module stringlengths 16 90 | startPos dict | endPos dict | nextStartPos dict | goals listlengths 0 96 | goalsAfter listlengths 0 96 | ppTac stringlengths 1 14.5k | elaborator stringclasses 375
values | kind stringclasses 379
values |
|---|---|---|---|---|---|---|---|---|
Mathlib.CategoryTheory.Abelian.SerreClass.Localization | {
"line": 123,
"column": 6
} | {
"line": 123,
"column": 58
} | {
"line": 123,
"column": 59
} | [
{
"pp": "case refine_2\nC : Type u\ninst✝⁵ : Category.{v, u} C\ninst✝⁴ : Abelian C\nD : Type u'\ninst✝³ : Category.{v', u'} D\nL : C ⥤ D\nP : ObjectProperty C\ninst✝² : P.IsSerreClass\nE : Type u''\ninst✝¹ : Category.{v'', u''} E\ninst✝ : Abelian E\nX Y Y' : C\nf₁ f₂ : X ⟶ Y\ns : Y ⟶ Y'\nhs : P.isoModSerre s\ne... | [
"case refine_2\nC : Type u\ninst✝⁵ : Category.{v, u} C\ninst✝⁴ : Abelian C\nD : Type u'\ninst✝³ : Category.{v', u'} D\nL : C ⥤ D\nP : ObjectProperty C\ninst✝² : P.IsSerreClass\nE : Type u''\ninst✝¹ : Category.{v'', u''} E\ninst✝ : Abelian E\nX Y Y' : C\nf₁ f₂ : X ⟶ Y\ns : Y ⟶ Y'\nhs : P.isoModSerre s\neq : f₁ ≫ s =... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.SerreClass.Localization | {
"line": 139,
"column": 2
} | {
"line": 139,
"column": 13
} | {
"line": 139,
"column": 14
} | [
{
"pp": "C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : Abelian C\nD : Type u'\ninst✝⁴ : Category.{v', u'} D\nL : C ⥤ D\nP : ObjectProperty C\ninst✝³ : P.IsSerreClass\ninst✝² : L.IsLocalization P.isoModSerre\ninst✝¹ : Preadditive D\ninst✝ : L.Additive\nX Y : C\nh : P.isoModSerre 0\n⊢ P X",
"ppTerm": "?m.4... | [
"C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : Abelian C\nD : Type u'\ninst✝⁴ : Category.{v', u'} D\nL : C ⥤ D\nP : ObjectProperty C\ninst✝³ : P.IsSerreClass\ninst✝² : L.IsLocalization P.isoModSerre\ninst✝¹ : Preadditive D\ninst✝ : L.Additive\nX Y : C\nh : P.isoModSerre 0\n⊢ P X"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Action.Concrete | {
"line": 146,
"column": 6
} | {
"line": 146,
"column": 29
} | {
"line": 146,
"column": 30
} | [
{
"pp": "G : Type u_1\ninst✝² : Group G\nH N : Subgroup G\ninst✝¹ : Fintype (G ⧸ N)\ninst✝ : N.Normal\nv a b : G\nh : a ≈ b\n⊢ (a * v⁻¹)⁻¹ * (b * v⁻¹) ∈ N",
"ppTerm": "?m.68",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Semigroup.toMul",
"DivInvMonoid.toInv",
"HMul.hMul",... | [
"G : Type u_1\ninst✝² : Group G\nH N : Subgroup G\ninst✝¹ : Fintype (G ⧸ N)\ninst✝ : N.Normal\nv a b : G\nh : a ≈ b\n⊢ v * (a⁻¹ * (b * v⁻¹)) ∈ N"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.SerreClass.Localization | {
"line": 231,
"column": 22
} | {
"line": 231,
"column": 57
} | {
"line": 231,
"column": 58
} | [
{
"pp": "C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : Abelian C\nD : Type u'\ninst✝⁴ : Category.{v', u'} D\nL : C ⥤ D\nP : ObjectProperty C\ninst✝³ : P.IsSerreClass\ninst✝² : L.IsLocalization P.isoModSerre\ninst✝¹ : Preadditive D\ninst✝ : L.Additive\nX✝ Y✝ : C\nf : X✝ ⟶ Y✝\nx✝ : Mono f\n⊢ Mono (L.map f)",
... | [
"C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : Abelian C\nD : Type u'\ninst✝⁴ : Category.{v', u'} D\nL : C ⥤ D\nP : ObjectProperty C\ninst✝³ : P.IsSerreClass\ninst✝² : L.IsLocalization P.isoModSerre\ninst✝¹ : Preadditive D\ninst✝ : L.Additive\nX✝ Y✝ : C\nf : X✝ ⟶ Y✝\nx✝ : Mono f\n⊢ P.monoModSerre f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.SerreClass.Localization | {
"line": 234,
"column": 22
} | {
"line": 234,
"column": 56
} | {
"line": 234,
"column": 57
} | [
{
"pp": "C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : Abelian C\nD : Type u'\ninst✝⁴ : Category.{v', u'} D\nL : C ⥤ D\nP : ObjectProperty C\ninst✝³ : P.IsSerreClass\ninst✝² : L.IsLocalization P.isoModSerre\ninst✝¹ : Preadditive D\ninst✝ : L.Additive\nX✝ Y✝ : C\nf : X✝ ⟶ Y✝\nx✝ : Epi f\n⊢ Epi (L.map f)",
... | [
"C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : Abelian C\nD : Type u'\ninst✝⁴ : Category.{v', u'} D\nL : C ⥤ D\nP : ObjectProperty C\ninst✝³ : P.IsSerreClass\ninst✝² : L.IsLocalization P.isoModSerre\ninst✝¹ : Preadditive D\ninst✝ : L.Additive\nX✝ Y✝ : C\nf : X✝ ⟶ Y✝\nx✝ : Epi f\n⊢ P.epiModSerre f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.SerreClass.Localization | {
"line": 258,
"column": 10
} | {
"line": 258,
"column": 21
} | {
"line": 258,
"column": 22
} | [
{
"pp": "C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : Abelian C\nD : Type u'\ninst✝⁴ : Category.{v', u'} D\nL : C ⥤ D\nP : ObjectProperty C\ninst✝³ : P.IsSerreClass\ninst✝² : L.IsLocalization P.isoModSerre\ninst✝¹ : Preadditive D\ninst✝ : L.Additive\nX Y : D\nf : X ⟶ Y\nthis✝ : L.PreservesMonomorphisms\nthi... | [
"C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : Abelian C\nD : Type u'\ninst✝⁴ : Category.{v', u'} D\nL : C ⥤ D\nP : ObjectProperty C\ninst✝³ : P.IsSerreClass\ninst✝² : L.IsLocalization P.isoModSerre\ninst✝¹ : Preadditive D\ninst✝ : L.Additive\nX Y : D\nf : X ⟶ Y\nthis✝ : L.PreservesMonomorphisms\nthis : L.mapArr... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.SerreClass.Localization | {
"line": 276,
"column": 4
} | {
"line": 276,
"column": 65
} | {
"line": 277,
"column": 4
} | [
{
"pp": "case refine_1\nC : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : Abelian C\nD : Type u'\ninst✝⁴ : Category.{v', u'} D\nL : C ⥤ D\nP : ObjectProperty C\ninst✝³ : P.IsSerreClass\ninst✝² : L.IsLocalization P.isoModSerre\ninst✝¹ : Preadditive D\ninst✝ : L.Additive\nX✝ Y✝ : D\nf✝ : X✝ ⟶ Y✝\nthis✝ : L.Preserv... | [
"case refine_1\nC : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : Abelian C\nD : Type u'\ninst✝⁴ : Category.{v', u'} D\nL : C ⥤ D\nP : ObjectProperty C\ninst✝³ : P.IsSerreClass\ninst✝² : L.IsLocalization P.isoModSerre\ninst✝¹ : Preadditive D\ninst✝ : L.Additive\nX✝ Y✝ : D\nf✝ : X✝ ⟶ Y✝\nthis✝ : L.PreservesEpimorphis... | refine ⟨_, _, Abelian.factorThruImage f, inferInstance, ⟨?_⟩⟩ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.CategoryTheory.Abelian.SerreClass.Localization | {
"line": 281,
"column": 10
} | {
"line": 281,
"column": 21
} | {
"line": 281,
"column": 22
} | [
{
"pp": "C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : Abelian C\nD : Type u'\ninst✝⁴ : Category.{v', u'} D\nL : C ⥤ D\nP : ObjectProperty C\ninst✝³ : P.IsSerreClass\ninst✝² : L.IsLocalization P.isoModSerre\ninst✝¹ : Preadditive D\ninst✝ : L.Additive\nX Y : D\nf : X ⟶ Y\nthis✝ : L.PreservesEpimorphisms\nthis... | [
"C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : Abelian C\nD : Type u'\ninst✝⁴ : Category.{v', u'} D\nL : C ⥤ D\nP : ObjectProperty C\ninst✝³ : P.IsSerreClass\ninst✝² : L.IsLocalization P.isoModSerre\ninst✝¹ : Preadditive D\ninst✝ : L.Additive\nX Y : D\nf : X ⟶ Y\nthis✝ : L.PreservesEpimorphisms\nthis : L.mapArro... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.SerreClass.Localization | {
"line": 295,
"column": 32
} | {
"line": 295,
"column": 57
} | {
"line": 295,
"column": 58
} | [
{
"pp": "C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : Abelian C\nD : Type u'\ninst✝⁴ : Category.{v', u'} D\nL : C ⥤ D\nP : ObjectProperty C\ninst✝³ : P.IsSerreClass\ninst✝² : L.IsLocalization P.isoModSerre\ninst✝¹ : Preadditive D\ninst✝ : L.Additive\nX Y : C\nf : X ⟶ Y\nthis✝¹ : L.PreservesMonomorphisms\nth... | [
"C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : Abelian C\nD : Type u'\ninst✝⁴ : Category.{v', u'} D\nL : C ⥤ D\nP : ObjectProperty C\ninst✝³ : P.IsSerreClass\ninst✝² : L.IsLocalization P.isoModSerre\ninst✝¹ : Preadditive D\ninst✝ : L.Additive\nX Y : C\nf : X ⟶ Y\nthis✝¹ : L.PreservesMonomorphisms\nthis✝ : L.EssS... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.SerreClass.Localization | {
"line": 326,
"column": 32
} | {
"line": 326,
"column": 56
} | {
"line": 326,
"column": 57
} | [
{
"pp": "C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : Abelian C\nD : Type u'\ninst✝⁴ : Category.{v', u'} D\nL : C ⥤ D\nP : ObjectProperty C\ninst✝³ : P.IsSerreClass\ninst✝² : L.IsLocalization P.isoModSerre\ninst✝¹ : Preadditive D\ninst✝ : L.Additive\nX Y : C\nf : X ⟶ Y\nthis✝¹ : L.PreservesEpimorphisms\nthi... | [
"C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : Abelian C\nD : Type u'\ninst✝⁴ : Category.{v', u'} D\nL : C ⥤ D\nP : ObjectProperty C\ninst✝³ : P.IsSerreClass\ninst✝² : L.IsLocalization P.isoModSerre\ninst✝¹ : Preadditive D\ninst✝ : L.Additive\nX Y : C\nf : X ⟶ Y\nthis✝¹ : L.PreservesEpimorphisms\nthis✝ : L.EssSu... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Action.Basic | {
"line": 288,
"column": 4
} | {
"line": 288,
"column": 15
} | {
"line": 288,
"column": 16
} | [
{
"pp": "V : Type u_1\ninst✝³ : Category.{v_1, u_1} V\nG : Type u_2\ninst✝² : Monoid G\nFV : V → V → Type u_3\nCV : V → Type u_4\ninst✝¹ : (X Y : V) → FunLike (FV X Y) (CV X) (CV Y)\ninst✝ : ConcreteCategory V FV\nX✝ Y✝ : Action V G\nf : X✝ ⟶ Y✝\ng : G\nx✝ : CV X✝.V\n⊢ (⇑(ConcreteCategory.hom f.hom) ∘ ⇑(Concret... | [
"V : Type u_1\ninst✝³ : Category.{v_1, u_1} V\nG : Type u_2\ninst✝² : Monoid G\nFV : V → V → Type u_3\nCV : V → Type u_4\ninst✝¹ : (X Y : V) → FunLike (FV X Y) (CV X) (CV Y)\ninst✝ : ConcreteCategory V FV\nX✝ Y✝ : Action V G\nf : X✝ ⟶ Y✝\ng : G\nx✝ : CV X✝.V\n⊢ (ConcreteCategory.hom f.hom) ((ConcreteCategory.hom (X... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Action.Basic | {
"line": 290,
"column": 4
} | {
"line": 290,
"column": 44
} | {
"line": 290,
"column": 45
} | [
{
"pp": "V : Type u_1\ninst✝³ : Category.{v_1, u_1} V\nG : Type u_2\ninst✝² : Monoid G\nFV : V → V → Type u_3\nCV : V → Type u_4\ninst✝¹ : (X Y : V) → FunLike (FV X Y) (CV X) (CV Y)\ninst✝ : ConcreteCategory V FV\nX✝ Y✝ : Action V G\nf : HomSubtype V G X✝ Y✝\ng : G\nx : CV X✝.V\n⊢ (ConcreteCategory.hom (X✝.ρ g ... | [
"V : Type u_1\ninst✝³ : Category.{v_1, u_1} V\nG : Type u_2\ninst✝² : Monoid G\nFV : V → V → Type u_3\nCV : V → Type u_4\ninst✝¹ : (X Y : V) → FunLike (FV X Y) (CV X) (CV Y)\ninst✝ : ConcreteCategory V FV\nX✝ Y✝ : Action V G\nf : HomSubtype V G X✝ Y✝\ng : G\nx : CV X✝.V\n⊢ ↑f ((ConcreteCategory.hom (X✝.ρ g)) x) = (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.SerreClass.Localization | {
"line": 516,
"column": 6
} | {
"line": 516,
"column": 50
} | {
"line": 516,
"column": 51
} | [
{
"pp": "C : Type u\ninst✝⁸ : Category.{v, u} C\ninst✝⁷ : Abelian C\nD : Type u'\ninst✝⁶ : Category.{v', u'} D\nL : C ⥤ D\nP : ObjectProperty C\ninst✝⁵ : P.IsSerreClass\nE : Type u''\ninst✝⁴ : Category.{v'', u''} E\ninst✝³ : Abelian E\ninst✝² : L.IsLocalization P.isoModSerre\ninst✝¹ : Preadditive D\ninst✝ : L.A... | [
"C : Type u\ninst✝⁸ : Category.{v, u} C\ninst✝⁷ : Abelian C\nD : Type u'\ninst✝⁶ : Category.{v', u'} D\nL : C ⥤ D\nP : ObjectProperty C\ninst✝⁵ : P.IsSerreClass\nE : Type u''\ninst✝⁴ : Category.{v'', u''} E\ninst✝³ : Abelian E\ninst✝² : L.IsLocalization P.isoModSerre\ninst✝¹ : Preadditive D\ninst✝ : L.Additive\nG✝ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monad.Coequalizer | {
"line": 72,
"column": 4
} | {
"line": 72,
"column": 36
} | {
"line": 73,
"column": 2
} | [
{
"pp": "C : Type u₁\ninst✝ : Category.{v₁, u₁} C\nT : Monad C\nX : T.Algebra\n⊢ T.free.obj X.A ⟶ T.free.obj (T.obj X.A)",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"CategoryTheory.Functor.id",
"CategoryTheory.Monad.Algebra.A",
"CategoryTheory.Functor.map",
"Cat... | [] | apply (free T).map (T.η.app X.A) | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.CategoryTheory.Monad.Coequalizer | {
"line": 72,
"column": 4
} | {
"line": 72,
"column": 36
} | {
"line": 73,
"column": 2
} | [
{
"pp": "C : Type u₁\ninst✝ : Category.{v₁, u₁} C\nT : Monad C\nX : T.Algebra\n⊢ T.free.obj X.A ⟶ T.free.obj (T.obj X.A)",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"CategoryTheory.Functor.id",
"CategoryTheory.Monad.Algebra.A",
"CategoryTheory.Functor.map",
"Cat... | [] | apply (free T).map (T.η.app X.A) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Monad.Coequalizer | {
"line": 72,
"column": 4
} | {
"line": 72,
"column": 36
} | {
"line": 73,
"column": 2
} | [
{
"pp": "C : Type u₁\ninst✝ : Category.{v₁, u₁} C\nT : Monad C\nX : T.Algebra\n⊢ T.free.obj X.A ⟶ T.free.obj (T.obj X.A)",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"CategoryTheory.Functor.id",
"CategoryTheory.Monad.Algebra.A",
"CategoryTheory.Functor.map",
"Cat... | [] | apply (free T).map (T.η.app X.A) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Action.Monoidal | {
"line": 374,
"column": 24
} | {
"line": 374,
"column": 32
} | {
"line": 375,
"column": 2
} | [
{
"pp": "V : Type u_1\ninst✝⁵ : Category.{v_1, u_1} V\nG : Type u_2\ninst✝⁴ : Monoid G\nW : Type u_3\ninst✝³ : Category.{v_2, u_3} W\ninst✝² : MonoidalCategory V\ninst✝¹ : MonoidalCategory W\nF : V ⥤ W\ninst✝ : F.Monoidal\n⊢ ε F ≫ η F = 𝟙 (𝟙_ W)",
"ppTerm": "?m.49",
"assigned": true,
"usedConstant... | [] | rw [ε_η] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.CategoryTheory.Adjunction.Triple | {
"line": 92,
"column": 6
} | {
"line": 93,
"column": 20
} | {
"line": 94,
"column": 4
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Category.{v_2, u_2} D\nF : C ⥤ D\nG : D ⥤ C\nH : C ⥤ D\nt : Triple F G H\nh : H.FullyFaithful\nthis✝ : H.Full\nthis : H.Faithful\n⊢ IsIso t.adj₁.unit",
"ppTerm": "?m.138",
"assigned": true,
"usedConstants": [
"Categor... | [] | rw [t.isIso_unit_iff_isIso_counit]
infer_instance | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Adjunction.Triple | {
"line": 92,
"column": 6
} | {
"line": 93,
"column": 20
} | {
"line": 94,
"column": 4
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Category.{v_2, u_2} D\nF : C ⥤ D\nG : D ⥤ C\nH : C ⥤ D\nt : Triple F G H\nh : H.FullyFaithful\nthis✝ : H.Full\nthis : H.Faithful\n⊢ IsIso t.adj₁.unit",
"ppTerm": "?m.138",
"assigned": true,
"usedConstants": [
"Categor... | [] | rw [t.isIso_unit_iff_isIso_counit]
infer_instance | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Adjunction.Quadruple | {
"line": 131,
"column": 2
} | {
"line": 131,
"column": 13
} | {
"line": 131,
"column": 14
} | [
{
"pp": "C : Type u₁\nD : Type u₂\ninst✝⁵ : Category.{v₁, u₁} C\ninst✝⁴ : Category.{v₂, u₂} D\nL : C ⥤ D\nF : D ⥤ C\nG : C ⥤ D\nR : D ⥤ C\nq : Quadruple L F G R\ninst✝³ : L.Full\ninst✝² : L.Faithful\ninst✝¹ : G.Full\ninst✝ : G.Faithful\nh :\n (∀ (a : D), Epi (q.op.leftTriple.rightToLeft.app (Opposite.equivToOp... | [
"C : Type u₁\nD : Type u₂\ninst✝⁵ : Category.{v₁, u₁} C\ninst✝⁴ : Category.{v₂, u₂} D\nL : C ⥤ D\nF : D ⥤ C\nG : C ⥤ D\nR : D ⥤ C\nq : Quadruple L F G R\ninst✝³ : L.Full\ninst✝² : L.Faithful\ninst✝¹ : G.Full\ninst✝ : G.Faithful\nh :\n (∀ (a : D), Epi (q.op.leftTriple.rightToLeft.app (Opposite.equivToOpposite a))) ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Adjunction.Triple | {
"line": 189,
"column": 2
} | {
"line": 189,
"column": 13
} | {
"line": 189,
"column": 14
} | [
{
"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\nF : C ⥤ D\nG : D ⥤ C\nH : C ⥤ D\nt : Triple F G H\ninst✝² : G.Full\ninst✝¹ : G.Faithful\ninst✝ : H.PreservesEpimorphisms\nX : C\nx✝ : G.IsLeftAdjoint\nh : Epi (t.adj₂.counit.app X ≫ t.adj₁.unit.app X)\n⊢ Epi (H.... | [
"C : Type u_1\nD : Type u_2\ninst✝⁴ : Category.{v_1, u_1} C\ninst✝³ : Category.{v_2, u_2} D\nF : C ⥤ D\nG : D ⥤ C\nH : C ⥤ D\nt : Triple F G H\ninst✝² : G.Full\ninst✝¹ : G.Faithful\ninst✝ : H.PreservesEpimorphisms\nX : C\nx✝ : G.IsLeftAdjoint\nh : Epi (t.adj₂.counit.app X ≫ t.adj₁.unit.app X)\n⊢ Epi (H.map (t.adj₁.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Adjunction.Triple | {
"line": 236,
"column": 2
} | {
"line": 236,
"column": 13
} | {
"line": 236,
"column": 14
} | [
{
"pp": "case e_a\nC : Type u_1\nD : Type u_2\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : Category.{v_2, u_2} D\nF : C ⥤ D\nG : D ⥤ C\nH : C ⥤ D\nt : Triple F G H\ninst✝¹ : F.Full\ninst✝ : F.Faithful\nX : D\n⊢ G.map (t.adj₁.counit.app X) ≫ 𝟙 (G.obj X) = inv (t.adj₁.unit.app (G.obj X))",
"ppTerm": "?e_a✝",
... | [
"case e_a\nC : Type u_1\nD : Type u_2\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : Category.{v_2, u_2} D\nF : C ⥤ D\nG : D ⥤ C\nH : C ⥤ D\nt : Triple F G H\ninst✝¹ : F.Full\ninst✝ : F.Faithful\nX : D\n⊢ G.map (t.adj₁.counit.app X) = inv (t.adj₁.unit.app (G.obj X))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Adjunction.Triple | {
"line": 297,
"column": 2
} | {
"line": 297,
"column": 13
} | {
"line": 297,
"column": 14
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : Category.{v_2, u_2} D\nF : C ⥤ D\nG : D ⥤ C\nH : C ⥤ D\nt : Triple F G H\ninst✝¹ : F.Full\ninst✝ : F.Faithful\nh : ∀ (X : D), Mono (t.adj₁.counit.app X ≫ t.adj₂.unit.app X)\nX : C\n⊢ Mono (t.adj₂.unit.app (F.obj X))",
"ppTerm": "?... | [
"C : Type u_1\nD : Type u_2\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : Category.{v_2, u_2} D\nF : C ⥤ D\nG : D ⥤ C\nH : C ⥤ D\nt : Triple F G H\ninst✝¹ : F.Full\ninst✝ : F.Faithful\nh : ∀ (X : D), Mono (t.adj₁.counit.app X ≫ t.adj₂.unit.app X)\nX : C\n⊢ Mono (t.adj₂.unit.app (F.obj X))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 323,
"column": 55
} | {
"line": 323,
"column": 82
} | {
"line": 323,
"column": 82
} | [
{
"pp": "case vcomp_right\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝¹ b✝ : B\nf✝ g✝ h✝ : Hom a✝¹ b✝\nη✝ : Hom₂ f✝ g✝\nθ₁✝ θ₂✝ : Hom₂ g✝ h✝\na✝ : Rel θ₁✝ θ₂✝\na_ih✝ : liftHom₂ F θ₁✝ = liftHom₂ F θ₂✝\n⊢ liftHom₂ F (η✝.vco... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 323,
"column": 55
} | {
"line": 323,
"column": 82
} | {
"line": 323,
"column": 82
} | [
{
"pp": "case vcomp_right\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝¹ b✝ : B\nf✝ g✝ h✝ : Hom a✝¹ b✝\nη✝ : Hom₂ f✝ g✝\nθ₁✝ θ₂✝ : Hom₂ g✝ h✝\na✝ : Rel θ₁✝ θ₂✝\na_ih✝ : liftHom₂ F θ₁✝ = liftHom₂ F θ₂✝\n⊢ liftHom₂ F (η✝.vco... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 323,
"column": 55
} | {
"line": 323,
"column": 82
} | {
"line": 323,
"column": 82
} | [
{
"pp": "case vcomp_left\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝¹ b✝ : B\nf✝ g✝ h✝ : Hom a✝¹ b✝\nη₁✝ η₂✝ : Hom₂ f✝ g✝\nθ✝ : Hom₂ g✝ h✝\na✝ : Rel η₁✝ η₂✝\na_ih✝ : liftHom₂ F η₁✝ = liftHom₂ F η₂✝\n⊢ liftHom₂ F (η₁✝.vco... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 323,
"column": 55
} | {
"line": 323,
"column": 82
} | {
"line": 323,
"column": 82
} | [
{
"pp": "case vcomp_left\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝¹ b✝ : B\nf✝ g✝ h✝ : Hom a✝¹ b✝\nη₁✝ η₂✝ : Hom₂ f✝ g✝\nθ✝ : Hom₂ g✝ h✝\na✝ : Rel η₁✝ η₂✝\na_ih✝ : liftHom₂ F η₁✝ = liftHom₂ F η₂✝\n⊢ liftHom₂ F (η₁✝.vco... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 323,
"column": 55
} | {
"line": 323,
"column": 82
} | {
"line": 323,
"column": 82
} | [
{
"pp": "case id_comp\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝ b✝ : B\nf✝ g✝ : Hom a✝ b✝\nη✝ : Hom₂ f✝ g✝\n⊢ liftHom₂ F ((Hom₂.id f✝).vcomp η✝) = liftHom₂ F η✝",
"ppTerm": "?id_comp",
"assigned": true,
"us... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 323,
"column": 55
} | {
"line": 323,
"column": 82
} | {
"line": 323,
"column": 82
} | [
{
"pp": "case id_comp\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝ b✝ : B\nf✝ g✝ : Hom a✝ b✝\nη✝ : Hom₂ f✝ g✝\n⊢ liftHom₂ F ((Hom₂.id f✝).vcomp η✝) = liftHom₂ F η✝",
"ppTerm": "?id_comp",
"assigned": true,
"us... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 323,
"column": 55
} | {
"line": 323,
"column": 82
} | {
"line": 323,
"column": 82
} | [
{
"pp": "case comp_id\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝ b✝ : B\nf✝ g✝ : Hom a✝ b✝\nη✝ : Hom₂ f✝ g✝\n⊢ liftHom₂ F (η✝.vcomp (Hom₂.id g✝)) = liftHom₂ F η✝",
"ppTerm": "?comp_id",
"assigned": true,
"us... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 323,
"column": 55
} | {
"line": 323,
"column": 82
} | {
"line": 323,
"column": 82
} | [
{
"pp": "case comp_id\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝ b✝ : B\nf✝ g✝ : Hom a✝ b✝\nη✝ : Hom₂ f✝ g✝\n⊢ liftHom₂ F (η✝.vcomp (Hom₂.id g✝)) = liftHom₂ F η✝",
"ppTerm": "?comp_id",
"assigned": true,
"us... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 323,
"column": 55
} | {
"line": 323,
"column": 82
} | {
"line": 323,
"column": 82
} | [
{
"pp": "case assoc\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝ b✝ : B\nf✝ g✝ h✝ i✝ : Hom a✝ b✝\nη✝ : Hom₂ f✝ g✝\nθ✝ : Hom₂ g✝ h✝\nι✝ : Hom₂ h✝ i✝\n⊢ liftHom₂ F ((η✝.vcomp θ✝).vcomp ι✝) = liftHom₂ F (η✝.vcomp (θ✝.vcomp ι... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 323,
"column": 55
} | {
"line": 323,
"column": 82
} | {
"line": 323,
"column": 82
} | [
{
"pp": "case assoc\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝ b✝ : B\nf✝ g✝ h✝ i✝ : Hom a✝ b✝\nη✝ : Hom₂ f✝ g✝\nθ✝ : Hom₂ g✝ h✝\nι✝ : Hom₂ h✝ i✝\n⊢ liftHom₂ F ((η✝.vcomp θ✝).vcomp ι✝) = liftHom₂ F (η✝.vcomp (θ✝.vcomp ι... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 323,
"column": 55
} | {
"line": 323,
"column": 82
} | {
"line": 323,
"column": 82
} | [
{
"pp": "case whisker_left\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝¹ b✝ c✝ : B\nf✝ : Hom a✝¹ b✝\ng✝ h✝ : Hom b✝ c✝\nη✝ η'✝ : Hom₂ g✝ h✝\na✝ : Rel η✝ η'✝\na_ih✝ : liftHom₂ F η✝ = liftHom₂ F η'✝\n⊢ liftHom₂ F (Hom₂.whis... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 323,
"column": 55
} | {
"line": 323,
"column": 82
} | {
"line": 323,
"column": 82
} | [
{
"pp": "case whisker_left\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝¹ b✝ c✝ : B\nf✝ : Hom a✝¹ b✝\ng✝ h✝ : Hom b✝ c✝\nη✝ η'✝ : Hom₂ g✝ h✝\na✝ : Rel η✝ η'✝\na_ih✝ : liftHom₂ F η✝ = liftHom₂ F η'✝\n⊢ liftHom₂ F (Hom₂.whis... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 323,
"column": 55
} | {
"line": 323,
"column": 82
} | {
"line": 323,
"column": 82
} | [
{
"pp": "case whisker_left_id\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝ b✝ c✝ : B\nf✝ : Hom a✝ b✝\ng✝ : Hom b✝ c✝\n⊢ liftHom₂ F (Hom₂.whisker_left f✝ (Hom₂.id g✝)) = liftHom₂ F (Hom₂.id (f✝.comp g✝))",
"ppTerm": "?... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 323,
"column": 55
} | {
"line": 323,
"column": 82
} | {
"line": 323,
"column": 82
} | [
{
"pp": "case whisker_left_id\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝ b✝ c✝ : B\nf✝ : Hom a✝ b✝\ng✝ : Hom b✝ c✝\n⊢ liftHom₂ F (Hom₂.whisker_left f✝ (Hom₂.id g✝)) = liftHom₂ F (Hom₂.id (f✝.comp g✝))",
"ppTerm": "?... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 323,
"column": 55
} | {
"line": 323,
"column": 82
} | {
"line": 323,
"column": 82
} | [
{
"pp": "case whisker_left_comp\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝ b✝ c✝ : B\nf✝ : Hom a✝ b✝\ng✝ h✝ i✝ : Hom b✝ c✝\nη✝ : Hom₂ g✝ h✝\nθ✝ : Hom₂ h✝ i✝\n⊢ liftHom₂ F (Hom₂.whisker_left f✝ (η✝.vcomp θ✝)) =\n lift... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 323,
"column": 55
} | {
"line": 323,
"column": 82
} | {
"line": 323,
"column": 82
} | [
{
"pp": "case whisker_left_comp\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝ b✝ c✝ : B\nf✝ : Hom a✝ b✝\ng✝ h✝ i✝ : Hom b✝ c✝\nη✝ : Hom₂ g✝ h✝\nθ✝ : Hom₂ h✝ i✝\n⊢ liftHom₂ F (Hom₂.whisker_left f✝ (η✝.vcomp θ✝)) =\n lift... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 323,
"column": 55
} | {
"line": 323,
"column": 82
} | {
"line": 323,
"column": 82
} | [
{
"pp": "case id_whisker_left\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝ b✝ : B\nf✝ g✝ : Hom a✝ b✝\nη✝ : Hom₂ f✝ g✝\n⊢ liftHom₂ F (Hom₂.whisker_left (Hom.id a✝) η✝) =\n liftHom₂ F ((Hom₂.left_unitor f✝).vcomp (η✝.vco... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 323,
"column": 55
} | {
"line": 323,
"column": 82
} | {
"line": 323,
"column": 82
} | [
{
"pp": "case id_whisker_left\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝ b✝ : B\nf✝ g✝ : Hom a✝ b✝\nη✝ : Hom₂ f✝ g✝\n⊢ liftHom₂ F (Hom₂.whisker_left (Hom.id a✝) η✝) =\n liftHom₂ F ((Hom₂.left_unitor f✝).vcomp (η✝.vco... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 323,
"column": 55
} | {
"line": 323,
"column": 82
} | {
"line": 323,
"column": 82
} | [
{
"pp": "case comp_whisker_left\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝ b✝ c✝ d✝ : B\nf✝ : Hom a✝ b✝\ng✝ : Hom b✝ c✝\nh✝ h'✝ : Hom c✝ d✝\nη✝ : Hom₂ h✝ h'✝\n⊢ liftHom₂ F (Hom₂.whisker_left (f✝.comp g✝) η✝) =\n lift... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 323,
"column": 55
} | {
"line": 323,
"column": 82
} | {
"line": 323,
"column": 82
} | [
{
"pp": "case comp_whisker_left\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝ b✝ c✝ d✝ : B\nf✝ : Hom a✝ b✝\ng✝ : Hom b✝ c✝\nh✝ h'✝ : Hom c✝ d✝\nη✝ : Hom₂ h✝ h'✝\n⊢ liftHom₂ F (Hom₂.whisker_left (f✝.comp g✝) η✝) =\n lift... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 323,
"column": 55
} | {
"line": 323,
"column": 82
} | {
"line": 323,
"column": 82
} | [
{
"pp": "case whisker_right\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝¹ b✝ c✝ : B\nf✝ g✝ : Hom a✝¹ b✝\nh✝ : Hom b✝ c✝\nη✝ η'✝ : Hom₂ f✝ g✝\na✝ : Rel η✝ η'✝\na_ih✝ : liftHom₂ F η✝ = liftHom₂ F η'✝\n⊢ liftHom₂ F (Hom₂.whi... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 323,
"column": 55
} | {
"line": 323,
"column": 82
} | {
"line": 323,
"column": 82
} | [
{
"pp": "case whisker_right\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝¹ b✝ c✝ : B\nf✝ g✝ : Hom a✝¹ b✝\nh✝ : Hom b✝ c✝\nη✝ η'✝ : Hom₂ f✝ g✝\na✝ : Rel η✝ η'✝\na_ih✝ : liftHom₂ F η✝ = liftHom₂ F η'✝\n⊢ liftHom₂ F (Hom₂.whi... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 323,
"column": 55
} | {
"line": 323,
"column": 82
} | {
"line": 323,
"column": 82
} | [
{
"pp": "case id_whisker_right\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝ b✝ c✝ : B\nf✝ : Hom a✝ b✝\ng✝ : Hom b✝ c✝\n⊢ liftHom₂ F (Hom₂.whisker_right g✝ (Hom₂.id f✝)) = liftHom₂ F (Hom₂.id (f✝.comp g✝))",
"ppTerm": ... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 323,
"column": 55
} | {
"line": 323,
"column": 82
} | {
"line": 323,
"column": 82
} | [
{
"pp": "case id_whisker_right\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝ b✝ c✝ : B\nf✝ : Hom a✝ b✝\ng✝ : Hom b✝ c✝\n⊢ liftHom₂ F (Hom₂.whisker_right g✝ (Hom₂.id f✝)) = liftHom₂ F (Hom₂.id (f✝.comp g✝))",
"ppTerm": ... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 323,
"column": 55
} | {
"line": 323,
"column": 82
} | {
"line": 323,
"column": 82
} | [
{
"pp": "case comp_whisker_right\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝ b✝ c✝ : B\nf✝ g✝ h✝ : Hom a✝ b✝\ni✝ : Hom b✝ c✝\nη✝ : Hom₂ f✝ g✝\nθ✝ : Hom₂ g✝ h✝\n⊢ liftHom₂ F (Hom₂.whisker_right i✝ (η✝.vcomp θ✝)) =\n li... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 323,
"column": 55
} | {
"line": 323,
"column": 82
} | {
"line": 323,
"column": 82
} | [
{
"pp": "case comp_whisker_right\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝ b✝ c✝ : B\nf✝ g✝ h✝ : Hom a✝ b✝\ni✝ : Hom b✝ c✝\nη✝ : Hom₂ f✝ g✝\nθ✝ : Hom₂ g✝ h✝\n⊢ liftHom₂ F (Hom₂.whisker_right i✝ (η✝.vcomp θ✝)) =\n li... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 323,
"column": 55
} | {
"line": 323,
"column": 82
} | {
"line": 323,
"column": 82
} | [
{
"pp": "case whisker_right_id\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝ b✝ : B\nf✝ g✝ : Hom a✝ b✝\nη✝ : Hom₂ f✝ g✝\n⊢ liftHom₂ F (Hom₂.whisker_right (Hom.id b✝) η✝) =\n liftHom₂ F ((Hom₂.right_unitor f✝).vcomp (η✝.... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 323,
"column": 55
} | {
"line": 323,
"column": 82
} | {
"line": 323,
"column": 82
} | [
{
"pp": "case whisker_right_id\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝ b✝ : B\nf✝ g✝ : Hom a✝ b✝\nη✝ : Hom₂ f✝ g✝\n⊢ liftHom₂ F (Hom₂.whisker_right (Hom.id b✝) η✝) =\n liftHom₂ F ((Hom₂.right_unitor f✝).vcomp (η✝.... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 323,
"column": 55
} | {
"line": 323,
"column": 82
} | {
"line": 323,
"column": 82
} | [
{
"pp": "case whisker_right_comp\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝ b✝ c✝ d✝ : B\nf✝ f'✝ : Hom a✝ b✝\ng✝ : Hom b✝ c✝\nh✝ : Hom c✝ d✝\nη✝ : Hom₂ f✝ f'✝\n⊢ liftHom₂ F (Hom₂.whisker_right (g✝.comp h✝) η✝) =\n li... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 323,
"column": 55
} | {
"line": 323,
"column": 82
} | {
"line": 323,
"column": 82
} | [
{
"pp": "case whisker_right_comp\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝ b✝ c✝ d✝ : B\nf✝ f'✝ : Hom a✝ b✝\ng✝ : Hom b✝ c✝\nh✝ : Hom c✝ d✝\nη✝ : Hom₂ f✝ f'✝\n⊢ liftHom₂ F (Hom₂.whisker_right (g✝.comp h✝) η✝) =\n li... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 323,
"column": 55
} | {
"line": 323,
"column": 82
} | {
"line": 323,
"column": 82
} | [
{
"pp": "case whisker_assoc\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝ b✝ c✝ d✝ : B\nf✝ : Hom a✝ b✝\ng✝ g'✝ : Hom b✝ c✝\nη✝ : Hom₂ g✝ g'✝\nh✝ : Hom c✝ d✝\n⊢ liftHom₂ F (Hom₂.whisker_right h✝ (Hom₂.whisker_left f✝ η✝)) =... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 323,
"column": 55
} | {
"line": 323,
"column": 82
} | {
"line": 323,
"column": 82
} | [
{
"pp": "case whisker_assoc\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝ b✝ c✝ d✝ : B\nf✝ : Hom a✝ b✝\ng✝ g'✝ : Hom b✝ c✝\nη✝ : Hom₂ g✝ g'✝\nh✝ : Hom c✝ d✝\n⊢ liftHom₂ F (Hom₂.whisker_right h✝ (Hom₂.whisker_left f✝ η✝)) =... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 323,
"column": 55
} | {
"line": 323,
"column": 82
} | {
"line": 323,
"column": 82
} | [
{
"pp": "case whisker_exchange\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝ b✝ c✝ : B\nf✝ g✝ : Hom a✝ b✝\nh✝ i✝ : Hom b✝ c✝\nη✝ : Hom₂ f✝ g✝\nθ✝ : Hom₂ h✝ i✝\n⊢ liftHom₂ F ((Hom₂.whisker_left f✝ θ✝).vcomp (Hom₂.whisker_ri... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 323,
"column": 55
} | {
"line": 323,
"column": 82
} | {
"line": 323,
"column": 82
} | [
{
"pp": "case whisker_exchange\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝ b✝ c✝ : B\nf✝ g✝ : Hom a✝ b✝\nh✝ i✝ : Hom b✝ c✝\nη✝ : Hom₂ f✝ g✝\nθ✝ : Hom₂ h✝ i✝\n⊢ liftHom₂ F ((Hom₂.whisker_left f✝ θ✝).vcomp (Hom₂.whisker_ri... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 323,
"column": 55
} | {
"line": 323,
"column": 82
} | {
"line": 323,
"column": 82
} | [
{
"pp": "case associator_hom_inv\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝ b✝ c✝ d✝ : B\nf✝ : Hom a✝ b✝\ng✝ : Hom b✝ c✝\nh✝ : Hom c✝ d✝\n⊢ liftHom₂ F ((Hom₂.associator f✝ g✝ h✝).vcomp (Hom₂.associator_inv f✝ g✝ h✝)) =\... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 323,
"column": 55
} | {
"line": 323,
"column": 82
} | {
"line": 323,
"column": 82
} | [
{
"pp": "case associator_hom_inv\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝ b✝ c✝ d✝ : B\nf✝ : Hom a✝ b✝\ng✝ : Hom b✝ c✝\nh✝ : Hom c✝ d✝\n⊢ liftHom₂ F ((Hom₂.associator f✝ g✝ h✝).vcomp (Hom₂.associator_inv f✝ g✝ h✝)) =\... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 323,
"column": 55
} | {
"line": 323,
"column": 82
} | {
"line": 323,
"column": 82
} | [
{
"pp": "case associator_inv_hom\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝ b✝ c✝ d✝ : B\nf✝ : Hom a✝ b✝\ng✝ : Hom b✝ c✝\nh✝ : Hom c✝ d✝\n⊢ liftHom₂ F ((Hom₂.associator_inv f✝ g✝ h✝).vcomp (Hom₂.associator f✝ g✝ h✝)) =\... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 323,
"column": 55
} | {
"line": 323,
"column": 82
} | {
"line": 323,
"column": 82
} | [
{
"pp": "case associator_inv_hom\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝ b✝ c✝ d✝ : B\nf✝ : Hom a✝ b✝\ng✝ : Hom b✝ c✝\nh✝ : Hom c✝ d✝\n⊢ liftHom₂ F ((Hom₂.associator_inv f✝ g✝ h✝).vcomp (Hom₂.associator f✝ g✝ h✝)) =\... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 323,
"column": 55
} | {
"line": 323,
"column": 82
} | {
"line": 323,
"column": 82
} | [
{
"pp": "case left_unitor_hom_inv\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝ b✝ : B\nf✝ : Hom a✝ b✝\n⊢ liftHom₂ F ((Hom₂.left_unitor f✝).vcomp (Hom₂.left_unitor_inv f✝)) = liftHom₂ F (Hom₂.id ((Hom.id a✝).comp f✝))",
... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 323,
"column": 55
} | {
"line": 323,
"column": 82
} | {
"line": 323,
"column": 82
} | [
{
"pp": "case left_unitor_hom_inv\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝ b✝ : B\nf✝ : Hom a✝ b✝\n⊢ liftHom₂ F ((Hom₂.left_unitor f✝).vcomp (Hom₂.left_unitor_inv f✝)) = liftHom₂ F (Hom₂.id ((Hom.id a✝).comp f✝))",
... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 323,
"column": 55
} | {
"line": 323,
"column": 82
} | {
"line": 323,
"column": 82
} | [
{
"pp": "case left_unitor_inv_hom\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝ b✝ : B\nf✝ : Hom a✝ b✝\n⊢ liftHom₂ F ((Hom₂.left_unitor_inv f✝).vcomp (Hom₂.left_unitor f✝)) = liftHom₂ F (Hom₂.id f✝)",
"ppTerm": "?left_... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 323,
"column": 55
} | {
"line": 323,
"column": 82
} | {
"line": 323,
"column": 82
} | [
{
"pp": "case left_unitor_inv_hom\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝ b✝ : B\nf✝ : Hom a✝ b✝\n⊢ liftHom₂ F ((Hom₂.left_unitor_inv f✝).vcomp (Hom₂.left_unitor f✝)) = liftHom₂ F (Hom₂.id f✝)",
"ppTerm": "?left_... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 323,
"column": 55
} | {
"line": 323,
"column": 82
} | {
"line": 323,
"column": 82
} | [
{
"pp": "case right_unitor_hom_inv\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝ b✝ : B\nf✝ : Hom a✝ b✝\n⊢ liftHom₂ F ((Hom₂.right_unitor f✝).vcomp (Hom₂.right_unitor_inv f✝)) = liftHom₂ F (Hom₂.id (f✝.comp (Hom.id b✝)))",... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 323,
"column": 55
} | {
"line": 323,
"column": 82
} | {
"line": 323,
"column": 82
} | [
{
"pp": "case right_unitor_hom_inv\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝ b✝ : B\nf✝ : Hom a✝ b✝\n⊢ liftHom₂ F ((Hom₂.right_unitor f✝).vcomp (Hom₂.right_unitor_inv f✝)) = liftHom₂ F (Hom₂.id (f✝.comp (Hom.id b✝)))",... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 323,
"column": 55
} | {
"line": 323,
"column": 82
} | {
"line": 323,
"column": 82
} | [
{
"pp": "case right_unitor_inv_hom\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝ b✝ : B\nf✝ : Hom a✝ b✝\n⊢ liftHom₂ F ((Hom₂.right_unitor_inv f✝).vcomp (Hom₂.right_unitor f✝)) = liftHom₂ F (Hom₂.id f✝)",
"ppTerm": "?ri... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 323,
"column": 55
} | {
"line": 323,
"column": 82
} | {
"line": 323,
"column": 82
} | [
{
"pp": "case right_unitor_inv_hom\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝ b✝ : B\nf✝ : Hom a✝ b✝\n⊢ liftHom₂ F ((Hom₂.right_unitor_inv f✝).vcomp (Hom₂.right_unitor f✝)) = liftHom₂ F (Hom₂.id f✝)",
"ppTerm": "?ri... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 323,
"column": 55
} | {
"line": 323,
"column": 82
} | {
"line": 323,
"column": 82
} | [
{
"pp": "case pentagon\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝ b✝ c✝ d✝ e✝ : B\nf✝ : Hom a✝ b✝\ng✝ : Hom b✝ c✝\nh✝ : Hom c✝ d✝\ni✝ : Hom d✝ e✝\n⊢ liftHom₂ F\n ((Hom₂.whisker_right i✝ (Hom₂.associator f✝ g✝ h✝)).... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 323,
"column": 55
} | {
"line": 323,
"column": 82
} | {
"line": 323,
"column": 82
} | [
{
"pp": "case pentagon\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝ b✝ c✝ d✝ e✝ : B\nf✝ : Hom a✝ b✝\ng✝ : Hom b✝ c✝\nh✝ : Hom c✝ d✝\ni✝ : Hom d✝ e✝\n⊢ liftHom₂ F\n ((Hom₂.whisker_right i✝ (Hom₂.associator f✝ g✝ h✝)).... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 323,
"column": 55
} | {
"line": 323,
"column": 82
} | {
"line": 323,
"column": 82
} | [
{
"pp": "case triangle\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝ b✝ c✝ : B\nf✝ : Hom a✝ b✝\ng✝ : Hom b✝ c✝\n⊢ liftHom₂ F ((Hom₂.associator f✝ (Hom.id b✝) g✝).vcomp (Hom₂.whisker_left f✝ (Hom₂.left_unitor g✝))) =\n l... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 323,
"column": 55
} | {
"line": 323,
"column": 82
} | {
"line": 323,
"column": 82
} | [
{
"pp": "case triangle\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝ b✝ c✝ : B\nf✝ : Hom a✝ b✝\ng✝ : Hom b✝ c✝\n⊢ liftHom₂ F ((Hom₂.associator f✝ (Hom.id b✝) g✝).vcomp (Hom₂.whisker_left f✝ (Hom₂.left_unitor g✝))) =\n l... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Bicategory.Modification.Lax | {
"line": 132,
"column": 4
} | {
"line": 132,
"column": 15
} | {
"line": 132,
"column": 16
} | [
{
"pp": "B : Type u₁\ninst✝¹ : Bicategory B\nC : Type u₂\ninst✝ : Bicategory C\nF G : B ⥤ᴸ C\nη θ : F ⟶ G\napp : (a : B) → η.app a ≅ θ.app a\nnaturality : ∀ {a b : B} (f : a ⟶ b), (app a).hom ▷ G.map f ≫ θ.naturality f = η.naturality f ≫ F.map f ◁ (app b).hom\na b : B\nf : a ⟶ b\n⊢ (app a).inv ▷ G.map f ≫ η.nat... | [
"B : Type u₁\ninst✝¹ : Bicategory B\nC : Type u₂\ninst✝ : Bicategory C\nF G : B ⥤ᴸ C\nη θ : F ⟶ G\napp : (a : B) → η.app a ≅ θ.app a\nnaturality : ∀ {a b : B} (f : a ⟶ b), (app a).hom ▷ G.map f ≫ θ.naturality f = η.naturality f ≫ F.map f ◁ (app b).hom\na b : B\nf : a ⟶ b\n⊢ (app a).inv ▷ G.map f ≫ η.naturality f = ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Bicategory.Modification.Lax | {
"line": 219,
"column": 4
} | {
"line": 219,
"column": 15
} | {
"line": 219,
"column": 16
} | [
{
"pp": "B : Type u₁\ninst✝¹ : Bicategory B\nC : Type u₂\ninst✝ : Bicategory C\nF G : B ⥤ᴸ C\nη θ : F ⟶ G\napp : (a : B) → η.app a ≅ θ.app a\nnaturality : ∀ {a b : B} (f : a ⟶ b), F.map f ◁ (app b).hom ≫ θ.naturality f = η.naturality f ≫ (app a).hom ▷ G.map f\na b : B\nf : a ⟶ b\n⊢ F.map f ◁ (app b).inv ≫ η.nat... | [
"B : Type u₁\ninst✝¹ : Bicategory B\nC : Type u₂\ninst✝ : Bicategory C\nF G : B ⥤ᴸ C\nη θ : F ⟶ G\napp : (a : B) → η.app a ≅ θ.app a\nnaturality : ∀ {a b : B} (f : a ⟶ b), F.map f ◁ (app b).hom ≫ θ.naturality f = η.naturality f ≫ (app a).hom ▷ G.map f\na b : B\nf : a ⟶ b\n⊢ F.map f ◁ (app b).inv ≫ η.naturality f = ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Bicategory.Modification.Oplax | {
"line": 159,
"column": 4
} | {
"line": 159,
"column": 15
} | {
"line": 159,
"column": 16
} | [
{
"pp": "B : Type u₁\ninst✝¹ : Bicategory B\nC : Type u₂\ninst✝ : Bicategory C\nF G : B ⥤ᵒᵖᴸ C\nη θ : F ⟶ G\napp : (a : B) → η.app a ≅ θ.app a\nnaturality : ∀ {a b : B} (f : a ⟶ b), (app a).hom ▷ G.map f ≫ θ.naturality f = η.naturality f ≫ F.map f ◁ (app b).hom\na b : B\nf : a ⟶ b\n⊢ (app a).inv ▷ G.map f ≫ η.n... | [
"B : Type u₁\ninst✝¹ : Bicategory B\nC : Type u₂\ninst✝ : Bicategory C\nF G : B ⥤ᵒᵖᴸ C\nη θ : F ⟶ G\napp : (a : B) → η.app a ≅ θ.app a\nnaturality : ∀ {a b : B} (f : a ⟶ b), (app a).hom ▷ G.map f ≫ θ.naturality f = η.naturality f ≫ F.map f ◁ (app b).hom\na b : B\nf : a ⟶ b\n⊢ (app a).inv ▷ G.map f ≫ η.naturality f ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Bicategory.Modification.Oplax | {
"line": 260,
"column": 4
} | {
"line": 260,
"column": 15
} | {
"line": 260,
"column": 16
} | [
{
"pp": "B : Type u₁\ninst✝¹ : Bicategory B\nC : Type u₂\ninst✝ : Bicategory C\nF G : B ⥤ᵒᵖᴸ C\nη θ : F ⟶ G\napp : (a : B) → η.app a ≅ θ.app a\nnaturality : ∀ {a b : B} (f : a ⟶ b), F.map f ◁ (app b).hom ≫ θ.naturality f = η.naturality f ≫ (app a).hom ▷ G.map f\na b : B\nf : a ⟶ b\n⊢ F.map f ◁ (app b).inv ≫ η.n... | [
"B : Type u₁\ninst✝¹ : Bicategory B\nC : Type u₂\ninst✝ : Bicategory C\nF G : B ⥤ᵒᵖᴸ C\nη θ : F ⟶ G\napp : (a : B) → η.app a ≅ θ.app a\nnaturality : ∀ {a b : B} (f : a ⟶ b), F.map f ◁ (app b).hom ≫ θ.naturality f = η.naturality f ≫ (app a).hom ▷ G.map f\na b : B\nf : a ⟶ b\n⊢ F.map f ◁ (app b).inv ≫ η.naturality f ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Bicategory.Modification.Oplax | {
"line": 387,
"column": 4
} | {
"line": 387,
"column": 15
} | {
"line": 387,
"column": 16
} | [
{
"pp": "B : Type u₁\ninst✝¹ : Bicategory B\nC : Type u₂\ninst✝ : Bicategory C\nF G : B ⥤ᵒᵖᴸ C\nη θ : F ⟶ G\napp : (a : B) → η.app a ≅ θ.app a\nnaturality :\n ∀ {a b : B} (f : a ⟶ b), F.map f ◁ (app b).hom ≫ (θ.naturality f).hom = (η.naturality f).hom ≫ (app a).hom ▷ G.map f\na b : B\nf : a ⟶ b\n⊢ F.map f ◁ (a... | [
"B : Type u₁\ninst✝¹ : Bicategory B\nC : Type u₂\ninst✝ : Bicategory C\nF G : B ⥤ᵒᵖᴸ C\nη θ : F ⟶ G\napp : (a : B) → η.app a ≅ θ.app a\nnaturality :\n ∀ {a b : B} (f : a ⟶ b), F.map f ◁ (app b).hom ≫ (θ.naturality f).hom = (η.naturality f).hom ≫ (app a).hom ▷ G.map f\na b : B\nf : a ⟶ b\n⊢ F.map f ◁ (app b).inv ≫ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Bicategory.Modification.Pseudo | {
"line": 165,
"column": 4
} | {
"line": 165,
"column": 15
} | {
"line": 165,
"column": 16
} | [
{
"pp": "B : Type u₁\ninst✝¹ : Bicategory B\nC : Type u₂\ninst✝ : Bicategory C\nF G : B ⥤ᵖ C\nη θ : F ⟶ G\napp : (a : B) → η.app a ≅ θ.app a\nnaturality :\n ∀ {a b : B} (f : a ⟶ b), F.map f ◁ (app b).hom ≫ (θ.naturality f).hom = (η.naturality f).hom ≫ (app a).hom ▷ G.map f\na b : B\nf : a ⟶ b\n⊢ F.map f ◁ (app... | [
"B : Type u₁\ninst✝¹ : Bicategory B\nC : Type u₂\ninst✝ : Bicategory C\nF G : B ⥤ᵖ C\nη θ : F ⟶ G\napp : (a : B) → η.app a ≅ θ.app a\nnaturality :\n ∀ {a b : B} (f : a ⟶ b), F.map f ◁ (app b).hom ≫ (θ.naturality f).hom = (η.naturality f).hom ≫ (app a).hom ▷ G.map f\na b : B\nf : a ⟶ b\n⊢ F.map f ◁ (app b).inv ≫ (η... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Bicategory.Grothendieck | {
"line": 126,
"column": 15
} | {
"line": 126,
"column": 30
} | {
"line": 127,
"column": 2
} | [
{
"pp": "𝒮 : Type u₁\ninst✝ : Category.{v₁, u₁} 𝒮\nF : LocallyDiscrete 𝒮 ⥤ᵖ Cat\na b : ∫ F\nf g : a ⟶ b\nhfg : f = g\n⊢ ∃ (hfg : f.base = g.base), eqToHom ⋯ ≫ f.fiber = g.fiber",
"ppTerm": "?m.50",
"assigned": true,
"usedConstants": [
"CategoryTheory.LocallyDiscrete.mk",
"CategoryTheo... | [] | subst hfg; simp | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Bicategory.Grothendieck | {
"line": 126,
"column": 15
} | {
"line": 126,
"column": 30
} | {
"line": 127,
"column": 2
} | [
{
"pp": "𝒮 : Type u₁\ninst✝ : Category.{v₁, u₁} 𝒮\nF : LocallyDiscrete 𝒮 ⥤ᵖ Cat\na b : ∫ F\nf g : a ⟶ b\nhfg : f = g\n⊢ ∃ (hfg : f.base = g.base), eqToHom ⋯ ≫ f.fiber = g.fiber",
"ppTerm": "?m.50",
"assigned": true,
"usedConstants": [
"CategoryTheory.LocallyDiscrete.mk",
"CategoryTheo... | [] | subst hfg; simp | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Bicategory.InducedBicategory | {
"line": 114,
"column": 50
} | {
"line": 114,
"column": 61
} | {
"line": 114,
"column": 62
} | [
{
"pp": "B : Type u_1\nC : Type u_2\ninst✝ : Bicategory C\nF : B → C\nx✝⁶ x✝⁵ x✝⁴ : InducedBicategory C F\nx✝³ x✝² : x✝⁶ ⟶ x✝⁵\nx✝¹ x✝ : x✝⁵ ⟶ x✝⁴\nη : x✝³ ⟶ x✝²\nθ : x✝¹ ⟶ x✝\n⊢ (mkHom₂ (x✝³.hom ◁ θ.hom) ≫ mkHom₂ (η.hom ▷ x✝.hom)).hom = (mkHom₂ (η.hom ▷ x✝¹.hom) ≫ mkHom₂ (x✝².hom ◁ θ.hom)).hom",
"ppTerm": ... | [
"B : Type u_1\nC : Type u_2\ninst✝ : Bicategory C\nF : B → C\nx✝⁶ x✝⁵ x✝⁴ : InducedBicategory C F\nx✝³ x✝² : x✝⁶ ⟶ x✝⁵\nx✝¹ x✝ : x✝⁵ ⟶ x✝⁴\nη : x✝³ ⟶ x✝²\nθ : x✝¹ ⟶ x✝\n⊢ x✝³.hom ◁ θ.hom ≫ η.hom ▷ x✝.hom = η.hom ▷ x✝¹.hom ≫ x✝².hom ◁ θ.hom"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Bicategory.Grothendieck | {
"line": 312,
"column": 4
} | {
"line": 314,
"column": 98
} | {
"line": 316,
"column": 0
} | [
{
"pp": "𝒮 : Type u₁\ninst✝ : Category.{v₁, u₁} 𝒮\nF : LocallyDiscrete 𝒮ᵒᵖ ⥤ᵖ Cat\nW✝ X✝ Y✝ Z✝ : ∫ᶜ F\nf : W✝ ⟶ X✝\ng : X✝ ⟶ Y✝\nh : Y✝ ⟶ Z✝\n⊢ (f ≫ g) ≫ h = f ≫ g ≫ h",
"ppTerm": "?m.48",
"assigned": true,
"usedConstants": [
"_private.Mathlib.CategoryTheory.Bicategory.Grothendieck.0.Catego... | [] | ext
· simp
· simp [← NatTrans.naturality_assoc, F.mapComp_assoc_right_inv_app, Strict.associator_eqToIso] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Bicategory.Grothendieck | {
"line": 312,
"column": 4
} | {
"line": 314,
"column": 98
} | {
"line": 316,
"column": 0
} | [
{
"pp": "𝒮 : Type u₁\ninst✝ : Category.{v₁, u₁} 𝒮\nF : LocallyDiscrete 𝒮ᵒᵖ ⥤ᵖ Cat\nW✝ X✝ Y✝ Z✝ : ∫ᶜ F\nf : W✝ ⟶ X✝\ng : X✝ ⟶ Y✝\nh : Y✝ ⟶ Z✝\n⊢ (f ≫ g) ≫ h = f ≫ g ≫ h",
"ppTerm": "?m.48",
"assigned": true,
"usedConstants": [
"_private.Mathlib.CategoryTheory.Bicategory.Grothendieck.0.Catego... | [] | ext
· simp
· simp [← NatTrans.naturality_assoc, F.mapComp_assoc_right_inv_app, Strict.associator_eqToIso] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Bicategory.Kan.Adjunction | {
"line": 68,
"column": 6
} | {
"line": 68,
"column": 37
} | {
"line": 68,
"column": 38
} | [
{
"pp": "B : Type u\ninst✝ : Bicategory B\na b c : B\nf : a ⟶ b\nu : b ⟶ a\nadj : f ⊣ u\nx : B\nh : a ⟶ x\ns : LeftExtension f (𝟙 a ≫ h)\nτ₀ : (LeftExtension.mk u adj.unit).whisker h ⟶ s\nτ : u ≫ h ⟶ s.extension := StructuredArrow.Hom.right τ₀\n⊢ adj.unit ▷ h ⊗≫ f ◁ τ = s.unit",
"ppTerm": "?m.2641",
"a... | [
"B : Type u\ninst✝ : Bicategory B\na b c : B\nf : a ⟶ b\nu : b ⟶ a\nadj : f ⊣ u\nx : B\nh : a ⟶ x\ns : LeftExtension f (𝟙 a ≫ h)\nτ₀ : (LeftExtension.mk u adj.unit).whisker h ⟶ s\nτ : u ≫ h ⟶ s.extension := StructuredArrow.Hom.right τ₀\n⊢ adj.unit ▷ h ≫ (α_ f u h).hom ≫ f ◁ τ = s.unit"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Bicategory.Kan.Adjunction | {
"line": 88,
"column": 4
} | {
"line": 88,
"column": 47
} | {
"line": 88,
"column": 48
} | [
{
"pp": "B : Type u\ninst✝ : Bicategory B\na b c : B\nf : a ⟶ b\nt : LeftExtension f (𝟙 a)\nH : t.IsKan\nH' : (t.whisker f).IsKan\nε : t.extension ≫ f ⟶ 𝟙 b := H'.desc (LeftExtension.mk (𝟙 b) ((λ_ f).hom ≫ (ρ_ f).inv))\n⊢ leftZigzag t.unit ε = (λ_ f).hom ≫ (ρ_ f).inv",
"ppTerm": "?m.149",
"assigned":... | [
"B : Type u\ninst✝ : Bicategory B\na b c : B\nf : a ⟶ b\nt : LeftExtension f (𝟙 a)\nH : t.IsKan\nH' : (t.whisker f).IsKan\nε : t.extension ≫ f ⟶ 𝟙 b := H'.desc (LeftExtension.mk (𝟙 b) ((λ_ f).hom ≫ (ρ_ f).inv))\n⊢ t.unit ▷ f ≫ (α_ f t.extension f).hom ≫ f ◁ ε = (λ_ f).hom ≫ (ρ_ f).inv"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Bicategory.Kan.Adjunction | {
"line": 151,
"column": 53
} | {
"line": 151,
"column": 84
} | {
"line": 151,
"column": 85
} | [
{
"pp": "B : Type u\ninst✝ : Bicategory B\na b c : B\nf : a ⟶ b\nu : b ⟶ a\nadj : f ⊣ u\nx : B\nh : x ⟶ a\ns : LeftLift u (h ≫ 𝟙 a)\nτ₀ : (LeftLift.mk f adj.unit).whisker h ⟶ s\nτ : h ≫ f ⟶ s.lift := StructuredArrow.Hom.right τ₀\n⊢ h ◁ adj.unit ⊗≫ τ ▷ u = s.unit",
"ppTerm": "?m.2518",
"assigned": true,... | [
"B : Type u\ninst✝ : Bicategory B\na b c : B\nf : a ⟶ b\nu : b ⟶ a\nadj : f ⊣ u\nx : B\nh : x ⟶ a\ns : LeftLift u (h ≫ 𝟙 a)\nτ₀ : (LeftLift.mk f adj.unit).whisker h ⟶ s\nτ : h ≫ f ⟶ s.lift := StructuredArrow.Hom.right τ₀\n⊢ h ◁ adj.unit ≫ (α_ h f u).inv ≫ τ ▷ u = s.unit"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Bicategory.Kan.Adjunction | {
"line": 171,
"column": 4
} | {
"line": 171,
"column": 48
} | {
"line": 171,
"column": 49
} | [
{
"pp": "B : Type u\ninst✝ : Bicategory B\na b c : B\nu : b ⟶ a\nt : LeftLift u (𝟙 a)\nH : t.IsKan\nH' : (t.whisker u).IsKan\nε : u ≫ t.lift ⟶ 𝟙 b := H'.desc (LeftLift.mk (𝟙 b) ((ρ_ u).hom ≫ (λ_ u).inv))\n⊢ rightZigzag t.unit ε = (ρ_ u).hom ≫ (λ_ u).inv",
"ppTerm": "?m.149",
"assigned": true,
"us... | [
"B : Type u\ninst✝ : Bicategory B\na b c : B\nu : b ⟶ a\nt : LeftLift u (𝟙 a)\nH : t.IsKan\nH' : (t.whisker u).IsKan\nε : u ≫ t.lift ⟶ 𝟙 b := H'.desc (LeftLift.mk (𝟙 b) ((ρ_ u).hom ≫ (λ_ u).inv))\n⊢ u ◁ t.unit ≫ (α_ u t.lift u).inv ≫ ε ▷ u = (ρ_ u).hom ≫ (λ_ u).inv"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Bicategory.Kan.Adjunction | {
"line": 229,
"column": 8
} | {
"line": 229,
"column": 39
} | {
"line": 229,
"column": 40
} | [
{
"pp": "B : Type u\ninst✝ : Bicategory B\na b c : B\nf : a ⟶ b\ng : a ⟶ c\nt : LeftExtension f g\nH : t.IsKan\nx : B\nh : c ⟶ x\nu : x ⟶ c\nadj : h ⊣ u\nη' : 𝟙 c ⟶ h ≫ u := adj.unit\nH' : (LeftLift.mk h η').IsAbsKan := fun {x_1} ↦ adj.isAbsoluteLeftKanLift\ns : LeftExtension f (g ≫ h)\nk : b ⟶ x := s.extensio... | [
"B : Type u\ninst✝ : Bicategory B\na b c : B\nf : a ⟶ b\ng : a ⟶ c\nt : LeftExtension f g\nH : t.IsKan\nx : B\nh : c ⟶ x\nu : x ⟶ c\nadj : h ⊣ u\nη' : 𝟙 c ⟶ h ≫ u := adj.unit\nH' : (LeftLift.mk h η').IsAbsKan := fun {x_1} ↦ adj.isAbsoluteLeftKanLift\ns : LeftExtension f (g ≫ h)\nk : b ⟶ x := s.extension\nθ : g ≫ h... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Bicategory.Kan.Adjunction | {
"line": 232,
"column": 6
} | {
"line": 244,
"column": 20
} | {
"line": 244,
"column": 20
} | [
{
"pp": "B : Type u\ninst✝ : Bicategory B\na b c : B\nf : a ⟶ b\ng : a ⟶ c\nt : LeftExtension f g\nH : t.IsKan\nx : B\nh : c ⟶ x\nu : x ⟶ c\nadj : h ⊣ u\nη' : 𝟙 c ⟶ h ≫ u := adj.unit\nH' : (LeftLift.mk h η').IsAbsKan := fun {x_1} ↦ adj.isAbsoluteLeftKanLift\ns : LeftExtension f (g ≫ h)\nk : b ⟶ x := s.extensio... | [] | calc _
_ = (g ◁ η' ≫ t.unit ▷ (h ≫ u)) ⊗≫ f ◁ σ ▷ u ⊗≫ 𝟙 _ := by
bicategory
_ = t.unit ▷ (𝟙 c) ⊗≫ f ◁ (t.extension ◁ η' ⊗≫ σ ▷ u) ⊗≫ 𝟙 _ := by
rw [whisker_exchange]; bicategory
_ = (ρ_ g).hom ≫ t.unit ≫ f ◁ H.desc sτ ≫ (α_ f s.extension u).inv := by
rw [Hσ]
... | Lean.Elab.Tactic._aux_Mathlib_Tactic_Widget_Calc___elabRules_Lean_calcTactic_1 | Lean.calcTactic |
Mathlib.CategoryTheory.Bicategory.Kan.Adjunction | {
"line": 247,
"column": 52
} | {
"line": 247,
"column": 83
} | {
"line": 247,
"column": 84
} | [
{
"pp": "B : Type u\ninst✝ : Bicategory B\na b c : B\nf : a ⟶ b\ng : a ⟶ c\nt : LeftExtension f g\nH : t.IsKan\nx : B\nh : c ⟶ x\nu : x ⟶ c\nadj : h ⊣ u\nη' : 𝟙 c ⟶ h ≫ u := adj.unit\nH' : (LeftLift.mk h η').IsAbsKan := fun {x_1} ↦ adj.isAbsoluteLeftKanLift\ns' : LeftExtension f (g ≫ h)\nτ₀' : t.whisker h ⟶ s'... | [
"B : Type u\ninst✝ : Bicategory B\na b c : B\nf : a ⟶ b\ng : a ⟶ c\nt : LeftExtension f g\nH : t.IsKan\nx : B\nh : c ⟶ x\nu : x ⟶ c\nadj : h ⊣ u\nη' : 𝟙 c ⟶ h ≫ u := adj.unit\nH' : (LeftLift.mk h η').IsAbsKan := fun {x_1} ↦ adj.isAbsoluteLeftKanLift\ns' : LeftExtension f (g ≫ h)\nτ₀' : t.whisker h ⟶ s'\nτ' : t.ext... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sigma.Basic | {
"line": 130,
"column": 4
} | {
"line": 130,
"column": 24
} | {
"line": 132,
"column": 0
} | [
{
"pp": "I : Type w₁\nC : I → Type u₁\ninst✝¹ : (i : I) → Category.{v₁, u₁} (C i)\nD : Type u₂\ninst✝ : Category.{v₂, u₂} D\nF : (i : I) → C i ⥤ D\ni : I\nX Y✝¹ : C i\nf : X ⟶ Y✝¹\nY✝ : C i\ng : Y✝¹ ⟶ Y✝\n⊢ descMap F ⟨i, X⟩ ⟨i, Y✝⟩ (SigmaHom.mk f ≫ SigmaHom.mk g) =\n descMap F ⟨i, X⟩ ⟨i, Y✝¹⟩ (SigmaHom.mk f)... | [] | apply (F i).map_comp | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.CategoryTheory.Category.Cat.Adjunction | {
"line": 67,
"column": 24
} | {
"line": 67,
"column": 35
} | {
"line": 67,
"column": 36
} | [
{
"pp": "X : Type u\nC : Cat\nx✝ : Cat\nx : ConnectedComponents ↑x✝\n⊢ (ConcreteCategory.hom (↾(𝟙 x✝).toFunctor.mapConnectedComponents)).toFun x =\n (ConcreteCategory.hom (𝟙 (ConnectedComponents ↑x✝))).toFun x",
"ppTerm": "?m.48",
"assigned": true,
"usedConstants": [
"CategoryTheory.Cat.c... | [
"X : Type u\nC : Cat\nx✝ : Cat\nx : ConnectedComponents ↑x✝\n⊢ (𝟭 ↑x✝).mapConnectedComponents x = x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Category.Cat.Adjunction | {
"line": 68,
"column": 28
} | {
"line": 68,
"column": 39
} | {
"line": 68,
"column": 40
} | [
{
"pp": "X : Type u\nC : Cat\nX✝ Y✝ Z✝ : Cat\nx✝¹ : X✝ ⟶ Y✝\nx✝ : Y✝ ⟶ Z✝\nx : ConnectedComponents ↑X✝\n⊢ (ConcreteCategory.hom (↾(x✝¹ ≫ x✝).toFunctor.mapConnectedComponents)).toFun x =\n (ConcreteCategory.hom (↾x✝¹.toFunctor.mapConnectedComponents ≫ ↾x✝.toFunctor.mapConnectedComponents)).toFun x",
"ppTe... | [
"X : Type u\nC : Cat\nX✝ Y✝ Z✝ : Cat\nx✝¹ : X✝ ⟶ Y✝\nx✝ : Y✝ ⟶ Z✝\nx : ConnectedComponents ↑X✝\n⊢ (x✝¹.toFunctor ⋙ x✝.toFunctor).mapConnectedComponents x =\n x✝.toFunctor.mapConnectedComponents (x✝¹.toFunctor.mapConnectedComponents x)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Category.PartialFun | {
"line": 154,
"column": 54
} | {
"line": 158,
"column": 54
} | {
"line": 159,
"column": 2
} | [
{
"pp": "X Y : Pointed\nf : X ⟶ Y\na : ((pointedToPartialFun ⋙ partialFunToPointed).obj X).X\n⊢ ((pointedToPartialFun ⋙ partialFunToPointed).map f ≫ (Pointed.Iso.mk (Equiv.optionSubtypeNe Y.point) ⋯).hom).toFun a =\n ((Pointed.Iso.mk (Equiv.optionSubtypeNe X.point) ⋯).hom ≫ (𝟭 Pointed).map f).toFun a",
... | [] | by
obtain _ | ⟨a, ha⟩ := a
· exact f.map_point.symm
simp_all [Equiv.optionSubtypeNe, Equiv.optionSubtype,
Option.casesOn'_eq_elim, Part.elim_toOption] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Monoidal.Cartesian.Comon_ | {
"line": 46,
"column": 4
} | {
"line": 46,
"column": 19
} | {
"line": 46,
"column": 19
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : CartesianMonoidalCategory C\nX✝ Y✝ : C\nf : X✝ ⟶ Y✝\n⊢ f ≫ Δ = Δ ≫ (f ⊗ₘ f)",
"ppTerm": "?m.58",
"assigned": true,
"usedConstants": [
"CategoryTheory.ComonObj.comul",
"CategoryTheory.cartesianComon._proof_6",
"CategoryTheory.... | [] | simp +instances | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.CategoryTheory.Monoidal.Cartesian.Comon_ | {
"line": 54,
"column": 4
} | {
"line": 54,
"column": 15
} | {
"line": 54,
"column": 16
} | [
{
"pp": "case h_fst\nC : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : CartesianMonoidalCategory C\nA : C\ninst✝ : ComonObj A\n⊢ Δ ≫ fst A A = lift (𝟙 A) (𝟙 A) ≫ fst A A",
"ppTerm": "?h_fst",
"assigned": true,
"usedConstants": [
"CategoryTheory.ComonObj.comul",
"Eq.mpr",
"Category... | [
"case h_fst\nC : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : CartesianMonoidalCategory C\nA : C\ninst✝ : ComonObj A\n⊢ Δ ≫ fst A A = 𝟙 A"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.Cartesian.Comon_ | {
"line": 55,
"column": 4
} | {
"line": 55,
"column": 15
} | {
"line": 55,
"column": 16
} | [
{
"pp": "case h_snd\nC : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : CartesianMonoidalCategory C\nA : C\ninst✝ : ComonObj A\n⊢ Δ ≫ snd A A = lift (𝟙 A) (𝟙 A) ≫ snd A A",
"ppTerm": "?h_snd",
"assigned": true,
"usedConstants": [
"CategoryTheory.ComonObj.comul",
"Eq.mpr",
"Category... | [
"case h_snd\nC : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : CartesianMonoidalCategory C\nA : C\ninst✝ : ComonObj A\n⊢ Δ ≫ snd A A = 𝟙 A"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Localization.Prod | {
"line": 58,
"column": 2
} | {
"line": 58,
"column": 60
} | {
"line": 58,
"column": 61
} | [
{
"pp": "C₁ : Type u₁\nC₂ : Type u₂\ninst✝² : Category.{v₁, u₁} C₁\ninst✝¹ : Category.{v₂, u₂} C₂\nW₁ : MorphismProperty C₁\nW₂ : MorphismProperty C₂\nE : Type u₅\ninst✝ : Category.{v₅, u₅} E\nF₁ F₂ : W₁.Localization × W₂.Localization ⥤ E\nh : W₁.Q.prod W₂.Q ⋙ F₁ = W₁.Q.prod W₂.Q ⋙ F₂\n⊢ uncurry.obj (W₂.Q ⋙ (W₁... | [
"C₁ : Type u₁\nC₂ : Type u₂\ninst✝² : Category.{v₁, u₁} C₁\ninst✝¹ : Category.{v₂, u₂} C₂\nW₁ : MorphismProperty C₁\nW₂ : MorphismProperty C₂\nE : Type u₅\ninst✝ : Category.{v₅, u₅} E\nF₁ F₂ : W₁.Localization × W₂.Localization ⥤ E\nh : W₁.Q.prod W₂.Q ⋙ F₁ = W₁.Q.prod W₂.Q ⋙ F₂\n⊢ W₁.Q.prod W₂.Q ⋙ F₁ = W₁.Q.prod W₂.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong | {
"line": 140,
"column": 41
} | {
"line": 141,
"column": 59
} | {
"line": 143,
"column": 0
} | [
{
"pp": "C : Type u₁\ninst✝³ : Category.{v₁, u₁} C\nX Y Z : C\nf : X ⟶ Y\ng : Y ⟶ Z\ninst✝² : ChosenPullbacksAlong f\ninst✝¹ : ChosenPullbacksAlong g\ninst✝ : ChosenPullbacksAlong (f ≫ g)\n⊢ Functor.whiskerRight (pullbackComp f g).hom (map (f ≫ g)) ≫ (mapPullbackAdj (f ≫ g)).counit =\n (mapPullbackAdj (f ≫ g... | [] | by
rw [pullbackComp, Adjunction.rightAdjointUniq_hom_counit] | [anonymous] | Lean.Parser.Term.byTactic |
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