module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Algebra.Homology.HomotopyCategory.Shift | {
"line": 301,
"column": 4
} | {
"line": 305,
"column": 13
} | {
"line": 305,
"column": 14
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : Preadditive C\nD : Type u'\ninst✝¹ : Category.{v', u'} D\ninst✝ : Preadditive D\nK L : CochainComplex C ℤ\nφ₁ φ₂ : K ⟶ L\nh : Homotopy φ₁ φ₂\nn i : ℤ\n⊢ φ₁.f (i + n) =\n (n.negOnePow • K.d (i + n) (i + 1 + n)) ≫ (n.negOnePow • h.hom (i + 1 + n) (i + n... | [
"C : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : Preadditive C\nD : Type u'\ninst✝¹ : Category.{v', u'} D\ninst✝ : Preadditive D\nK L : CochainComplex C ℤ\nφ₁ φ₂ : K ⟶ L\nh : Homotopy φ₁ φ₂\nn i : ℤ\n⊢ φ₁.f (i + n) =\n K.d (i + n) (i + 1 + n) ≫ h.hom (i + 1 + n) (i + n) + h.hom (i + n) (i - 1 + n) ≫ L.d (i - 1 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Shift.Induced | {
"line": 112,
"column": 10
} | {
"line": 112,
"column": 21
} | {
"line": 112,
"column": 22
} | [
{
"pp": "C : Type ?u.2\nD : Type ?u.4\ninst✝⁵ : Category.{v_1, ?u.2} C\ninst✝⁴ : Category.{v_2, ?u.4} D\nF : C ⥤ D\nA : Type ?u.15\ninst✝³ : AddMonoid A\ninst✝² : HasShift C A\ns : A → D ⥤ D\ni : (a : A) → F ⋙ s a ≅ shiftFunctor C a ⋙ F\ninst✝¹ : ((whiskeringLeft C D D).obj F).Full\ninst✝ : ((whiskeringLeft C D... | [
"C : Type ?u.2\nD : Type ?u.4\ninst✝⁵ : Category.{v_1, ?u.2} C\ninst✝⁴ : Category.{v_2, ?u.4} D\nF : C ⥤ D\nA : Type ?u.15\ninst✝³ : AddMonoid A\ninst✝² : HasShift C A\ns : A → D ⥤ D\ni : (a : A) → F ⋙ s a ≅ shiftFunctor C a ⋙ F\ninst✝¹ : ((whiskeringLeft C D D).obj F).Full\ninst✝ : ((whiskeringLeft C D D).obj F).F... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Shift.CommShift | {
"line": 565,
"column": 2
} | {
"line": 565,
"column": 13
} | {
"line": 565,
"column": 14
} | [
{
"pp": "C : Type u_1\nD : Type u_2\nE : Type u_3\ninst✝¹⁰ : Category.{v_1, u_1} C\ninst✝⁹ : Category.{v_2, u_2} D\ninst✝⁸ : Category.{v_3, u_3} E\nF : C ⥤ D\nG : D ⥤ E\nH : C ⥤ E\ne : F ⋙ G ≅ H\ninst✝⁷ : G.Full\ninst✝⁶ : G.Faithful\nA : Type u_5\ninst✝⁵ : AddMonoid A\ninst✝⁴ : HasShift C A\ninst✝³ : HasShift D... | [
"C : Type u_1\nD : Type u_2\nE : Type u_3\ninst✝¹⁰ : Category.{v_1, u_1} C\ninst✝⁹ : Category.{v_2, u_2} D\ninst✝⁸ : Category.{v_3, u_3} E\nF : C ⥤ D\nG : D ⥤ E\nH : C ⥤ E\ne : F ⋙ G ≅ H\ninst✝⁷ : G.Full\ninst✝⁶ : G.Faithful\nA : Type u_5\ninst✝⁵ : AddMonoid A\ninst✝⁴ : HasShift C A\ninst✝³ : HasShift D A\ninst✝² :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Shift.CommShift | {
"line": 574,
"column": 2
} | {
"line": 574,
"column": 13
} | {
"line": 574,
"column": 14
} | [
{
"pp": "C : Type u_1\nD : Type u_2\nE : Type u_3\ninst✝¹⁰ : Category.{v_1, u_1} C\ninst✝⁹ : Category.{v_2, u_2} D\ninst✝⁸ : Category.{v_3, u_3} E\nF : C ⥤ D\nG : D ⥤ E\nH : C ⥤ E\ne : F ⋙ G ≅ H\ninst✝⁷ : G.Full\ninst✝⁶ : G.Faithful\nA : Type u_5\ninst✝⁵ : AddMonoid A\ninst✝⁴ : HasShift C A\ninst✝³ : HasShift D... | [
"C : Type u_1\nD : Type u_2\nE : Type u_3\ninst✝¹⁰ : Category.{v_1, u_1} C\ninst✝⁹ : Category.{v_2, u_2} D\ninst✝⁸ : Category.{v_3, u_3} E\nF : C ⥤ D\nG : D ⥤ E\nH : C ⥤ E\ne : F ⋙ G ≅ H\ninst✝⁷ : G.Full\ninst✝⁶ : G.Faithful\nA : Type u_5\ninst✝⁵ : AddMonoid A\ninst✝⁴ : HasShift C A\ninst✝³ : HasShift D A\ninst✝² :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Shift.Induced | {
"line": 126,
"column": 10
} | {
"line": 126,
"column": 21
} | {
"line": 126,
"column": 22
} | [
{
"pp": "C : Type ?u.2\nD : Type ?u.4\ninst✝⁵ : Category.{v_1, ?u.2} C\ninst✝⁴ : Category.{v_2, ?u.4} D\nF : C ⥤ D\nA : Type ?u.15\ninst✝³ : AddMonoid A\ninst✝² : HasShift C A\ns : A → D ⥤ D\ni : (a : A) → F ⋙ s a ≅ shiftFunctor C a ⋙ F\ninst✝¹ : ((whiskeringLeft C D D).obj F).Full\ninst✝ : ((whiskeringLeft C D... | [
"C : Type ?u.2\nD : Type ?u.4\ninst✝⁵ : Category.{v_1, ?u.2} C\ninst✝⁴ : Category.{v_2, ?u.4} D\nF : C ⥤ D\nA : Type ?u.15\ninst✝³ : AddMonoid A\ninst✝² : HasShift C A\ns : A → D ⥤ D\ni : (a : A) → F ⋙ s a ≅ shiftFunctor C a ⋙ F\ninst✝¹ : ((whiskeringLeft C D D).obj F).Full\ninst✝ : ((whiskeringLeft C D D).obj F).F... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.Pretriangulated | {
"line": 126,
"column": 2
} | {
"line": 126,
"column": 57
} | {
"line": 126,
"column": 58
} | [
{
"pp": "C : Type u\ninst✝⁴ : Category.{v, u} C\ninst✝³ : HasZeroObject C\ninst✝² : HasShift C ℤ\ninst✝¹ : Preadditive C\ninst✝ : ∀ (n : ℤ), (shiftFunctor C n).Additive\nhC : Pretriangulated C\nT : Triangle C\nH : T ∈ distinguishedTriangles\nc : (contractibleTriangle T.obj₁).obj₃ ⟶ T.obj₃\nhc :\n (contractible... | [
"C : Type u\ninst✝⁴ : Category.{v, u} C\ninst✝³ : HasZeroObject C\ninst✝² : HasShift C ℤ\ninst✝¹ : Preadditive C\ninst✝ : ∀ (n : ℤ), (shiftFunctor C n).Additive\nhC : Pretriangulated C\nT : Triangle C\nH : T ∈ distinguishedTriangles\nc : (contractibleTriangle T.obj₁).obj₃ ⟶ T.obj₃\nhc :\n (contractibleTriangle T.o... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.Pretriangulated | {
"line": 150,
"column": 2
} | {
"line": 150,
"column": 13
} | {
"line": 150,
"column": 14
} | [
{
"pp": "C : Type u\ninst✝⁴ : Category.{v, u} C\ninst✝³ : HasZeroObject C\ninst✝² : HasShift C ℤ\ninst✝¹ : Preadditive C\ninst✝ : ∀ (n : ℤ), (shiftFunctor C n).Additive\nhC : Pretriangulated C\nT : Triangle C\nH : T ∈ distinguishedTriangles\nH₂ : T.rotate.rotate ∈ distinguishedTriangles\n⊢ T.mor₃ ≫ (shiftFuncto... | [
"C : Type u\ninst✝⁴ : Category.{v, u} C\ninst✝³ : HasZeroObject C\ninst✝² : HasShift C ℤ\ninst✝¹ : Preadditive C\ninst✝ : ∀ (n : ℤ), (shiftFunctor C n).Additive\nhC : Pretriangulated C\nT : Triangle C\nH : T ∈ distinguishedTriangles\nH₂ : T.rotate.rotate ∈ distinguishedTriangles\n⊢ T.mor₃ ≫ (shiftFunctor C 1).map T... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.Pretriangulated | {
"line": 250,
"column": 15
} | {
"line": 250,
"column": 26
} | {
"line": 250,
"column": 27
} | [
{
"pp": "C : Type u\ninst✝⁴ : Category.{v, u} C\ninst✝³ : HasZeroObject C\ninst✝² : HasShift C ℤ\ninst✝¹ : Preadditive C\ninst✝ : ∀ (n : ℤ), (CategoryTheory.shiftFunctor C n).Additive\nhC : Pretriangulated C\nT : Triangle C\nhT : T ∈ distinguishedTriangles\nX : C\nf : T.obj₂ ⟶ X\nhf : T.mor₁ ≫ f = 0\ng : T.obj₃... | [
"C : Type u\ninst✝⁴ : Category.{v, u} C\ninst✝³ : HasZeroObject C\ninst✝² : HasShift C ℤ\ninst✝¹ : Preadditive C\ninst✝ : ∀ (n : ℤ), (CategoryTheory.shiftFunctor C n).Additive\nhC : Pretriangulated C\nT : Triangle C\nhT : T ∈ distinguishedTriangles\nX : C\nf : T.obj₂ ⟶ X\nhf : T.mor₁ ≫ f = 0\ng : T.obj₃ ⟶ (mk 0 (𝟙... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.Pretriangulated | {
"line": 261,
"column": 15
} | {
"line": 261,
"column": 26
} | {
"line": 261,
"column": 27
} | [
{
"pp": "C : Type u\ninst✝⁴ : Category.{v, u} C\ninst✝³ : HasZeroObject C\ninst✝² : HasShift C ℤ\ninst✝¹ : Preadditive C\ninst✝ : ∀ (n : ℤ), (CategoryTheory.shiftFunctor C n).Additive\nhC : Pretriangulated C\nT : Triangle C\nhT : T ∈ distinguishedTriangles\nX : C\nf : X ⟶ T.obj₂\nhf : f ≫ T.mor₂ = 0\na : (contr... | [
"C : Type u\ninst✝⁴ : Category.{v, u} C\ninst✝³ : HasZeroObject C\ninst✝² : HasShift C ℤ\ninst✝¹ : Preadditive C\ninst✝ : ∀ (n : ℤ), (CategoryTheory.shiftFunctor C n).Additive\nhC : Pretriangulated C\nT : Triangle C\nhT : T ∈ distinguishedTriangles\nX : C\nf : X ⟶ T.obj₂\nhf : f ≫ T.mor₂ = 0\na : (contractibleTrian... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.Triangulated | {
"line": 124,
"column": 4
} | {
"line": 124,
"column": 46
} | {
"line": 124,
"column": 47
} | [
{
"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\nX₁ X₂ X₃ Z₁₂ Z₂₃ Z₁₃ : C\nu₁₂ : X₁ ⟶ X₂\nu₂₃ : X₂ ⟶ X₃\nu₁₃ : X₁ ⟶ X₃\ncomm : u₁₂ ≫ u₂₃ = u₁₃\nv₁₂ : X₂ ⟶ Z₁... | [
"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\nX₁ X₂ X₃ Z₁₂ Z₂₃ Z₁₃ : C\nu₁₂ : X₁ ⟶ X₂\nu₂₃ : X₂ ⟶ X₃\nu₁₃ : X₁ ⟶ X₃\ncomm : u₁₂ ≫ u₂₃ = u₁₃\nv₁₂ : X₂ ⟶ Z₁₂\nw₁₂ : Z₁₂... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.TriangleShift | {
"line": 172,
"column": 10
} | {
"line": 172,
"column": 85
} | {
"line": 173,
"column": 10
} | [
{
"pp": "case h₁\nC : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : Preadditive C\ninst✝¹ : HasShift C ℤ\ninst✝ : ∀ (n : ℤ), (CategoryTheory.shiftFunctor C n).Additive\na b c : ℤ\nT : Triangle C\n⊢ (CategoryTheory.shiftFunctorAdd' C (a + b) c (a + b + c) ⋯).hom.app T.obj₁ ≫\n (CategoryTheory.shiftFunctor C ... | [
"case h₁\nC : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : Preadditive C\ninst✝¹ : HasShift C ℤ\ninst✝ : ∀ (n : ℤ), (CategoryTheory.shiftFunctor C n).Additive\na b c : ℤ\nT : Triangle C\n⊢ (CategoryTheory.shiftFunctorAdd' C (a + b) c (a + b + c) ⋯).hom.app T.obj₁ ≫\n (CategoryTheory.shiftFunctor C c).map ((Cat... | rw [← shiftFunctorAdd'_assoc_hom_app a b c _ _ _ rfl rfl (add_assoc a b c)] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.CategoryTheory.Triangulated.Pretriangulated | {
"line": 360,
"column": 2
} | {
"line": 360,
"column": 44
} | {
"line": 362,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝⁴ : Category.{v, u} C\ninst✝³ : HasZeroObject C\ninst✝² : HasShift C ℤ\ninst✝¹ : Preadditive C\ninst✝ : ∀ (n : ℤ), (CategoryTheory.shiftFunctor C n).Additive\nhC : Pretriangulated C\nT : Triangle C\nhT : T ∈ distinguishedTriangles\nh₁ : IsZero T.obj₁\nh₃ : IsZero T.obj₃\n⊢ T.mor₁ = 0 ∧... | [] | exact ⟨h₁.eq_of_src _ _, h₃.eq_of_tgt _ _⟩ | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.CategoryTheory.Triangulated.TriangleShift | {
"line": 172,
"column": 10
} | {
"line": 172,
"column": 85
} | {
"line": 173,
"column": 10
} | [
{
"pp": "case h₂\nC : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : Preadditive C\ninst✝¹ : HasShift C ℤ\ninst✝ : ∀ (n : ℤ), (CategoryTheory.shiftFunctor C n).Additive\na b c : ℤ\nT : Triangle C\n⊢ (CategoryTheory.shiftFunctorAdd' C (a + b) c (a + b + c) ⋯).hom.app T.obj₂ ≫\n (CategoryTheory.shiftFunctor C ... | [
"case h₂\nC : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : Preadditive C\ninst✝¹ : HasShift C ℤ\ninst✝ : ∀ (n : ℤ), (CategoryTheory.shiftFunctor C n).Additive\na b c : ℤ\nT : Triangle C\n⊢ (CategoryTheory.shiftFunctorAdd' C (a + b) c (a + b + c) ⋯).hom.app T.obj₂ ≫\n (CategoryTheory.shiftFunctor C c).map ((Cat... | rw [← shiftFunctorAdd'_assoc_hom_app a b c _ _ _ rfl rfl (add_assoc a b c)] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.CategoryTheory.Triangulated.TriangleShift | {
"line": 172,
"column": 10
} | {
"line": 172,
"column": 85
} | {
"line": 173,
"column": 10
} | [
{
"pp": "case h₃\nC : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : Preadditive C\ninst✝¹ : HasShift C ℤ\ninst✝ : ∀ (n : ℤ), (CategoryTheory.shiftFunctor C n).Additive\na b c : ℤ\nT : Triangle C\n⊢ (CategoryTheory.shiftFunctorAdd' C (a + b) c (a + b + c) ⋯).hom.app T.obj₃ ≫\n (CategoryTheory.shiftFunctor C ... | [
"case h₃\nC : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : Preadditive C\ninst✝¹ : HasShift C ℤ\ninst✝ : ∀ (n : ℤ), (CategoryTheory.shiftFunctor C n).Additive\na b c : ℤ\nT : Triangle C\n⊢ (CategoryTheory.shiftFunctorAdd' C (a + b) c (a + b + c) ⋯).hom.app T.obj₃ ≫\n (CategoryTheory.shiftFunctor C c).map ((Cat... | rw [← shiftFunctorAdd'_assoc_hom_app a b c _ _ _ rfl rfl (add_assoc a b c)] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.CategoryTheory.Triangulated.Pretriangulated | {
"line": 494,
"column": 4
} | {
"line": 494,
"column": 43
} | {
"line": 494,
"column": 44
} | [
{
"pp": "case refine_1\nC : Type u\ninst✝⁴ : Category.{v, u} C\ninst✝³ : HasZeroObject C\ninst✝² : HasShift C ℤ\ninst✝¹ : Preadditive C\ninst✝ : ∀ (n : ℤ), (shiftFunctor C n).Additive\nhC : Pretriangulated C\nT T' : Triangle C\nφ : T ⟶ T'\nhT : T ∈ distinguishedTriangles\nhT' : T' ∈ distinguishedTriangles\nh₁ :... | [
"case refine_1\nC : Type u\ninst✝⁴ : Category.{v, u} C\ninst✝³ : HasZeroObject C\ninst✝² : HasShift C ℤ\ninst✝¹ : Preadditive C\ninst✝ : ∀ (n : ℤ), (shiftFunctor C n).Additive\nhC : Pretriangulated C\nT T' : Triangle C\nφ : T ⟶ T'\nhT : T ∈ distinguishedTriangles\nhT' : T' ∈ distinguishedTriangles\nh₁ : IsIso φ.hom... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.Pretriangulated | {
"line": 587,
"column": 4
} | {
"line": 587,
"column": 19
} | {
"line": 587,
"column": 20
} | [
{
"pp": "case h₀\nC : Type u\ninst✝⁴ : Category.{v, u} C\ninst✝³ : HasZeroObject C\ninst✝² : HasShift C ℤ\ninst✝¹ : Preadditive C\ninst✝ : ∀ (n : ℤ), (shiftFunctor C n).Additive\nhC : Pretriangulated C\nT : Triangle C\nhT : T ∈ distinguishedTriangles\nzero : T.mor₃ = 0\nthis✝ : Epi T.mor₂\nthis : IsSplitEpi T.m... | [
"case h₀\nC : Type u\ninst✝⁴ : Category.{v, u} C\ninst✝³ : HasZeroObject C\ninst✝² : HasShift C ℤ\ninst✝¹ : Preadditive C\ninst✝ : ∀ (n : ℤ), (shiftFunctor C n).Additive\nhC : Pretriangulated C\nT : Triangle C\nhT : T ∈ distinguishedTriangles\nzero : T.mor₃ = 0\nthis✝ : Epi T.mor₂\nthis : IsSplitEpi T.mor₂\nfst : T... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.Pretriangulated | {
"line": 588,
"column": 4
} | {
"line": 588,
"column": 19
} | {
"line": 588,
"column": 20
} | [
{
"pp": "case h₁\nC : Type u\ninst✝⁴ : Category.{v, u} C\ninst✝³ : HasZeroObject C\ninst✝² : HasShift C ℤ\ninst✝¹ : Preadditive C\ninst✝ : ∀ (n : ℤ), (shiftFunctor C n).Additive\nhC : Pretriangulated C\nT : Triangle C\nhT : T ∈ distinguishedTriangles\nzero : T.mor₃ = 0\nthis✝ : Epi T.mor₂\nthis : IsSplitEpi T.m... | [
"case h₁\nC : Type u\ninst✝⁴ : Category.{v, u} C\ninst✝³ : HasZeroObject C\ninst✝² : HasShift C ℤ\ninst✝¹ : Preadditive C\ninst✝ : ∀ (n : ℤ), (shiftFunctor C n).Additive\nhC : Pretriangulated C\nT : Triangle C\nhT : T ∈ distinguishedTriangles\nzero : T.mor₃ = 0\nthis✝ : Epi T.mor₂\nthis : IsSplitEpi T.mor₂\nfst : T... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.Pretriangulated | {
"line": 652,
"column": 6
} | {
"line": 652,
"column": 46
} | {
"line": 652,
"column": 47
} | [
{
"pp": "C : Type u\ninst✝⁸ : Category.{v, u} C\ninst✝⁷ : HasZeroObject C\ninst✝⁶ : HasShift C ℤ\ninst✝⁵ : Preadditive C\ninst✝⁴ : ∀ (n : ℤ), (shiftFunctor C n).Additive\nhC : Pretriangulated C\nJ : Type u_1\nT : J → Triangle C\nhT : ∀ (j : J), T j ∈ distinguishedTriangles\ninst✝³ : HasProduct fun j ↦ (T j).obj... | [
"C : Type u\ninst✝⁸ : Category.{v, u} C\ninst✝⁷ : HasZeroObject C\ninst✝⁶ : HasShift C ℤ\ninst✝⁵ : Preadditive C\ninst✝⁴ : ∀ (n : ℤ), (shiftFunctor C n).Additive\nhC : Pretriangulated C\nJ : Type u_1\nT : J → Triangle C\nhT : ∀ (j : J), T j ∈ distinguishedTriangles\ninst✝³ : HasProduct fun j ↦ (T j).obj₁\ninst✝² : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.Pretriangulated | {
"line": 662,
"column": 6
} | {
"line": 662,
"column": 17
} | {
"line": 662,
"column": 18
} | [
{
"pp": "C : Type u\ninst✝⁸ : Category.{v, u} C\ninst✝⁷ : HasZeroObject C\ninst✝⁶ : HasShift C ℤ\ninst✝⁵ : Preadditive C\ninst✝⁴ : ∀ (n : ℤ), (shiftFunctor C n).Additive\nhC : Pretriangulated C\nJ : Type u_1\nT : J → Triangle C\nhT : ∀ (j : J), T j ∈ distinguishedTriangles\ninst✝³ : HasProduct fun j ↦ (T j).obj... | [
"C : Type u\ninst✝⁸ : Category.{v, u} C\ninst✝⁷ : HasZeroObject C\ninst✝⁶ : HasShift C ℤ\ninst✝⁵ : Preadditive C\ninst✝⁴ : ∀ (n : ℤ), (shiftFunctor C n).Additive\nhC : Pretriangulated C\nJ : Type u_1\nT : J → Triangle C\nhT : ∀ (j : J), T j ∈ distinguishedTriangles\ninst✝³ : HasProduct fun j ↦ (T j).obj₁\ninst✝² : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.HomotopyCategory.Pretriangulated | {
"line": 563,
"column": 4
} | {
"line": 567,
"column": 50
} | {
"line": 567,
"column": 51
} | [
{
"pp": "case refine_1\nC : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Preadditive C\ninst✝ : HasBinaryBiproducts C\nT₁ T₂ : Triangle (HomotopyCategory C (ComplexShape.up ℤ))\na : T₁.obj₁ ⟶ T₂.obj₁\nb : T₁.obj₂ ⟶ T₂.obj₂\nfac : T₁.mor₁ ≫ b = a ≫ T₂.mor₁\nK₁ L₁ : CochainComplex C ℤ\nφ₁ : K₁ ⟶ L₁\ne₁ : T₁... | [
"case refine_1\nC : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Preadditive C\ninst✝ : HasBinaryBiproducts C\nT₁ T₂ : Triangle (HomotopyCategory C (ComplexShape.up ℤ))\na : T₁.obj₁ ⟶ T₂.obj₁\nb : T₁.obj₂ ⟶ T₂.obj₂\nfac : T₁.mor₁ ≫ b = a ≫ T₂.mor₁\nK₁ L₁ : CochainComplex C ℤ\nφ₁ : K₁ ⟶ L₁\ne₁ : T₁ ≅ triangleh... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.HomotopyCategory.Pretriangulated | {
"line": 569,
"column": 4
} | {
"line": 572,
"column": 50
} | {
"line": 572,
"column": 51
} | [
{
"pp": "case refine_2\nC : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Preadditive C\ninst✝ : HasBinaryBiproducts C\nT₁ T₂ : Triangle (HomotopyCategory C (ComplexShape.up ℤ))\na : T₁.obj₁ ⟶ T₂.obj₁\nb : T₁.obj₂ ⟶ T₂.obj₂\nfac : T₁.mor₁ ≫ b = a ≫ T₂.mor₁\nK₁ L₁ : CochainComplex C ℤ\nφ₁ : K₁ ⟶ L₁\ne₁ : T₁... | [
"case refine_2\nC : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Preadditive C\ninst✝ : HasBinaryBiproducts C\nT₁ T₂ : Triangle (HomotopyCategory C (ComplexShape.up ℤ))\na : T₁.obj₁ ⟶ T₂.obj₁\nb : T₁.obj₂ ⟶ T₂.obj₂\nfac : T₁.mor₁ ≫ b = a ≫ T₂.mor₁\nK₁ L₁ : CochainComplex C ℤ\nφ₁ : K₁ ⟶ L₁\ne₁ : T₁ ≅ triangleh... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.Functor | {
"line": 95,
"column": 6
} | {
"line": 96,
"column": 64
} | {
"line": 96,
"column": 64
} | [
{
"pp": "C : Type u_1\nD : Type u_2\nE : Type u_3\ninst✝¹⁰ : Category.{v_1, u_1} C\ninst✝⁹ : Category.{v_2, u_2} D\ninst✝⁸ : Category.{v_3, u_3} E\ninst✝⁷ : HasShift C ℤ\ninst✝⁶ : HasShift D ℤ\ninst✝⁵ : HasShift E ℤ\nF : C ⥤ D\ninst✝⁴ : F.CommShift ℤ\nG : D ⥤ E\ninst✝³ : G.CommShift ℤ\ninst✝² : Preadditive C\ni... | [] | simp only [comp_obj, assoc, Iso.inv_hom_id_app_assoc,
← Functor.map_comp, Iso.inv_hom_id_app, map_id, comp_id] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.CategoryTheory.Triangulated.Functor | {
"line": 332,
"column": 14
} | {
"line": 332,
"column": 25
} | {
"line": 332,
"column": 26
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝¹³ : Category.{v_1, u_1} C\ninst✝¹² : Category.{v_2, u_2} D\ninst✝¹¹ : HasShift C ℤ\ninst✝¹⁰ : HasShift D ℤ\ninst✝⁹ : HasZeroObject C\ninst✝⁸ : HasZeroObject D\ninst✝⁷ : Preadditive C\ninst✝⁶ : Preadditive D\ninst✝⁵ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝⁴ : ∀ (... | [
"C : Type u_1\nD : Type u_2\ninst✝¹³ : Category.{v_1, u_1} C\ninst✝¹² : Category.{v_2, u_2} D\ninst✝¹¹ : HasShift C ℤ\ninst✝¹⁰ : HasShift D ℤ\ninst✝⁹ : HasZeroObject C\ninst✝⁸ : HasZeroObject D\ninst✝⁷ : Preadditive C\ninst✝⁶ : Preadditive D\ninst✝⁵ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝⁴ : ∀ (n : ℤ), (shi... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.Functor | {
"line": 333,
"column": 14
} | {
"line": 333,
"column": 25
} | {
"line": 333,
"column": 26
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝¹³ : Category.{v_1, u_1} C\ninst✝¹² : Category.{v_2, u_2} D\ninst✝¹¹ : HasShift C ℤ\ninst✝¹⁰ : HasShift D ℤ\ninst✝⁹ : HasZeroObject C\ninst✝⁸ : HasZeroObject D\ninst✝⁷ : Preadditive C\ninst✝⁶ : Preadditive D\ninst✝⁵ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝⁴ : ∀ (... | [
"C : Type u_1\nD : Type u_2\ninst✝¹³ : Category.{v_1, u_1} C\ninst✝¹² : Category.{v_2, u_2} D\ninst✝¹¹ : HasShift C ℤ\ninst✝¹⁰ : HasShift D ℤ\ninst✝⁹ : HasZeroObject C\ninst✝⁸ : HasZeroObject D\ninst✝⁷ : Preadditive C\ninst✝⁶ : Preadditive D\ninst✝⁵ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝⁴ : ∀ (n : ℤ), (shi... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.Functor | {
"line": 334,
"column": 14
} | {
"line": 334,
"column": 25
} | {
"line": 334,
"column": 26
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝¹³ : Category.{v_1, u_1} C\ninst✝¹² : Category.{v_2, u_2} D\ninst✝¹¹ : HasShift C ℤ\ninst✝¹⁰ : HasShift D ℤ\ninst✝⁹ : HasZeroObject C\ninst✝⁸ : HasZeroObject D\ninst✝⁷ : Preadditive C\ninst✝⁶ : Preadditive D\ninst✝⁵ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝⁴ : ∀ (... | [
"C : Type u_1\nD : Type u_2\ninst✝¹³ : Category.{v_1, u_1} C\ninst✝¹² : Category.{v_2, u_2} D\ninst✝¹¹ : HasShift C ℤ\ninst✝¹⁰ : HasShift D ℤ\ninst✝⁹ : HasZeroObject C\ninst✝⁸ : HasZeroObject D\ninst✝⁷ : Preadditive C\ninst✝⁶ : Preadditive D\ninst✝⁵ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝⁴ : ∀ (n : ℤ), (shi... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.Functor | {
"line": 335,
"column": 14
} | {
"line": 335,
"column": 25
} | {
"line": 335,
"column": 26
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝¹³ : Category.{v_1, u_1} C\ninst✝¹² : Category.{v_2, u_2} D\ninst✝¹¹ : HasShift C ℤ\ninst✝¹⁰ : HasShift D ℤ\ninst✝⁹ : HasZeroObject C\ninst✝⁸ : HasZeroObject D\ninst✝⁷ : Preadditive C\ninst✝⁶ : Preadditive D\ninst✝⁵ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝⁴ : ∀ (... | [
"C : Type u_1\nD : Type u_2\ninst✝¹³ : Category.{v_1, u_1} C\ninst✝¹² : Category.{v_2, u_2} D\ninst✝¹¹ : HasShift C ℤ\ninst✝¹⁰ : HasShift D ℤ\ninst✝⁹ : HasZeroObject C\ninst✝⁸ : HasZeroObject D\ninst✝⁷ : Preadditive C\ninst✝⁶ : Preadditive D\ninst✝⁵ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝⁴ : ∀ (n : ℤ), (shi... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.Functor | {
"line": 379,
"column": 37
} | {
"line": 379,
"column": 48
} | {
"line": 379,
"column": 49
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝¹⁶ : Category.{v_1, u_1} C\ninst✝¹⁵ : Category.{v_2, u_2} D\ninst✝¹⁴ : HasShift C ℤ\ninst✝¹³ : HasShift D ℤ\ninst✝¹² : HasZeroObject C\ninst✝¹¹ : HasZeroObject D\ninst✝¹⁰ : Preadditive C\ninst✝⁹ : Preadditive D\ninst✝⁸ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝⁷ : ... | [
"C : Type u_1\nD : Type u_2\ninst✝¹⁶ : Category.{v_1, u_1} C\ninst✝¹⁵ : Category.{v_2, u_2} D\ninst✝¹⁴ : HasShift C ℤ\ninst✝¹³ : HasShift D ℤ\ninst✝¹² : HasZeroObject C\ninst✝¹¹ : HasZeroObject D\ninst✝¹⁰ : Preadditive C\ninst✝⁹ : Preadditive D\ninst✝⁸ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝⁷ : ∀ (n : ℤ), (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.Functor | {
"line": 381,
"column": 10
} | {
"line": 381,
"column": 75
} | {
"line": 381,
"column": 76
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝¹⁶ : Category.{v_1, u_1} C\ninst✝¹⁵ : Category.{v_2, u_2} D\ninst✝¹⁴ : HasShift C ℤ\ninst✝¹³ : HasShift D ℤ\ninst✝¹² : HasZeroObject C\ninst✝¹¹ : HasZeroObject D\ninst✝¹⁰ : Preadditive C\ninst✝⁹ : Preadditive D\ninst✝⁸ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝⁷ : ... | [
"C : Type u_1\nD : Type u_2\ninst✝¹⁶ : Category.{v_1, u_1} C\ninst✝¹⁵ : Category.{v_2, u_2} D\ninst✝¹⁴ : HasShift C ℤ\ninst✝¹³ : HasShift D ℤ\ninst✝¹² : HasZeroObject C\ninst✝¹¹ : HasZeroObject D\ninst✝¹⁰ : Preadditive C\ninst✝⁹ : Preadditive D\ninst✝⁸ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝⁷ : ∀ (n : ℤ), (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.Functor | {
"line": 382,
"column": 37
} | {
"line": 382,
"column": 48
} | {
"line": 382,
"column": 49
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝¹⁶ : Category.{v_1, u_1} C\ninst✝¹⁵ : Category.{v_2, u_2} D\ninst✝¹⁴ : HasShift C ℤ\ninst✝¹³ : HasShift D ℤ\ninst✝¹² : HasZeroObject C\ninst✝¹¹ : HasZeroObject D\ninst✝¹⁰ : Preadditive C\ninst✝⁹ : Preadditive D\ninst✝⁸ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝⁷ : ... | [
"C : Type u_1\nD : Type u_2\ninst✝¹⁶ : Category.{v_1, u_1} C\ninst✝¹⁵ : Category.{v_2, u_2} D\ninst✝¹⁴ : HasShift C ℤ\ninst✝¹³ : HasShift D ℤ\ninst✝¹² : HasZeroObject C\ninst✝¹¹ : HasZeroObject D\ninst✝¹⁰ : Preadditive C\ninst✝⁹ : Preadditive D\ninst✝⁸ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝⁷ : ∀ (n : ℤ), (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.Functor | {
"line": 384,
"column": 10
} | {
"line": 384,
"column": 75
} | {
"line": 384,
"column": 76
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝¹⁶ : Category.{v_1, u_1} C\ninst✝¹⁵ : Category.{v_2, u_2} D\ninst✝¹⁴ : HasShift C ℤ\ninst✝¹³ : HasShift D ℤ\ninst✝¹² : HasZeroObject C\ninst✝¹¹ : HasZeroObject D\ninst✝¹⁰ : Preadditive C\ninst✝⁹ : Preadditive D\ninst✝⁸ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝⁷ : ... | [
"C : Type u_1\nD : Type u_2\ninst✝¹⁶ : Category.{v_1, u_1} C\ninst✝¹⁵ : Category.{v_2, u_2} D\ninst✝¹⁴ : HasShift C ℤ\ninst✝¹³ : HasShift D ℤ\ninst✝¹² : HasZeroObject C\ninst✝¹¹ : HasZeroObject D\ninst✝¹⁰ : Preadditive C\ninst✝⁹ : Preadditive D\ninst✝⁸ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝⁷ : ∀ (n : ℤ), (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.Functor | {
"line": 385,
"column": 18
} | {
"line": 385,
"column": 57
} | {
"line": 385,
"column": 58
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝¹⁶ : Category.{v_1, u_1} C\ninst✝¹⁵ : Category.{v_2, u_2} D\ninst✝¹⁴ : HasShift C ℤ\ninst✝¹³ : HasShift D ℤ\ninst✝¹² : HasZeroObject C\ninst✝¹¹ : HasZeroObject D\ninst✝¹⁰ : Preadditive C\ninst✝⁹ : Preadditive D\ninst✝⁸ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝⁷ : ... | [
"C : Type u_1\nD : Type u_2\ninst✝¹⁶ : Category.{v_1, u_1} C\ninst✝¹⁵ : Category.{v_2, u_2} D\ninst✝¹⁴ : HasShift C ℤ\ninst✝¹³ : HasShift D ℤ\ninst✝¹² : HasZeroObject C\ninst✝¹¹ : HasZeroObject D\ninst✝¹⁰ : Preadditive C\ninst✝⁹ : Preadditive D\ninst✝⁸ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝⁷ : ∀ (n : ℤ), (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Shift.ShiftSequence | {
"line": 161,
"column": 50
} | {
"line": 162,
"column": 45
} | {
"line": 164,
"column": 0
} | [
{
"pp": "C : Type u_1\nA : Type u_3\ninst✝⁴ : Category.{v_1, u_1} C\ninst✝³ : Category.{v_3, u_3} A\nF : C ⥤ A\nM : Type u_4\ninst✝² : AddMonoid M\ninst✝¹ : HasShift C M\ninst✝ : F.ShiftSequence M\nn m a a' a'' : M\nha' : n + a = a'\nha'' : m + a' = a''\nX : C\n⊢ (F.shiftIso (m + n) a a'' ⋯).hom.app X =\n (F... | [] | by
simp [F.shiftIso_add n m a a' a'' ha' ha''] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Shift.ShiftSequence | {
"line": 169,
"column": 65
} | {
"line": 170,
"column": 45
} | {
"line": 172,
"column": 0
} | [
{
"pp": "C : Type u_1\nA : Type u_3\ninst✝⁴ : Category.{v_1, u_1} C\ninst✝³ : Category.{v_3, u_3} A\nF : C ⥤ A\nM : Type u_4\ninst✝² : AddMonoid M\ninst✝¹ : HasShift C M\ninst✝ : F.ShiftSequence M\nn m a a' a'' : M\nha' : n + a = a'\nha'' : m + a' = a''\nX : C\n⊢ (F.shiftIso (m + n) a a'' ⋯).inv.app X =\n (F... | [] | by
simp [F.shiftIso_add n m a a' a'' ha' ha''] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.PathCategory.MorphismProperty | {
"line": 40,
"column": 2
} | {
"line": 40,
"column": 51
} | {
"line": 42,
"column": 0
} | [
{
"pp": "case mpr\nV : Type u₁\ninst✝ : Quiver V\nP : MorphismProperty (Paths V)\nid : ∀ {v : V}, P (𝟙 ((of V).obj v))\ncomp : ∀ {u v w : V} (p : (of V).obj u ⟶ (of V).obj v) (q : v ⟶ w), P p → P (p ≫ (of V).map q)\nX✝ Y✝ : Paths V\nf✝ : X✝ ⟶ Y✝\n⊢ ⊤ f✝ → P f✝",
"ppTerm": "?mpr",
"assigned": true,
... | [] | · exact fun _ ↦ induction (fun f ↦ P f) id comp _ | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.CategoryTheory.PathCategory.MorphismProperty | {
"line": 124,
"column": 13
} | {
"line": 124,
"column": 24
} | {
"line": 124,
"column": 25
} | [
{
"pp": "case refine_1.nil\nC : Type u_1\ninst✝ : Category.{v_1, u_1} C\nW : MorphismProperty C\nX Y Z : C\np : Path X Y\nh : W.paths (p.comp Path.nil)\n⊢ W.paths p",
"ppTerm": "?refine_1.nil",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case refine_1.nil\nC : Type u_1\ninst✝ : Category.{v_1, u_1} C\nW : MorphismProperty C\nX Y Z : C\np : Path X Y\nh : W.paths (p.comp Path.nil)\n⊢ W.paths p"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.PathCategory.MorphismProperty | {
"line": 161,
"column": 4
} | {
"line": 161,
"column": 23
} | {
"line": 161,
"column": 24
} | [
{
"pp": "case nil\nC : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\nW : MorphismProperty C\ninst✝ : W.IsStableUnderComposition\nX Y : C\np : Path X Y\nc✝ : C\nf : X ⟶ c✝\nhp : W.paths Path.nil → 0 < Path.nil.length → W (composePath Path.nil)\nhp' : W.paths (Path.nil.cons f)\nhp'' : 0 < (Path.nil.cons f).length\n⊢ ... | [
"case nil\nC : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\nW : MorphismProperty C\ninst✝ : W.IsStableUnderComposition\nX Y : C\np : Path X Y\nc✝ : C\nf : X ⟶ c✝\nhp : W.paths Path.nil → 0 < Path.nil.length → W (composePath Path.nil)\nhp' : W.paths (Path.nil.cons f)\nhp'' : 0 < (Path.nil.cons f).length\n⊢ W f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.HomologySequence | {
"line": 340,
"column": 2
} | {
"line": 340,
"column": 26
} | {
"line": 340,
"column": 27
} | [
{
"pp": "C : Type u_1\nι : Type u_2\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Abelian C\nc : ComplexShape ι\nS : ShortComplex (HomologicalComplex C c)\nhS : S.ShortExact\ni j : ι\nhij : c.Rel i j\nA : C\nx₃ : A ⟶ S.X₃.X i\nhx₃ : x₃ ≫ S.X₃.d i j = 0\nx₂ : A ⟶ S.X₂.X i\nhx₂ : x₂ ≫ S.g.f i = x₃\nx₁ : A ⟶ S.X₁.X j\n... | [
"C : Type u_1\nι : Type u_2\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Abelian C\nc : ComplexShape ι\nS : ShortComplex (HomologicalComplex C c)\nhS : S.ShortExact\ni j : ι\nhij : c.Rel i j\nA : C\nx₃ : A ⟶ S.X₃.X i\nhx₃ : x₃ ≫ S.X₃.d i j = 0\nx₂ : A ⟶ S.X₂.X i\nhx₂ : x₂ ≫ S.g.f i = x₃\nx₁ : A ⟶ S.X₁.X j\nhx₁ : x₁ ≫ S... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Localization.Construction | {
"line": 128,
"column": 35
} | {
"line": 128,
"column": 85
} | {
"line": 128,
"column": 85
} | [
{
"pp": "C : Type uC\ninst✝¹ : Category.{uC', uC} C\nW : MorphismProperty C\nD : Type uD\ninst✝ : Category.{uD', uD} D\nX Y : C\nw : X ⟶ Y\nhw : W w\n⊢ (Paths.of (LocQuiver W)).obj { obj := Y } ⟶ (Paths.of (LocQuiver W)).obj { obj := X }",
"ppTerm": "?m.41",
"assigned": true,
"usedConstants": [
... | [] | by dsimp; exact (Paths.of _).map (Sum.inr ⟨w, hw⟩) | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Localization.Construction | {
"line": 161,
"column": 27
} | {
"line": 161,
"column": 42
} | {
"line": 161,
"column": 42
} | [
{
"pp": "case id\nC : Type uC\ninst✝¹ : Category.{uC', uC} C\nW : MorphismProperty C\nD : Type uD\ninst✝ : Category.{uD', uD} D\nG : C ⥤ D\nhG : W.IsInvertedBy G\nX✝ : C\nX Y : Paths (LocQuiver W)\n⊢ (liftToPathCategory G hG).map (ψ₁ W (𝟙 X✝)) = (liftToPathCategory G hG).map (𝟙 (ιPaths W X✝))",
"ppTerm": ... | [] | all_goals aesop | Lean.Elab.Tactic.evalAllGoals | Lean.Parser.Tactic.allGoals |
Mathlib.CategoryTheory.Localization.Construction | {
"line": 161,
"column": 27
} | {
"line": 161,
"column": 42
} | {
"line": 161,
"column": 42
} | [
{
"pp": "case comp\nC : Type uC\ninst✝¹ : Category.{uC', uC} C\nW : MorphismProperty C\nD : Type uD\ninst✝ : Category.{uD', uD} D\nG : C ⥤ D\nhG : W.IsInvertedBy G\nX✝ Y✝¹ : C\nX Y : Paths (LocQuiver W)\nY✝ : C\nf✝ : X✝ ⟶ Y✝\ng✝ : Y✝ ⟶ Y✝¹\n⊢ (liftToPathCategory G hG).map (ψ₁ W (f✝ ≫ g✝)) = (liftToPathCategory ... | [] | all_goals aesop | Lean.Elab.Tactic.evalAllGoals | Lean.Parser.Tactic.allGoals |
Mathlib.CategoryTheory.Localization.Construction | {
"line": 161,
"column": 27
} | {
"line": 161,
"column": 42
} | {
"line": 161,
"column": 42
} | [
{
"pp": "case Winv₁\nC : Type uC\ninst✝¹ : Category.{uC', uC} C\nW : MorphismProperty C\nD : Type uD\ninst✝ : Category.{uD', uD} D\nG : C ⥤ D\nhG : W.IsInvertedBy G\nX✝ : C\nX Y : Paths (LocQuiver W)\nY✝ : C\nw✝ : X✝ ⟶ Y✝\nhw✝ : W w✝\n⊢ (liftToPathCategory G hG).map (ψ₁ W w✝ ≫ ψ₂ W w✝ hw✝) = (liftToPathCategory... | [] | all_goals aesop | Lean.Elab.Tactic.evalAllGoals | Lean.Parser.Tactic.allGoals |
Mathlib.CategoryTheory.Localization.Construction | {
"line": 161,
"column": 27
} | {
"line": 161,
"column": 42
} | {
"line": 161,
"column": 42
} | [
{
"pp": "case Winv₂\nC : Type uC\ninst✝¹ : Category.{uC', uC} C\nW : MorphismProperty C\nD : Type uD\ninst✝ : Category.{uD', uD} D\nG : C ⥤ D\nhG : W.IsInvertedBy G\nX✝¹ : C\nX Y : Paths (LocQuiver W)\nX✝ : C\nw✝ : X✝ ⟶ X✝¹\nhw✝ : W w✝\n⊢ (liftToPathCategory G hG).map (ψ₂ W w✝ hw✝ ≫ ψ₁ W w✝) = (liftToPathCatego... | [] | all_goals aesop | Lean.Elab.Tactic.evalAllGoals | Lean.Parser.Tactic.allGoals |
Mathlib.CategoryTheory.Localization.CalculusOfFractions | {
"line": 253,
"column": 32
} | {
"line": 253,
"column": 67
} | {
"line": 253,
"column": 68
} | [
{
"pp": "C : Type u_1\ninst✝ : Category.{v_1, u_1} C\nW : MorphismProperty C\nX Y : C\nz : W.LeftFraction X Y\n⊢ W (z.s ≫ 𝟙 z.Y')",
"ppTerm": "?m.34",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"Ca... | [
"C : Type u_1\ninst✝ : Category.{v_1, u_1} C\nW : MorphismProperty C\nX Y : C\nz : W.LeftFraction X Y\n⊢ W z.s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Localization.CalculusOfFractions | {
"line": 258,
"column": 43
} | {
"line": 258,
"column": 67
} | {
"line": 258,
"column": 68
} | [
{
"pp": "C : Type u_1\ninst✝ : Category.{v_1, u_1} C\nW : MorphismProperty C\nX Y : C\nz₁ z₂ : W.LeftFraction X Y\nZ : C\nt₁ : z₁.Y' ⟶ Z\nt₂ : z₂.Y' ⟶ Z\nhst : z₁.s ≫ t₁ = z₂.s ≫ t₂\nhft : z₁.f ≫ t₁ = z₂.f ≫ t₂\nht : W (z₁.s ≫ t₁)\n⊢ W (z₂.s ≫ t₂)",
"ppTerm": "?m.69",
"assigned": true,
"usedConstant... | [
"C : Type u_1\ninst✝ : Category.{v_1, u_1} C\nW : MorphismProperty C\nX Y : C\nz₁ z₂ : W.LeftFraction X Y\nZ : C\nt₁ : z₁.Y' ⟶ Z\nt₂ : z₂.Y' ⟶ Z\nhst : z₁.s ≫ t₁ = z₂.s ≫ t₂\nhft : z₁.f ≫ t₁ = z₂.f ≫ t₂\nht : W (z₁.s ≫ t₁)\n⊢ W (z₁.s ≫ t₁)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Localization.CalculusOfFractions | {
"line": 270,
"column": 4
} | {
"line": 270,
"column": 57
} | {
"line": 270,
"column": 58
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\nW : MorphismProperty C\nX Y : C\nz₁ z₂ z₃ : W.LeftFraction X Y\ninst✝ : W.HasLeftCalculusOfFractions\nZ₄ : C\nt₁ : z₁.Y' ⟶ Z₄\nt₂ : z₂.Y' ⟶ Z₄\nhst : z₁.s ≫ t₁ = z₂.s ≫ t₂\nhft : z₁.f ≫ t₁ = z₂.f ≫ t₂\nht : W (z₁.s ≫ t₁)\nZ₅ : C\nu₂ : z₂.Y' ⟶ Z₅\nu₃ : z₃.Y'... | [
"C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\nW : MorphismProperty C\nX Y : C\nz₁ z₂ z₃ : W.LeftFraction X Y\ninst✝ : W.HasLeftCalculusOfFractions\nZ₄ : C\nt₁ : z₁.Y' ⟶ Z₄\nt₂ : z₂.Y' ⟶ Z₄\nhst : z₁.s ≫ t₁ = z₂.s ≫ t₂\nhft : z₁.f ≫ t₁ = z₂.f ≫ t₂\nht : W (z₁.s ≫ t₁)\nZ₅ : C\nu₂ : z₂.Y' ⟶ Z₅\nu₃ : z₃.Y' ⟶ Z₅\nhsu :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Localization.CalculusOfFractions | {
"line": 372,
"column": 8
} | {
"line": 372,
"column": 28
} | {
"line": 372,
"column": 29
} | [
{
"pp": "case refine_1\nC : Type u_1\nD : Type u_2\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Category.{v_2, u_2} D\nW : MorphismProperty C\ninst✝ : W.HasLeftCalculusOfFractions\nX Y Z✝ : C\nz₁✝ : Hom W X Y\nz₂✝ : Hom W Y Z✝\na : W.LeftFraction X Y\nb₁ b₂ : W.LeftFraction Y Z✝\nU : C\nt₁ : b₁.Y' ⟶ U\nt₂ : b₂.Y' ... | [
"case refine_1\nC : Type u_1\nD : Type u_2\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Category.{v_2, u_2} D\nW : MorphismProperty C\ninst✝ : W.HasLeftCalculusOfFractions\nX Y Z✝ : C\nz₁✝ : Hom W X Y\nz₂✝ : Hom W Y Z✝\na : W.LeftFraction X Y\nb₁ b₂ : W.LeftFraction Y Z✝\nU : C\nt₁ : b₁.Y' ⟶ U\nt₂ : b₂.Y' ⟶ U\nhst : b... | comp_eq _ _ z₁ fac₁, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.CategoryTheory.Shift.Localization | {
"line": 56,
"column": 33
} | {
"line": 56,
"column": 55
} | {
"line": 56,
"column": 56
} | [
{
"pp": "C : Type u₁\nD : Type u₂\ninst✝⁵ : Category.{v₁, u₁} C\ninst✝⁴ : Category.{v₂, u₂} D\nL : C ⥤ D\nW : MorphismProperty C\ninst✝³ : L.IsLocalization W\nA : Type w\ninst✝² : AddMonoid A\ninst✝¹ : HasShift C A\ninst✝ : W.IsCompatibleWithShift A\na : A\nx✝¹ x✝ : C\nf : x✝¹ ⟶ x✝\nhf : W f\n⊢ W ((shiftFunctor... | [
"C : Type u₁\nD : Type u₂\ninst✝⁵ : Category.{v₁, u₁} C\ninst✝⁴ : Category.{v₂, u₂} D\nL : C ⥤ D\nW : MorphismProperty C\ninst✝³ : L.IsLocalization W\nA : Type w\ninst✝² : AddMonoid A\ninst✝¹ : HasShift C A\ninst✝ : W.IsCompatibleWithShift A\na : A\nx✝¹ x✝ : C\nf : x✝¹ ⟶ x✝\nhf : W f\n⊢ W f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Shift.Localization | {
"line": 62,
"column": 2
} | {
"line": 62,
"column": 52
} | {
"line": 62,
"column": 53
} | [
{
"pp": "C : Type u₁\ninst✝³ : Category.{v₁, u₁} C\nW : MorphismProperty C\nA : Type w\ninst✝² : AddMonoid A\ninst✝¹ : HasShift C A\ninst✝ : W.IsCompatibleWithShift A\nX Y : C\nf : X ⟶ Y\nhf : W f\na : A\n⊢ W ((shiftFunctor C a).map f)",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
... | [
"C : Type u₁\ninst✝³ : Category.{v₁, u₁} C\nW : MorphismProperty C\nA : Type w\ninst✝² : AddMonoid A\ninst✝¹ : HasShift C A\ninst✝ : W.IsCompatibleWithShift A\nX Y : C\nf : X ⟶ Y\nhf : W f\na : A\n⊢ W f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Localization.CalculusOfFractions | {
"line": 376,
"column": 6
} | {
"line": 377,
"column": 42
} | {
"line": 378,
"column": 4
} | [
{
"pp": "case refine_1.refine_1\nC : Type u_1\nD : Type u_2\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Category.{v_2, u_2} D\nW : MorphismProperty C\ninst✝ : W.HasLeftCalculusOfFractions\nX Y Z✝ : C\nz₁✝ : Hom W X Y\nz₂✝ : Hom W Y Z✝\na : W.LeftFraction X Y\nb₁ b₂ : W.LeftFraction Y Z✝\nU : C\nt₁ : b₁.Y' ⟶ U\nt₂... | [] | simp only [assoc, ← reassoc_of% fac₁', ← reassoc_of% fac₂',
reassoc_of% hst, reassoc_of% fac₃] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.CategoryTheory.Localization.CalculusOfFractions.Fractions | {
"line": 337,
"column": 2
} | {
"line": 337,
"column": 77
} | {
"line": 338,
"column": 4
} | [
{
"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\nL : C ⥤ D\nW : MorphismProperty C\ninst✝² : L.IsLocalization W\nE : Type u_3\ninst✝¹ : Category.{v_3, u_3} E\nF : D ⥤ E\ninst✝ : W.HasLeftCalculusOfFractions\nh : ∀ ⦃X₁ X₂ : C⦄ (f g : X₁ ⟶ X₂), F.map (L.map f) =... | [
"C : Type u_1\nD : Type u_2\ninst✝⁴ : Category.{v_1, u_1} C\ninst✝³ : Category.{v_2, u_2} D\nL : C ⥤ D\nW : MorphismProperty C\ninst✝² : L.IsLocalization W\nE : Type u_3\ninst✝¹ : Category.{v_3, u_3} E\nF : D ⥤ E\ninst✝ : W.HasLeftCalculusOfFractions\nh : ∀ ⦃X₁ X₂ : C⦄ (f g : X₁ ⟶ X₂), F.map (L.map f) = F.map (L.ma... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Localization.CalculusOfFractions | {
"line": 396,
"column": 8
} | {
"line": 396,
"column": 28
} | {
"line": 396,
"column": 29
} | [
{
"pp": "case refine_2\nC : Type u_1\nD : Type u_2\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Category.{v_2, u_2} D\nW : MorphismProperty C\ninst✝ : W.HasLeftCalculusOfFractions\nX Y Z : C\nz₁✝ : Hom W X Y\nz₂✝ : Hom W Y Z\na₁ a₂ : W.LeftFraction X Y\nb : W.LeftFraction Y Z\nU : C\nt₁ : a₁.Y' ⟶ U\nt₂ : a₂.Y' ⟶ U... | [
"case refine_2\nC : Type u_1\nD : Type u_2\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Category.{v_2, u_2} D\nW : MorphismProperty C\ninst✝ : W.HasLeftCalculusOfFractions\nX Y Z : C\nz₁✝ : Hom W X Y\nz₂✝ : Hom W Y Z\na₁ a₂ : W.LeftFraction X Y\nb : W.LeftFraction Y Z\nU : C\nt₁ : a₁.Y' ⟶ U\nt₂ : a₂.Y' ⟶ U\nhst : a₁.s... | comp_eq _ _ z₁ fac₁, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.CategoryTheory.Localization.CalculusOfFractions.Preadditive | {
"line": 327,
"column": 2
} | {
"line": 328,
"column": 18
} | {
"line": 329,
"column": 2
} | [
{
"pp": "case mp\nC : Type u_1\nD : Type u_2\ninst✝⁸ : Category.{v_1, u_1} C\ninst✝⁷ : Category.{v_2, u_2} D\ninst✝⁶ : Preadditive C\nL : C ⥤ D\nW : MorphismProperty C\ninst✝⁵ : L.IsLocalization W\ninst✝⁴ : W.HasLeftCalculusOfFractions\nE : Type u_3\ninst✝³ : Category.{v_3, u_3} E\ninst✝² : Preadditive E\ninst✝... | [
"case mpr\nC : Type u_1\nD : Type u_2\ninst✝⁸ : Category.{v_1, u_1} C\ninst✝⁷ : Category.{v_2, u_2} D\ninst✝⁶ : Preadditive C\nL : C ⥤ D\nW : MorphismProperty C\ninst✝⁵ : L.IsLocalization W\ninst✝⁴ : W.HasLeftCalculusOfFractions\nE : Type u_3\ninst✝³ : Category.{v_3, u_3} E\ninst✝² : Preadditive E\ninst✝¹ : Preaddi... | · intro
infer_instance | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Order.TransfiniteIteration | {
"line": 83,
"column": 29
} | {
"line": 83,
"column": 40
} | {
"line": 83,
"column": 41
} | [
{
"pp": "I : Type u\ninst✝⁴ : CompleteLattice I\nφ : I → I\ni₀ : I\nJ : Type w\ninst✝³ : LinearOrder J\ninst✝² : OrderBot J\ninst✝¹ : SuccOrder J\ninst✝ : WellFoundedLT J\nhφ : ∀ (i : I), i ≤ φ i\nk : J\nhk : IsMin ⊥\nhkj : k ≤ ⊥\n⊢ k = ⊥",
"ppTerm": "?m.65",
"assigned": false,
"usedConstants": [],
... | [
"I : Type u\ninst✝⁴ : CompleteLattice I\nφ : I → I\ni₀ : I\nJ : Type w\ninst✝³ : LinearOrder J\ninst✝² : OrderBot J\ninst✝¹ : SuccOrder J\ninst✝ : WellFoundedLT J\nhφ : ∀ (i : I), i ≤ φ i\nk : J\nhk : IsMin ⊥\nhkj : k ≤ ⊥\n⊢ k = ⊥"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Cardinal.HasCardinalLT | {
"line": 42,
"column": 2
} | {
"line": 42,
"column": 55
} | {
"line": 42,
"column": 56
} | [
{
"pp": "X : Type u\nκ : Cardinal.{v}\nh : Cardinal.lift.{v + 1, u} (Cardinal.mk X) < Cardinal.lift.{max u (v + 1), v} κ\n⊢ Small.{v, u} X",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"Cardinal",
"Cardinal.univ",
"PartialOrder.toP... | [
"X : Type u\nκ : Cardinal.{v}\nh : Cardinal.lift.{v + 1, u} (Cardinal.mk X) < Cardinal.lift.{max u (v + 1), v} κ\n⊢ Cardinal.lift.{v + 1, u} (Cardinal.mk X) < Cardinal.univ.{v, max u (v + 1)}"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Cardinal.HasCardinalLT | {
"line": 46,
"column": 23
} | {
"line": 46,
"column": 58
} | {
"line": 46,
"column": 59
} | [
{
"pp": "X : Type u\nκ : Cardinal.{v}\nh : HasCardinalLT X κ\nκ' : Cardinal.{v}\nhκ' : κ ≤ κ'\n⊢ Cardinal.lift.{u, v} κ ≤ Cardinal.lift.{u, v} κ'",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Cardinal",
"PartialOrder.toPreorder",
"Cardinal.lift",
"... | [
"X : Type u\nκ : Cardinal.{v}\nh : HasCardinalLT X κ\nκ' : Cardinal.{v}\nhκ' : κ ≤ κ'\n⊢ κ ≤ κ'"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Cardinal.HasCardinalLT | {
"line": 80,
"column": 2
} | {
"line": 80,
"column": 29
} | {
"line": 80,
"column": 30
} | [
{
"pp": "X : Type u\n⊢ HasCardinalLT X Cardinal.aleph0 ↔ Finite X",
"ppTerm": "?m.1",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"HasCardinalLT",
"Cardinal",
"congrArg",
"Finite",
"PartialOrder.toPreorder",
"Cardinal.lift",
"... | [
"X : Type u\n⊢ Cardinal.mk X < Cardinal.aleph0 ↔ Finite X"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Cardinal.HasCardinalLT | {
"line": 109,
"column": 36
} | {
"line": 109,
"column": 47
} | {
"line": 109,
"column": 48
} | [
{
"pp": "X : Type u\nY : Type u'\nκ : Cardinal.{w}\nhκ : Cardinal.aleph0 ≤ κ\nhX : Cardinal.lift.{max w u', u} (Cardinal.mk X) < Cardinal.lift.{max u u', w} κ\nhY : Cardinal.lift.{max w u, u'} (Cardinal.mk Y) < Cardinal.lift.{max u' u, w} κ\n⊢ Cardinal.aleph0 ≤ Cardinal.lift.{max u' u, w} κ",
"ppTerm": "?m.... | [
"X : Type u\nY : Type u'\nκ : Cardinal.{w}\nhκ : Cardinal.aleph0 ≤ κ\nhX : Cardinal.lift.{max w u', u} (Cardinal.mk X) < Cardinal.lift.{max u u', w} κ\nhY : Cardinal.lift.{max w u, u'} (Cardinal.mk Y) < Cardinal.lift.{max u' u, w} κ\n⊢ Cardinal.aleph0 ≤ κ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Cardinal.HasCardinalLT | {
"line": 155,
"column": 16
} | {
"line": 155,
"column": 27
} | {
"line": 155,
"column": 28
} | [
{
"pp": "ι : Type u\nα : ι → Type v\nκ : Cardinal.{w}\ninst✝ : Fact κ.IsRegular\nhι : HasCardinalLT ι κ\nhα : ∀ (i : ι), HasCardinalLT (α i) κ\nthis : Fact (Cardinal.lift.{max u v, w} κ).IsRegular\ni : ULift.{max v w, u} ι\n⊢ HasCardinalLT (ULift.{max u w, v} (α i.down)) (Cardinal.lift.{max u v, w} κ)",
"pp... | [
"ι : Type u\nα : ι → Type v\nκ : Cardinal.{w}\ninst✝ : Fact κ.IsRegular\nhι : HasCardinalLT ι κ\nhα : ∀ (i : ι), HasCardinalLT (α i) κ\nthis : Fact (Cardinal.lift.{max u v, w} κ).IsRegular\ni : ULift.{max v w, u} ι\n⊢ HasCardinalLT (α i.down) κ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Localization.CalculusOfFractions | {
"line": 415,
"column": 41
} | {
"line": 415,
"column": 57
} | {
"line": 415,
"column": 58
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Category.{v_2, u_2} D\nW : MorphismProperty C\ninst✝ : W.HasLeftCalculusOfFractions\nX Y Z : C\nz₁✝ : Hom W X Y\nz₂✝ : Hom W Y Z\na₁ a₂ : W.LeftFraction X Y\nb : W.LeftFraction Y Z\nU : C\nt₁ : a₁.Y' ⟶ U\nt₂ : a₂.Y' ⟶ U\nhst : a₁.s ≫ ... | [
"C : Type u_1\nD : Type u_2\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Category.{v_2, u_2} D\nW : MorphismProperty C\ninst✝ : W.HasLeftCalculusOfFractions\nX Y Z : C\nz₁✝ : Hom W X Y\nz₂✝ : Hom W Y Z\na₁ a₂ : W.LeftFraction X Y\nb : W.LeftFraction Y Z\nU : C\nt₁ : a₁.Y' ⟶ U\nt₂ : a₂.Y' ⟶ U\nhst : a₁.s ≫ t₁ = a₂.s ≫ ... | reassoc_of% hst, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.SetTheory.Cardinal.HasCardinalLT | {
"line": 184,
"column": 2
} | {
"line": 184,
"column": 13
} | {
"line": 184,
"column": 14
} | [
{
"pp": "T₁ T₂ : Type w\nκ : Cardinal.{w}\nhκ : Cardinal.aleph0 ≤ κ\nh₁ : Cardinal.mk T₁ < κ\nh₂ : Cardinal.mk T₂ < κ\n⊢ Cardinal.mk (T₁ × T₂) < κ",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"HMul.hMul",
"Cardinal",
"congrArg",
... | [
"T₁ T₂ : Type w\nκ : Cardinal.{w}\nhκ : Cardinal.aleph0 ≤ κ\nh₁ : Cardinal.mk T₁ < κ\nh₂ : Cardinal.mk T₂ < κ\n⊢ Cardinal.mk T₁ * Cardinal.mk T₂ < κ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.ObjectProperty.FiniteProducts | {
"line": 226,
"column": 24
} | {
"line": 233,
"column": 68
} | {
"line": 235,
"column": 0
} | [
{
"pp": "C : Type u_1\ninst✝² : Category.{v_1, u_1} C\nP : ObjectProperty C\ninst✝¹ : P.ContainsZero\ninst✝ : P.IsClosedUnderIsomorphisms\n⊢ P.colimitsOfShape (Discrete PEmpty.{1}) ≤ P",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"CategoryTheory.Limits.ColimitPresentation.isColimi... | [] | by
rintro X ⟨p⟩
obtain ⟨Z, hZ, hZ₂⟩ := P.exists_prop_of_containsZero
have hX : IsInitial X :=
(IsColimit.equivOfNatIsoOfIso p.diag.uniqueFromEmpty _ _
(by exact Cocone.ext (Iso.refl _) (by rintro ⟨⟨⟩⟩))).1 p.isColimit
exact P.prop_of_isZero (IsZero.of_iso hZ
(IsColimit.coconePointUni... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Localization.CalculusOfFractions | {
"line": 546,
"column": 4
} | {
"line": 546,
"column": 37
} | {
"line": 547,
"column": 4
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Category.{v_2, u_2} D\nW : MorphismProperty C\ninst✝ : W.HasLeftCalculusOfFractions\nX Y : C\ns : X ⟶ Y\nhs : W s\n⊢ homMk { Y' := Y, f := s, s := s, hs := hs } = 𝟙 ((Q W).obj X)",
"ppTerm": "?m.56",
"assigned": true,
"us... | [
"C : Type u_1\nD : Type u_2\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Category.{v_2, u_2} D\nW : MorphismProperty C\ninst✝ : W.HasLeftCalculusOfFractions\nX Y : C\ns : X ⟶ Y\nhs : W s\n⊢ LeftFractionRel { Y' := Y, f := s, s := s, hs := hs } (ofHom W (𝟙 ((Q W).obj X)))"
] | apply homMk_eq_of_leftFractionRel | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.CategoryTheory.Localization.CalculusOfFractions | {
"line": 547,
"column": 43
} | {
"line": 547,
"column": 54
} | {
"line": 547,
"column": 55
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Category.{v_2, u_2} D\nW : MorphismProperty C\ninst✝ : W.HasLeftCalculusOfFractions\nX Y : C\ns : X ⟶ Y\nhs : W s\n⊢ W ({ Y' := Y, f := s, s := s, hs := hs }.s ≫ 𝟙 Y)",
"ppTerm": "?m.81",
"assigned": true,
"usedConstants"... | [
"C : Type u_1\nD : Type u_2\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Category.{v_2, u_2} D\nW : MorphismProperty C\ninst✝ : W.HasLeftCalculusOfFractions\nX Y : C\ns : X ⟶ Y\nhs : W s\n⊢ W s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Localization.CalculusOfFractions | {
"line": 551,
"column": 4
} | {
"line": 551,
"column": 37
} | {
"line": 552,
"column": 4
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Category.{v_2, u_2} D\nW : MorphismProperty C\ninst✝ : W.HasLeftCalculusOfFractions\nX Y : C\ns : X ⟶ Y\nhs : W s\n⊢ homMk ((ofInv s hs).comp₀ (ofHom W s) (ofHom W (𝟙 Y))) = 𝟙 ((Q W).obj Y)",
"ppTerm": "?m.115",
"assigned": ... | [
"C : Type u_1\nD : Type u_2\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Category.{v_2, u_2} D\nW : MorphismProperty C\ninst✝ : W.HasLeftCalculusOfFractions\nX Y : C\ns : X ⟶ Y\nhs : W s\n⊢ LeftFractionRel ((ofInv s hs).comp₀ (ofHom W s) (ofHom W (𝟙 Y))) (ofHom W (𝟙 ((Q W).obj Y)))"
] | apply homMk_eq_of_leftFractionRel | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.CategoryTheory.Localization.CalculusOfFractions | {
"line": 552,
"column": 45
} | {
"line": 552,
"column": 56
} | {
"line": 552,
"column": 57
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Category.{v_2, u_2} D\nW : MorphismProperty C\ninst✝ : W.HasLeftCalculusOfFractions\nX Y : C\ns : X ⟶ Y\nhs : W s\n⊢ W (((ofInv s hs).comp₀ (ofHom W s) (ofHom W (𝟙 Y))).s ≫ 𝟙 Y)",
"ppTerm": "?m.142",
"assigned": true,
"u... | [
"C : Type u_1\nD : Type u_2\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Category.{v_2, u_2} D\nW : MorphismProperty C\ninst✝ : W.HasLeftCalculusOfFractions\nX Y : C\ns : X ⟶ Y\nhs : W s\n⊢ W (𝟙 Y)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.HomologicalFunctor | {
"line": 143,
"column": 35
} | {
"line": 143,
"column": 67
} | {
"line": 143,
"column": 67
} | [
{
"pp": "C : Type u_1\nD : Type u_2\nA : Type u_3\ninst✝¹⁴ : Category.{v_1, u_1} C\ninst✝¹³ : HasShift C ℤ\ninst✝¹² : Category.{v_2, u_2} D\ninst✝¹¹ : HasZeroObject D\ninst✝¹⁰ : HasShift D ℤ\ninst✝⁹ : Preadditive D\ninst✝⁸ : ∀ (n : ℤ), (shiftFunctor D n).Additive\ninst✝⁷ : Pretriangulated D\ninst✝⁶ : Category.{... | [] | by simpa using! hf =≫ biprod.snd | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Localization.CalculusOfFractions | {
"line": 705,
"column": 2
} | {
"line": 705,
"column": 56
} | {
"line": 705,
"column": 57
} | [
{
"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\nW : MorphismProperty C\nX Y : C\nφ : W.LeftFraction X Y\nE : Type u_3\ninst✝² : Category.{v_3, u_3} E\nL₁ : C ⥤ D\nL₂ : C ⥤ E\ninst✝¹ : L₁.IsLocalization W\ninst✝ : L₂.IsLocalization W\ne : L₁ ⋙ (Localization.un... | [
"C : Type u_1\nD : Type u_2\ninst✝⁴ : Category.{v_1, u_1} C\ninst✝³ : Category.{v_2, u_2} D\nW : MorphismProperty C\nX Y : C\nφ : W.LeftFraction X Y\nE : Type u_3\ninst✝² : Category.{v_3, u_3} E\nL₁ : C ⥤ D\nL₂ : C ⥤ E\ninst✝¹ : L₁.IsLocalization W\ninst✝ : L₂.IsLocalization W\ne : L₁ ⋙ (Localization.uniq L₁ L₂ W).... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Localization.CalculusOfFractions | {
"line": 713,
"column": 2
} | {
"line": 713,
"column": 64
} | {
"line": 715,
"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\nW : MorphismProperty C\nX Y : C\nφ₁ φ₂ : W.LeftFraction X Y\nE : Type u_3\ninst✝² : Category.{v_3, u_3} E\nL₁ : C ⥤ D\nL₂ : C ⥤ E\ninst✝¹ : L₁.IsLocalization W\ninst✝ : L₂.IsLocalization W\nh : φ₁.map L₁ ⋯ = φ₂.... | [] | rw [map_compatibility φ₁ L₂ L₁, map_compatibility φ₂ L₂ L₁, h] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.CategoryTheory.Localization.CalculusOfFractions | {
"line": 781,
"column": 4
} | {
"line": 781,
"column": 26
} | {
"line": 782,
"column": 4
} | [
{
"pp": "case mpr\nC : Type u_1\nD : Type u_2\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : Category.{v_2, u_2} D\nL : C ⥤ D\nW : MorphismProperty C\ninst✝¹ : L.IsLocalization W\ninst✝ : W.HasLeftCalculusOfFractions\nX Y : C\nf₁ f₂ : X ⟶ Y\n⊢ (∃ Z s, ∃ (_ : W s), f₁ ≫ s = f₂ ≫ s) → L.map f₁ = L.map f₂",
"ppTerm... | [
"case mpr\nC : Type u_1\nD : Type u_2\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : Category.{v_2, u_2} D\nL : C ⥤ D\nW : MorphismProperty C\ninst✝¹ : L.IsLocalization W\ninst✝ : W.HasLeftCalculusOfFractions\nX Y : C\nf₁ f₂ : X ⟶ Y\nZ : C\ns : Y ⟶ Z\nhs : W s\nfac : f₁ ≫ s = f₂ ≫ s\n⊢ L.map f₁ = L.map f₂"
] | rintro ⟨Z, s, hs, fac⟩ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRIntro | Lean.Parser.Tactic.rintro |
Mathlib.CategoryTheory.Localization.CalculusOfFractions | {
"line": 796,
"column": 4
} | {
"line": 796,
"column": 40
} | {
"line": 797,
"column": 4
} | [
{
"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\nL : C ⥤ D\nW : MorphismProperty C\ninst✝¹ : L.IsLocalization W\ninst✝ : W.HasLeftCalculusOfFractions\nf : Arrow D\nthis : L.EssSurj\nX : C\neX : L.obj X ≅ f.left\nY : C\neY : L.obj Y ≅ f.right\nφ : W.LeftFractio... | [
"C : Type u_1\nD : Type u_2\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : Category.{v_2, u_2} D\nL : C ⥤ D\nW : MorphismProperty C\ninst✝¹ : L.IsLocalization W\ninst✝ : W.HasLeftCalculusOfFractions\nf : Arrow D\nthis : L.EssSurj\nX : C\neX : L.obj X ≅ f.left\nY : C\neY : L.obj Y ≅ f.right\nφ : W.LeftFraction X Y\nhφ : ... | refine ⟨Arrow.mk φ.f, ⟨Iso.symm ?_⟩⟩ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.CategoryTheory.Localization.CalculusOfFractions | {
"line": 993,
"column": 4
} | {
"line": 993,
"column": 26
} | {
"line": 994,
"column": 4
} | [
{
"pp": "case mpr\nC : Type u_1\nD : Type u_2\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : Category.{v_2, u_2} D\nL : C ⥤ D\nW : MorphismProperty C\ninst✝¹ : L.IsLocalization W\ninst✝ : W.HasRightCalculusOfFractions\nY Z : C\nf₁ f₂ : Y ⟶ Z\n⊢ (∃ X s, ∃ (_ : W s), s ≫ f₁ = s ≫ f₂) → L.map f₁ = L.map f₂",
"ppTer... | [
"case mpr\nC : Type u_1\nD : Type u_2\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : Category.{v_2, u_2} D\nL : C ⥤ D\nW : MorphismProperty C\ninst✝¹ : L.IsLocalization W\ninst✝ : W.HasRightCalculusOfFractions\nY Z✝ : C\nf₁ f₂ : Y ⟶ Z✝\nZ : C\ns : Z ⟶ Y\nhs : W s\nfac : s ≫ f₁ = s ≫ f₂\n⊢ L.map f₁ = L.map f₂"
] | rintro ⟨Z, s, hs, fac⟩ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRIntro | Lean.Parser.Tactic.rintro |
Mathlib.CategoryTheory.Triangulated.Subcategory | {
"line": 124,
"column": 2
} | {
"line": 124,
"column": 39
} | {
"line": 124,
"column": 40
} | [
{
"pp": "C : Type u_1\ninst✝⁷ : Category.{v_1, u_1} C\ninst✝⁶ : HasZeroObject C\ninst✝⁵ : HasShift C ℤ\ninst✝⁴ : Preadditive C\ninst✝³ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝² : Pretriangulated C\nP : ObjectProperty C\ninst✝¹ : P.IsTriangulatedClosed₁\ninst✝ : P.IsClosedUnderIsomorphisms\nT : Triangle C... | [
"C : Type u_1\ninst✝⁷ : Category.{v_1, u_1} C\ninst✝⁶ : HasZeroObject C\ninst✝⁵ : HasShift C ℤ\ninst✝⁴ : Preadditive C\ninst✝³ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝² : Pretriangulated C\nP : ObjectProperty C\ninst✝¹ : P.IsTriangulatedClosed₁\ninst✝ : P.IsClosedUnderIsomorphisms\nT : Triangle C\nhT : T ∈ d... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.Subcategory | {
"line": 130,
"column": 2
} | {
"line": 130,
"column": 39
} | {
"line": 130,
"column": 40
} | [
{
"pp": "C : Type u_1\ninst✝⁷ : Category.{v_1, u_1} C\ninst✝⁶ : HasZeroObject C\ninst✝⁵ : HasShift C ℤ\ninst✝⁴ : Preadditive C\ninst✝³ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝² : Pretriangulated C\nP : ObjectProperty C\ninst✝¹ : P.IsTriangulatedClosed₂\ninst✝ : P.IsClosedUnderIsomorphisms\nT : Triangle C... | [
"C : Type u_1\ninst✝⁷ : Category.{v_1, u_1} C\ninst✝⁶ : HasZeroObject C\ninst✝⁵ : HasShift C ℤ\ninst✝⁴ : Preadditive C\ninst✝³ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝² : Pretriangulated C\nP : ObjectProperty C\ninst✝¹ : P.IsTriangulatedClosed₂\ninst✝ : P.IsClosedUnderIsomorphisms\nT : Triangle C\nhT : T ∈ d... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.Subcategory | {
"line": 136,
"column": 2
} | {
"line": 136,
"column": 39
} | {
"line": 136,
"column": 40
} | [
{
"pp": "C : Type u_1\ninst✝⁷ : Category.{v_1, u_1} C\ninst✝⁶ : HasZeroObject C\ninst✝⁵ : HasShift C ℤ\ninst✝⁴ : Preadditive C\ninst✝³ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝² : Pretriangulated C\nP : ObjectProperty C\ninst✝¹ : P.IsTriangulatedClosed₃\ninst✝ : P.IsClosedUnderIsomorphisms\nT : Triangle C... | [
"C : Type u_1\ninst✝⁷ : Category.{v_1, u_1} C\ninst✝⁶ : HasZeroObject C\ninst✝⁵ : HasShift C ℤ\ninst✝⁴ : Preadditive C\ninst✝³ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝² : Pretriangulated C\nP : ObjectProperty C\ninst✝¹ : P.IsTriangulatedClosed₃\ninst✝ : P.IsClosedUnderIsomorphisms\nT : Triangle C\nhT : T ∈ d... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.Subcategory | {
"line": 143,
"column": 14
} | {
"line": 143,
"column": 51
} | {
"line": 143,
"column": 52
} | [
{
"pp": "C : Type u_1\ninst✝⁶ : Category.{v_1, u_1} C\ninst✝⁵ : HasZeroObject C\ninst✝⁴ : HasShift C ℤ\ninst✝³ : Preadditive C\ninst✝² : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝¹ : Pretriangulated C\nP : ObjectProperty C\ninst✝ : P.IsClosedUnderIsomorphisms\nhP : ∀ T ∈ distinguishedTriangles, P T.obj₂ → P ... | [
"C : Type u_1\ninst✝⁶ : Category.{v_1, u_1} C\ninst✝⁵ : HasZeroObject C\ninst✝⁴ : HasShift C ℤ\ninst✝³ : Preadditive C\ninst✝² : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝¹ : Pretriangulated C\nP : ObjectProperty C\ninst✝ : P.IsClosedUnderIsomorphisms\nhP : ∀ T ∈ distinguishedTriangles, P T.obj₂ → P T.obj₃ → P T... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.Subcategory | {
"line": 148,
"column": 14
} | {
"line": 148,
"column": 51
} | {
"line": 148,
"column": 52
} | [
{
"pp": "C : Type u_1\ninst✝⁶ : Category.{v_1, u_1} C\ninst✝⁵ : HasZeroObject C\ninst✝⁴ : HasShift C ℤ\ninst✝³ : Preadditive C\ninst✝² : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝¹ : Pretriangulated C\nP : ObjectProperty C\ninst✝ : P.IsClosedUnderIsomorphisms\nhP : ∀ T ∈ distinguishedTriangles, P T.obj₁ → P ... | [
"C : Type u_1\ninst✝⁶ : Category.{v_1, u_1} C\ninst✝⁵ : HasZeroObject C\ninst✝⁴ : HasShift C ℤ\ninst✝³ : Preadditive C\ninst✝² : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝¹ : Pretriangulated C\nP : ObjectProperty C\ninst✝ : P.IsClosedUnderIsomorphisms\nhP : ∀ T ∈ distinguishedTriangles, P T.obj₁ → P T.obj₃ → P T... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.Subcategory | {
"line": 153,
"column": 14
} | {
"line": 153,
"column": 51
} | {
"line": 153,
"column": 52
} | [
{
"pp": "C : Type u_1\ninst✝⁶ : Category.{v_1, u_1} C\ninst✝⁵ : HasZeroObject C\ninst✝⁴ : HasShift C ℤ\ninst✝³ : Preadditive C\ninst✝² : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝¹ : Pretriangulated C\nP : ObjectProperty C\ninst✝ : P.IsClosedUnderIsomorphisms\nhP : ∀ T ∈ distinguishedTriangles, P T.obj₁ → P ... | [
"C : Type u_1\ninst✝⁶ : Category.{v_1, u_1} C\ninst✝⁵ : HasZeroObject C\ninst✝⁴ : HasShift C ℤ\ninst✝³ : Preadditive C\ninst✝² : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝¹ : Pretriangulated C\nP : ObjectProperty C\ninst✝ : P.IsClosedUnderIsomorphisms\nhP : ∀ T ∈ distinguishedTriangles, P T.obj₁ → P T.obj₂ → P T... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Localization.Composition | {
"line": 48,
"column": 4
} | {
"line": 48,
"column": 70
} | {
"line": 48,
"column": 71
} | [
{
"pp": "C₁ : Type u₁\nC₂ : Type u₂\nC₃ : Type u₃\nE : Type u₄\ninst✝³ : Category.{v₁, u₁} C₁\ninst✝² : Category.{v₂, u₂} C₂\ninst✝¹ : Category.{v₃, u₃} C₃\ninst✝ : Category.{v₄, u₄} E\nL₁ : C₁ ⥤ C₂\nL₂ : C₂ ⥤ C₃\nW₁ : MorphismProperty C₁\nW₂ : MorphismProperty C₂\nh₁ : StrictUniversalPropertyFixedTarget L₁ W₁ ... | [
"C₁ : Type u₁\nC₂ : Type u₂\nC₃ : Type u₃\nE : Type u₄\ninst✝³ : Category.{v₁, u₁} C₁\ninst✝² : Category.{v₂, u₂} C₂\ninst✝¹ : Category.{v₃, u₃} C₃\ninst✝ : Category.{v₄, u₄} E\nL₁ : C₁ ⥤ C₂\nL₂ : C₂ ⥤ C₃\nW₁ : MorphismProperty C₁\nW₂ : MorphismProperty C₂\nh₁ : StrictUniversalPropertyFixedTarget L₁ W₁ E\nh₂ : Stri... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Localization.Composition | {
"line": 50,
"column": 45
} | {
"line": 50,
"column": 77
} | {
"line": 50,
"column": 78
} | [
{
"pp": "C₁ : Type u₁\nC₂ : Type u₂\nC₃ : Type u₃\nE : Type u₄\ninst✝³ : Category.{v₁, u₁} C₁\ninst✝² : Category.{v₂, u₂} C₂\ninst✝¹ : Category.{v₃, u₃} C₃\ninst✝ : Category.{v₄, u₄} E\nL₁ : C₁ ⥤ C₂\nL₂ : C₂ ⥤ C₃\nW₁ : MorphismProperty C₁\nW₂ : MorphismProperty C₂\nh₁ : StrictUniversalPropertyFixedTarget L₁ W₁ ... | [
"C₁ : Type u₁\nC₂ : Type u₂\nC₃ : Type u₃\nE : Type u₄\ninst✝³ : Category.{v₁, u₁} C₁\ninst✝² : Category.{v₂, u₂} C₂\ninst✝¹ : Category.{v₃, u₃} C₃\ninst✝ : Category.{v₄, u₄} E\nL₁ : C₁ ⥤ C₂\nL₂ : C₂ ⥤ C₃\nW₁ : MorphismProperty C₁\nW₂ : MorphismProperty C₂\nh₁ : StrictUniversalPropertyFixedTarget L₁ W₁ E\nh₂ : Stri... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Localization.Composition | {
"line": 100,
"column": 4
} | {
"line": 101,
"column": 60
} | {
"line": 101,
"column": 61
} | [
{
"pp": "C₁ : Type u₁\nC₂ : Type u₂\nC₃ : Type u₃\ninst✝⁴ : Category.{v₁, u₁} C₁\ninst✝³ : Category.{v₂, u₂} C₂\ninst✝² : Category.{v₃, u₃} C₃\nL₁ : C₁ ⥤ C₂\nL₂ : C₂ ⥤ C₃\nW₁ : MorphismProperty C₁\nW₂ : MorphismProperty C₂\ninst✝¹ : L₁.IsLocalization W₁\ninst✝ : L₂.IsLocalization W₂\nW₃ : MorphismProperty C₁\nh... | [
"C₁ : Type u₁\nC₂ : Type u₂\nC₃ : Type u₃\ninst✝⁴ : Category.{v₁, u₁} C₁\ninst✝³ : Category.{v₂, u₂} C₂\ninst✝² : Category.{v₃, u₃} C₃\nL₁ : C₁ ⥤ C₂\nL₂ : C₂ ⥤ C₃\nW₁ : MorphismProperty C₁\nW₂ : MorphismProperty C₂\ninst✝¹ : L₁.IsLocalization W₁\ninst✝ : L₂.IsLocalization W₂\nW₃ : MorphismProperty C₁\nhW₃ : W₃.IsIn... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Localization.Composition | {
"line": 103,
"column": 8
} | {
"line": 104,
"column": 11
} | {
"line": 104,
"column": 12
} | [
{
"pp": "C₁ : Type u₁\nC₂ : Type u₂\nC₃ : Type u₃\ninst✝⁴ : Category.{v₁, u₁} C₁\ninst✝³ : Category.{v₂, u₂} C₂\ninst✝² : Category.{v₃, u₃} C₃\nL₁ : C₁ ⥤ C₂\nL₂ : C₂ ⥤ C₃\nW₁ : MorphismProperty C₁\nW₂ : MorphismProperty C₂\ninst✝¹ : L₁.IsLocalization W₁\ninst✝ : L₂.IsLocalization W₂\nW₃ : MorphismProperty C₁\nh... | [
"C₁ : Type u₁\nC₂ : Type u₂\nC₃ : Type u₃\ninst✝⁴ : Category.{v₁, u₁} C₁\ninst✝³ : Category.{v₂, u₂} C₂\ninst✝² : Category.{v₃, u₃} C₃\nL₁ : C₁ ⥤ C₂\nL₂ : C₂ ⥤ C₃\nW₁ : MorphismProperty C₁\nW₂ : MorphismProperty C₂\ninst✝¹ : L₁.IsLocalization W₁\ninst✝ : L₂.IsLocalization W₂\nW₃ : MorphismProperty C₁\nhW₃ : W₃.IsIn... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Localization.Composition | {
"line": 120,
"column": 12
} | {
"line": 120,
"column": 35
} | {
"line": 120,
"column": 36
} | [
{
"pp": "C₁ : Type u₁\nC₂ : Type u₂\nC₃ : Type u₃\ninst✝⁴ : Category.{v₁, u₁} C₁\ninst✝³ : Category.{v₂, u₂} C₂\ninst✝² : Category.{v₃, u₃} C₃\nL₁ : C₁ ⥤ C₂\nL₂ : C₂ ⥤ C₃\nW₁ : MorphismProperty C₁\nW₂ : MorphismProperty C₂\nW₃ : MorphismProperty C₁\ninst✝¹ : L₁.IsLocalization W₁\ninst✝ : (L₁ ⋙ L₂).IsLocalizatio... | [
"C₁ : Type u₁\nC₂ : Type u₂\nC₃ : Type u₃\ninst✝⁴ : Category.{v₁, u₁} C₁\ninst✝³ : Category.{v₂, u₂} C₂\ninst✝² : Category.{v₃, u₃} C₃\nL₁ : C₁ ⥤ C₂\nL₂ : C₂ ⥤ C₃\nW₁ : MorphismProperty C₁\nW₂ : MorphismProperty C₂\nW₃ : MorphismProperty C₁\ninst✝¹ : L₁.IsLocalization W₁\ninst✝ : (L₁ ⋙ L₂).IsLocalization W₃\nhW₁₃ :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.QuasiIso | {
"line": 179,
"column": 2
} | {
"line": 180,
"column": 18
} | {
"line": 182,
"column": 0
} | [
{
"pp": "case mpr\nι : Type u_1\nC : Type u\ninst✝⁴ : Category.{v, u} C\ninst✝³ : HasZeroMorphisms C\nc : ComplexShape ι\nK L M : HomologicalComplex C c\nφ : K ⟶ L\nφ' : L ⟶ M\ni : ι\ninst✝² : K.HasHomology i\ninst✝¹ : L.HasHomology i\ninst✝ : M.HasHomology i\nhφ : QuasiIsoAt φ i\n⊢ QuasiIsoAt φ' i → QuasiIsoAt... | [] | · intro
infer_instance | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Algebra.Homology.QuasiIso | {
"line": 210,
"column": 2
} | {
"line": 211,
"column": 18
} | {
"line": 213,
"column": 0
} | [
{
"pp": "case mpr\nι : Type u_1\nC : Type u\ninst✝⁴ : Category.{v, u} C\ninst✝³ : HasZeroMorphisms C\nc : ComplexShape ι\nK L M : HomologicalComplex C c\nφ : K ⟶ L\nφ' : L ⟶ M\ni : ι\ninst✝² : K.HasHomology i\ninst✝¹ : L.HasHomology i\ninst✝ : M.HasHomology i\nhφ' : QuasiIsoAt φ' i\n⊢ QuasiIsoAt φ i → QuasiIsoA... | [] | · intro
infer_instance | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Algebra.Homology.HomotopyCategory.Acyclic | {
"line": 56,
"column": 2
} | {
"line": 56,
"column": 33
} | {
"line": 57,
"column": 2
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Abelian C\nK : CochainComplex C ℤ\n⊢ subcategoryAcyclic C ((quotient C (ComplexShape.up ℤ)).obj K) ↔ ∀ (n : ℤ), HomologicalComplex.ExactAt K n",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"Int.instAddCommGroup",
"Categ... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Abelian C\nK : CochainComplex C ℤ\n⊢ (∀ (n : ℤ), IsZero ((homologyFunctor C (ComplexShape.up ℤ) n).obj ((quotient C (ComplexShape.up ℤ)).obj K))) ↔\n ∀ (n : ℤ), HomologicalComplex.ExactAt K n"
] | rw [mem_subcategoryAcyclic_iff] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.CategoryTheory.Shift.SingleFunctors | {
"line": 65,
"column": 45
} | {
"line": 66,
"column": 45
} | {
"line": 68,
"column": 0
} | [
{
"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\nA : Type u_5\ninst✝¹ : AddMonoid A\ninst✝ : HasShift D A\nF : SingleFunctors C D A\nn m a a' a'' : A\nha' : n + a = a'\nha'' : m + a' = a''\nX : C\n⊢ (F.shiftIso (m + n) a a'' ⋯).hom.app X =\n (shiftFunctorAd... | [] | by
simp [F.shiftIso_add n m a a' a'' ha' ha''] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Shift.SingleFunctors | {
"line": 73,
"column": 65
} | {
"line": 74,
"column": 45
} | {
"line": 76,
"column": 0
} | [
{
"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\nA : Type u_5\ninst✝¹ : AddMonoid A\ninst✝ : HasShift D A\nF : SingleFunctors C D A\nn m a a' a'' : A\nha' : n + a = a'\nha'' : m + a' = a''\nX : C\n⊢ (F.shiftIso (m + n) a a'' ⋯).inv.app X =\n (F.shiftIso n a... | [] | by
simp [F.shiftIso_add n m a a' a'' ha' ha''] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Shift.SingleFunctors | {
"line": 244,
"column": 8
} | {
"line": 244,
"column": 19
} | {
"line": 244,
"column": 20
} | [
{
"pp": "C : Type u_1\nD : Type u_2\nE : Type u_3\nE' : Type u_4\ninst✝⁸ : Category.{v_1, u_1} C\ninst✝⁷ : Category.{v_2, u_2} D\ninst✝⁶ : Category.{v_3, u_3} E\ninst✝⁵ : Category.{v_4, u_4} E'\nA : Type u_5\ninst✝⁴ : AddMonoid A\ninst✝³ : HasShift D A\ninst✝² : HasShift E A\ninst✝¹ : HasShift E' A\nF G✝ H : Si... | [
"C : Type u_1\nD : Type u_2\nE : Type u_3\nE' : Type u_4\ninst✝⁸ : Category.{v_1, u_1} C\ninst✝⁷ : Category.{v_2, u_2} D\ninst✝⁶ : Category.{v_3, u_3} E\ninst✝⁵ : Category.{v_4, u_4} E'\nA : Type u_5\ninst✝⁴ : AddMonoid A\ninst✝³ : HasShift D A\ninst✝² : HasShift E A\ninst✝¹ : HasShift E' A\nF G✝ H : SingleFunctors... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.Subcategory | {
"line": 594,
"column": 8
} | {
"line": 594,
"column": 47
} | {
"line": 594,
"column": 48
} | [
{
"pp": "C : Type u_1\ninst✝¹⁶ : Category.{v_1, u_1} C\ninst✝¹⁵ : HasZeroObject C\ninst✝¹⁴ : HasShift C ℤ\ninst✝¹³ : Preadditive C\ninst✝¹² : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝¹¹ : Pretriangulated C\nD : Type u_2\ninst✝¹⁰ : Category.{v_2, u_2} D\ninst✝⁹ : Preadditive D\ninst✝⁸ : HasZeroObject D\ninst... | [
"C : Type u_1\ninst✝¹⁶ : Category.{v_1, u_1} C\ninst✝¹⁵ : HasZeroObject C\ninst✝¹⁴ : HasShift C ℤ\ninst✝¹³ : Preadditive C\ninst✝¹² : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝¹¹ : Pretriangulated C\nD : Type u_2\ninst✝¹⁰ : Category.{v_2, u_2} D\ninst✝⁹ : Preadditive D\ninst✝⁸ : HasZeroObject D\ninst✝⁷ : HasShif... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.Subcategory | {
"line": 647,
"column": 7
} | {
"line": 647,
"column": 22
} | {
"line": 647,
"column": 23
} | [
{
"pp": "C : Type u_1\ninst✝¹⁵ : Category.{v_1, u_1} C\ninst✝¹⁴ : HasZeroObject C\ninst✝¹³ : HasShift C ℤ\ninst✝¹² : Preadditive C\ninst✝¹¹ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝¹⁰ : Pretriangulated C\nD : Type u_2\ninst✝⁹ : Category.{v_2, u_2} D\ninst✝⁸ : Preadditive D\ninst✝⁷ : HasZeroObject D\ninst✝... | [
"C : Type u_1\ninst✝¹⁵ : Category.{v_1, u_1} C\ninst✝¹⁴ : HasZeroObject C\ninst✝¹³ : HasShift C ℤ\ninst✝¹² : Preadditive C\ninst✝¹¹ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝¹⁰ : Pretriangulated C\nD : Type u_2\ninst✝⁹ : Category.{v_2, u_2} D\ninst✝⁸ : Preadditive D\ninst✝⁷ : HasZeroObject D\ninst✝⁶ : HasShift... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.Subcategory | {
"line": 647,
"column": 35
} | {
"line": 647,
"column": 50
} | {
"line": 647,
"column": 51
} | [
{
"pp": "C : Type u_1\ninst✝¹⁵ : Category.{v_1, u_1} C\ninst✝¹⁴ : HasZeroObject C\ninst✝¹³ : HasShift C ℤ\ninst✝¹² : Preadditive C\ninst✝¹¹ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝¹⁰ : Pretriangulated C\nD : Type u_2\ninst✝⁹ : Category.{v_2, u_2} D\ninst✝⁸ : Preadditive D\ninst✝⁷ : HasZeroObject D\ninst✝... | [
"C : Type u_1\ninst✝¹⁵ : Category.{v_1, u_1} C\ninst✝¹⁴ : HasZeroObject C\ninst✝¹³ : HasShift C ℤ\ninst✝¹² : Preadditive C\ninst✝¹¹ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝¹⁰ : Pretriangulated C\nD : Type u_2\ninst✝⁹ : Category.{v_2, u_2} D\ninst✝⁸ : Preadditive D\ninst✝⁷ : HasZeroObject D\ninst✝⁶ : HasShift... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.Subcategory | {
"line": 708,
"column": 10
} | {
"line": 708,
"column": 21
} | {
"line": 708,
"column": 22
} | [
{
"pp": "C : Type u_1\ninst✝¹⁴ : Category.{v_1, u_1} C\ninst✝¹³ : HasZeroObject C\ninst✝¹² : HasShift C ℤ\ninst✝¹¹ : Preadditive C\ninst✝¹⁰ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝⁹ : Pretriangulated C\nD : Type u_2\ninst✝⁸ : Category.{v_2, u_2} D\ninst✝⁷ : Preadditive D\ninst✝⁶ : HasZeroObject D\ninst✝⁵... | [
"C : Type u_1\ninst✝¹⁴ : Category.{v_1, u_1} C\ninst✝¹³ : HasZeroObject C\ninst✝¹² : HasShift C ℤ\ninst✝¹¹ : Preadditive C\ninst✝¹⁰ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝⁹ : Pretriangulated C\nD : Type u_2\ninst✝⁸ : Category.{v_2, u_2} D\ninst✝⁷ : Preadditive D\ninst✝⁶ : HasZeroObject D\ninst✝⁵ : HasShift ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.Basic | {
"line": 168,
"column": 4
} | {
"line": 168,
"column": 15
} | {
"line": 168,
"column": 16
} | [
{
"pp": "case pos.e_a\nι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\ni k : ι\nhi : some k = some i\n⊢ i = k",
"ppTerm": "?pos.e_a✝",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case pos.e_a\nι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\ni k : ι\nhi : some k = some i\n⊢ i = k"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.Basic | {
"line": 169,
"column": 29
} | {
"line": 169,
"column": 40
} | {
"line": 169,
"column": 41
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\ni : ι\ni' : ι'\nhi : e.r i' = some i\nh : ¬∃ k, e.f k = i'\n⊢ ∀ (i : ι), e.f i ≠ i'",
"ppTerm": "?m.87",
"assigned": true,
"usedConstants": [
"id",
"Ne",
"ComplexShape.Embedding.f"
... | [
"ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\ni : ι\ni' : ι'\nhi : e.r i' = some i\nh : ¬∃ k, e.f k = i'\n⊢ ∀ (i : ι), ¬e.f i = i'"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.Basic | {
"line": 182,
"column": 21
} | {
"line": 182,
"column": 32
} | {
"line": 182,
"column": 33
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nA : Type u_3\ninst✝² : AddCommSemigroup A\ninst✝¹ : IsRightCancelAdd A\ninst✝ : One A\na b x✝¹ x✝ : A\nh : (fun x ↦ x + b) x✝¹ = (fun x ↦ x + b) x✝\n⊢ x✝¹ = x✝",
"ppTerm": "?m.25",
"assigned": false,
"usedConstants": [],... | [
"ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nA : Type u_3\ninst✝² : AddCommSemigroup A\ninst✝¹ : IsRightCancelAdd A\ninst✝ : One A\na b x✝¹ x✝ : A\nh : (fun x ↦ x + b) x✝¹ = (fun x ↦ x + b) x✝\n⊢ x✝¹ = x✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.Basic | {
"line": 195,
"column": 21
} | {
"line": 195,
"column": 32
} | {
"line": 195,
"column": 33
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nA : Type u_3\ninst✝² : AddCommSemigroup A\ninst✝¹ : IsRightCancelAdd A\ninst✝ : One A\na b x✝¹ x✝ : A\nh : (fun x ↦ x + b) x✝¹ = (fun x ↦ x + b) x✝\n⊢ x✝¹ = x✝",
"ppTerm": "?m.25",
"assigned": false,
"usedConstants": [],... | [
"ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nA : Type u_3\ninst✝² : AddCommSemigroup A\ninst✝¹ : IsRightCancelAdd A\ninst✝ : One A\na b x✝¹ x✝ : A\nh : (fun x ↦ x + b) x✝¹ = (fun x ↦ x + b) x✝\n⊢ x✝¹ = x✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.Basic | {
"line": 211,
"column": 21
} | {
"line": 211,
"column": 32
} | {
"line": 211,
"column": 33
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nx✝¹ x✝ : ℕ\nh : (fun n ↦ ↑n) x✝¹ = (fun n ↦ ↑n) x✝\n⊢ x✝¹ = x✝",
"ppTerm": "?m.20",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nx✝¹ x✝ : ℕ\nh : (fun n ↦ ↑n) x✝¹ = (fun n ↦ ↑n) x✝\n⊢ x✝¹ = x✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.Basic | {
"line": 224,
"column": 21
} | {
"line": 224,
"column": 32
} | {
"line": 224,
"column": 33
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nx✝¹ x✝ : ℕ\nh : (fun n ↦ -↑n) x✝¹ = (fun n ↦ -↑n) x✝\n⊢ x✝¹ = x✝",
"ppTerm": "?m.22",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nx✝¹ x✝ : ℕ\nh : (fun n ↦ -↑n) x✝¹ = (fun n ↦ -↑n) x✝\n⊢ x✝¹ = x✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.Basic | {
"line": 280,
"column": 4
} | {
"line": 280,
"column": 41
} | {
"line": 281,
"column": 2
} | [
{
"pp": "case mp\np n : ℤ\nh : ∀ (i : ℕ), (embeddingUpIntGE p).f i ≠ n\nthis : ¬n < p\n⊢ False",
"ppTerm": "?mp",
"assigned": true,
"usedConstants": [
"Nat.instOne",
"AddGroupWithOne.toAddMonoidWithOne",
"HSub.hSub",
"AddCancelMonoid.toAddRightCancelMonoid",
"_private.M... | [] | exact h (n - p).natAbs (by simp; lia) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Algebra.Homology.Embedding.IsSupported | {
"line": 146,
"column": 54
} | {
"line": 146,
"column": 65
} | {
"line": 146,
"column": 66
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝¹ : Category.{v_1, u_3} C\ninst✝ : HasZeroMorphisms C\nK : HomologicalComplex C c'\ne : c.Embedding c'\nh₁ : K.IsStrictlySupported e\nh₂ : K.IsStrictlySupportedOutside e\nn : ι'\nhn : ¬∃ i, e.f i = n\n⊢ ∀ (i : ι),... | [
"ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝¹ : Category.{v_1, u_3} C\ninst✝ : HasZeroMorphisms C\nK : HomologicalComplex C c'\ne : c.Embedding c'\nh₁ : K.IsStrictlySupported e\nh₂ : K.IsStrictlySupportedOutside e\nn : ι'\nhn : ¬∃ i, e.f i = n\n⊢ ∀ (i : ι), ¬e.f i = n"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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