module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.CategoryTheory.Quotient | {
"line": 119,
"column": 18
} | {
"line": 119,
"column": 23
} | {
"line": 120,
"column": 2
} | [
{
"pp": "C✝ : Type u_1\ninst✝² : Category.{v_1, u_1} C✝\nr : HomRel C✝\nC : Type u_2\nD : Type u_3\ninst✝¹ : Category.{v_2, u_2} C\ninst✝ : Category.{v_3, u_3} D\nF : C ⥤ D\n⊢ ∀ {X Y Z : C} (f : X ⟶ Y) {g g' : Y ⟶ Z}, F.homRel g g' → F.homRel (f ≫ g) (f ≫ g')",
"ppTerm": "?m.13",
"assigned": true,
"... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.Quotient | {
"line": 119,
"column": 18
} | {
"line": 119,
"column": 23
} | {
"line": 120,
"column": 2
} | [
{
"pp": "C✝ : Type u_1\ninst✝² : Category.{v_1, u_1} C✝\nr : HomRel C✝\nC : Type u_2\nD : Type u_3\ninst✝¹ : Category.{v_2, u_2} C\ninst✝ : Category.{v_3, u_3} D\nF : C ⥤ D\n⊢ ∀ {X Y Z : C} (f : X ⟶ Y) {g g' : Y ⟶ Z}, F.homRel g g' → F.homRel (f ≫ g) (f ≫ g')",
"ppTerm": "?m.13",
"assigned": true,
"... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Quotient | {
"line": 119,
"column": 18
} | {
"line": 119,
"column": 23
} | {
"line": 120,
"column": 2
} | [
{
"pp": "C✝ : Type u_1\ninst✝² : Category.{v_1, u_1} C✝\nr : HomRel C✝\nC : Type u_2\nD : Type u_3\ninst✝¹ : Category.{v_2, u_2} C\ninst✝ : Category.{v_3, u_3} D\nF : C ⥤ D\n⊢ ∀ {X Y Z : C} (f : X ⟶ Y) {g g' : Y ⟶ Z}, F.homRel g g' → F.homRel (f ≫ g) (f ≫ g')",
"ppTerm": "?m.13",
"assigned": true,
"... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Quotient | {
"line": 120,
"column": 19
} | {
"line": 120,
"column": 24
} | {
"line": 122,
"column": 0
} | [
{
"pp": "C✝ : Type u_1\ninst✝² : Category.{v_1, u_1} C✝\nr : HomRel C✝\nC : Type u_2\nD : Type u_3\ninst✝¹ : Category.{v_2, u_2} C\ninst✝ : Category.{v_3, u_3} D\nF : C ⥤ D\n⊢ ∀ {X Y Z : C} {f f' : X ⟶ Y} (g : Y ⟶ Z), F.homRel f f' → F.homRel (f ≫ g) (f' ≫ g)",
"ppTerm": "?m.14",
"assigned": true,
"... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.Quotient | {
"line": 120,
"column": 19
} | {
"line": 120,
"column": 24
} | {
"line": 122,
"column": 0
} | [
{
"pp": "C✝ : Type u_1\ninst✝² : Category.{v_1, u_1} C✝\nr : HomRel C✝\nC : Type u_2\nD : Type u_3\ninst✝¹ : Category.{v_2, u_2} C\ninst✝ : Category.{v_3, u_3} D\nF : C ⥤ D\n⊢ ∀ {X Y Z : C} {f f' : X ⟶ Y} (g : Y ⟶ Z), F.homRel f f' → F.homRel (f ≫ g) (f' ≫ g)",
"ppTerm": "?m.14",
"assigned": true,
"... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Quotient | {
"line": 120,
"column": 19
} | {
"line": 120,
"column": 24
} | {
"line": 122,
"column": 0
} | [
{
"pp": "C✝ : Type u_1\ninst✝² : Category.{v_1, u_1} C✝\nr : HomRel C✝\nC : Type u_2\nD : Type u_3\ninst✝¹ : Category.{v_2, u_2} C\ninst✝ : Category.{v_3, u_3} D\nF : C ⥤ D\n⊢ ∀ {X Y Z : C} {f f' : X ⟶ Y} (g : Y ⟶ Z), F.homRel f f' → F.homRel (f ≫ g) (f' ≫ g)",
"ppTerm": "?m.14",
"assigned": true,
"... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Quotient | {
"line": 117,
"column": 17
} | {
"line": 117,
"column": 22
} | {
"line": 118,
"column": 6
} | [
{
"pp": "C✝ : Type u_1\ninst✝² : Category.{v_1, u_1} C✝\nr : HomRel C✝\nC : Type u_2\nD : Type u_3\ninst✝¹ : Category.{v_2, u_2} C\ninst✝ : Category.{v_3, u_3} D\nF : C ⥤ D\nX✝ Y✝ : C\n⊢ ∀ {x y : X✝ ⟶ Y✝}, F.homRel x y → F.homRel y x",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"C... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.Quotient | {
"line": 117,
"column": 17
} | {
"line": 117,
"column": 22
} | {
"line": 118,
"column": 6
} | [
{
"pp": "C✝ : Type u_1\ninst✝² : Category.{v_1, u_1} C✝\nr : HomRel C✝\nC : Type u_2\nD : Type u_3\ninst✝¹ : Category.{v_2, u_2} C\ninst✝ : Category.{v_3, u_3} D\nF : C ⥤ D\nX✝ Y✝ : C\n⊢ ∀ {x y : X✝ ⟶ Y✝}, F.homRel x y → F.homRel y x",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"C... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Quotient | {
"line": 117,
"column": 17
} | {
"line": 117,
"column": 22
} | {
"line": 118,
"column": 6
} | [
{
"pp": "C✝ : Type u_1\ninst✝² : Category.{v_1, u_1} C✝\nr : HomRel C✝\nC : Type u_2\nD : Type u_3\ninst✝¹ : Category.{v_2, u_2} C\ninst✝ : Category.{v_3, u_3} D\nF : C ⥤ D\nX✝ Y✝ : C\n⊢ ∀ {x y : X✝ ⟶ Y✝}, F.homRel x y → F.homRel y x",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"C... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Quotient | {
"line": 118,
"column": 18
} | {
"line": 118,
"column": 23
} | {
"line": 118,
"column": 24
} | [
{
"pp": "C✝ : Type u_1\ninst✝² : Category.{v_1, u_1} C✝\nr : HomRel C✝\nC : Type u_2\nD : Type u_3\ninst✝¹ : Category.{v_2, u_2} C\ninst✝ : Category.{v_3, u_3} D\nF : C ⥤ D\nX✝ Y✝ : C\n⊢ ∀ {x y z : X✝ ⟶ Y✝}, F.homRel x y → F.homRel y z → F.homRel x z",
"ppTerm": "?m.21",
"assigned": true,
"usedConst... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.Quotient | {
"line": 118,
"column": 18
} | {
"line": 118,
"column": 23
} | {
"line": 118,
"column": 24
} | [
{
"pp": "C✝ : Type u_1\ninst✝² : Category.{v_1, u_1} C✝\nr : HomRel C✝\nC : Type u_2\nD : Type u_3\ninst✝¹ : Category.{v_2, u_2} C\ninst✝ : Category.{v_3, u_3} D\nF : C ⥤ D\nX✝ Y✝ : C\n⊢ ∀ {x y z : X✝ ⟶ Y✝}, F.homRel x y → F.homRel y z → F.homRel x z",
"ppTerm": "?m.21",
"assigned": true,
"usedConst... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Quotient | {
"line": 118,
"column": 18
} | {
"line": 118,
"column": 23
} | {
"line": 118,
"column": 24
} | [
{
"pp": "C✝ : Type u_1\ninst✝² : Category.{v_1, u_1} C✝\nr : HomRel C✝\nC : Type u_2\nD : Type u_3\ninst✝¹ : Category.{v_2, u_2} C\ninst✝ : Category.{v_3, u_3} D\nF : C ⥤ D\nX✝ Y✝ : C\n⊢ ∀ {x y z : X✝ ⟶ Y✝}, F.homRel x y → F.homRel y z → F.homRel x z",
"ppTerm": "?m.21",
"assigned": true,
"usedConst... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Homology.HomotopyCategory.HomComplexShift | {
"line": 74,
"column": 62
} | {
"line": 74,
"column": 66
} | {
"line": 74,
"column": 67
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : Preadditive C\nR : Type u_1\ninst✝¹ : Ring R\ninst✝ : Linear R C\nK L M : CochainComplex C ℤ\nn : ℤ\nγ γ₁ γ₂ : Cochain K L n\na n' : ℤ\nhn' : n + a = n'\np q : ℤ\nhpq : p + n' = q\np' : ℤ\nhp' : p' + n = q\n⊢ q = p + (n + a)",
"ppTerm": "?m.118",
... | [
"C : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : Preadditive C\nR : Type u_1\ninst✝¹ : Ring R\ninst✝ : Linear R C\nK L M : CochainComplex C ℤ\nn : ℤ\nγ γ₁ γ₂ : Cochain K L n\na n' : ℤ\nhn' : n + a = n'\np q : ℤ\nhpq : p + n' = q\np' : ℤ\nhp' : p' + n = q\n⊢ q = p + n'"
] | hn', | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.CategoryTheory.Triangulated.Basic | {
"line": 311,
"column": 17
} | {
"line": 311,
"column": 22
} | {
"line": 312,
"column": 2
} | [
{
"pp": "C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : HasShift C ℤ\nT₁ T₂ T₃ : Triangle C\ninst✝⁴ : Preadditive C\nR : Type u_1\ninst✝³ : Semiring R\ninst✝² : Linear R C\ninst✝¹ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝ : ∀ (n : ℤ), Functor.Linear R (shiftFunctor C n)\n⊢ ∀ (x y : R) (b : T₁ ⟶ T₂), (x ... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.Triangulated.Basic | {
"line": 311,
"column": 17
} | {
"line": 311,
"column": 22
} | {
"line": 312,
"column": 2
} | [
{
"pp": "C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : HasShift C ℤ\nT₁ T₂ T₃ : Triangle C\ninst✝⁴ : Preadditive C\nR : Type u_1\ninst✝³ : Semiring R\ninst✝² : Linear R C\ninst✝¹ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝ : ∀ (n : ℤ), Functor.Linear R (shiftFunctor C n)\n⊢ ∀ (x y : R) (b : T₁ ⟶ T₂), (x ... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Triangulated.Basic | {
"line": 311,
"column": 17
} | {
"line": 311,
"column": 22
} | {
"line": 312,
"column": 2
} | [
{
"pp": "C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : HasShift C ℤ\nT₁ T₂ T₃ : Triangle C\ninst✝⁴ : Preadditive C\nR : Type u_1\ninst✝³ : Semiring R\ninst✝² : Linear R C\ninst✝¹ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝ : ∀ (n : ℤ), Functor.Linear R (shiftFunctor C n)\n⊢ ∀ (x y : R) (b : T₁ ⟶ T₂), (x ... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Triangulated.Basic | {
"line": 310,
"column": 17
} | {
"line": 310,
"column": 22
} | {
"line": 311,
"column": 2
} | [
{
"pp": "C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : HasShift C ℤ\nT₁ T₂ T₃ : Triangle C\ninst✝⁴ : Preadditive C\nR : Type u_1\ninst✝³ : Semiring R\ninst✝² : Linear R C\ninst✝¹ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝ : ∀ (n : ℤ), Functor.Linear R (shiftFunctor C n)\n⊢ ∀ (b : T₁ ⟶ T₂), 1 • b = b",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.Triangulated.Basic | {
"line": 310,
"column": 17
} | {
"line": 310,
"column": 22
} | {
"line": 311,
"column": 2
} | [
{
"pp": "C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : HasShift C ℤ\nT₁ T₂ T₃ : Triangle C\ninst✝⁴ : Preadditive C\nR : Type u_1\ninst✝³ : Semiring R\ninst✝² : Linear R C\ninst✝¹ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝ : ∀ (n : ℤ), Functor.Linear R (shiftFunctor C n)\n⊢ ∀ (b : T₁ ⟶ T₂), 1 • b = b",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Triangulated.Basic | {
"line": 310,
"column": 17
} | {
"line": 310,
"column": 22
} | {
"line": 311,
"column": 2
} | [
{
"pp": "C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : HasShift C ℤ\nT₁ T₂ T₃ : Triangle C\ninst✝⁴ : Preadditive C\nR : Type u_1\ninst✝³ : Semiring R\ninst✝² : Linear R C\ninst✝¹ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝ : ∀ (n : ℤ), Functor.Linear R (shiftFunctor C n)\n⊢ ∀ (b : T₁ ⟶ T₂), 1 • b = b",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Triangulated.Basic | {
"line": 312,
"column": 18
} | {
"line": 312,
"column": 23
} | {
"line": 313,
"column": 2
} | [
{
"pp": "C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : HasShift C ℤ\nT₁ T₂ T₃ : Triangle C\ninst✝⁴ : Preadditive C\nR : Type u_1\ninst✝³ : Semiring R\ninst✝² : Linear R C\ninst✝¹ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝ : ∀ (n : ℤ), Functor.Linear R (shiftFunctor C n)\n⊢ ∀ (a : R), a • 0 = 0",
"pp... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.Triangulated.Basic | {
"line": 312,
"column": 18
} | {
"line": 312,
"column": 23
} | {
"line": 313,
"column": 2
} | [
{
"pp": "C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : HasShift C ℤ\nT₁ T₂ T₃ : Triangle C\ninst✝⁴ : Preadditive C\nR : Type u_1\ninst✝³ : Semiring R\ninst✝² : Linear R C\ninst✝¹ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝ : ∀ (n : ℤ), Functor.Linear R (shiftFunctor C n)\n⊢ ∀ (a : R), a • 0 = 0",
"pp... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Triangulated.Basic | {
"line": 312,
"column": 18
} | {
"line": 312,
"column": 23
} | {
"line": 313,
"column": 2
} | [
{
"pp": "C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : HasShift C ℤ\nT₁ T₂ T₃ : Triangle C\ninst✝⁴ : Preadditive C\nR : Type u_1\ninst✝³ : Semiring R\ninst✝² : Linear R C\ninst✝¹ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝ : ∀ (n : ℤ), Functor.Linear R (shiftFunctor C n)\n⊢ ∀ (a : R), a • 0 = 0",
"pp... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Triangulated.Basic | {
"line": 313,
"column": 17
} | {
"line": 313,
"column": 22
} | {
"line": 314,
"column": 2
} | [
{
"pp": "C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : HasShift C ℤ\nT₁ T₂ T₃ : Triangle C\ninst✝⁴ : Preadditive C\nR : Type u_1\ninst✝³ : Semiring R\ninst✝² : Linear R C\ninst✝¹ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝ : ∀ (n : ℤ), Functor.Linear R (shiftFunctor C n)\n⊢ ∀ (a : R) (x y : T₁ ⟶ T₂), a •... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.Triangulated.Basic | {
"line": 313,
"column": 17
} | {
"line": 313,
"column": 22
} | {
"line": 314,
"column": 2
} | [
{
"pp": "C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : HasShift C ℤ\nT₁ T₂ T₃ : Triangle C\ninst✝⁴ : Preadditive C\nR : Type u_1\ninst✝³ : Semiring R\ninst✝² : Linear R C\ninst✝¹ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝ : ∀ (n : ℤ), Functor.Linear R (shiftFunctor C n)\n⊢ ∀ (a : R) (x y : T₁ ⟶ T₂), a •... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Triangulated.Basic | {
"line": 313,
"column": 17
} | {
"line": 313,
"column": 22
} | {
"line": 314,
"column": 2
} | [
{
"pp": "C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : HasShift C ℤ\nT₁ T₂ T₃ : Triangle C\ninst✝⁴ : Preadditive C\nR : Type u_1\ninst✝³ : Semiring R\ninst✝² : Linear R C\ninst✝¹ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝ : ∀ (n : ℤ), Functor.Linear R (shiftFunctor C n)\n⊢ ∀ (a : R) (x y : T₁ ⟶ T₂), a •... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Triangulated.Basic | {
"line": 314,
"column": 17
} | {
"line": 314,
"column": 22
} | {
"line": 315,
"column": 2
} | [
{
"pp": "C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : HasShift C ℤ\nT₁ T₂ T₃ : Triangle C\ninst✝⁴ : Preadditive C\nR : Type u_1\ninst✝³ : Semiring R\ninst✝² : Linear R C\ninst✝¹ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝ : ∀ (n : ℤ), Functor.Linear R (shiftFunctor C n)\n⊢ ∀ (r s : R) (x : T₁ ⟶ T₂), (r ... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.Triangulated.Basic | {
"line": 314,
"column": 17
} | {
"line": 314,
"column": 22
} | {
"line": 315,
"column": 2
} | [
{
"pp": "C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : HasShift C ℤ\nT₁ T₂ T₃ : Triangle C\ninst✝⁴ : Preadditive C\nR : Type u_1\ninst✝³ : Semiring R\ninst✝² : Linear R C\ninst✝¹ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝ : ∀ (n : ℤ), Functor.Linear R (shiftFunctor C n)\n⊢ ∀ (r s : R) (x : T₁ ⟶ T₂), (r ... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Triangulated.Basic | {
"line": 314,
"column": 17
} | {
"line": 314,
"column": 22
} | {
"line": 315,
"column": 2
} | [
{
"pp": "C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : HasShift C ℤ\nT₁ T₂ T₃ : Triangle C\ninst✝⁴ : Preadditive C\nR : Type u_1\ninst✝³ : Semiring R\ninst✝² : Linear R C\ninst✝¹ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝ : ∀ (n : ℤ), Functor.Linear R (shiftFunctor C n)\n⊢ ∀ (r s : R) (x : T₁ ⟶ T₂), (r ... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Triangulated.Basic | {
"line": 315,
"column": 18
} | {
"line": 315,
"column": 23
} | {
"line": 317,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : HasShift C ℤ\nT₁ T₂ T₃ : Triangle C\ninst✝⁴ : Preadditive C\nR : Type u_1\ninst✝³ : Semiring R\ninst✝² : Linear R C\ninst✝¹ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝ : ∀ (n : ℤ), Functor.Linear R (shiftFunctor C n)\n⊢ ∀ (x : T₁ ⟶ T₂), 0 • x = 0",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.Triangulated.Basic | {
"line": 315,
"column": 18
} | {
"line": 315,
"column": 23
} | {
"line": 317,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : HasShift C ℤ\nT₁ T₂ T₃ : Triangle C\ninst✝⁴ : Preadditive C\nR : Type u_1\ninst✝³ : Semiring R\ninst✝² : Linear R C\ninst✝¹ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝ : ∀ (n : ℤ), Functor.Linear R (shiftFunctor C n)\n⊢ ∀ (x : T₁ ⟶ T₂), 0 • x = 0",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Triangulated.Basic | {
"line": 315,
"column": 18
} | {
"line": 315,
"column": 23
} | {
"line": 317,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : HasShift C ℤ\nT₁ T₂ T₃ : Triangle C\ninst✝⁴ : Preadditive C\nR : Type u_1\ninst✝³ : Semiring R\ninst✝² : Linear R C\ninst✝¹ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝ : ∀ (n : ℤ), Functor.Linear R (shiftFunctor C n)\n⊢ ∀ (x : T₁ ⟶ T₂), 0 • x = 0",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Triangulated.Basic | {
"line": 401,
"column": 2
} | {
"line": 408,
"column": 12
} | {
"line": 410,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : HasShift C ℤ\nJ : Type u_1\nT : J → Triangle C\ninst✝⁴ : HasProduct fun j ↦ (T j).obj₁\ninst✝³ : HasProduct fun j ↦ (T j).obj₂\ninst✝² : HasProduct fun j ↦ (T j).obj₃\ninst✝¹ : HasProduct fun j ↦ (shiftFunctor C 1).obj (T j).obj₁\ninst✝ : HasZeroMorphism... | [] | have : HasProduct (fun j => (T j).obj₂⟦(1 : ℤ)⟧) :=
⟨_, isLimitFanMkObjOfIsLimit (shiftFunctor C (1 : ℤ)) _ _
(productIsProduct (fun j => (T j).obj₂))⟩
dsimp
change _ ≫ (Pi.lift (fun j => Pi.π _ j ≫ (T j).mor₁))⟦(1 : ℤ)⟧' = 0
rw [assoc, ← cancel_mono (piComparison _ _), zero_comp, assoc, assoc]
ext j
... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Triangulated.Basic | {
"line": 401,
"column": 2
} | {
"line": 408,
"column": 12
} | {
"line": 410,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : HasShift C ℤ\nJ : Type u_1\nT : J → Triangle C\ninst✝⁴ : HasProduct fun j ↦ (T j).obj₁\ninst✝³ : HasProduct fun j ↦ (T j).obj₂\ninst✝² : HasProduct fun j ↦ (T j).obj₃\ninst✝¹ : HasProduct fun j ↦ (shiftFunctor C 1).obj (T j).obj₁\ninst✝ : HasZeroMorphism... | [] | have : HasProduct (fun j => (T j).obj₂⟦(1 : ℤ)⟧) :=
⟨_, isLimitFanMkObjOfIsLimit (shiftFunctor C (1 : ℤ)) _ _
(productIsProduct (fun j => (T j).obj₂))⟩
dsimp
change _ ≫ (Pi.lift (fun j => Pi.π _ j ≫ (T j).mor₁))⟦(1 : ℤ)⟧' = 0
rw [assoc, ← cancel_mono (piComparison _ _), zero_comp, assoc, assoc]
ext j
... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Triangulated.Pretriangulated | {
"line": 373,
"column": 4
} | {
"line": 373,
"column": 18
} | {
"line": 374,
"column": 4
} | [
{
"pp": "case mp\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), (CategoryTheory.shiftFunctor C n).Additive\nhC : Pretriangulated C\nT : Triangle C\nhT : T ∈ distinguishedTriangles\n⊢ T.mor₁ = 0 ∧ T.mor₃ = 0 → IsIso T.mor₂",
... | [
"case mp\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), (CategoryTheory.shiftFunctor C n).Additive\nhC : Pretriangulated C\nT : Triangle C\nhT : T ∈ distinguishedTriangles\nh₁ : T.mor₁ = 0\nh₃ : T.mor₃ = 0\n⊢ IsIso T.mor₂"
] | intro ⟨h₁, h₃⟩ | Lean.Elab.Tactic.evalIntro | null |
Mathlib.CategoryTheory.Triangulated.Pretriangulated | {
"line": 373,
"column": 4
} | {
"line": 373,
"column": 18
} | {
"line": 374,
"column": 4
} | [
{
"pp": "case mp\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), (CategoryTheory.shiftFunctor C n).Additive\nhC : Pretriangulated C\nT : Triangle C\nhT : T ∈ distinguishedTriangles\n⊢ T.mor₁ = 0 ∧ T.mor₃ = 0 → IsIso T.mor₂",
... | [
"case mp\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), (CategoryTheory.shiftFunctor C n).Additive\nhC : Pretriangulated C\nT : Triangle C\nhT : T ∈ distinguishedTriangles\nh₁ : T.mor₁ = 0\nh₃ : T.mor₃ = 0\n⊢ IsIso T.mor₂"
] | intro ⟨h₁, h₃⟩ | Lean.Elab.Tactic.evalIntro | Lean.Parser.Tactic.intro |
Mathlib.Algebra.Homology.HomotopyCategory.Pretriangulated | {
"line": 111,
"column": 45
} | {
"line": 112,
"column": 22
} | {
"line": 114,
"column": 0
} | [
{
"pp": "C : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Preadditive C\ninst✝ : HasBinaryBiproducts C\nK₁ L₁ K₂ L₂ : CochainComplex C ℤ\nφ₁ : K₁ ⟶ L₁\nφ₂ : K₂ ⟶ L₂\na : K₁ ⟶ K₂\nb : L₁ ⟶ L₂\nH : Homotopy (φ₁ ≫ b) (a ≫ φ₂)\n⊢ inr φ₁ ≫ mapOfHomotopy H = b ≫ inr φ₂",
"ppTerm": "?m.101",
"assigned": ... | [] | by
simp [mapOfHomotopy] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Homology.HomotopyCategory.Pretriangulated | {
"line": 382,
"column": 2
} | {
"line": 382,
"column": 91
} | {
"line": 383,
"column": 2
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝⁵ : Category.{v_1, u_1} C\ninst✝⁴ : Category.{v_2, u_2} D\ninst✝³ : Preadditive C\ninst✝² : HasBinaryBiproducts C\ninst✝¹ : Preadditive D\ninst✝ : HasBinaryBiproducts D\nK L : CochainComplex C ℤ\nφ : K ⟶ L\nn : ℤ\n⊢ (Triangle.shiftFunctor (CochainComplex C ℤ) n).obj (tr... | [
"case refine_1\nC : Type u_1\nD : Type u_2\ninst✝⁵ : Category.{v_1, u_1} C\ninst✝⁴ : Category.{v_2, u_2} D\ninst✝³ : Preadditive C\ninst✝² : HasBinaryBiproducts C\ninst✝¹ : Preadditive D\ninst✝ : HasBinaryBiproducts D\nK L : CochainComplex C ℤ\nφ : K ⟶ L\nn : ℤ\n⊢ ((Triangle.shiftFunctor (CochainComplex C ℤ) n).obj... | refine Triangle.isoMk _ _ (Iso.refl _) (n.negOnePow • Iso.refl _) (shiftIso φ n) ?_ ?_ ?_ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.CategoryTheory.Triangulated.Functor | {
"line": 204,
"column": 4
} | {
"line": 204,
"column": 71
} | {
"line": 206,
"column": 0
} | [
{
"pp": "C : Type u_1\nD : Type u_2\nE : Type u_3\ninst✝²⁰ : Category.{v_1, u_1} C\ninst✝¹⁹ : Category.{v_2, u_2} D\ninst✝¹⁸ : Category.{v_3, u_3} E\ninst✝¹⁷ : HasShift C ℤ\ninst✝¹⁶ : HasShift D ℤ\ninst✝¹⁵ : HasShift E ℤ\nF : C ⥤ D\ninst✝¹⁴ : F.CommShift ℤ\nG : D ⥤ E\ninst✝¹³ : G.CommShift ℤ\ninst✝¹² : HasZeroO... | [] | rw [h₁, F.map_comp, F.map_comp, F.map_id, h₂, zero_comp, comp_zero] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.CategoryTheory.PathCategory.Basic | {
"line": 138,
"column": 2
} | {
"line": 138,
"column": 33
} | {
"line": 139,
"column": 2
} | [
{
"pp": "V : Type u₁\ninst✝¹ : Quiver V\nC : Type u_1\ninst✝ : Category.{v_1, u_1} C\nφ : V ⥤q C\nX Y : V\nf : X ⟶ Y\n⊢ (lift φ).map f.toPath = φ.map f",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.... | [
"V : Type u₁\ninst✝¹ : Quiver V\nC : Type u_1\ninst✝ : Category.{v_1, u_1} C\nφ : V ⥤q C\nX Y : V\nf : X ⟶ Y\n⊢ 𝟙 (φ.obj X) ≫ φ.map f = φ.map f"
] | dsimp [Quiver.Hom.toPath, lift] | Lean.Elab.Tactic.evalDSimp | Lean.Parser.Tactic.dsimp |
Mathlib.CategoryTheory.Localization.Construction | {
"line": 161,
"column": 37
} | {
"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": ... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.Localization.Construction | {
"line": 161,
"column": 37
} | {
"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": ... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Localization.Construction | {
"line": 161,
"column": 37
} | {
"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": ... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Localization.Construction | {
"line": 161,
"column": 37
} | {
"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 ... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.Localization.Construction | {
"line": 161,
"column": 37
} | {
"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 ... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Localization.Construction | {
"line": 161,
"column": 37
} | {
"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 ... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Localization.Construction | {
"line": 161,
"column": 37
} | {
"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... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.Localization.Construction | {
"line": 161,
"column": 37
} | {
"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... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Localization.Construction | {
"line": 161,
"column": 37
} | {
"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... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Localization.Construction | {
"line": 161,
"column": 37
} | {
"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... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.Localization.Construction | {
"line": 161,
"column": 37
} | {
"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... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Localization.Construction | {
"line": 161,
"column": 37
} | {
"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... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Localization.Construction | {
"line": 174,
"column": 2
} | {
"line": 179,
"column": 32
} | {
"line": 180,
"column": 2
} | [
{
"pp": "C : Type uC\ninst✝¹ : Category.{uC', uC} C\nW : MorphismProperty C\nD : Type uD\ninst✝ : Category.{uD', uD} D\nG₁ G₂ : W.Localization ⥤ D\nh : W.Q ⋙ G₁ = W.Q ⋙ G₂\n⊢ G₁ = G₂",
"ppTerm": "?m.34",
"assigned": true,
"usedConstants": [
"CategoryTheory.Functor",
"CategoryTheory.Categ... | [
"C : Type uC\ninst✝¹ : Category.{uC', uC} C\nW : MorphismProperty C\nD : Type uD\ninst✝ : Category.{uD', uD} D\nG₁ G₂ : W.Localization ⥤ D\nh : W.Q ⋙ G₁ = W.Q ⋙ G₂\n⊢ Quotient.functor (relations W) ⋙ G₁ = Quotient.functor (relations W) ⋙ G₂"
] | suffices h' : Quotient.functor _ ⋙ G₁ = Quotient.functor _ ⋙ G₂ by
refine Functor.ext ?_ ?_
· rintro ⟨⟨X⟩⟩
apply Functor.congr_obj h
· rintro ⟨⟨X⟩⟩ ⟨⟨Y⟩⟩ ⟨f⟩
apply Functor.congr_hom h' | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticSuffices__1 | Lean.Parser.Tactic.tacticSuffices_ |
Mathlib.CategoryTheory.Localization.Construction | {
"line": 224,
"column": 6
} | {
"line": 226,
"column": 70
} | {
"line": 227,
"column": 4
} | [
{
"pp": "C : Type uC\ninst✝¹ : Category.{uC', uC} C\nW : MorphismProperty C\nP : MorphismProperty W.Localization\ninst✝ : P.IsStableUnderComposition\nhP₁ : ∀ ⦃X Y : C⦄ (f : X ⟶ Y), P (W.Q.map f)\nhP₂ : ∀ ⦃X Y : C⦄ (w : X ⟶ Y) (hw : W w), P (wInv w hw)\nX Y : W.Localization\nf : X ⟶ Y\na✝ : ⊤ f\nG : Paths (LocQu... | [] | rcases X with ⟨⟨X⟩⟩
rcases Y with ⟨⟨Y⟩⟩
simpa only [Functor.map_preimage] using! this _ _ (G.preimage f) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Localization.Construction | {
"line": 224,
"column": 6
} | {
"line": 226,
"column": 70
} | {
"line": 227,
"column": 4
} | [
{
"pp": "C : Type uC\ninst✝¹ : Category.{uC', uC} C\nW : MorphismProperty C\nP : MorphismProperty W.Localization\ninst✝ : P.IsStableUnderComposition\nhP₁ : ∀ ⦃X Y : C⦄ (f : X ⟶ Y), P (W.Q.map f)\nhP₂ : ∀ ⦃X Y : C⦄ (w : X ⟶ Y) (hw : W w), P (wInv w hw)\nX Y : W.Localization\nf : X ⟶ Y\na✝ : ⊤ f\nG : Paths (LocQu... | [] | rcases X with ⟨⟨X⟩⟩
rcases Y with ⟨⟨Y⟩⟩
simpa only [Functor.map_preimage] using! this _ _ (G.preimage f) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Localization.CalculusOfFractions.ComposableArrows | {
"line": 43,
"column": 6
} | {
"line": 43,
"column": 68
} | {
"line": 44,
"column": 6
} | [
{
"pp": "case succ\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\nthis : L.EssSurj\nn : ℕ\nhn : ∀ (Y : ComposableArrows D n), (L.mapComposableArrows n).essImage Y\... | [
"case succ\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\nthis : L.EssSurj\nn : ℕ\nhn : ∀ (Y : ComposableArrows D n), (L.mapComposableArrows n).essImage Y\nY : Composa... | obtain ⟨Y, Z, f, rfl⟩ := ComposableArrows.precomp_surjective Y | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.CategoryTheory.Localization.Predicate | {
"line": 444,
"column": 10
} | {
"line": 444,
"column": 15
} | {
"line": 446,
"column": 0
} | [
{
"pp": "case functor\nC : Type u_1\ninst✝⁴ : Category.{v_1, u_1} C\nD₁ : Type u_4\nD₂ : Type u_5\ninst✝³ : Category.{v_4, u_4} D₁\ninst✝² : Category.{v_5, u_5} D₂\nL₁ : C ⥤ D₁\nL₂ : C ⥤ D₂\nW' : MorphismProperty C\ninst✝¹ : L₁.IsLocalization W'\ninst✝ : L₂.IsLocalization W'\n⊢ { functor := (equivalenceFromMode... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.Localization.Predicate | {
"line": 444,
"column": 10
} | {
"line": 444,
"column": 15
} | {
"line": 446,
"column": 0
} | [
{
"pp": "case inverse\nC : Type u_1\ninst✝⁴ : Category.{v_1, u_1} C\nD₁ : Type u_4\nD₂ : Type u_5\ninst✝³ : Category.{v_4, u_4} D₁\ninst✝² : Category.{v_5, u_5} D₂\nL₁ : C ⥤ D₁\nL₂ : C ⥤ D₂\nW' : MorphismProperty C\ninst✝¹ : L₁.IsLocalization W'\ninst✝ : L₂.IsLocalization W'\n⊢ { functor := (equivalenceFromMode... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.Localization.Predicate | {
"line": 444,
"column": 10
} | {
"line": 444,
"column": 15
} | {
"line": 446,
"column": 0
} | [
{
"pp": "case unitIso\nC : Type u_1\ninst✝⁴ : Category.{v_1, u_1} C\nD₁ : Type u_4\nD₂ : Type u_5\ninst✝³ : Category.{v_4, u_4} D₁\ninst✝² : Category.{v_5, u_5} D₂\nL₁ : C ⥤ D₁\nL₂ : C ⥤ D₂\nW' : MorphismProperty C\ninst✝¹ : L₁.IsLocalization W'\ninst✝ : L₂.IsLocalization W'\n⊢ { functor := (equivalenceFromMode... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.Localization.Predicate | {
"line": 444,
"column": 10
} | {
"line": 444,
"column": 15
} | {
"line": 446,
"column": 0
} | [
{
"pp": "case counitIso\nC : Type u_1\ninst✝⁴ : Category.{v_1, u_1} C\nD₁ : Type u_4\nD₂ : Type u_5\ninst✝³ : Category.{v_4, u_4} D₁\ninst✝² : Category.{v_5, u_5} D₂\nL₁ : C ⥤ D₁\nL₂ : C ⥤ D₂\nW' : MorphismProperty C\ninst✝¹ : L₁.IsLocalization W'\ninst✝ : L₂.IsLocalization W'\n⊢ { functor := (equivalenceFromMo... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.Localization.CalculusOfFractions | {
"line": 269,
"column": 2
} | {
"line": 270,
"column": 61
} | {
"line": 271,
"column": 2
} | [
{
"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 :... | have eq : z₂.s ≫ u₂ ≫ v₅ = z₂.s ≫ t₂ ≫ v₄ := by
simpa only [← reassoc_of% hsu, reassoc_of% hst] using fac | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.CategoryTheory.Localization.CalculusOfFractions | {
"line": 319,
"column": 2
} | {
"line": 319,
"column": 34
} | {
"line": 320,
"column": 2
} | [
{
"pp": "case refine_2\nC : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\nW : MorphismProperty C\ninst✝ : W.HasLeftCalculusOfFractions\nX Y✝ Z : C\nz₁ : W.LeftFraction X Y✝\nz₂ : W.LeftFraction Y✝ Z\nz₃ z₃' : W.LeftFraction z₁.Y' z₂.Y'\nh₃ : z₂.f ≫ z₃.s = z₁.s ≫ z₃.f\nh₃' : z₂.f ≫ z₃'.s = z₁.s ≫ z₃'.f\nz₄ : W.LeftF... | [
"case refine_3\nC : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\nW : MorphismProperty C\ninst✝ : W.HasLeftCalculusOfFractions\nX Y✝ Z : C\nz₁ : W.LeftFraction X Y✝\nz₂ : W.LeftFraction Y✝ Z\nz₃ z₃' : W.LeftFraction z₁.Y' z₂.Y'\nh₃ : z₂.f ≫ z₃.s = z₁.s ≫ z₃.f\nh₃' : z₂.f ≫ z₃'.s = z₁.s ≫ z₃'.f\nz₄ : W.LeftFraction z₃.Y... | · simp only [comp₀, assoc, fac'] | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.CategoryTheory.Localization.CalculusOfFractions.Fractions | {
"line": 293,
"column": 4
} | {
"line": 296,
"column": 17
} | {
"line": 298,
"column": 0
} | [
{
"pp": "case refine_2\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\nf f' : L.obj X ⟶ L.obj Y\nφ : W.LeftFraction X Y\nhφ : f = φ.map L ⋯\nφ' : W.LeftFrac... | [] | rw [← cancel_mono (L.map (φ'.s ≫ α.s)), hφ']
nth_rw 1 [L.map_comp]
rw [LeftFraction.map_comp_map_s_assoc, LeftFraction.map_comp_map_s,
L.map_comp] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Localization.CalculusOfFractions.Fractions | {
"line": 293,
"column": 4
} | {
"line": 296,
"column": 17
} | {
"line": 298,
"column": 0
} | [
{
"pp": "case refine_2\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\nf f' : L.obj X ⟶ L.obj Y\nφ : W.LeftFraction X Y\nhφ : f = φ.map L ⋯\nφ' : W.LeftFrac... | [] | rw [← cancel_mono (L.map (φ'.s ≫ α.s)), hφ']
nth_rw 1 [L.map_comp]
rw [LeftFraction.map_comp_map_s_assoc, LeftFraction.map_comp_map_s,
L.map_comp] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Shift.Localization | {
"line": 313,
"column": 2
} | {
"line": 313,
"column": 91
} | {
"line": 315,
"column": 0
} | [
{
"pp": "C₁ : Type u_1\nC₂ : Type u_2\ninst✝¹² : Category.{v_1, u_1} C₁\ninst✝¹¹ : Category.{v_2, u_2} C₂\nW₁ : MorphismProperty C₁\nW₂ : MorphismProperty C₂\nΦ : LocalizerMorphism W₁ W₂\nM : Type u_3\ninst✝¹⁰ : AddMonoid M\ninst✝⁹ : HasShift C₁ M\ninst✝⁸ : HasShift C₂ M\ninst✝⁷ : Φ.functor.CommShift M\nD₁ : Ty... | [] | simp [Functor.commShiftIso_comp_hom_app, commShift_iso_hom_app, ← Functor.map_comp_assoc] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.CategoryTheory.Localization.CalculusOfFractions.Preadditive | {
"line": 337,
"column": 10
} | {
"line": 337,
"column": 60
} | {
"line": 338,
"column": 8
} | [
{
"pp": "C : 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 : Pread... | [
"C : 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 : Preadditive D\nin... | ← cancel_mono (G.map (L.objObjPreimageIso Y).inv), | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.SetTheory.Cardinal.HasCardinalLT | {
"line": 115,
"column": 36
} | {
"line": 115,
"column": 56
} | {
"line": 115,
"column": 56
} | [
{
"pp": "X : Type u\nκ : Cardinal.{w}\nhκ : Cardinal.aleph0 ≤ κ\n⊢ HasCardinalLT X κ ∧ HasCardinalLT PUnit.{1} κ ↔ HasCardinalLT X κ",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"HasCardinalLT",
"congrArg",
"id",
"And",
"Iff",
"PUnit",... | [
"X : Type u\nκ : Cardinal.{w}\nhκ : Cardinal.aleph0 ≤ κ\n⊢ HasCardinalLT X κ → HasCardinalLT PUnit.{1} κ"
] | and_iff_left_iff_imp | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.SetTheory.Cardinal.HasCardinalLT | {
"line": 176,
"column": 2
} | {
"line": 176,
"column": 7
} | {
"line": 178,
"column": 0
} | [
{
"pp": "ι : Type u_1\nX : Type u_2\nS : ι → Set X\nκ : Cardinal.{u_3}\ninst✝ : Fact κ.IsRegular\nhι : HasCardinalLT ι κ\nhS : ∀ (i : ι), HasCardinalLT (↑(S i)) κ\n⊢ ⋃ i, S i = setOf (⨆ i, S i)",
"ppTerm": "?m.121",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"congrAr... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.ObjectProperty.LimitsClosure | {
"line": 160,
"column": 22
} | {
"line": 160,
"column": 27
} | {
"line": 160,
"column": 27
} | [
{
"pp": "C : Type u\ninst✝¹¹ : Category.{v, u} C\nP : ObjectProperty C\nα : Type t\nJ : α → Type u'\ninst✝¹⁰ : (a : α) → Category.{v', u'} (J a)\nβ : Type w'\ninst✝⁹ : LinearOrder β\ninst✝⁸ : OrderBot β\ninst✝⁷ : SuccOrder β\ninst✝⁶ : WellFoundedLT β\ninst✝⁵ : ObjectProperty.Small.{w, v, u} P\ninst✝⁴ : LocallyS... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.ObjectProperty.LimitsClosure | {
"line": 160,
"column": 22
} | {
"line": 160,
"column": 27
} | {
"line": 160,
"column": 27
} | [
{
"pp": "C : Type u\ninst✝¹¹ : Category.{v, u} C\nP : ObjectProperty C\nα : Type t\nJ : α → Type u'\ninst✝¹⁰ : (a : α) → Category.{v', u'} (J a)\nβ : Type w'\ninst✝⁹ : LinearOrder β\ninst✝⁸ : OrderBot β\ninst✝⁷ : SuccOrder β\ninst✝⁶ : WellFoundedLT β\ninst✝⁵ : ObjectProperty.Small.{w, v, u} P\ninst✝⁴ : LocallyS... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.ObjectProperty.LimitsClosure | {
"line": 160,
"column": 22
} | {
"line": 160,
"column": 27
} | {
"line": 160,
"column": 27
} | [
{
"pp": "C : Type u\ninst✝¹¹ : Category.{v, u} C\nP : ObjectProperty C\nα : Type t\nJ : α → Type u'\ninst✝¹⁰ : (a : α) → Category.{v', u'} (J a)\nβ : Type w'\ninst✝⁹ : LinearOrder β\ninst✝⁸ : OrderBot β\ninst✝⁷ : SuccOrder β\ninst✝⁶ : WellFoundedLT β\ninst✝⁵ : ObjectProperty.Small.{w, v, u} P\ninst✝⁴ : LocallyS... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.ObjectProperty.FiniteProducts | {
"line": 137,
"column": 2
} | {
"line": 137,
"column": 70
} | {
"line": 138,
"column": 2
} | [
{
"pp": "C : Type u_1\ninst✝³ : Category.{v_1, u_1} C\nP : ObjectProperty C\ninst✝² : HasFiniteProducts C\ninst✝¹ : P.IsClosedUnderLimitsOfShape (Discrete PEmpty.{1})\ninst✝ : P.IsClosedUnderBinaryProducts\nthis✝ : P.IsClosedUnderIsomorphisms\nthis : HasFiniteProducts P.FullSubcategory\n⊢ P.IsClosedUnderFiniteP... | [
"C : Type u_1\ninst✝³ : Category.{v_1, u_1} C\nP : ObjectProperty C\ninst✝² : HasFiniteProducts C\ninst✝¹ : P.IsClosedUnderLimitsOfShape (Discrete PEmpty.{1})\ninst✝ : P.IsClosedUnderBinaryProducts\nthis✝¹ : P.IsClosedUnderIsomorphisms\nthis✝ : HasFiniteProducts P.FullSubcategory\nthis : PreservesFiniteProducts P.ι... | have := PreservesFiniteProducts.of_preserves_binary_and_terminal P.ι | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.CategoryTheory.ObjectProperty.Shift | {
"line": 87,
"column": 4
} | {
"line": 87,
"column": 25
} | {
"line": 88,
"column": 4
} | [
{
"pp": "C : Type u_1\ninst✝⁵ : Category.{v_1, u_1} C\nP Q : ObjectProperty C\nA : Type u_2\ninst✝⁴ : AddMonoid A\ninst✝³ : HasShift C A\nE : Type u_3\ninst✝² : Category.{v_2, u_3} E\ninst✝¹ : HasShift E A\na : A\ninst✝ : P.IsStableUnderShiftBy a\n⊢ P.isoClosure ≤ P.isoClosure.shift a",
"ppTerm": "?m.26",
... | [
"C : Type u_1\ninst✝⁵ : Category.{v_1, u_1} C\nP Q : ObjectProperty C\nA : Type u_2\ninst✝⁴ : AddMonoid A\ninst✝³ : HasShift C A\nE : Type u_3\ninst✝² : Category.{v_2, u_3} E\ninst✝¹ : HasShift E A\na : A\ninst✝ : P.IsStableUnderShiftBy a\nX Y : C\nhY : P Y\ne : X ≅ Y\n⊢ P.isoClosure.shift a X"
] | rintro X ⟨Y, hY, ⟨e⟩⟩ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRIntro | Lean.Parser.Tactic.rintro |
Mathlib.CategoryTheory.ObjectProperty.Shift | {
"line": 143,
"column": 2
} | {
"line": 143,
"column": 48
} | {
"line": 145,
"column": 0
} | [
{
"pp": "C : Type u_1\ninst✝⁴ : Category.{v_1, u_1} C\nP : ObjectProperty C\nA : Type u_2\ninst✝³ : AddMonoid A\ninst✝² : HasShift C A\ninst✝¹ : P.IsClosedUnderIsomorphisms\ninst✝ : P.IsStableUnderShift A\nX Y : C\na : A\ni : X ≅ (shiftFunctor C a).obj Y\nhY : P Y\n⊢ P X",
"ppTerm": "?m.52",
"assigned":... | [] | exact P.prop_of_iso i.symm (P.le_shift a Y hY) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.CategoryTheory.ObjectProperty.Shift | {
"line": 171,
"column": 43
} | {
"line": 171,
"column": 70
} | {
"line": 171,
"column": 70
} | [
{
"pp": "C : Type u_1\ninst✝³ : Category.{v_1, u_1} C\nP : ObjectProperty C\nA : Type u_2\ninst✝² : AddMonoid A\ninst✝¹ : HasShift C A\ninst✝ : P.IsClosedUnderIsomorphisms\nh : P.shiftClosure A = P\n⊢ P.IsStableUnderShift A",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"Eq.mpr",
... | [] | by rw [← h]; infer_instance | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Localization.CalculusOfFractions | {
"line": 979,
"column": 2
} | {
"line": 979,
"column": 29
} | {
"line": 980,
"column": 2
} | [
{
"pp": "case mp\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\nX Y : C\nφ ψ : W.RightFraction X Y\n⊢ φ.map L ⋯ = ψ.map L ⋯ → (φ.map L ⋯).op = (ψ.map L ⋯).op",
... | [
"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\nX Y : C\nφ ψ : W.RightFraction X Y\n⊢ (φ.map L ⋯).op = (ψ.map L ⋯).op → φ.map L ⋯ = ψ.map L ⋯"
] | · apply Quiver.Hom.unop_inj | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.CategoryTheory.Shift.ShiftedHom | {
"line": 186,
"column": 69
} | {
"line": 187,
"column": 47
} | {
"line": 189,
"column": 0
} | [
{
"pp": "C : Type u_1\ninst✝⁸ : Category.{v_1, u_1} C\nD : Type u_2\ninst✝⁷ : Category.{v_2, u_2} D\nE : Type u_3\ninst✝⁶ : Category.{v_3, u_3} E\nM : Type u_4\ninst✝⁵ : AddMonoid M\ninst✝⁴ : HasShift C M\ninst✝³ : HasShift D M\ninst✝² : HasShift E M\nX Y : C\na : M\nf : ShiftedHom X Y a\nF : C ⥤ D\ninst✝¹ : F.... | [] | by
simp [map, Functor.commShiftIso_comp_hom_app] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Triangulated.Subcategory | {
"line": 378,
"column": 32
} | {
"line": 378,
"column": 45
} | {
"line": 378,
"column": 46
} | [
{
"pp": "case succ\nC : 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✝ : IsTriangulated C\nm m' : ℕ\nh : m = m' + 1\nn : ℕ\nhn : P.extensio... | [
"case succ\nC : 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✝ : IsTriangulated C\nm m' : ℕ\nh : m = m' + 1\nn : ℕ\nhn : P.extensionProductIter... | add_comm 1 m, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Homology.HomotopyCategory.ShiftSequence | {
"line": 80,
"column": 2
} | {
"line": 80,
"column": 15
} | {
"line": 80,
"column": 16
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Preadditive C\nn m mn : ℤ\nhmn : m + n = mn\na a' a'' : ℤ\nha' : n + a = a'\nha'' : m + a' = a''\nK : CochainComplex C ℤ\n⊢ (shiftShortComplexFunctorIso C mn a a'' ⋯).hom.app K =\n (shortComplexFunctor C (up ℤ) a).map ((CategoryTheory.shiftFuncto... | [
"case h₁\nC : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Preadditive C\nn m mn : ℤ\nhmn : m + n = mn\na a' a'' : ℤ\nha' : n + a = a'\nha'' : m + a' = a''\nK : CochainComplex C ℤ\n⊢ mn.negOnePow • (XIsoOfEq K ⋯).hom =\n ((CategoryTheory.shiftFunctorAdd' (CochainComplex C ℤ) m n mn hmn).hom.app K).f ((up ℤ)... | ext <;> dsimp | Lean.Parser.Tactic.«_aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tactic_<;>__1» | Lean.Parser.Tactic.«tactic_<;>_» |
Mathlib.Algebra.Homology.HomotopyCategory.SingleFunctors | {
"line": 76,
"column": 4
} | {
"line": 76,
"column": 9
} | {
"line": 78,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝⁴ : Category.{v, u} C\ninst✝³ : Preadditive C\ninst✝² : HasZeroObject C\nR : Type u_1\ninst✝¹ : Ring R\nn : ℤ\ninst✝ : Linear R C\nX✝ Y✝ : C\nf : X✝ ⟶ Y✝\nr : R\n⊢ { f := fun i ↦ if h : i = n then eqToHom ⋯ ≫ (r • f) ≫ eqToHom ⋯ else 0, comm' := ⋯ } =\n r • { f := fun i ↦ if h : i =... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.Triangulated.Subcategory | {
"line": 621,
"column": 32
} | {
"line": 626,
"column": 76
} | {
"line": 627,
"column": 2
} | [
{
"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✝... | [] | by
obtain ⟨Z, f, g, H, mem⟩ := φ.hs
obtain ⟨X', f', h', mem'⟩ := distinguished_cocone_triangle₁ (φ.f ≫ f)
obtain ⟨a, ⟨ha₁, _⟩⟩ := complete_distinguished_triangle_morphism₁ _ _
mem' H φ.f (𝟙 Z) (by simp)
exact ⟨MorphismProperty.RightFraction.mk f' ⟨_, _, _, mem', mem⟩ a, ha₁⟩ | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Triangulated.Subcategory | {
"line": 731,
"column": 4
} | {
"line": 737,
"column": 45
} | {
"line": 737,
"column": 45
} | [
{
"pp": "C : Type u_1\ninst✝¹⁷ : Category.{v_1, u_1} C\ninst✝¹⁶ : HasZeroObject C\ninst✝¹⁵ : HasShift C ℤ\ninst✝¹⁴ : Preadditive C\ninst✝¹³ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝¹² : Pretriangulated C\nD : Type u_2\ninst✝¹¹ : Category.{v_2, u_2} D\ninst✝¹⁰ : Preadditive D\ninst✝⁹ : HasZeroObject D\nins... | [] | rintro T hT ⟨X₁, ⟨e₁⟩⟩ ⟨X₃, ⟨e₃⟩⟩
have ⟨h, hh⟩ := F.map_surjective (e₃.hom ≫ T.mor₃ ≫ e₁.inv⟦1⟧' ≫
(F.commShiftIso (1 : ℤ)).inv.app X₁)
obtain ⟨X₂, f, g, H⟩ := distinguished_cocone_triangle₂ h
exact ⟨X₂, ⟨Triangle.π₂.mapIso
(isoTriangleOfIso₁₃ _ _ (F.map_distinguished _ H) hT e₁ e₃
(by s... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Triangulated.Subcategory | {
"line": 731,
"column": 4
} | {
"line": 737,
"column": 45
} | {
"line": 737,
"column": 45
} | [
{
"pp": "C : Type u_1\ninst✝¹⁷ : Category.{v_1, u_1} C\ninst✝¹⁶ : HasZeroObject C\ninst✝¹⁵ : HasShift C ℤ\ninst✝¹⁴ : Preadditive C\ninst✝¹³ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝¹² : Pretriangulated C\nD : Type u_2\ninst✝¹¹ : Category.{v_2, u_2} D\ninst✝¹⁰ : Preadditive D\ninst✝⁹ : HasZeroObject D\nins... | [] | rintro T hT ⟨X₁, ⟨e₁⟩⟩ ⟨X₃, ⟨e₃⟩⟩
have ⟨h, hh⟩ := F.map_surjective (e₃.hom ≫ T.mor₃ ≫ e₁.inv⟦1⟧' ≫
(F.commShiftIso (1 : ℤ)).inv.app X₁)
obtain ⟨X₂, f, g, H⟩ := distinguished_cocone_triangle₂ h
exact ⟨X₂, ⟨Triangle.π₂.mapIso
(isoTriangleOfIso₁₃ _ _ (F.map_distinguished _ H) hT e₁ e₃
(by s... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Homology.Embedding.Extend | {
"line": 224,
"column": 4
} | {
"line": 224,
"column": 63
} | {
"line": 226,
"column": 0
} | [
{
"pp": "case neg\nι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝² : Category.{v_1, u_3} C\ninst✝¹ : HasZeroObject C\ninst✝ : HasZeroMorphisms C\nK L M : HomologicalComplex C c\nφ : K ⟶ L\nφ' : L ⟶ M\ne : c.Embedding c'\ni' : ι'\nhi' : ¬∃ i, e.f i = i'\n⊢ (extendMap (... | [] | simp [extendMap_f_eq_zero _ e i' (fun i hi => hi' ⟨i, hi⟩)] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.Homology.Embedding.Extend | {
"line": 224,
"column": 4
} | {
"line": 224,
"column": 63
} | {
"line": 226,
"column": 0
} | [
{
"pp": "case neg\nι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝² : Category.{v_1, u_3} C\ninst✝¹ : HasZeroObject C\ninst✝ : HasZeroMorphisms C\nK L M : HomologicalComplex C c\nφ : K ⟶ L\nφ' : L ⟶ M\ne : c.Embedding c'\ni' : ι'\nhi' : ¬∃ i, e.f i = i'\n⊢ (extendMap (... | [] | simp [extendMap_f_eq_zero _ e i' (fun i hi => hi' ⟨i, hi⟩)] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Homology.Embedding.Extend | {
"line": 224,
"column": 4
} | {
"line": 224,
"column": 63
} | {
"line": 226,
"column": 0
} | [
{
"pp": "case neg\nι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝² : Category.{v_1, u_3} C\ninst✝¹ : HasZeroObject C\ninst✝ : HasZeroMorphisms C\nK L M : HomologicalComplex C c\nφ : K ⟶ L\nφ' : L ⟶ M\ne : c.Embedding c'\ni' : ι'\nhi' : ¬∃ i, e.f i = i'\n⊢ (extendMap (... | [] | simp [extendMap_f_eq_zero _ e i' (fun i hi => hi' ⟨i, hi⟩)] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Homology.Embedding.Boundary | {
"line": 144,
"column": 4
} | {
"line": 144,
"column": 45
} | {
"line": 146,
"column": 0
} | [
{
"pp": "case neg\nι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\ninst✝ : e.IsRelIff\nj : ι\nhjk' : ¬c.Rel j j\nhj' : c'.Rel (e.f j) (c'.next (e.f j))\nhj : c'.Rel (e.f j) (c'.next (e.f j)) → ∃ x, c'.Rel (e.f j) (e.f x)\nk : ι\nhjk : k = j\nhk : c.Rel j k\n⊢ False",
... | [] | exact hjk' (by simpa only [hjk] using hk) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Algebra.Homology.HomotopyCategory.Triangulated | {
"line": 164,
"column": 44
} | {
"line": 167,
"column": 63
} | {
"line": 169,
"column": 0
} | [
{
"pp": "C : Type u_1\ninst✝² : Category.{v, u_1} C\ninst✝¹ : Preadditive C\ninst✝ : HasBinaryBiproducts C\nX₁ X₂ X₃ : CochainComplex C ℤ\nf : X₁ ⟶ X₂\ng : X₂ ⟶ X₃\n⊢ (mappingConeCompHomotopyEquiv f g).hom ≫ (triangle (mappingConeCompTriangle f g).mor₁).mor₃ =\n (mappingConeCompTriangle f g).mor₃",
"ppTe... | [] | by
ext n
simp [mappingConeCompHomotopyEquiv, MappingConeCompHomotopyEquiv.hom,
lift_f _ _ _ _ _ (n + 1) rfl, ext_from_iff _ (n + 1) _ rfl] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Homology.Embedding.TruncGE | {
"line": 219,
"column": 2
} | {
"line": 219,
"column": 28
} | {
"line": 221,
"column": 0
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝⁴ : Category.{v_1, u_3} C\ninst✝³ : HasZeroMorphisms C\nK : HomologicalComplex C c'\ne : c.Embedding c'\ninst✝² : e.IsTruncGE\ninst✝¹ : ∀ (i' : ι'), K.HasHomology i'\ninst✝ : HasZeroObject C\n⊢ truncGEMap (𝟙 K) e... | [] | simp [truncGEMap, truncGE] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.Homology.Embedding.TruncGE | {
"line": 219,
"column": 2
} | {
"line": 219,
"column": 28
} | {
"line": 221,
"column": 0
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝⁴ : Category.{v_1, u_3} C\ninst✝³ : HasZeroMorphisms C\nK : HomologicalComplex C c'\ne : c.Embedding c'\ninst✝² : e.IsTruncGE\ninst✝¹ : ∀ (i' : ι'), K.HasHomology i'\ninst✝ : HasZeroObject C\n⊢ truncGEMap (𝟙 K) e... | [] | simp [truncGEMap, truncGE] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Homology.Embedding.TruncGE | {
"line": 219,
"column": 2
} | {
"line": 219,
"column": 28
} | {
"line": 221,
"column": 0
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝⁴ : Category.{v_1, u_3} C\ninst✝³ : HasZeroMorphisms C\nK : HomologicalComplex C c'\ne : c.Embedding c'\ninst✝² : e.IsTruncGE\ninst✝¹ : ∀ (i' : ι'), K.HasHomology i'\ninst✝ : HasZeroObject C\n⊢ truncGEMap (𝟙 K) e... | [] | simp [truncGEMap, truncGE] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Homology.Embedding.TruncGE | {
"line": 223,
"column": 2
} | {
"line": 223,
"column": 28
} | {
"line": 225,
"column": 0
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝⁶ : Category.{v_1, u_3} C\ninst✝⁵ : HasZeroMorphisms C\nK L M : HomologicalComplex C c'\nφ : K ⟶ L\nφ' : L ⟶ M\ne : c.Embedding c'\ninst✝⁴ : e.IsTruncGE\ninst✝³ : ∀ (i' : ι'), K.HasHomology i'\ninst✝² : ∀ (i' : ι'... | [] | simp [truncGEMap, truncGE] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.Homology.Embedding.TruncGE | {
"line": 223,
"column": 2
} | {
"line": 223,
"column": 28
} | {
"line": 225,
"column": 0
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝⁶ : Category.{v_1, u_3} C\ninst✝⁵ : HasZeroMorphisms C\nK L M : HomologicalComplex C c'\nφ : K ⟶ L\nφ' : L ⟶ M\ne : c.Embedding c'\ninst✝⁴ : e.IsTruncGE\ninst✝³ : ∀ (i' : ι'), K.HasHomology i'\ninst✝² : ∀ (i' : ι'... | [] | simp [truncGEMap, truncGE] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Homology.Embedding.TruncGE | {
"line": 223,
"column": 2
} | {
"line": 223,
"column": 28
} | {
"line": 225,
"column": 0
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝⁶ : Category.{v_1, u_3} C\ninst✝⁵ : HasZeroMorphisms C\nK L M : HomologicalComplex C c'\nφ : K ⟶ L\nφ' : L ⟶ M\ne : c.Embedding c'\ninst✝⁴ : e.IsTruncGE\ninst✝³ : ∀ (i' : ι'), K.HasHomology i'\ninst✝² : ∀ (i' : ι'... | [] | simp [truncGEMap, truncGE] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Homology.Embedding.ExtendHomology | {
"line": 381,
"column": 6
} | {
"line": 381,
"column": 52
} | {
"line": 381,
"column": 53
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝⁴ : Category.{v_1, u_3} C\ninst✝³ : HasZeroMorphisms C\ninst✝² : HasZeroObject C\nK : HomologicalComplex C c\ne : c.Embedding c'\nj : ι\nj' : ι'\nhj' : e.f j = j'\ninst✝¹ : K.HasHomology j\ninst✝ : (K.extend e).Ha... | [
"ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝⁴ : Category.{v_1, u_3} C\ninst✝³ : HasZeroMorphisms C\ninst✝² : HasZeroObject C\nK : HomologicalComplex C c\ne : c.Embedding c'\nj : ι\nj' : ι'\nhj' : e.f j = j'\ninst✝¹ : K.HasHomology j\ninst✝ : (K.extend e).HasHomology j'... | ← cancel_mono (K.extendOpcyclesIso e hj').hom, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Homology.Embedding.CochainComplex | {
"line": 164,
"column": 4
} | {
"line": 167,
"column": 16
} | {
"line": 169,
"column": 0
} | [
{
"pp": "case mpr\nC : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : HasZeroMorphisms C\nK : CochainComplex C ℤ\nn : ℤ\n⊢ (∀ i < n, ExactAt K i) → K.IsGE n",
"ppTerm": "?mpr",
"assigned": true,
"usedConstants": [
"HomologicalComplex.ExactAt",
"Nat.instOne",
"CochainComplex.trun... | [] | intro h
refine IsSupported.mk (fun i hi ↦ ?_)
rw [notMem_range_embeddingUpIntGE_iff] at hi
exact h i hi | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Homology.Embedding.CochainComplex | {
"line": 164,
"column": 4
} | {
"line": 167,
"column": 16
} | {
"line": 169,
"column": 0
} | [
{
"pp": "case mpr\nC : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : HasZeroMorphisms C\nK : CochainComplex C ℤ\nn : ℤ\n⊢ (∀ i < n, ExactAt K i) → K.IsGE n",
"ppTerm": "?mpr",
"assigned": true,
"usedConstants": [
"HomologicalComplex.ExactAt",
"Nat.instOne",
"CochainComplex.trun... | [] | intro h
refine IsSupported.mk (fun i hi ↦ ?_)
rw [notMem_range_embeddingUpIntGE_iff] at hi
exact h i hi | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Homology.Embedding.CochainComplex | {
"line": 229,
"column": 42
} | {
"line": 229,
"column": 47
} | {
"line": 229,
"column": 47
} | [
{
"pp": "C : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : HasZeroMorphisms C\nK L : CochainComplex C ℤ\nφ : K ⟶ L\ne : K ≅ L\ninst✝ : HasZeroObject C\nX : CochainComplex C ℕ\nx✝¹ : ℤ\nx✝ : ∀ (i : ℕ), (embeddingUpIntGE 0).f i ≠ x✝¹\n⊢ ∀ (i : ℕ), embeddingUpNat.f i ≠ x✝¹",
"ppTerm": "?m.54",
"assign... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Algebra.Homology.Embedding.CochainComplex | {
"line": 229,
"column": 42
} | {
"line": 229,
"column": 47
} | {
"line": 229,
"column": 47
} | [
{
"pp": "C : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : HasZeroMorphisms C\nK L : CochainComplex C ℤ\nφ : K ⟶ L\ne : K ≅ L\ninst✝ : HasZeroObject C\nX : CochainComplex C ℕ\nx✝¹ : ℤ\nx✝ : ∀ (i : ℕ), (embeddingUpIntGE 0).f i ≠ x✝¹\n⊢ ∀ (i : ℕ), embeddingUpNat.f i ≠ x✝¹",
"ppTerm": "?m.54",
"assign... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Homology.Embedding.CochainComplex | {
"line": 229,
"column": 42
} | {
"line": 229,
"column": 47
} | {
"line": 229,
"column": 47
} | [
{
"pp": "C : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : HasZeroMorphisms C\nK L : CochainComplex C ℤ\nφ : K ⟶ L\ne : K ≅ L\ninst✝ : HasZeroObject C\nX : CochainComplex C ℕ\nx✝¹ : ℤ\nx✝ : ∀ (i : ℕ), (embeddingUpIntGE 0).f i ≠ x✝¹\n⊢ ∀ (i : ℕ), embeddingUpNat.f i ≠ x✝¹",
"ppTerm": "?m.54",
"assign... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Homology.Embedding.CochainComplex | {
"line": 233,
"column": 42
} | {
"line": 233,
"column": 47
} | {
"line": 233,
"column": 47
} | [
{
"pp": "C : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : HasZeroMorphisms C\nK L : CochainComplex C ℤ\nφ : K ⟶ L\ne : K ≅ L\ninst✝ : HasZeroObject C\nX : ChainComplex C ℕ\nx✝¹ : ℤ\nx✝ : ∀ (i : ℕ), (embeddingUpIntLE 0).f i ≠ x✝¹\n⊢ ∀ (i : ℕ), embeddingDownNat.f i ≠ x✝¹",
"ppTerm": "?m.54",
"assign... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
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