module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Algebra.Homology.HomotopyCategory.Triangulated | {
"line": 112,
"column": 30
} | {
"line": 112,
"column": 36
} | {
"line": 112,
"column": 36
} | [
{
"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⊢ -1 + -1 = -2",
"ppTerm": "?m.148",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Int.instDecidableEq",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Homology.HomotopyCategory.Triangulated | {
"line": 112,
"column": 30
} | {
"line": 112,
"column": 36
} | {
"line": 112,
"column": 36
} | [
{
"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⊢ -1 + -1 = -2",
"ppTerm": "?m.148",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Int.instDecidableEq",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Homology.HomotopyCategory.Triangulated | {
"line": 112,
"column": 62
} | {
"line": 112,
"column": 68
} | {
"line": 112,
"column": 68
} | [
{
"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⊢ 1 + -2 = -1",
"ppTerm": "?m.149",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Int.instDecidableEq",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Algebra.Homology.HomotopyCategory.Triangulated | {
"line": 112,
"column": 62
} | {
"line": 112,
"column": 68
} | {
"line": 112,
"column": 68
} | [
{
"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⊢ 1 + -2 = -1",
"ppTerm": "?m.149",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Int.instDecidableEq",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Homology.HomotopyCategory.Triangulated | {
"line": 112,
"column": 62
} | {
"line": 112,
"column": 68
} | {
"line": 112,
"column": 68
} | [
{
"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⊢ 1 + -2 = -1",
"ppTerm": "?m.149",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Int.instDecidableEq",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Homology.HomotopyCategory.Triangulated | {
"line": 115,
"column": 42
} | {
"line": 115,
"column": 48
} | {
"line": 115,
"column": 48
} | [
{
"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⊢ 1 + -2 = -1",
"ppTerm": "?m.219",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Int.instDecidableEq",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Algebra.Homology.HomotopyCategory.Triangulated | {
"line": 115,
"column": 42
} | {
"line": 115,
"column": 48
} | {
"line": 115,
"column": 48
} | [
{
"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⊢ 1 + -2 = -1",
"ppTerm": "?m.219",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Int.instDecidableEq",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Homology.HomotopyCategory.Triangulated | {
"line": 115,
"column": 42
} | {
"line": 115,
"column": 48
} | {
"line": 115,
"column": 48
} | [
{
"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⊢ 1 + -2 = -1",
"ppTerm": "?m.219",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Int.instDecidableEq",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Homology.HomotopyCategory.Triangulated | {
"line": 115,
"column": 63
} | {
"line": 115,
"column": 69
} | {
"line": 115,
"column": 69
} | [
{
"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⊢ -1 + 1 = 0",
"ppTerm": "?m.228",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Int.instDecidableEq",
"... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Algebra.Homology.HomotopyCategory.Triangulated | {
"line": 115,
"column": 63
} | {
"line": 115,
"column": 69
} | {
"line": 115,
"column": 69
} | [
{
"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⊢ -1 + 1 = 0",
"ppTerm": "?m.228",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Int.instDecidableEq",
"... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Homology.HomotopyCategory.Triangulated | {
"line": 115,
"column": 63
} | {
"line": 115,
"column": 69
} | {
"line": 115,
"column": 69
} | [
{
"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⊢ -1 + 1 = 0",
"ppTerm": "?m.228",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Int.instDecidableEq",
"... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Homology.HomotopyCategory.Triangulated | {
"line": 116,
"column": 14
} | {
"line": 116,
"column": 20
} | {
"line": 116,
"column": 20
} | [
{
"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⊢ 1 + 1 = 2",
"ppTerm": "?m.229",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Int.instDecidableEq",
"i... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Algebra.Homology.HomotopyCategory.Triangulated | {
"line": 116,
"column": 14
} | {
"line": 116,
"column": 20
} | {
"line": 116,
"column": 20
} | [
{
"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⊢ 1 + 1 = 2",
"ppTerm": "?m.229",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Int.instDecidableEq",
"i... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Homology.HomotopyCategory.Triangulated | {
"line": 116,
"column": 14
} | {
"line": 116,
"column": 20
} | {
"line": 116,
"column": 20
} | [
{
"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⊢ 1 + 1 = 2",
"ppTerm": "?m.229",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Int.instDecidableEq",
"i... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Homology.HomotopyCategory.Triangulated | {
"line": 116,
"column": 26
} | {
"line": 116,
"column": 32
} | {
"line": 116,
"column": 32
} | [
{
"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⊢ -2 + 1 = -1",
"ppTerm": "?m.230",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Int.instDecidableEq",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Algebra.Homology.HomotopyCategory.Triangulated | {
"line": 116,
"column": 26
} | {
"line": 116,
"column": 32
} | {
"line": 116,
"column": 32
} | [
{
"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⊢ -2 + 1 = -1",
"ppTerm": "?m.230",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Int.instDecidableEq",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Homology.HomotopyCategory.Triangulated | {
"line": 116,
"column": 26
} | {
"line": 116,
"column": 32
} | {
"line": 116,
"column": 32
} | [
{
"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⊢ -2 + 1 = -1",
"ppTerm": "?m.230",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Int.instDecidableEq",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Homology.HomotopyCategory.Triangulated | {
"line": 117,
"column": 45
} | {
"line": 117,
"column": 51
} | {
"line": 117,
"column": 51
} | [
{
"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⊢ -1 + -1 = -2",
"ppTerm": "?m.261",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Int.instDecidableEq",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Algebra.Homology.HomotopyCategory.Triangulated | {
"line": 117,
"column": 45
} | {
"line": 117,
"column": 51
} | {
"line": 117,
"column": 51
} | [
{
"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⊢ -1 + -1 = -2",
"ppTerm": "?m.261",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Int.instDecidableEq",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Homology.HomotopyCategory.Triangulated | {
"line": 117,
"column": 45
} | {
"line": 117,
"column": 51
} | {
"line": 117,
"column": 51
} | [
{
"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⊢ -1 + -1 = -2",
"ppTerm": "?m.261",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Int.instDecidableEq",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Homology.HomotopyCategory.Triangulated | {
"line": 117,
"column": 66
} | {
"line": 117,
"column": 72
} | {
"line": 117,
"column": 72
} | [
{
"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⊢ -2 + 1 = -1",
"ppTerm": "?m.270",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Int.instDecidableEq",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Algebra.Homology.HomotopyCategory.Triangulated | {
"line": 117,
"column": 66
} | {
"line": 117,
"column": 72
} | {
"line": 117,
"column": 72
} | [
{
"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⊢ -2 + 1 = -1",
"ppTerm": "?m.270",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Int.instDecidableEq",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Homology.HomotopyCategory.Triangulated | {
"line": 117,
"column": 66
} | {
"line": 117,
"column": 72
} | {
"line": 117,
"column": 72
} | [
{
"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⊢ -2 + 1 = -1",
"ppTerm": "?m.270",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Int.instDecidableEq",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Homology.HomotopyCategory.Triangulated | {
"line": 118,
"column": 14
} | {
"line": 118,
"column": 20
} | {
"line": 118,
"column": 20
} | [
{
"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⊢ -1 + 1 = 0",
"ppTerm": "?m.271",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Int.instDecidableEq",
"... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Algebra.Homology.HomotopyCategory.Triangulated | {
"line": 118,
"column": 14
} | {
"line": 118,
"column": 20
} | {
"line": 118,
"column": 20
} | [
{
"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⊢ -1 + 1 = 0",
"ppTerm": "?m.271",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Int.instDecidableEq",
"... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Homology.HomotopyCategory.Triangulated | {
"line": 118,
"column": 14
} | {
"line": 118,
"column": 20
} | {
"line": 118,
"column": 20
} | [
{
"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⊢ -1 + 1 = 0",
"ppTerm": "?m.271",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Int.instDecidableEq",
"... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Homology.HomotopyCategory.Triangulated | {
"line": 118,
"column": 26
} | {
"line": 118,
"column": 32
} | {
"line": 118,
"column": 32
} | [
{
"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⊢ -1 + 1 = 0",
"ppTerm": "?m.272",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Int.instDecidableEq",
"... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Algebra.Homology.HomotopyCategory.Triangulated | {
"line": 118,
"column": 26
} | {
"line": 118,
"column": 32
} | {
"line": 118,
"column": 32
} | [
{
"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⊢ -1 + 1 = 0",
"ppTerm": "?m.272",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Int.instDecidableEq",
"... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Homology.HomotopyCategory.Triangulated | {
"line": 118,
"column": 26
} | {
"line": 118,
"column": 32
} | {
"line": 118,
"column": 32
} | [
{
"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⊢ -1 + 1 = 0",
"ppTerm": "?m.272",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Int.instDecidableEq",
"... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Homology.HomotopyCategory.Triangulated | {
"line": 117,
"column": 8
} | {
"line": 118,
"column": 34
} | {
"line": 118,
"column": 35
} | [
{
"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⊢ Cochain.ofHom (inv f g ≫ hom f g) =\n -((snd (mappingConeCompTriangle f g).mor₁).comp\n ((↑(fst (f ≫ g))).comp\n (δ ... | [
"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⊢ Cochain.ofHom (inv f g ≫ hom f g) =\n -((snd (mappingConeCompTriangle f g).mor₁).comp\n ((↑(fst (f ≫ g))).comp\n ((inl f).comp (... | δ_comp _ _ (show (-1) + (-1) = -2 by decide) 0 0 (-1) (by decide)
(by decide) (by decide), | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Homology.HomotopyCategory.Triangulated | {
"line": 119,
"column": 36
} | {
"line": 119,
"column": 42
} | {
"line": 119,
"column": 42
} | [
{
"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⊢ 2 = 1 + 1",
"ppTerm": "?m.284",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Int.instDecidableEq",
"i... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Algebra.Homology.HomotopyCategory.Triangulated | {
"line": 119,
"column": 36
} | {
"line": 119,
"column": 42
} | {
"line": 119,
"column": 42
} | [
{
"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⊢ 2 = 1 + 1",
"ppTerm": "?m.284",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Int.instDecidableEq",
"i... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Homology.HomotopyCategory.Triangulated | {
"line": 119,
"column": 36
} | {
"line": 119,
"column": 42
} | {
"line": 119,
"column": 42
} | [
{
"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⊢ 2 = 1 + 1",
"ppTerm": "?m.284",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Int.instDecidableEq",
"i... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Homology.Embedding.Boundary | {
"line": 108,
"column": 4
} | {
"line": 110,
"column": 41
} | {
"line": 112,
"column": 0
} | [
{
"pp": "case right\nι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\nk' : ι'\nj : ι\nhj : c'.Rel (e.f j) k'\nhk' : ∀ (i : ι), e.f i ≠ k'\n⊢ ∀ (k : ι), ¬c'.Rel (e.f j) (e.f k)",
"ppTerm": "?right",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"... | [] | intro k hk
apply hk' k
rw [← c'.next_eq' hj, c'.next_eq' hk] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Homology.Embedding.Boundary | {
"line": 108,
"column": 4
} | {
"line": 110,
"column": 41
} | {
"line": 112,
"column": 0
} | [
{
"pp": "case right\nι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\nk' : ι'\nj : ι\nhj : c'.Rel (e.f j) k'\nhk' : ∀ (i : ι), e.f i ≠ k'\n⊢ ∀ (k : ι), ¬c'.Rel (e.f j) (e.f k)",
"ppTerm": "?right",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"... | [] | intro k hk
apply hk' k
rw [← c'.next_eq' hj, c'.next_eq' hk] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Homology.Embedding.Extend | {
"line": 331,
"column": 2
} | {
"line": 332,
"column": 66
} | {
"line": 333,
"column": 2
} | [
{
"pp": "case pos\nι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝³ : Category.{v_1, u_3} C\ninst✝² : HasZeroObject C\ninst✝¹ : HasZeroMorphisms C\ne : c.Embedding c'\nK : HomologicalComplex C c\ninst✝ : ∀ (i : ι), Projective (K.X i)\ni' : ι'\nhi' : ∃ i, e.f i = i'\n⊢ ... | [
"case neg\nι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝³ : Category.{v_1, u_3} C\ninst✝² : HasZeroObject C\ninst✝¹ : HasZeroMorphisms C\ne : c.Embedding c'\nK : HomologicalComplex C c\ninst✝ : ∀ (i : ι), Projective (K.X i)\ni' : ι'\nhi' : ∀ (i : ι), e.f i ≠ i'\n⊢ Projec... | · obtain ⟨i, hi⟩ := hi'
exact Projective.of_iso (K.extendXIso e hi).symm inferInstance | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Algebra.Homology.HomotopyCategory.Triangulated | {
"line": 128,
"column": 48
} | {
"line": 128,
"column": 54
} | {
"line": 128,
"column": 54
} | [
{
"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\nn : ℤ\n⊢ 1 + -2 = -1",
"ppTerm": "?m.474",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Int.instDecidableEq",... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Algebra.Homology.HomotopyCategory.Triangulated | {
"line": 128,
"column": 48
} | {
"line": 128,
"column": 54
} | {
"line": 128,
"column": 54
} | [
{
"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\nn : ℤ\n⊢ 1 + -2 = -1",
"ppTerm": "?m.474",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Int.instDecidableEq",... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Homology.HomotopyCategory.Triangulated | {
"line": 128,
"column": 48
} | {
"line": 128,
"column": 54
} | {
"line": 128,
"column": 54
} | [
{
"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\nn : ℤ\n⊢ 1 + -2 = -1",
"ppTerm": "?m.474",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Int.instDecidableEq",... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Homology.HomotopyCategory.Triangulated | {
"line": 130,
"column": 51
} | {
"line": 130,
"column": 57
} | {
"line": 130,
"column": 57
} | [
{
"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\nn : ℤ\n⊢ -1 + -1 = -2",
"ppTerm": "?m.476",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Int.instDecidableEq"... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Algebra.Homology.HomotopyCategory.Triangulated | {
"line": 130,
"column": 51
} | {
"line": 130,
"column": 57
} | {
"line": 130,
"column": 57
} | [
{
"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\nn : ℤ\n⊢ -1 + -1 = -2",
"ppTerm": "?m.476",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Int.instDecidableEq"... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Homology.HomotopyCategory.Triangulated | {
"line": 130,
"column": 51
} | {
"line": 130,
"column": 57
} | {
"line": 130,
"column": 57
} | [
{
"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\nn : ℤ\n⊢ -1 + -1 = -2",
"ppTerm": "?m.476",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Int.instDecidableEq"... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Homology.Embedding.RestrictionHomology | {
"line": 143,
"column": 2
} | {
"line": 143,
"column": 6
} | {
"line": 144,
"column": 2
} | [
{
"pp": "case e_a\nι : 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.IsRelIff\ni j k : ι\nhi : c.prev j = i\nhk : c.next j = k\ni' j' k' : ι'\nhi' : e.f i =... | [
"case e_a\nι : 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.IsRelIff\ni j k : ι\nhi : c.prev j = i\nhk : c.next j = k\ni' j' k' : ι'\nhi' : e.f i = i'\nhj' : e... | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.Algebra.Homology.Embedding.ExtendHomology | {
"line": 249,
"column": 8
} | {
"line": 249,
"column": 62
} | {
"line": 249,
"column": 62
} | [
{
"pp": "ι : 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 : HasZeroMorphisms C\ninst✝ : HasZeroObject C\nK L M : HomologicalComplex C c\nφ : K ⟶ L\nφ' : L ⟶ M\ne : c.Embedding c'\ni j k : ι\ni' j' k' : ι'\nhj' : e.f j = j'\nhi : c.prev j... | [
"ι : 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 : HasZeroMorphisms C\ninst✝ : HasZeroObject C\nK L M : HomologicalComplex C c\nφ : K ⟶ L\nφ' : L ⟶ M\ne : c.Embedding c'\ni j k : ι\ni' j' k' : ι'\nhj' : e.f j = j'\nhi : c.prev j = i\nhi' : ... | ← d_comp_desc_eq_zero_iff K e hj' hi hi' hk hk' _ h.hp | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Homology.Embedding.TruncGE | {
"line": 268,
"column": 4
} | {
"line": 268,
"column": 45
} | {
"line": 270,
"column": 0
} | [
{
"pp": "case neg\nι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝³ : Category.{v_1, u_3} C\ninst✝² : HasZeroMorphisms C\nK : HomologicalComplex C c'\ne : c.Embedding c'\ninst✝¹ : e.IsTruncGE\ninst✝ : ∀ (i' : ι'), K.HasHomology i'\ni j : ι\nhij : ¬c.Rel i j\n⊢ f K e i ... | [] | simp [HomologicalComplex.shape _ _ _ hij] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.Homology.Embedding.TruncGE | {
"line": 268,
"column": 4
} | {
"line": 268,
"column": 45
} | {
"line": 270,
"column": 0
} | [
{
"pp": "case neg\nι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝³ : Category.{v_1, u_3} C\ninst✝² : HasZeroMorphisms C\nK : HomologicalComplex C c'\ne : c.Embedding c'\ninst✝¹ : e.IsTruncGE\ninst✝ : ∀ (i' : ι'), K.HasHomology i'\ni j : ι\nhij : ¬c.Rel i j\n⊢ f K e i ... | [] | simp [HomologicalComplex.shape _ _ _ hij] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Homology.Embedding.TruncGE | {
"line": 268,
"column": 4
} | {
"line": 268,
"column": 45
} | {
"line": 270,
"column": 0
} | [
{
"pp": "case neg\nι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝³ : Category.{v_1, u_3} C\ninst✝² : HasZeroMorphisms C\nK : HomologicalComplex C c'\ne : c.Embedding c'\ninst✝¹ : e.IsTruncGE\ninst✝ : ∀ (i' : ι'), K.HasHomology i'\ni j : ι\nhij : ¬c.Rel i j\n⊢ f K e i ... | [] | simp [HomologicalComplex.shape _ _ _ hij] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Homology.Embedding.TruncGE | {
"line": 326,
"column": 4
} | {
"line": 329,
"column": 59
} | {
"line": 330,
"column": 4
} | [
{
"pp": "case pos\nι : 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 : ... | [
"case pos\nι : 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'),... | have : IsIso (K.pOpcycles (e.f i)) := K.isIso_pOpcycles _ _ rfl (by
obtain ⟨hi₁, hi₂⟩ := hi
apply IsZero.eq_of_src (K.isZero_X_of_isStrictlySupported e _
(fun j hj ↦ hi₂ j (by simpa only [hj] using hi₁)))) | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Algebra.Homology.Embedding.ExtendHomology | {
"line": 427,
"column": 54
} | {
"line": 430,
"column": 73
} | {
"line": 432,
"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\ninst✝⁴ : HasZeroObject C\nK L : HomologicalComplex C c\nφ : K ⟶ L\ne : c.Embedding c'\nj : ι\nj' : ι'\nhj' : e.f j = j'\ninst✝³ : K.HasHomology j\ninst✝² : L... | [] | by
simp only [quasiIsoAt_iff_isIso_homologyMap]
exact (MorphismProperty.isomorphisms C).arrow_mk_iso_iff
(Arrow.isoMk (K.extendHomologyIso e hj') (L.extendHomologyIso e hj')) | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Homology.Embedding.AreComplementary | {
"line": 80,
"column": 6
} | {
"line": 80,
"column": 36
} | {
"line": 81,
"column": 4
} | [
{
"pp": "case left.inl.inr\nι : Type u_1\nι₁ : Type u_2\nι₂ : Type u_3\nc : ComplexShape ι\nc₁ : ComplexShape ι₁\nc₂ : ComplexShape ι₂\ne₁ : c₁.Embedding c\ne₂ : c₂.Embedding c\nac : e₁.AreComplementary e₂\ni₁ : ι₁\nj₂ : ι₂\nh : fromSum e₁ e₂ (Sum.inl i₁) = fromSum e₁ e₂ (Sum.inr j₂)\n⊢ Sum.inl i₁ = Sum.inr j₂"... | [] | exact (ac.disjoint _ _ h).elim | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Algebra.Homology.Embedding.AreComplementary | {
"line": 80,
"column": 6
} | {
"line": 80,
"column": 36
} | {
"line": 81,
"column": 4
} | [
{
"pp": "case left.inl.inr\nι : Type u_1\nι₁ : Type u_2\nι₂ : Type u_3\nc : ComplexShape ι\nc₁ : ComplexShape ι₁\nc₂ : ComplexShape ι₂\ne₁ : c₁.Embedding c\ne₂ : c₂.Embedding c\nac : e₁.AreComplementary e₂\ni₁ : ι₁\nj₂ : ι₂\nh : fromSum e₁ e₂ (Sum.inl i₁) = fromSum e₁ e₂ (Sum.inr j₂)\n⊢ Sum.inl i₁ = Sum.inr j₂"... | [] | exact (ac.disjoint _ _ h).elim | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Homology.Embedding.AreComplementary | {
"line": 80,
"column": 6
} | {
"line": 80,
"column": 36
} | {
"line": 81,
"column": 4
} | [
{
"pp": "case left.inl.inr\nι : Type u_1\nι₁ : Type u_2\nι₂ : Type u_3\nc : ComplexShape ι\nc₁ : ComplexShape ι₁\nc₂ : ComplexShape ι₂\ne₁ : c₁.Embedding c\ne₂ : c₂.Embedding c\nac : e₁.AreComplementary e₂\ni₁ : ι₁\nj₂ : ι₂\nh : fromSum e₁ e₂ (Sum.inl i₁) = fromSum e₁ e₂ (Sum.inr j₂)\n⊢ Sum.inl i₁ = Sum.inr j₂"... | [] | exact (ac.disjoint _ _ h).elim | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Localization.HomEquiv | {
"line": 144,
"column": 30
} | {
"line": 145,
"column": 35
} | {
"line": 147,
"column": 0
} | [
{
"pp": "C : Type u_1\nD₁ : Type u_5\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Category.{v_5, u_5} D₁\nW : MorphismProperty C\nL₁ : C ⥤ D₁\ninst✝ : L₁.IsLocalization W\nX Y : C\nf : L₁.obj X ⟶ L₁.obj Y\n⊢ (homEquiv W L₁ L₁) f = f",
"ppTerm": "?m.42",
"assigned": true,
"usedConstants": [
"Categ... | [] | by
apply LocalizerMorphism.id_homMap | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic | {
"line": 89,
"column": 80
} | {
"line": 91,
"column": 16
} | {
"line": 93,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : Abelian C\ninst✝ : HasDerivedCategory C\n⊢ HasExt C",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instCategoryDerivedCategory",
"DerivedCategory",
"CategoryTheory.CategoryStruct.toQuiver",
"... | [] | by
rw [hasExt_iff.{w}]
infer_instance | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic | {
"line": 216,
"column": 4
} | {
"line": 216,
"column": 8
} | {
"line": 217,
"column": 4
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : Abelian C\ninst✝ : HasExt C\nX Y : C\nthis : HasDerivedCategory C := ⋯\nh : (singleFunctor C 0).FullyFaithful\ne : (X ⟶ Y) ≃ Ext X Y 0 := ⋯\nf : X ⟶ Y\n⊢ (ShiftedHom.homEquiv 0 ⋯) (h.homEquiv f) = homEquiv (mk₀ f)",
"ppTerm": "?m.117",
"assigned"... | [
"C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : Abelian C\ninst✝ : HasExt C\nX Y : C\nthis : HasDerivedCategory C := ⋯\nh : (singleFunctor C 0).FullyFaithful\ne : (X ⟶ Y) ≃ Ext X Y 0 := ⋯\nf : X ⟶ Y\n⊢ homEquiv (mk₀ f) = (ShiftedHom.homEquiv 0 ⋯) (h.homEquiv f)"
] | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic | {
"line": 430,
"column": 4
} | {
"line": 430,
"column": 8
} | {
"line": 431,
"column": 4
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : Abelian C\ninst✝ : HasExt C\nX : C\nn : ℕ\nX✝ Y✝ Z✝ : C\nf : X✝ ⟶ Y✝\nf' : Y✝ ⟶ Z✝\nα : ↑(AddCommGrpCat.of (Ext X X✝ n))\n⊢ Ext.comp α ((Ext.mk₀ f).comp (Ext.mk₀ f') ⋯) ⋯ = (Ext.comp α (Ext.mk₀ f) ⋯).comp (Ext.mk₀ f') ⋯",
"ppTerm": "?m.71",
"assi... | [
"C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : Abelian C\ninst✝ : HasExt C\nX : C\nn : ℕ\nX✝ Y✝ Z✝ : C\nf : X✝ ⟶ Y✝\nf' : Y✝ ⟶ Z✝\nα : ↑(AddCommGrpCat.of (Ext X X✝ n))\n⊢ (Ext.comp α (Ext.mk₀ f) ⋯).comp (Ext.mk₀ f') ⋯ = Ext.comp α ((Ext.mk₀ f).comp (Ext.mk₀ f') ⋯) ⋯"
] | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic | {
"line": 447,
"column": 8
} | {
"line": 447,
"column": 12
} | {
"line": 448,
"column": 8
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : Abelian C\ninst✝ : HasExt C\nn : ℕ\nX₁ X₂ : Cᵒᵖ\nf : X₁ ⟶ X₂\nY₁ Y₂ : C\ng : Y₁ ⟶ Y₂\nα : ↑((extFunctorObj (Opposite.unop X₁) n).obj Y₁)\n⊢ (Ext.mk₀ f.unop).comp (Ext.comp α (Ext.mk₀ g) ⋯) ⋯ = ((Ext.mk₀ f.unop).comp α ⋯).comp (Ext.mk₀ g) ⋯",
"ppTerm"... | [
"C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : Abelian C\ninst✝ : HasExt C\nn : ℕ\nX₁ X₂ : Cᵒᵖ\nf : X₁ ⟶ X₂\nY₁ Y₂ : C\ng : Y₁ ⟶ Y₂\nα : ↑((extFunctorObj (Opposite.unop X₁) n).obj Y₁)\n⊢ ((Ext.mk₀ f.unop).comp α ⋯).comp (Ext.mk₀ g) ⋯ = (Ext.mk₀ f.unop).comp (Ext.comp α (Ext.mk₀ g) ⋯) ⋯"
] | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.CategoryTheory.Shift.Adjunction | {
"line": 192,
"column": 2
} | {
"line": 193,
"column": 51
} | {
"line": 194,
"column": 2
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝⁴ : Category.{v_1, u_1} C\ninst✝³ : Category.{v_2, u_2} D\nF : C ⥤ D\nG : D ⥤ C\nadj : F ⊣ G\nA : Type u_3\ninst✝² : AddMonoid A\ninst✝¹ : HasShift C A\ninst✝ : HasShift D A\na b : A\ne₁ : shiftFunctor C a ⋙ F ≅ F ⋙ shiftFunctor D a\nf₁ : shiftFunctor C b ⋙ F ≅ F ⋙ shif... | [
"C : Type u_1\nD : Type u_2\ninst✝⁴ : Category.{v_1, u_1} C\ninst✝³ : Category.{v_2, u_2} D\nF : C ⥤ D\nG : D ⥤ C\nadj : F ⊣ G\nA : Type u_3\ninst✝² : AddMonoid A\ninst✝¹ : HasShift C A\ninst✝ : HasShift D A\na b : A\ne₁ : shiftFunctor C a ⋙ F ≅ F ⋙ shiftFunctor D a\nf₁ : shiftFunctor C b ⋙ F ≅ F ⋙ shiftFunctor D b... | simp only [Functor.id_obj, Functor.comp_obj, Functor.CommShift.isoAdd_hom_app,
Functor.map_comp, assoc, unit_naturality_assoc] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.Homology.HomotopyCategory.ShortExact | {
"line": 188,
"column": 2
} | {
"line": 188,
"column": 6
} | {
"line": 189,
"column": 2
} | [
{
"pp": "C : Type u_1\ninst✝⁴ : Category.{v_1, u_1} C\ninst✝³ : Abelian C\nD : Type u_2\ninst✝² : Category.{v_2, u_2} D\ninst✝¹ : Abelian D\nF : C ⥤ D\ninst✝ : F.Additive\nS : ShortComplex (CochainComplex C ℤ)\n⊢ (mapHomologicalComplexIso S.f F).hom ≫ descShortComplex (S.map (F.mapHomologicalComplex (up ℤ))) =\... | [
"C : Type u_1\ninst✝⁴ : Category.{v_1, u_1} C\ninst✝³ : Abelian C\nD : Type u_2\ninst✝² : Category.{v_2, u_2} D\ninst✝¹ : Abelian D\nF : C ⥤ D\ninst✝ : F.Additive\nS : ShortComplex (CochainComplex C ℤ)\n⊢ (F.mapHomologicalComplex (up ℤ)).map (descShortComplex S) =\n (mapHomologicalComplexIso S.f F).hom ≫ descSho... | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.CategoryTheory.Shift.Adjunction | {
"line": 278,
"column": 20
} | {
"line": 280,
"column": 18
} | {
"line": 282,
"column": 0
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝¹² : Category.{v_1, u_1} C\ninst✝¹¹ : Category.{v_2, u_2} D\nF : C ⥤ D\nG : D ⥤ C\nadj : F ⊣ G\nA : Type u_3\ninst✝¹⁰ : AddMonoid A\ninst✝⁹ : HasShift C A\ninst✝⁸ : HasShift D A\ninst✝⁷ : F.CommShift A\ninst✝⁶ : G.CommShift A\nE : Type u_4\ninst✝⁵ : Category.{v_3, u_4} ... | [] | by
rw [comp_unit]
infer_instance | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Shift.Pullback | {
"line": 218,
"column": 18
} | {
"line": 225,
"column": 42
} | {
"line": 227,
"column": 0
} | [
{
"pp": "C : Type u_1\ninst✝⁸ : Category.{v_1, u_1} C\nA : Type u_2\nB : Type u_3\ninst✝⁷ : AddMonoid A\ninst✝⁶ : AddMonoid B\ninst✝⁵ : HasShift C B\nφ : A →+ B\nX : PullbackShift C φ\na₁ a₂ a₃ : A\nh : a₁ + a₂ = a₃\nb₁ b₂ b₃ : B\nh₁ : b₁ = φ a₁\nh₂ : b₂ = φ a₂\nh₃ : b₃ = φ a₃\nD : Type u_4\ninst✝⁴ : Category.{... | [] | by
ext
dsimp [PullbackShift.natTrans]
simp only [commShiftPullback_iso_eq φ _ _ _ rfl, Iso.trans_hom, isoWhiskerRight_hom,
isoWhiskerLeft_hom, Iso.symm_hom, comp_app, whiskerRight_app, whiskerLeft_app,
assoc]
rw [← τ.naturality_assoc]
simp [← NatTrans.shift_app_comm_assoc] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Triangulated.Yoneda | {
"line": 94,
"column": 2
} | {
"line": 94,
"column": 6
} | {
"line": 95,
"column": 2
} | [
{
"pp": "C : Type u_1\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : Preadditive C\ninst✝¹ : HasShift C ℤ\ninst✝ : ∀ (n : ℤ), (shiftFunctor C n).Additive\nB : C\nX Y : Cᵒᵖ\nn : ℤ\nf : X ⟶ (shiftFunctor Cᵒᵖ n).obj Y\na a' : ℤ\nh : n + a = a'\nz : unop X ⟶ (shiftFunctor C a).obj B\n⊢ (ConcreteCategory.hom ((preadditiv... | [
"C : Type u_1\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : Preadditive C\ninst✝¹ : HasShift C ℤ\ninst✝ : ∀ (n : ℤ), (shiftFunctor C n).Additive\nB : C\nX Y : Cᵒᵖ\nn : ℤ\nf : X ⟶ (shiftFunctor Cᵒᵖ n).obj Y\na a' : ℤ\nh : n + a = a'\nz : unop X ⟶ (shiftFunctor C a).obj B\n⊢ ((ShiftedHom.opEquiv n).symm f).comp z ⋯ = (Co... | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.Algebra.Category.ModuleCat.Ext.Basic | {
"line": 36,
"column": 87
} | {
"line": 41,
"column": 36
} | {
"line": 43,
"column": 0
} | [
{
"pp": "R : Type u\ninst✝¹ : CommRing R\ninst✝ : Small.{v, u} R\nM N : ModuleCat R\nr : R\nmem_ann : r ∈ Module.annihilator R ↑N\nn : ℕ\n⊢ AddCommGrpCat.ofHom ((mk₀ (r • 𝟙 M)).postcomp N ⋯) = 0",
"ppTerm": "?m.43",
"assigned": true,
"usedConstants": [
"CategoryTheory.Abelian.Ext.zero_comp",
... | [] | by
ext h
have : r • 𝟙 N = 0 := by
simp [← ModuleCat.lsmul_eq_smul_id, Module.mem_annihilator_iff_lsmul_eq_zero.mp mem_ann]
have smul_eq : r • h = (Ext.mk₀ (r • 𝟙 N)).comp h (zero_add n) := by simp [Ext.mk₀_smul]
simp [Ext.mk₀_smul, this, smul_eq] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.RingTheory.RootsOfUnity.Basic | {
"line": 151,
"column": 12
} | {
"line": 151,
"column": 72
} | {
"line": 151,
"column": 73
} | [
{
"pp": "M : Type u_1\nN : Type u_2\nG : Type u_3\nR : Type u_4\nS : Type u_5\nF : Type u_6\ninst✝⁶ : CommMonoid M\ninst✝⁵ : CommMonoid N\ninst✝⁴ : DivisionCommMonoid G\nk l : ℕ\ninst✝³ : CommMonoid R\ninst✝² : CommMonoid S\ninst✝¹ : FunLike F R S\ninst✝ : MonoidHomClass F R S\nσ : F\nn : ℕ\nξ₁ ξ₂ : ↥(rootsOfUn... | [] | simp only [Subgroup.coe_mul, map_mul, MulMemClass.mk_mul_mk] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.LinearAlgebra.Matrix.SpecialLinearGroup | {
"line": 174,
"column": 2
} | {
"line": 174,
"column": 16
} | {
"line": 175,
"column": 2
} | [
{
"pp": "n : Type u\ninst✝³ : DecidableEq n\ninst✝² : Fintype n\nR : Type v\ninst✝¹ : CommRing R\ninst✝ : Nontrivial R\ng : SpecialLinearGroup n R\n⊢ (↑g).det ≠ 0",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"CommSemiring.toSemiring",
"Matri... | [
"n : Type u\ninst✝³ : DecidableEq n\ninst✝² : Fintype n\nR : Type v\ninst✝¹ : CommRing R\ninst✝ : Nontrivial R\ng : SpecialLinearGroup n R\n⊢ 1 ≠ 0"
] | rw [g.det_coe] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.LinearAlgebra.Matrix.SpecialLinearGroup | {
"line": 388,
"column": 49
} | {
"line": 388,
"column": 72
} | {
"line": 388,
"column": 72
} | [
{
"pp": "R : Type v\ninst✝ : CommRing R\nP : SL(2, R) → Prop\nh : ∀ (a b c d : R) (hdet : a * d - b * c = 1), P ⟨!![a, b; c, d], ⋯⟩\nm : Matrix (Fin 2) (Fin 2) R\nhm : m.det = 1\n⊢ m 0 0 * m 1 1 - m 0 1 * m 1 0 = 1",
"ppTerm": "?m.86",
"assigned": true,
"usedConstants": [
"HMul.hMul",
"A... | [] | rwa [det_fin_two] at hm | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticRwa___1 | Lean.Parser.Tactic.tacticRwa__ |
Mathlib.LinearAlgebra.Matrix.SpecialLinearGroup | {
"line": 388,
"column": 49
} | {
"line": 388,
"column": 72
} | {
"line": 388,
"column": 72
} | [
{
"pp": "R : Type v\ninst✝ : CommRing R\nP : SL(2, R) → Prop\nh : ∀ (a b c d : R) (hdet : a * d - b * c = 1), P ⟨!![a, b; c, d], ⋯⟩\nm : Matrix (Fin 2) (Fin 2) R\nhm : m.det = 1\n⊢ m 0 0 * m 1 1 - m 0 1 * m 1 0 = 1",
"ppTerm": "?m.86",
"assigned": true,
"usedConstants": [
"HMul.hMul",
"A... | [] | rwa [det_fin_two] at hm | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.Matrix.SpecialLinearGroup | {
"line": 388,
"column": 49
} | {
"line": 388,
"column": 72
} | {
"line": 388,
"column": 72
} | [
{
"pp": "R : Type v\ninst✝ : CommRing R\nP : SL(2, R) → Prop\nh : ∀ (a b c d : R) (hdet : a * d - b * c = 1), P ⟨!![a, b; c, d], ⋯⟩\nm : Matrix (Fin 2) (Fin 2) R\nhm : m.det = 1\n⊢ m 0 0 * m 1 1 - m 0 1 * m 1 0 = 1",
"ppTerm": "?m.86",
"assigned": true,
"usedConstants": [
"HMul.hMul",
"A... | [] | rwa [det_fin_two] at hm | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.Matrix.SpecialLinearGroup | {
"line": 434,
"column": 4
} | {
"line": 434,
"column": 35
} | {
"line": 435,
"column": 4
} | [
{
"pp": "case refine_1\nR : Type u_1\ninst✝ : CommRing R\na b : R\nj : Fin 2\nu v : R\nh : u * a + v * b = 1\n⊢ !![a, -v; b, u].det = 1",
"ppTerm": "?refine_1",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Eq... | [
"case refine_1\nR : Type u_1\ninst✝ : CommRing R\na b : R\nj : Fin 2\nu v : R\nh : u * a + v * b = 1\n⊢ a * u - -v * b = u * a + v * b"
] | rw [Matrix.det_fin_two_of, ← h] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.LinearAlgebra.Matrix.SpecialLinearGroup | {
"line": 434,
"column": 4
} | {
"line": 434,
"column": 35
} | {
"line": 435,
"column": 4
} | [
{
"pp": "case refine_2\nR : Type u_1\ninst✝ : CommRing R\na b : R\nj : Fin 2\nu v : R\nh : u * a + v * b = 1\n⊢ !![v, a; -u, b].det = 1",
"ppTerm": "?refine_2",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Eq... | [
"case refine_2\nR : Type u_1\ninst✝ : CommRing R\na b : R\nj : Fin 2\nu v : R\nh : u * a + v * b = 1\n⊢ v * b - a * -u = u * a + v * b"
] | rw [Matrix.det_fin_two_of, ← h] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.LinearAlgebra.CliffordAlgebra.Basic | {
"line": 294,
"column": 65
} | {
"line": 294,
"column": 73
} | {
"line": 294,
"column": 73
} | [
{
"pp": "R : Type u_1\ninst✝² : CommRing R\nM : Type u_2\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nQ : QuadraticForm R M\nx : CliffordAlgebra Q\na b : M\nh : QuadraticMap.IsOrtho Q a b\ny : CliffordAlgebra Q\n⊢ 0 - x * (ι Q) b * ((ι Q) a * y) = -(x * (ι Q) b * ((ι Q) a * y))",
"ppTerm": "?m.113",
"a... | [
"R : Type u_1\ninst✝² : CommRing R\nM : Type u_2\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nQ : QuadraticForm R M\nx : CliffordAlgebra Q\na b : M\nh : QuadraticMap.IsOrtho Q a b\ny : CliffordAlgebra Q\n⊢ -(x * (ι Q) b * ((ι Q) a * y)) = -(x * (ι Q) b * ((ι Q) a * y))"
] | zero_sub | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.LinearAlgebra.Matrix.SpecialLinearGroup | {
"line": 445,
"column": 4
} | {
"line": 445,
"column": 35
} | {
"line": 446,
"column": 4
} | [
{
"pp": "case refine_1\nR : Type u_1\ninst✝ : CommRing R\na b : R\ni : Fin 2\nu v : R\nh : u * a + v * b = 1\n⊢ !![a, b; -v, u].det = 1",
"ppTerm": "?refine_1",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Eq... | [
"case refine_1\nR : Type u_1\ninst✝ : CommRing R\na b : R\ni : Fin 2\nu v : R\nh : u * a + v * b = 1\n⊢ a * u - b * -v = u * a + v * b"
] | rw [Matrix.det_fin_two_of, ← h] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.LinearAlgebra.Matrix.SpecialLinearGroup | {
"line": 445,
"column": 4
} | {
"line": 445,
"column": 35
} | {
"line": 446,
"column": 4
} | [
{
"pp": "case refine_2\nR : Type u_1\ninst✝ : CommRing R\na b : R\ni : Fin 2\nu v : R\nh : u * a + v * b = 1\n⊢ !![v, -u; a, b].det = 1",
"ppTerm": "?refine_2",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Eq... | [
"case refine_2\nR : Type u_1\ninst✝ : CommRing R\na b : R\ni : Fin 2\nu v : R\nh : u * a + v * b = 1\n⊢ v * b - -u * a = u * a + v * b"
] | rw [Matrix.det_fin_two_of, ← h] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.LinearAlgebra.Matrix.SpecialLinearGroup | {
"line": 652,
"column": 35
} | {
"line": 652,
"column": 69
} | {
"line": 653,
"column": 4
} | [
{
"pp": "F : Type u_1\ninst✝² : Field F\nι : Type u_2\ninst✝¹ : Fintype ι\ninst✝ : DecidableEq ι\ni₀ : ι\nD : ι → F\nhD : D i₀ * ∏ x with x ≠ i₀, D x = 1\n⊢ (∏ i with i ≠ i₀, fun k ↦ if k = i then D i else if k = i₀ then (D i)⁻¹ else 1) = D",
"ppTerm": "?m.79",
"assigned": true,
"usedConstants": [
... | [
"F : Type u_1\ninst✝² : Field F\nι : Type u_2\ninst✝¹ : Fintype ι\ninst✝ : DecidableEq ι\ni₀ : ι\nD : ι → F\nhD : D i₀ = (∏ x with x ≠ i₀, D x)⁻¹\n⊢ (∏ i with i ≠ i₀, fun k ↦ if k = i then D i else if k = i₀ then (D i)⁻¹ else 1) = D"
] | mul_eq_one_iff_eq_inv₀ (by grind), | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.DirectSum.Ring | {
"line": 420,
"column": 13
} | {
"line": 420,
"column": 69
} | {
"line": 422,
"column": 0
} | [
{
"pp": "ι : Type u_1\ninst✝³ : DecidableEq ι\nA : ι → Type u_2\ninst✝² : (i : ι) → AddCommMonoid (A i)\ninst✝¹ : AddMonoid ι\ninst✝ : GSemiring A\na : A 0\nn : ℕ\n⊢ (of A 0) (a ^ (n + 1)) = (of A 0) a ^ (n + 1)",
"ppTerm": "?m.39",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"HMul.hM... | [] | by rw [pow_succ, pow_succ, of_zero_mul, of_zero_pow _ n] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.LinearAlgebra.Matrix.SpecialLinearGroup | {
"line": 829,
"column": 29
} | {
"line": 829,
"column": 35
} | {
"line": 831,
"column": 0
} | [
{
"pp": "⊢ S⁻¹ = -S",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"Fintype.card_fin_two",
"Matrix.SpecialLinearGroup",
"of_decide_eq_true",
"Matrix.SpecialLinearGroup.instNeg",
"instDecidableEqFin",
"Int.instDecidableEq",
"id",
"instOfNatNat... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.LinearAlgebra.Matrix.SpecialLinearGroup | {
"line": 829,
"column": 29
} | {
"line": 829,
"column": 35
} | {
"line": 831,
"column": 0
} | [
{
"pp": "⊢ S⁻¹ = -S",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"Fintype.card_fin_two",
"Matrix.SpecialLinearGroup",
"of_decide_eq_true",
"Matrix.SpecialLinearGroup.instNeg",
"instDecidableEqFin",
"Int.instDecidableEq",
"id",
"instOfNatNat... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.Matrix.SpecialLinearGroup | {
"line": 829,
"column": 29
} | {
"line": 829,
"column": 35
} | {
"line": 831,
"column": 0
} | [
{
"pp": "⊢ S⁻¹ = -S",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"Fintype.card_fin_two",
"Matrix.SpecialLinearGroup",
"of_decide_eq_true",
"Matrix.SpecialLinearGroup.instNeg",
"instDecidableEqFin",
"Int.instDecidableEq",
"id",
"instOfNatNat... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.Matrix.SesquilinearForm | {
"line": 503,
"column": 6
} | {
"line": 503,
"column": 36
} | {
"line": 503,
"column": 37
} | [
{
"pp": "R : Type u_1\nM₁ : Type u_6\nM₂ : Type u_7\nn : Type u_11\nm : Type u_12\nn' : Type u_13\nm' : Type u_14\ninst✝¹² : CommSemiring R\ninst✝¹¹ : AddCommMonoid M₁\ninst✝¹⁰ : Module R M₁\ninst✝⁹ : AddCommMonoid M₂\ninst✝⁸ : Module R M₂\ninst✝⁷ : Fintype n\ninst✝⁶ : Fintype m\ninst✝⁵ : DecidableEq m\ninst✝⁴ ... | [
"R : Type u_1\nM₁ : Type u_6\nM₂ : Type u_7\nn : Type u_11\nm : Type u_12\nn' : Type u_13\nm' : Type u_14\ninst✝¹² : CommSemiring R\ninst✝¹¹ : AddCommMonoid M₁\ninst✝¹⁰ : Module R M₁\ninst✝⁹ : AddCommMonoid M₂\ninst✝⁸ : Module R M₂\ninst✝⁷ : Fintype n\ninst✝⁶ : Fintype m\ninst✝⁵ : DecidableEq m\ninst✝⁴ : DecidableE... | ← LinearMap.toMatrix₂_compl₁₂, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.LinearAlgebra.Matrix.SesquilinearForm | {
"line": 525,
"column": 5
} | {
"line": 527,
"column": 23
} | {
"line": 527,
"column": 23
} | [
{
"pp": "R : Type u_1\nM₁ : Type u_6\nM₂ : Type u_7\nM₁' : Type u_8\nM₂' : Type u_9\nn : Type u_11\nm : Type u_12\nn' : Type u_13\nm' : Type u_14\ninst✝¹⁶ : CommSemiring R\ninst✝¹⁵ : AddCommMonoid M₁\ninst✝¹⁴ : Module R M₁\ninst✝¹³ : AddCommMonoid M₂\ninst✝¹² : Module R M₂\ninst✝¹¹ : Fintype n\ninst✝¹⁰ : Fintyp... | [] | by
simp only [LinearMap.toMatrix₂_compl₁₂ b₁ b₂, LinearMap.toMatrix₂_toLinearMap₂,
toMatrix_toLin] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.LinearAlgebra.QuadraticForm.Basic | {
"line": 582,
"column": 55
} | {
"line": 582,
"column": 74
} | {
"line": 582,
"column": 74
} | [
{
"pp": "S : Type u_1\nT : Type u_2\nR : Type u_3\nM : Type u_4\nN : Type u_5\nP : Type u_6\nA : Type u_7\ninst✝⁶ : CommSemiring R\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : Module R M\ninst✝³ : AddCommMonoid N\ninst✝² : Module R N\ninst✝¹ : AddCommMonoid P\ninst✝ : Module R P\nQ : QuadraticMap R N P\nf : M →ₗ[R] N\nB... | [] | exact h (f x) (f y) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Data.Set.PowersetCard | {
"line": 83,
"column": 9
} | {
"line": 83,
"column": 24
} | {
"line": 83,
"column": 24
} | [
{
"pp": "α : Type u_1\nn : ℕ\nhn : 1 ≤ n\nhα : ↑n < ENat.card α\na b : α\nhab : a ≠ b\nha' : ↑n ≤ {b}ᶜ.encard\ns : Set α\nhas : {a} ⊆ s\nhas' : s ⊆ {b}ᶜ\nhs : s.encard = ↑n\nthis : s.Finite\n⊢ a ∈ ⟨this.toFinset, ⋯⟩",
"ppTerm": "?m.120",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Se... | [] | simpa using has | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Data.Set.PowersetCard | {
"line": 83,
"column": 9
} | {
"line": 83,
"column": 24
} | {
"line": 83,
"column": 24
} | [
{
"pp": "α : Type u_1\nn : ℕ\nhn : 1 ≤ n\nhα : ↑n < ENat.card α\na b : α\nhab : a ≠ b\nha' : ↑n ≤ {b}ᶜ.encard\ns : Set α\nhas : {a} ⊆ s\nhas' : s ⊆ {b}ᶜ\nhs : s.encard = ↑n\nthis : s.Finite\n⊢ a ∈ ⟨this.toFinset, ⋯⟩",
"ppTerm": "?m.120",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Se... | [] | simpa using has | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Set.PowersetCard | {
"line": 83,
"column": 9
} | {
"line": 83,
"column": 24
} | {
"line": 83,
"column": 24
} | [
{
"pp": "α : Type u_1\nn : ℕ\nhn : 1 ≤ n\nhα : ↑n < ENat.card α\na b : α\nhab : a ≠ b\nha' : ↑n ≤ {b}ᶜ.encard\ns : Set α\nhas : {a} ⊆ s\nhas' : s ⊆ {b}ᶜ\nhs : s.encard = ↑n\nthis : s.Finite\n⊢ a ∈ ⟨this.toFinset, ⋯⟩",
"ppTerm": "?m.120",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Se... | [] | simpa using has | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.CliffordAlgebra.Grading | {
"line": 121,
"column": 6
} | {
"line": 121,
"column": 88
} | {
"line": 121,
"column": 88
} | [
{
"pp": "R : Type u_1\nM : Type u_2\ninst✝² : CommRing R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nQ : QuadraticForm R M\nm : M\n⊢ (DirectSum.coeAlgHom (evenOdd Q)) (((lift Q) ⟨GradedAlgebra.ι Q, ⋯⟩) ((ι Q) m)) = (ι Q) m",
"ppTerm": "?m.88",
"assigned": true,
"usedConstants": [
"Subtype.co... | [] | rw [lift_ι_apply, GradedAlgebra.ι_apply Q, DirectSum.coeAlgHom_of, Subtype.coe_mk] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Order.Hom.PowersetCard | {
"line": 40,
"column": 19
} | {
"line": 40,
"column": 23
} | {
"line": 40,
"column": 23
} | [
{
"pp": "n : ℕ\nI : Type u_1\ninst✝ : LinearOrder I\nf : Fin n ↪o I\n⊢ (fun s ↦ (↑s).orderEmbOfFin ⋯) ((fun f ↦ ofFinEmb n I f.toEmbedding) f) = f",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"Set.powersetCard.ofFinEmb",
"Finset.orderEmbOfFin",
"Finset",
"Partial... | [
"n : ℕ\nI : Type u_1\ninst✝ : LinearOrder I\nf : Fin n ↪o I\n⊢ f = (fun s ↦ (↑s).orderEmbOfFin ⋯) ((fun f ↦ ofFinEmb n I f.toEmbedding) f)"
] | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.LinearAlgebra.ExteriorAlgebra.Basic | {
"line": 214,
"column": 60
} | {
"line": 214,
"column": 74
} | {
"line": 214,
"column": 75
} | [
{
"pp": "R : Type u1\ninst✝² : CommRing R\nM : Type u2\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nx : M\n⊢ (ι R) x = 0 ↔ x = 0",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"ExteriorAlgebra.ι_inj",
"Semiring.toModule",
"QuadraticMap.instZero",
"... | [
"R : Type u1\ninst✝² : CommRing R\nM : Type u2\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nx : M\n⊢ (ι R) x = 0 ↔ (ι R) x = (ι R) 0"
] | ← ι_inj R x 0, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Category.ModuleCat.FilteredColimits | {
"line": 121,
"column": 8
} | {
"line": 121,
"column": 57
} | {
"line": 121,
"column": 58
} | [
{
"pp": "R : Type u\ninst✝² : Ring R\nJ : Type v\ninst✝¹ : SmallCategory J\ninst✝ : IsFiltered J\nF : J ⥤ ModuleCat R\nr : R\n⊢ r • 0 = 0",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instHSMul",
"ModuleCat",
"congrArg",
"ModuleCat.FilteredColimit... | [
"R : Type u\ninst✝² : Ring R\nJ : Type v\ninst✝¹ : SmallCategory J\ninst✝ : IsFiltered J\nF : J ⥤ ModuleCat R\nr : R\n⊢ r • M.mk F ⟨⋯.some, 0⟩ = M.mk F ⟨⋯.some, 0⟩"
] | colimit_zero_eq _ (IsFiltered.nonempty.some : J), | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.LinearAlgebra.ExteriorPower.Basic | {
"line": 98,
"column": 10
} | {
"line": 98,
"column": 27
} | {
"line": 98,
"column": 28
} | [
{
"pp": "case a.refine_1\nR : Type u\ninst✝² : CommRing R\nn : ℕ\nM : Type u_1\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\ns : Set M\nhs : span R s = ⊤\nf : Fin n → ↑(⇑(ExteriorAlgebra.ι R) '' s)\nhx : (List.ofFn fun i ↦ ↑(f i)).prod ∈ (⇑(ExteriorAlgebra.ι R) '' s) ^ n\n⊢ ⇑ExteriorAlgebra.ιInv ∘ Subtype.val ∘... | [
"case a.refine_1\nR : Type u\ninst✝² : CommRing R\nn : ℕ\nM : Type u_1\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\ns : Set M\nhs : span R s = ⊤\nf : Fin n → ↑(⇑(ExteriorAlgebra.ι R) '' s)\nhx : (List.ofFn fun i ↦ ↑(f i)).prod ∈ (⇑(ExteriorAlgebra.ι R) '' s) ^ n\n⊢ range (⇑ExteriorAlgebra.ιInv ∘ Subtype.val ∘ f) ⊆... | Set.mem_setOf_eq, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.CategoryTheory.Monoidal.Closed.Cartesian | {
"line": 119,
"column": 4
} | {
"line": 120,
"column": 23
} | {
"line": 121,
"column": 2
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : CartesianMonoidalCategory C\nA : C\ninst✝ : Closed A\nI : C\nt : IsInitial I\nf : A ⟶ I\n⊢ Mono f",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"CategoryTheory.zeroMul_hom",
"CategoryTheory.Mono",
... | [] | rw [← lift_snd (𝟙 A) f, ← zeroMul_hom t]
exact mono_comp _ _ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Monoidal.Closed.Cartesian | {
"line": 119,
"column": 4
} | {
"line": 120,
"column": 23
} | {
"line": 121,
"column": 2
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : CartesianMonoidalCategory C\nA : C\ninst✝ : Closed A\nI : C\nt : IsInitial I\nf : A ⟶ I\n⊢ Mono f",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"CategoryTheory.zeroMul_hom",
"CategoryTheory.Mono",
... | [] | rw [← lift_snd (𝟙 A) f, ← zeroMul_hom t]
exact mono_comp _ _ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Monoidal.ExternalProduct.Basic | {
"line": 82,
"column": 54
} | {
"line": 82,
"column": 77
} | {
"line": 82,
"column": 77
} | [
{
"pp": "J₁ : Type u₁\nJ₂ : Type u₂\nC : Type u₃\ninst✝⁴ : Category.{v₁, u₁} J₁\ninst✝³ : Category.{v₂, u₂} J₂\ninst✝² : Category.{v₃, u₃} C\ninst✝¹ : MonoidalCategory C\ninst✝ : BraidedCategory C\nx✝ : (J₁ ⥤ C) × (J₂ ⥤ C)\n⊢ ∀ {X Y : J₂ × J₁} (f : X ⟶ Y),\n ((externalProductBifunctor J₁ J₂ C ⋙ (whiskeringLe... | [] | simp [whisker_exchange] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.CategoryTheory.Monoidal.ExternalProduct.Basic | {
"line": 82,
"column": 54
} | {
"line": 82,
"column": 77
} | {
"line": 82,
"column": 77
} | [
{
"pp": "J₁ : Type u₁\nJ₂ : Type u₂\nC : Type u₃\ninst✝⁴ : Category.{v₁, u₁} J₁\ninst✝³ : Category.{v₂, u₂} J₂\ninst✝² : Category.{v₃, u₃} C\ninst✝¹ : MonoidalCategory C\ninst✝ : BraidedCategory C\nx✝ : (J₁ ⥤ C) × (J₂ ⥤ C)\n⊢ ∀ {X Y : J₂ × J₁} (f : X ⟶ Y),\n ((externalProductBifunctor J₁ J₂ C ⋙ (whiskeringLe... | [] | simp [whisker_exchange] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Monoidal.ExternalProduct.Basic | {
"line": 82,
"column": 54
} | {
"line": 82,
"column": 77
} | {
"line": 82,
"column": 77
} | [
{
"pp": "J₁ : Type u₁\nJ₂ : Type u₂\nC : Type u₃\ninst✝⁴ : Category.{v₁, u₁} J₁\ninst✝³ : Category.{v₂, u₂} J₂\ninst✝² : Category.{v₃, u₃} C\ninst✝¹ : MonoidalCategory C\ninst✝ : BraidedCategory C\nx✝ : (J₁ ⥤ C) × (J₂ ⥤ C)\n⊢ ∀ {X Y : J₂ × J₁} (f : X ⟶ Y),\n ((externalProductBifunctor J₁ J₂ C ⋙ (whiskeringLe... | [] | simp [whisker_exchange] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Monoidal.ExternalProduct.Basic | {
"line": 83,
"column": 21
} | {
"line": 83,
"column": 44
} | {
"line": 83,
"column": 44
} | [
{
"pp": "J₁ : Type u₁\nJ₂ : Type u₂\nC : Type u₃\ninst✝⁴ : Category.{v₁, u₁} J₁\ninst✝³ : Category.{v₂, u₂} J₂\ninst✝² : Category.{v₃, u₃} C\ninst✝¹ : MonoidalCategory C\ninst✝ : BraidedCategory C\nX✝ Y✝ : (J₁ ⥤ C) × (J₂ ⥤ C)\nx✝¹ : X✝ ⟶ Y✝\nx✝ : J₂ × J₁\n⊢ ((externalProductBifunctor J₁ J₂ C ⋙ (whiskeringLeft (... | [] | simp [whisker_exchange] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.CategoryTheory.Limits.Sifted | {
"line": 206,
"column": 2
} | {
"line": 206,
"column": 6
} | {
"line": 207,
"column": 2
} | [
{
"pp": "C : Type u\ninst✝¹ : SmallCategory C\nX Y : C ⥤ Type u\ninst✝ : IsSifted C\n⊢ colim.obj (⊤_ C ⥤ Type u) ≅ ⊤_ Type u",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"CategoryTheory.Limits.Types.hasColimitsOfShape",
"CategoryTheory.Functor",
"CategoryTheory.typesCa... | [
"C : Type u\ninst✝¹ : SmallCategory C\nX Y : C ⥤ Type u\ninst✝ : IsSifted C\n⊢ ⊤_ Type u ≅ colim.obj (⊤_ C ⥤ Type u)"
] | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.CategoryTheory.Limits.Preserves.Bifunctor | {
"line": 231,
"column": 10
} | {
"line": 231,
"column": 14
} | {
"line": 232,
"column": 10
} | [
{
"pp": "case refine_2\nJ₁ : Type u_1\nJ₂ : Type u_2\ninst✝⁷ : Category.{v_1, u_1} J₁\ninst✝⁶ : Category.{v_2, u_2} J₂\nC₁ : Type u_3\nC₂ : Type u_4\nC : Type u_5\ninst✝⁵ : Category.{v_3, u_3} C₁\ninst✝⁴ : Category.{v_4, u_4} C₂\ninst✝³ : Category.{v_5, u_5} C\nK₁ : J₁ ⥤ C₁\nK₂ : J₂ ⥤ C₂\nG : C₁ ⥤ C₂ ⥤ C\ninst✝... | [
"case refine_2\nJ₁ : Type u_1\nJ₂ : Type u_2\ninst✝⁷ : Category.{v_1, u_1} J₁\ninst✝⁶ : Category.{v_2, u_2} J₂\nC₁ : Type u_3\nC₂ : Type u_4\nC : Type u_5\ninst✝⁵ : Category.{v_3, u_3} C₁\ninst✝⁴ : Category.{v_4, u_4} C₂\ninst✝³ : Category.{v_5, u_5} C\nK₁ : J₁ ⥤ C₁\nK₂ : J₂ ⥤ C₂\nG : C₁ ⥤ C₂ ⥤ C\ninst✝² : Preserve... | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.CategoryTheory.Limits.Preserves.Bifunctor | {
"line": 361,
"column": 10
} | {
"line": 361,
"column": 14
} | {
"line": 362,
"column": 10
} | [
{
"pp": "case refine_2\nJ₁ : Type u_1\nJ₂ : Type u_2\ninst✝⁷ : Category.{v_1, u_1} J₁\ninst✝⁶ : Category.{v_2, u_2} J₂\nC₁ : Type u_3\nC₂ : Type u_4\nC : Type u_5\ninst✝⁵ : Category.{v_3, u_3} C₁\ninst✝⁴ : Category.{v_4, u_4} C₂\ninst✝³ : Category.{v_5, u_5} C\nK₁ : J₁ ⥤ C₁\nK₂ : J₂ ⥤ C₂\nG : C₁ ⥤ C₂ ⥤ C\ninst✝... | [
"case refine_2\nJ₁ : Type u_1\nJ₂ : Type u_2\ninst✝⁷ : Category.{v_1, u_1} J₁\ninst✝⁶ : Category.{v_2, u_2} J₂\nC₁ : Type u_3\nC₂ : Type u_4\nC : Type u_5\ninst✝⁵ : Category.{v_3, u_3} C₁\ninst✝⁴ : Category.{v_4, u_4} C₂\ninst✝³ : Category.{v_5, u_5} C\nK₁ : J₁ ⥤ C₁\nK₂ : J₂ ⥤ C₂\nG : C₁ ⥤ C₂ ⥤ C\ninst✝² : Preserve... | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.Algebra.Category.ModuleCat.Presheaf.ColimitFunctor | {
"line": 176,
"column": 2
} | {
"line": 179,
"column": 72
} | {
"line": 180,
"column": 2
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : LocallySmall.{w, v, u} C\ninst✝¹ : IsCofiltered C\ninst✝ : InitiallySmall C\nR : Cᵒᵖ ⥤ RingCat\ncR : Cocone R\nhcR : IsColimit cR\nM : PresheafOfModules R\ncM : Cocone M.presheaf\nhcM : IsColimit cM\nM' : PresheafOfModules R\ncM' : Cocone M'.presheaf\nhc... | [
"C : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : LocallySmall.{w, v, u} C\ninst✝¹ : IsCofiltered C\ninst✝ : InitiallySmall C\nR : Cᵒᵖ ⥤ RingCat\ncR : Cocone R\nhcR : IsColimit cR\nM : PresheafOfModules R\ncM : Cocone M.presheaf\nhcM : IsColimit cM\nM' : PresheafOfModules R\ncM' : Cocone M'.presheaf\nhcM' : IsColim... | obtain ⟨U, ⟨a, x₁, x₂⟩, h⟩ := Types.jointly_surjective_of_isColimit
((isColimitOfPreserves (forget RingCat) hcR).tensor
((isColimitOfPreserves (forget AddCommGrpCat) hcM).tensor
(isColimitOfPreserves (forget AddCommGrpCat) hcM'))) ⟨r, m₁, m₂⟩ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.CategoryTheory.Sites.Grothendieck | {
"line": 450,
"column": 61
} | {
"line": 450,
"column": 69
} | {
"line": 450,
"column": 69
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nX Y✝ : C\nS R : Sieve X\nJ : GrothendieckTopology C\nx✝¹ x✝ : J.Cover X\nh1 : x✝¹ ≤ x✝\nh2 : x✝ ≤ x✝¹\nY : C\nf : Y ⟶ X\n⊢ (↑x✝¹).arrows f → (↑x✝).arrows f",
"ppTerm": "?m.89",
"assigned": true,
"usedConstants": [],
"usedFVars": [
"h1",
... | [] | apply h1 | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
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