_epi ((shiftFunctorAdd' C (1 : ℤ) 1 2 (by lia)).hom.app _), comp_zero]
exact eq_zero_of_hom_shift_pos hι _ (by lia) | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Triangulated.TStructure.ETrunc | {
"line": 50,
"column": 53
} | {
"line": 50,
"column": 64
} | {
"line": 50,
"column": 65
} | [
{
"pp": "C : Type u_1\ninst✝⁵ : Category.{v_1, u_1} C\ninst✝⁴ : Preadditive C\ninst✝³ : HasZeroObject C\ninst✝² : HasShift C ℤ\ninst✝¹ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝ : Pretriangulated C\nt : TStructure C\na b : ℤ\nf : WithBotTop.coe a ⟶ WithBotTop.coe b\n⊢ a ≤ b",
"ppTerm": "?m.141",
"a... | [
"C : Type u_1\ninst✝⁵ : Category.{v_1, u_1} C\ninst✝⁴ : Preadditive C\ninst✝³ : HasZeroObject C\ninst✝² : HasShift C ℤ\ninst✝¹ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝ : Pretriangulated C\nt : TStructure C\na b : ℤ\nf : WithBotTop.coe a ⟶ WithBotTop.coe b\n⊢ a ≤ b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.AP.Three.Defs | {
"line": 154,
"column": 2
} | {
"line": 155,
"column": 91
} | {
"line": 157,
"column": 0
} | [
{
"pp": "F : Type u_1\nα : Type u_2\nβ : Type u_3\ninst✝³ : CommMonoid α\ninst✝² : CommMonoid β\ns : Set α\ninst✝¹ : FunLike F α β\ninst✝ : MulHomClass F α β\nf : F\nhf : InjOn (⇑f) (s * s)\nh : ThreeGPFree s\n⊢ ThreeGPFree (⇑f '' s)",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"E... | [] | rintro _ ⟨a, ha, rfl⟩ _ ⟨b, hb, rfl⟩ _ ⟨c, hc, rfl⟩ habc
rw [h ha hb hc (hf (mul_mem_mul ha hc) (mul_mem_mul hb hb) <| by rwa [map_mul, map_mul])] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.Additive.AP.Three.Defs | {
"line": 154,
"column": 2
} | {
"line": 155,
"column": 91
} | {
"line": 157,
"column": 0
} | [
{
"pp": "F : Type u_1\nα : Type u_2\nβ : Type u_3\ninst✝³ : CommMonoid α\ninst✝² : CommMonoid β\ns : Set α\ninst✝¹ : FunLike F α β\ninst✝ : MulHomClass F α β\nf : F\nhf : InjOn (⇑f) (s * s)\nh : ThreeGPFree s\n⊢ ThreeGPFree (⇑f '' s)",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"E... | [] | rintro _ ⟨a, ha, rfl⟩ _ ⟨b, hb, rfl⟩ _ ⟨c, hc, rfl⟩ habc
rw [h ha hb hc (hf (mul_mem_mul ha hc) (mul_mem_mul hb hb) <| by rwa [map_mul, map_mul])] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.Additive.AP.Three.Defs | {
"line": 167,
"column": 2
} | {
"line": 167,
"column": 13
} | {
"line": 167,
"column": 14
} | [
{
"pp": "α : Type u_2\ninst✝¹ : CommMonoid α\ninst✝ : IsCancelMul α\ns : Set α\nhs : ThreeGPFree s\na : α\nha : a ∈ s\nc : α\nhc : c ∈ s\nhb : a ∈ s\nhabc : a * c = a * a\n⊢ a = c",
"ppTerm": "?m.53",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝¹ : CommMonoid α\ninst✝ : IsCancelMul α\ns : Set α\nhs : ThreeGPFree s\na : α\nha : a ∈ s\nc : α\nhc : c ∈ s\nhb : a ∈ s\nhabc : a * c = a * a\n⊢ a = c"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.TStructure.AbelianSubcategory | {
"line": 326,
"column": 6
} | {
"line": 326,
"column": 72
} | {
"line": 327,
"column": 4
} | [
{
"pp": "C : Type u_1\nA : Type u_2\ninst✝¹² : Category.{v_1, u_1} C\ninst✝¹¹ : HasZeroObject C\ninst✝¹⁰ : Preadditive C\ninst✝⁹ : HasShift C ℤ\ninst✝⁸ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝⁷ : Pretriangulated C\ninst✝⁶ : Category.{v_2, u_2} A\nι : A ⥤ C\nhι : ∀ ⦃X Y : A⦄ ⦃n : ℤ⦄ (f : ι.obj X ⟶ (shiftF... | [] | exact Triangle.isoMk _ _ (-(Iso.refl _)) (Iso.refl _) (Iso.refl _) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.CategoryTheory.Triangulated.TStructure.AbelianSubcategory | {
"line": 339,
"column": 60
} | {
"line": 339,
"column": 77
} | {
"line": 339,
"column": 78
} | [
{
"pp": "C : Type u_1\nA : Type u_2\ninst✝¹² : Category.{v_1, u_1} C\ninst✝¹¹ : HasZeroObject C\ninst✝¹⁰ : Preadditive C\ninst✝⁹ : HasShift C ℤ\ninst✝⁸ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝⁷ : Pretriangulated C\ninst✝⁶ : Category.{v_2, u_2} A\nι : A ⥤ C\nhι : ∀ ⦃X Y : A⦄ ⦃n : ℤ⦄ (f : ι.obj X ⟶ (shiftF... | [
"C : Type u_1\nA : Type u_2\ninst✝¹² : Category.{v_1, u_1} C\ninst✝¹¹ : HasZeroObject C\ninst✝¹⁰ : Preadditive C\ninst✝⁹ : HasShift C ℤ\ninst✝⁸ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝⁷ : Pretriangulated C\ninst✝⁶ : Category.{v_2, u_2} A\nι : A ⥤ C\nhι : ∀ ⦃X Y : A⦄ ⦃n : ℤ⦄ (f : ι.obj X ⟶ (shiftFunctor C n).... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.AP.Three.Defs | {
"line": 192,
"column": 47
} | {
"line": 192,
"column": 83
} | {
"line": 192,
"column": 84
} | [
{
"pp": "α : Type u_2\ninst✝¹ : CommMonoid α\ninst✝ : IsCancelMul α\ns : Set α\na : α\nhs : ThreeGPFree s\nb : α\nhb : b ∈ s\nc : α\nhc : c ∈ s\nd : α\nhd : d ∈ s\nh : (fun x ↦ a • x) b * (fun x ↦ a • x) d = (fun x ↦ a • x) c * (fun x ↦ a • x) c\n⊢ b * d = c * c",
"ppTerm": "?m.99",
"assigned": false,
... | [
"α : Type u_2\ninst✝¹ : CommMonoid α\ninst✝ : IsCancelMul α\ns : Set α\na : α\nhs : ThreeGPFree s\nb : α\nhb : b ∈ s\nc : α\nhc : c ∈ s\nd : α\nhd : d ∈ s\nh : (fun x ↦ a • x) b * (fun x ↦ a • x) d = (fun x ↦ a • x) c * (fun x ↦ a • x) c\n⊢ b * d = c * c"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.AP.Three.Defs | {
"line": 222,
"column": 47
} | {
"line": 222,
"column": 87
} | {
"line": 222,
"column": 88
} | [
{
"pp": "α : Type u_2\ninst✝² : CommMonoidWithZero α\ninst✝¹ : IsCancelMulZero α\ninst✝ : NoZeroDivisors α\ns : Set α\na : α\nhs : ThreeGPFree s\nha : a ≠ 0\nb : α\nhb : b ∈ s\nc : α\nhc : c ∈ s\nd : α\nhd : d ∈ s\nh : (fun x ↦ a • x) b * (fun x ↦ a • x) d = (fun x ↦ a • x) c * (fun x ↦ a • x) c\n⊢ b * d = c * ... | [
"α : Type u_2\ninst✝² : CommMonoidWithZero α\ninst✝¹ : IsCancelMulZero α\ninst✝ : NoZeroDivisors α\ns : Set α\na : α\nhs : ThreeGPFree s\nha : a ≠ 0\nb : α\nhb : b ∈ s\nc : α\nhc : c ∈ s\nd : α\nhd : d ∈ s\nh : (fun x ↦ a • x) b * (fun x ↦ a • x) d = (fun x ↦ a • x) c * (fun x ↦ a • x) c\n⊢ b * d = c * c"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.AP.Three.Defs | {
"line": 348,
"column": 2
} | {
"line": 348,
"column": 13
} | {
"line": 348,
"column": 14
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\ninst✝³ : DecidableEq α\ninst✝² : CommMonoid α\ninst✝¹ : CommMonoid β\ninst✝ : DecidableEq β\nA : Finset α\nB : Finset β\nf : α → β\nhf : IsMulFreimanHom 2 (↑A) (↑B) f\nhf' : Set.BijOn f ↑A ↑B\ns : Finset β\nhsB : s ⊆ B\nhcard : #s = mulRothNumber B\nhs : ThreeGPFree ↑s\nhsA ... | [
"α : Type u_2\nβ : Type u_3\ninst✝³ : DecidableEq α\ninst✝² : CommMonoid α\ninst✝¹ : CommMonoid β\ninst✝ : DecidableEq β\nA : Finset α\nB : Finset β\nf : α → β\nhf : IsMulFreimanHom 2 (↑A) (↑B) f\nhf' : Set.BijOn f ↑A ↑B\ns : Finset β\nhsB : s ⊆ B\nhcard : #s = mulRothNumber B\nhs : ThreeGPFree ↑s\nhsA : invFunOn f... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.FreimanHom | {
"line": 149,
"column": 4
} | {
"line": 149,
"column": 19
} | {
"line": 151,
"column": 0
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\ninst✝¹ : CommMonoid α\ninst✝ : CommMonoid β\nA : Set α\nB : Set β\nf : α → β\nn : ℕ\ng : β → α\nhg₁ : MapsTo g B A\nhg₂ : RightInvOn g f B\nhf : IsMulFreimanIso n A B f\ns t : Multiset β\nhsB : ∀ ⦃x : β⦄, x ∈ s → x ∈ B\nhtB : ∀ ⦃x : β⦄, x ∈ t → x ∈ B\nhs : s.card = n\nht : t... | [] | all_goals aesop | Lean.Elab.Tactic.evalAllGoals | Lean.Parser.Tactic.allGoals |
Mathlib.Combinatorics.Pigeonhole | {
"line": 316,
"column": 27
} | {
"line": 316,
"column": 66
} | {
"line": 317,
"column": 4
} | [
{
"pp": "α : Type u\nβ : Type v\ninst✝² : DecidableEq β\ns : Finset α\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf : α → Finset β\nh₁ : s.Nonempty\nh₂ : ∀ j ∈ s, 0 < #(f j)\nk : ℕ := s.inf' h₁ fun j ↦ #(f j)\nhk : k = s.inf' h₁ fun j ↦ #(f j)\nh₃ : ∀ a ∈ s, ∀ x ∈ f a, #{j | j ∈ s ∧ x ∈ f j} ≤ k\n⊢ ∑ j ∈ s, k ≤... | [] | by gcongr with i hi; exact inf'_le _ hi | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Combinatorics.Additive.CovBySMul | {
"line": 69,
"column": 29
} | {
"line": 69,
"column": 40
} | {
"line": 69,
"column": 41
} | [
{
"pp": "M : Type u_1\nX : Type u_3\ninst✝¹ : Monoid M\ninst✝ : MulAction M X\nK : ℝ\nA₁ A₂ B : Set X\nhA : A₁ ⊆ A₂\nhAB : CovBySMul M K A₂ B\n⊢ CovBySMul M K A₁ B",
"ppTerm": "?m.11",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"M : Type u_1\nX : Type u_3\ninst✝¹ : Monoid M\ninst✝ : MulAction M X\nK : ℝ\nA₁ A₂ B : Set X\nhA : A₁ ⊆ A₂\nhAB : CovBySMul M K A₂ B\n⊢ CovBySMul M K A₁ B"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.CovBySMul | {
"line": 73,
"column": 29
} | {
"line": 73,
"column": 40
} | {
"line": 73,
"column": 41
} | [
{
"pp": "M : Type u_1\nX : Type u_3\ninst✝¹ : Monoid M\ninst✝ : MulAction M X\nK : ℝ\nA B₁ B₂ : Set X\nhB : B₁ ⊆ B₂\nhAB : CovBySMul M K A B₁\n⊢ CovBySMul M K A B₂",
"ppTerm": "?m.11",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"M : Type u_1\nX : Type u_3\ninst✝¹ : Monoid M\ninst✝ : MulAction M X\nK : ℝ\nA B₁ B₂ : Set X\nhB : B₁ ⊆ B₂\nhAB : CovBySMul M K A B₁\n⊢ CovBySMul M K A B₂"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.FreimanHom | {
"line": 185,
"column": 2
} | {
"line": 185,
"column": 13
} | {
"line": 185,
"column": 14
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\ninst✝¹ : CommMonoid α\ninst✝ : CommMonoid β\nA : Set α\nB : Set β\nf : α → β\nn : ℕ\nhf : IsMulFreimanHom n A B f\ns t : Finset α\nhsA : ↑s ⊆ A\nhtA : ↑t ⊆ A\nhs : s.card = n\nht : t.card = n\n⊢ ∏ i ∈ s, i = ∏ i ∈ t, i → ∏ i ∈ s, f i = ∏ i ∈ t, f i",
"ppTerm": "?m.35",
... | [
"α : Type u_2\nβ : Type u_3\ninst✝¹ : CommMonoid α\ninst✝ : CommMonoid β\nA : Set α\nB : Set β\nf : α → β\nn : ℕ\nhf : IsMulFreimanHom n A B f\ns t : Finset α\nhsA : ↑s ⊆ A\nhtA : ↑t ⊆ A\nhs : s.card = n\nht : t.card = n\n⊢ ∏ i ∈ s, i = ∏ i ∈ t, i → ∏ i ∈ s, f i = ∏ i ∈ t, f i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.FreimanHom | {
"line": 219,
"column": 43
} | {
"line": 219,
"column": 54
} | {
"line": 219,
"column": 55
} | [
{
"pp": "α : Type u_2\ninst✝ : CommMonoid α\nA₁ A₂ : Set α\nn : ℕ\nhA : A₁ ⊆ A₂\ns t : Multiset α\nx✝³ : ∀ ⦃x : α⦄, x ∈ s → x ∈ A₁\nx✝² : ∀ ⦃x : α⦄, x ∈ t → x ∈ A₁\nx✝¹ : s.card = n\nx✝ : t.card = n\nh : s.prod = t.prod\n⊢ (map id s).prod = (map id t).prod",
"ppTerm": "?m.23",
"assigned": true,
"use... | [
"α : Type u_2\ninst✝ : CommMonoid α\nA₁ A₂ : Set α\nn : ℕ\nhA : A₁ ⊆ A₂\ns t : Multiset α\nx✝³ : ∀ ⦃x : α⦄, x ∈ s → x ∈ A₁\nx✝² : ∀ ⦃x : α⦄, x ∈ t → x ∈ A₁\nx✝¹ : s.card = n\nx✝ : t.card = n\nh : s.prod = t.prod\n⊢ s.prod = t.prod"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.FreimanHom | {
"line": 232,
"column": 6
} | {
"line": 232,
"column": 17
} | {
"line": 232,
"column": 18
} | [
{
"pp": "case refine_1\nα : Type u_2\nβ : Type u_3\nγ : Type u_4\ninst✝² : CommMonoid α\ninst✝¹ : CommMonoid β\ninst✝ : CommMonoid γ\nA : Set α\nB : Set β\nC : Set γ\nf : α → β\ng : β → γ\nn : ℕ\nhg : IsMulFreimanHom n B C g\nhf : IsMulFreimanHom n A B f\ns t : Multiset α\nhsA : ∀ ⦃x : α⦄, x ∈ s → x ∈ A\nhtA : ... | [
"case refine_1\nα : Type u_2\nβ : Type u_3\nγ : Type u_4\ninst✝² : CommMonoid α\ninst✝¹ : CommMonoid β\ninst✝ : CommMonoid γ\nA : Set α\nB : Set β\nC : Set γ\nf : α → β\ng : β → γ\nn : ℕ\nhg : IsMulFreimanHom n B C g\nhf : IsMulFreimanHom n A B f\ns t : Multiset α\nhsA : ∀ ⦃x : α⦄, x ∈ s → x ∈ A\nhtA : ∀ ⦃x : α⦄, x... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.FreimanHom | {
"line": 233,
"column": 6
} | {
"line": 233,
"column": 17
} | {
"line": 233,
"column": 18
} | [
{
"pp": "case refine_2\nα : Type u_2\nβ : Type u_3\nγ : Type u_4\ninst✝² : CommMonoid α\ninst✝¹ : CommMonoid β\ninst✝ : CommMonoid γ\nA : Set α\nB : Set β\nC : Set γ\nf : α → β\ng : β → γ\nn : ℕ\nhg : IsMulFreimanHom n B C g\nhf : IsMulFreimanHom n A B f\ns t : Multiset α\nhsA : ∀ ⦃x : α⦄, x ∈ s → x ∈ A\nhtA : ... | [
"case refine_2\nα : Type u_2\nβ : Type u_3\nγ : Type u_4\ninst✝² : CommMonoid α\ninst✝¹ : CommMonoid β\ninst✝ : CommMonoid γ\nA : Set α\nB : Set β\nC : Set γ\nf : α → β\ng : β → γ\nn : ℕ\nhg : IsMulFreimanHom n B C g\nhf : IsMulFreimanHom n A B f\ns t : Multiset α\nhsA : ∀ ⦃x : α⦄, x ∈ s → x ∈ A\nhtA : ∀ ⦃x : α⦄, x... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.FreimanHom | {
"line": 242,
"column": 6
} | {
"line": 242,
"column": 17
} | {
"line": 242,
"column": 18
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\nγ : Type u_4\ninst✝² : CommMonoid α\ninst✝¹ : CommMonoid β\ninst✝ : CommMonoid γ\nA : Set α\nB : Set β\nC : Set γ\nf : α → β\ng : β → γ\nn : ℕ\nhg : IsMulFreimanIso n B C g\nhf : IsMulFreimanIso n A B f\ns t : Multiset α\nhsA : ∀ ⦃x : α⦄, x ∈ s → x ∈ A\nhtA : ∀ ⦃x : α⦄, x ∈ ... | [
"α : Type u_2\nβ : Type u_3\nγ : Type u_4\ninst✝² : CommMonoid α\ninst✝¹ : CommMonoid β\ninst✝ : CommMonoid γ\nA : Set α\nB : Set β\nC : Set γ\nf : α → β\ng : β → γ\nn : ℕ\nhg : IsMulFreimanIso n B C g\nhf : IsMulFreimanIso n A B f\ns t : Multiset α\nhsA : ∀ ⦃x : α⦄, x ∈ s → x ∈ A\nhtA : ∀ ⦃x : α⦄, x ∈ t → x ∈ A\nh... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.FreimanHom | {
"line": 242,
"column": 6
} | {
"line": 242,
"column": 51
} | {
"line": 243,
"column": 4
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\nγ : Type u_4\ninst✝² : CommMonoid α\ninst✝¹ : CommMonoid β\ninst✝ : CommMonoid γ\nA : Set α\nB : Set β\nC : Set γ\nf : α → β\ng : β → γ\nn : ℕ\nhg : IsMulFreimanIso n B C g\nhf : IsMulFreimanIso n A B f\ns t : Multiset α\nhsA : ∀ ⦃x : α⦄, x ∈ s → x ∈ A\nhtA : ∀ ⦃x : α⦄, x ∈ ... | [] | simpa using fun a h ↦ hf.bijOn.mapsTo (hsA h) | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Combinatorics.Additive.FreimanHom | {
"line": 242,
"column": 6
} | {
"line": 242,
"column": 51
} | {
"line": 243,
"column": 4
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\nγ : Type u_4\ninst✝² : CommMonoid α\ninst✝¹ : CommMonoid β\ninst✝ : CommMonoid γ\nA : Set α\nB : Set β\nC : Set γ\nf : α → β\ng : β → γ\nn : ℕ\nhg : IsMulFreimanIso n B C g\nhf : IsMulFreimanIso n A B f\ns t : Multiset α\nhsA : ∀ ⦃x : α⦄, x ∈ s → x ∈ A\nhtA : ∀ ⦃x : α⦄, x ∈ ... | [] | simpa using fun a h ↦ hf.bijOn.mapsTo (hsA h) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.Additive.FreimanHom | {
"line": 242,
"column": 6
} | {
"line": 242,
"column": 51
} | {
"line": 243,
"column": 4
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\nγ : Type u_4\ninst✝² : CommMonoid α\ninst✝¹ : CommMonoid β\ninst✝ : CommMonoid γ\nA : Set α\nB : Set β\nC : Set γ\nf : α → β\ng : β → γ\nn : ℕ\nhg : IsMulFreimanIso n B C g\nhf : IsMulFreimanIso n A B f\ns t : Multiset α\nhsA : ∀ ⦃x : α⦄, x ∈ s → x ∈ A\nhtA : ∀ ⦃x : α⦄, x ∈ ... | [] | simpa using fun a h ↦ hf.bijOn.mapsTo (hsA h) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.Additive.FreimanHom | {
"line": 243,
"column": 6
} | {
"line": 243,
"column": 17
} | {
"line": 243,
"column": 18
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\nγ : Type u_4\ninst✝² : CommMonoid α\ninst✝¹ : CommMonoid β\ninst✝ : CommMonoid γ\nA : Set α\nB : Set β\nC : Set γ\nf : α → β\ng : β → γ\nn : ℕ\nhg : IsMulFreimanIso n B C g\nhf : IsMulFreimanIso n A B f\ns t : Multiset α\nhsA : ∀ ⦃x : α⦄, x ∈ s → x ∈ A\nhtA : ∀ ⦃x : α⦄, x ∈ ... | [
"α : Type u_2\nβ : Type u_3\nγ : Type u_4\ninst✝² : CommMonoid α\ninst✝¹ : CommMonoid β\ninst✝ : CommMonoid γ\nA : Set α\nB : Set β\nC : Set γ\nf : α → β\ng : β → γ\nn : ℕ\nhg : IsMulFreimanIso n B C g\nhf : IsMulFreimanIso n A B f\ns t : Multiset α\nhsA : ∀ ⦃x : α⦄, x ∈ s → x ∈ A\nhtA : ∀ ⦃x : α⦄, x ∈ t → x ∈ A\nh... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.FreimanHom | {
"line": 336,
"column": 8
} | {
"line": 336,
"column": 23
} | {
"line": 336,
"column": 24
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\ninst✝¹ : CommMonoid α\ninst✝ : CancelCommMonoid β\nA : Set α\nB : Set β\nf : α → β\nn✝ : ℕ\ns t : Multiset α\nhsA : ∀ ⦃x : α⦄, x ∈ s → x ∈ A\nhtA : ∀ ⦃x : α⦄, x ∈ t → x ∈ A\nh : s.prod = t.prod\nn : ℕ\nhf : IsMulFreimanHom (n + 1 + 1) A B f\nhs : s.card = n + 1\nx✝ : t.card ... | [
"α : Type u_2\nβ : Type u_3\ninst✝¹ : CommMonoid α\ninst✝ : CancelCommMonoid β\nA : Set α\nB : Set β\nf : α → β\nn✝ : ℕ\ns t : Multiset α\nhsA : ∀ ⦃x : α⦄, x ∈ s → x ∈ A\nhtA : ∀ ⦃x : α⦄, x ∈ t → x ∈ A\nh : s.prod = t.prod\nn : ℕ\nhf : IsMulFreimanHom (n + 1 + 1) A B f\nhs : s.card = n + 1\nx✝ : t.card = n + 1\na :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.FreimanHom | {
"line": 370,
"column": 20
} | {
"line": 370,
"column": 33
} | {
"line": 370,
"column": 34
} | [
{
"pp": "α : Type u_2\ninst✝¹ : CommMonoid α\nA : Set α\nn : ℕ\nβ : Type u_5\ninst✝ : DivisionCommMonoid β\nB₁ B₂ : Set β\nf₁ f₂ : α → β\nh₁ : IsMulFreimanHom n A B₁ f₁\nh₂ : IsMulFreimanHom n A B₂ f₂\ns t : Multiset α\nhsA : ∀ ⦃x : α⦄, x ∈ s → x ∈ A\nhtA : ∀ ⦃x : α⦄, x ∈ t → x ∈ A\nhs : s.card = n\nht : t.card... | [
"α : Type u_2\ninst✝¹ : CommMonoid α\nA : Set α\nn : ℕ\nβ : Type u_5\ninst✝ : DivisionCommMonoid β\nB₁ B₂ : Set β\nf₁ f₂ : α → β\nh₁ : IsMulFreimanHom n A B₁ f₁\nh₂ : IsMulFreimanHom n A B₂ f₂\ns t : Multiset α\nhsA : ∀ ⦃x : α⦄, x ∈ s → x ∈ A\nhtA : ∀ ⦃x : α⦄, x ∈ t → x ∈ A\nhs : s.card = n\nht : t.card = n\nh : s.... | prod_map_div, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Combinatorics.Additive.FreimanHom | {
"line": 370,
"column": 34
} | {
"line": 370,
"column": 47
} | {
"line": 370,
"column": 48
} | [
{
"pp": "α : Type u_2\ninst✝¹ : CommMonoid α\nA : Set α\nn : ℕ\nβ : Type u_5\ninst✝ : DivisionCommMonoid β\nB₁ B₂ : Set β\nf₁ f₂ : α → β\nh₁ : IsMulFreimanHom n A B₁ f₁\nh₂ : IsMulFreimanHom n A B₂ f₂\ns t : Multiset α\nhsA : ∀ ⦃x : α⦄, x ∈ s → x ∈ A\nhtA : ∀ ⦃x : α⦄, x ∈ t → x ∈ A\nhs : s.card = n\nht : t.card... | [
"α : Type u_2\ninst✝¹ : CommMonoid α\nA : Set α\nn : ℕ\nβ : Type u_5\ninst✝ : DivisionCommMonoid β\nB₁ B₂ : Set β\nf₁ f₂ : α → β\nh₁ : IsMulFreimanHom n A B₁ f₁\nh₂ : IsMulFreimanHom n A B₂ f₂\ns t : Multiset α\nhsA : ∀ ⦃x : α⦄, x ∈ s → x ∈ A\nhtA : ∀ ⦃x : α⦄, x ∈ t → x ∈ A\nhs : s.card = n\nht : t.card = n\nh : s.... | prod_map_div, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Combinatorics.Additive.FreimanHom | {
"line": 448,
"column": 6
} | {
"line": 448,
"column": 81
} | {
"line": 448,
"column": 82
} | [
{
"pp": "k m n : ℕ\nhm : m ≠ 0\nhkmn : m * k ≤ n\ns t : Multiset (Fin (n + 1))\nhsA : ∀ ⦃x : Fin (n + 1)⦄, x ∈ s → x ∈ Iic ↑k\nhtA : ∀ ⦃x : Fin (n + 1)⦄, x ∈ t → x ∈ Iic ↑k\nhs : s.card = m\nht : t.card = m\nthis : ∀ (u : Multiset (Fin (n + 1))), (Nat.castRingHom (Fin (n + 1))) (map val u).sum = u.sum\nu : Mult... | [
"k m n : ℕ\nhm : m ≠ 0\nhkmn : m * k ≤ n\ns t : Multiset (Fin (n + 1))\nhsA : ∀ ⦃x : Fin (n + 1)⦄, x ∈ s → x ∈ Iic ↑k\nhtA : ∀ ⦃x : Fin (n + 1)⦄, x ∈ t → x ∈ Iic ↑k\nhs : s.card = m\nht : t.card = m\nthis : ∀ (u : Multiset (Fin (n + 1))), (Nat.castRingHom (Fin (n + 1))) (map val u).sum = u.sum\nu : Multiset (Fin (n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.RuzsaCovering | {
"line": 69,
"column": 64
} | {
"line": 69,
"column": 94
} | {
"line": 69,
"column": 95
} | [
{
"pp": "G : Type u_1\ninst✝ : Group G\nK : ℝ\nA B : Finset G\nhB₀ : (↑B).Nonempty\nhK : ↑(Nat.card ↑(↑A * ↑B)) ≤ K * ↑(Nat.card ↑↑B)\n⊢ ↑(?m.82 * B).card ≤ ?m.80 * ↑B.card",
"ppTerm": "?m.84",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"G : Type u_1\ninst✝ : Group G\nK : ℝ\nA B : Finset G\nhB₀ : (↑B).Nonempty\nhK : ↑(Nat.card ↑(↑A * ↑B)) ≤ K * ↑(Nat.card ↑↑B)\n⊢ ↑(?m.82 * B).card ≤ ?m.80 * ↑B.card"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.PluenneckeRuzsa | {
"line": 71,
"column": 2
} | {
"line": 71,
"column": 30
} | {
"line": 71,
"column": 31
} | [
{
"pp": "G : Type u_1\ninst✝¹ : DecidableEq G\ninst✝ : Group G\nA B C : Finset G\n⊢ #(A * C⁻¹) * #B ≤ #(A * B⁻¹) * #(C * B⁻¹)",
"ppTerm": "?m.33",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"G : Type u_1\ninst✝¹ : DecidableEq G\ninst✝ : Group G\nA B C : Finset G\n⊢ #(A * C⁻¹) * #B ≤ #(A * B⁻¹) * #(C * B⁻¹)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.PluenneckeRuzsa | {
"line": 77,
"column": 2
} | {
"line": 77,
"column": 68
} | {
"line": 78,
"column": 4
} | [
{
"pp": "G : Type u_1\ninst✝¹ : DecidableEq G\ninst✝ : Group G\nA B C : Finset G\n⊢ #B * #(A⁻¹ * C) ≤ #(B⁻¹ * A) * #(B⁻¹ * C)",
"ppTerm": "?m.33",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"G : Type u_1\ninst✝¹ : DecidableEq G\ninst✝ : Group G\nA B C : Finset G\n⊢ #B * #(A⁻¹ * C) ≤ #(B⁻¹ * A) * #(B⁻¹ * C)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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