module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 287,
"column": 4
} | {
"line": 293,
"column": 31
} | {
"line": 295,
"column": 0
} | [
{
"pp": "case inr\nn : ℕ\ni : Fin (n + 2)\nj : Fin (n + 1)\nH : i ≤ j.castSucc\nk : Fin (⦋n + 1⦌.len + 1)\nhik : k < i\n⊢ j.succ.predAbove (i.castSucc.succAbove k) = i.succAbove (j.predAbove k)",
"ppTerm": "?inr",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Fin.succAbove",
"Eq... | [] | rw [Fin.succAbove_of_castSucc_lt _ _ (Fin.castSucc_lt_castSucc_iff.mpr hik)]
have hjk := H.trans_lt' hik
rw [Fin.predAbove_of_le_castSucc _ _ (Fin.castSucc_le_castSucc_iff.mpr
(hjk.trans Fin.castSucc_lt_succ).le),
Fin.predAbove_of_le_castSucc _ _ hjk.le, Fin.castPred_castSucc, Fin.succAbove_of_castS... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 287,
"column": 4
} | {
"line": 293,
"column": 31
} | {
"line": 295,
"column": 0
} | [
{
"pp": "case inr\nn : ℕ\ni : Fin (n + 2)\nj : Fin (n + 1)\nH : i ≤ j.castSucc\nk : Fin (⦋n + 1⦌.len + 1)\nhik : k < i\n⊢ j.succ.predAbove (i.castSucc.succAbove k) = i.succAbove (j.predAbove k)",
"ppTerm": "?inr",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Fin.succAbove",
"Eq... | [] | rw [Fin.succAbove_of_castSucc_lt _ _ (Fin.castSucc_lt_castSucc_iff.mpr hik)]
have hjk := H.trans_lt' hik
rw [Fin.predAbove_of_le_castSucc _ _ (Fin.castSucc_le_castSucc_iff.mpr
(hjk.trans Fin.castSucc_lt_succ).le),
Fin.predAbove_of_le_castSucc _ _ hjk.le, Fin.castPred_castSucc, Fin.succAbove_of_castS... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 338,
"column": 4
} | {
"line": 338,
"column": 76
} | {
"line": 339,
"column": 4
} | [
{
"pp": "case inl\nn : ℕ\ni : Fin (n + 2)\nj : Fin (n + 1)\nH : j.castSucc < i\nk : Fin (⦋n + 1⦌.len + 1)\nhik : k ≤ i\n⊢ j.castSucc.predAbove (i.succ.succAbove k) = i.succAbove (j.predAbove k)",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Fin.succAbove",
"Eq... | [
"case inl\nn : ℕ\ni : Fin (n + 2)\nj : Fin (n + 1)\nH : j.castSucc < i\nk : Fin (⦋n + 1⦌.len + 1)\nhik : k ≤ i\n⊢ j.castSucc.predAbove k.castSucc = i.succAbove (j.predAbove k)"
] | rw [Fin.succAbove_of_castSucc_lt _ _ (Fin.castSucc_lt_succ_iff.mpr hik)] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.AlgebraicTopology.AlternatingFaceMapComplex | {
"line": 335,
"column": 4
} | {
"line": 335,
"column": 8
} | {
"line": 336,
"column": 4
} | [
{
"pp": "case e_a\nC : Type u_1\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : Preadditive C\nA : Type u_2\ninst✝¹ : Category.{v_2, u_2} A\ninst✝ : Abelian A\nX Y : CosimplicialObject C\nf : X ⟶ Y\nn : ℕ\nx : Fin (n + 2)\nx✝ : x ∈ Finset.univ\n⊢ f.app ⦋n⦌ ≫ Y.δ x = X.δ x ≫ f.app ⦋n + 1⦌",
"ppTerm": "?e_a✝",
... | [
"case e_a\nC : Type u_1\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : Preadditive C\nA : Type u_2\ninst✝¹ : Category.{v_2, u_2} A\ninst✝ : Abelian A\nX Y : CosimplicialObject C\nf : X ⟶ Y\nn : ℕ\nx : Fin (n + 2)\nx✝ : x ∈ Finset.univ\n⊢ X.δ x ≫ f.app ⦋n + 1⦌ = f.app ⦋n⦌ ≫ Y.δ x"
] | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 400,
"column": 58
} | {
"line": 400,
"column": 64
} | {
"line": 402,
"column": 0
} | [
{
"pp": "⊢ δ 0 = ⦋0⦌.const ⦋0 + 1⦌ 1",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"instNeZeroNatHAdd_1",
"of_decide_eq_true",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"SimplexCategory.instDecidableEqHom",
"SimplexCategory.δ",
"id"... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 400,
"column": 58
} | {
"line": 400,
"column": 64
} | {
"line": 402,
"column": 0
} | [
{
"pp": "⊢ δ 0 = ⦋0⦌.const ⦋0 + 1⦌ 1",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"instNeZeroNatHAdd_1",
"of_decide_eq_true",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"SimplexCategory.instDecidableEqHom",
"SimplexCategory.δ",
"id"... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 400,
"column": 58
} | {
"line": 400,
"column": 64
} | {
"line": 402,
"column": 0
} | [
{
"pp": "⊢ δ 0 = ⦋0⦌.const ⦋0 + 1⦌ 1",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"instNeZeroNatHAdd_1",
"of_decide_eq_true",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"SimplexCategory.instDecidableEqHom",
"SimplexCategory.δ",
"id"... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 402,
"column": 57
} | {
"line": 402,
"column": 63
} | {
"line": 404,
"column": 0
} | [
{
"pp": "⊢ δ 1 = ⦋0⦌.const ⦋0 + 1⦌ 0",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"instNeZeroNatHAdd_1",
"of_decide_eq_true",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"SimplexCategory.instDecidableEqHom",
"SimplexCategory.δ",
"id"... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 402,
"column": 57
} | {
"line": 402,
"column": 63
} | {
"line": 404,
"column": 0
} | [
{
"pp": "⊢ δ 1 = ⦋0⦌.const ⦋0 + 1⦌ 0",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"instNeZeroNatHAdd_1",
"of_decide_eq_true",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"SimplexCategory.instDecidableEqHom",
"SimplexCategory.δ",
"id"... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 402,
"column": 57
} | {
"line": 402,
"column": 63
} | {
"line": 404,
"column": 0
} | [
{
"pp": "⊢ δ 1 = ⦋0⦌.const ⦋0 + 1⦌ 0",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"instNeZeroNatHAdd_1",
"of_decide_eq_true",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"SimplexCategory.instDecidableEqHom",
"SimplexCategory.δ",
"id"... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 476,
"column": 59
} | {
"line": 476,
"column": 65
} | {
"line": 478,
"column": 0
} | [
{
"pp": "⊢ mkOfSucc 1 = δ 0",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"instNeZeroNatHAdd_1",
"of_decide_eq_true",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"SimplexCategory.instDecidableEqHom",
"SimplexCategory.δ",
"id",
"... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 476,
"column": 59
} | {
"line": 476,
"column": 65
} | {
"line": 478,
"column": 0
} | [
{
"pp": "⊢ mkOfSucc 1 = δ 0",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"instNeZeroNatHAdd_1",
"of_decide_eq_true",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"SimplexCategory.instDecidableEqHom",
"SimplexCategory.δ",
"id",
"... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 476,
"column": 59
} | {
"line": 476,
"column": 65
} | {
"line": 478,
"column": 0
} | [
{
"pp": "⊢ mkOfSucc 1 = δ 0",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"instNeZeroNatHAdd_1",
"of_decide_eq_true",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"SimplexCategory.instDecidableEqHom",
"SimplexCategory.δ",
"id",
"... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 478,
"column": 60
} | {
"line": 478,
"column": 66
} | {
"line": 480,
"column": 0
} | [
{
"pp": "⊢ mkOfSucc 0 = δ 2",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"instNeZeroNatHAdd_1",
"of_decide_eq_true",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"SimplexCategory.instDecidableEqHom",
"SimplexCategory.δ",
"id",
"... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 478,
"column": 60
} | {
"line": 478,
"column": 66
} | {
"line": 480,
"column": 0
} | [
{
"pp": "⊢ mkOfSucc 0 = δ 2",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"instNeZeroNatHAdd_1",
"of_decide_eq_true",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"SimplexCategory.instDecidableEqHom",
"SimplexCategory.δ",
"id",
"... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 478,
"column": 60
} | {
"line": 478,
"column": 66
} | {
"line": 480,
"column": 0
} | [
{
"pp": "⊢ mkOfSucc 0 = δ 2",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"instNeZeroNatHAdd_1",
"of_decide_eq_true",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"SimplexCategory.instDecidableEqHom",
"SimplexCategory.δ",
"id",
"... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 482,
"column": 70
} | {
"line": 482,
"column": 76
} | {
"line": 482,
"column": 77
} | [
{
"pp": "f : ⦋1⦌ ⟶ ⦋2⦌\n⊢ 0 ≤ 1",
"ppTerm": "?m.47",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"Fin.instOfNat",
"instOfNatNat",
"LE.le",
"instLEFin",
"Bool.true",
"Nat.instNeZeroSucc",
"Nat",
"Bool",
"Eq.refl",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 482,
"column": 70
} | {
"line": 482,
"column": 76
} | {
"line": 482,
"column": 77
} | [
{
"pp": "f : ⦋1⦌ ⟶ ⦋2⦌\n⊢ 0 ≤ 1",
"ppTerm": "?m.47",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"Fin.instOfNat",
"instOfNatNat",
"LE.le",
"instLEFin",
"Bool.true",
"Nat.instNeZeroSucc",
"Nat",
"Bool",
"Eq.refl",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 482,
"column": 70
} | {
"line": 482,
"column": 76
} | {
"line": 482,
"column": 77
} | [
{
"pp": "f : ⦋1⦌ ⟶ ⦋2⦌\n⊢ 0 ≤ 1",
"ppTerm": "?m.47",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"Fin.instOfNat",
"instOfNatNat",
"LE.le",
"instLEFin",
"Bool.true",
"Nat.instNeZeroSucc",
"Nat",
"Bool",
"Eq.refl",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 510,
"column": 23
} | {
"line": 510,
"column": 29
} | {
"line": 510,
"column": 29
} | [
{
"pp": "f : ⦋1⦌ ⟶ ⦋2⦌\nthis : 1 ≤ 0\ne0 : (Hom.toOrderHom f) 0 = 1\ne1 : (Hom.toOrderHom f) 1 = 0\n⊢ ¬1 ≤ 0",
"ppTerm": "?m.2440",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
"Fin.instOfNat",
"instOfNatNat",
"LE.le",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 510,
"column": 23
} | {
"line": 510,
"column": 29
} | {
"line": 510,
"column": 29
} | [
{
"pp": "f : ⦋1⦌ ⟶ ⦋2⦌\nthis : 1 ≤ 0\ne0 : (Hom.toOrderHom f) 0 = 1\ne1 : (Hom.toOrderHom f) 1 = 0\n⊢ ¬1 ≤ 0",
"ppTerm": "?m.2440",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
"Fin.instOfNat",
"instOfNatNat",
"LE.le",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 510,
"column": 23
} | {
"line": 510,
"column": 29
} | {
"line": 510,
"column": 29
} | [
{
"pp": "f : ⦋1⦌ ⟶ ⦋2⦌\nthis : 1 ≤ 0\ne0 : (Hom.toOrderHom f) 0 = 1\ne1 : (Hom.toOrderHom f) 1 = 0\n⊢ ¬1 ≤ 0",
"ppTerm": "?m.2440",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
"Fin.instOfNat",
"instOfNatNat",
"LE.le",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 510,
"column": 23
} | {
"line": 510,
"column": 29
} | {
"line": 510,
"column": 29
} | [
{
"pp": "f : ⦋1⦌ ⟶ ⦋2⦌\nthis : 2 ≤ 0\ne0 : (Hom.toOrderHom f) 0 = 2\ne1 : (Hom.toOrderHom f) 1 = 0\n⊢ ¬2 ≤ 0",
"ppTerm": "?m.2457",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
"Fin.instOfNat",
"instOfNatNat",
"LE.le",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 510,
"column": 23
} | {
"line": 510,
"column": 29
} | {
"line": 510,
"column": 29
} | [
{
"pp": "f : ⦋1⦌ ⟶ ⦋2⦌\nthis : 2 ≤ 0\ne0 : (Hom.toOrderHom f) 0 = 2\ne1 : (Hom.toOrderHom f) 1 = 0\n⊢ ¬2 ≤ 0",
"ppTerm": "?m.2457",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
"Fin.instOfNat",
"instOfNatNat",
"LE.le",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 510,
"column": 23
} | {
"line": 510,
"column": 29
} | {
"line": 510,
"column": 29
} | [
{
"pp": "f : ⦋1⦌ ⟶ ⦋2⦌\nthis : 2 ≤ 0\ne0 : (Hom.toOrderHom f) 0 = 2\ne1 : (Hom.toOrderHom f) 1 = 0\n⊢ ¬2 ≤ 0",
"ppTerm": "?m.2457",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
"Fin.instOfNat",
"instOfNatNat",
"LE.le",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 510,
"column": 23
} | {
"line": 510,
"column": 29
} | {
"line": 510,
"column": 29
} | [
{
"pp": "f : ⦋1⦌ ⟶ ⦋2⦌\nthis : 2 ≤ 1\ne0 : (Hom.toOrderHom f) 0 = 2\ne1 : (Hom.toOrderHom f) 1 = 1\n⊢ ¬2 ≤ 1",
"ppTerm": "?m.2474",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
"Fin.instOfNat",
"instOfNatNat",
"LE.le",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 510,
"column": 23
} | {
"line": 510,
"column": 29
} | {
"line": 510,
"column": 29
} | [
{
"pp": "f : ⦋1⦌ ⟶ ⦋2⦌\nthis : 2 ≤ 1\ne0 : (Hom.toOrderHom f) 0 = 2\ne1 : (Hom.toOrderHom f) 1 = 1\n⊢ ¬2 ≤ 1",
"ppTerm": "?m.2474",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
"Fin.instOfNat",
"instOfNatNat",
"LE.le",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 510,
"column": 23
} | {
"line": 510,
"column": 29
} | {
"line": 510,
"column": 29
} | [
{
"pp": "f : ⦋1⦌ ⟶ ⦋2⦌\nthis : 2 ≤ 1\ne0 : (Hom.toOrderHom f) 0 = 2\ne1 : (Hom.toOrderHom f) 1 = 1\n⊢ ¬2 ≤ 1",
"ppTerm": "?m.2474",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
"Fin.instOfNat",
"instOfNatNat",
"LE.le",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 704,
"column": 28
} | {
"line": 704,
"column": 68
} | {
"line": 704,
"column": 68
} | [
{
"pp": "n : SimplexCategory\nf : n ⟶ n\nhf : Function.Surjective ⇑(Hom.toOrderHom f)\nh : n.len = n.len\n⊢ Function.Injective (Hom.toOrderHom f).toFun",
"ppTerm": "?m.51",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"SimplexCategory.instFintypeToTypeOrderHomFinHAddNatLenOfNat",
... | [] | by rwa [Finite.injective_iff_surjective] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.AlgebraicTopology.SimplexCategory.DeltaZeroIter | {
"line": 169,
"column": 6
} | {
"line": 169,
"column": 81
} | {
"line": 170,
"column": 4
} | [
{
"pp": "case pos.inl\ni n m : ℕ\nh : n + (i + 1) = m\nk : Fin (⦋m⦌.len + 1)\nhk✝ : ↑k ≤ i\nhk : ↑k < i\n⊢ 0 = ↑(Fin.predAbove 0 ((ConcreteCategory.hom (σ₀Iter i ⋯)) k))",
"ppTerm": "?pos.inl✝",
"assigned": true,
"usedConstants": [
"_private.Mathlib.AlgebraicTopology.SimplexCategory.DeltaZeroI... | [] | grind [Fin.predAbove_of_le_castSucc, Fin.coe_castPred, σ₀Iter_coe_eq_of_lt] | Lean.Elab.Tactic.evalGrind | Lean.Parser.Tactic.grind |
Mathlib.AlgebraicTopology.SimplexCategory.DeltaZeroIter | {
"line": 169,
"column": 6
} | {
"line": 169,
"column": 81
} | {
"line": 170,
"column": 4
} | [
{
"pp": "case pos.inl\ni n m : ℕ\nh : n + (i + 1) = m\nk : Fin (⦋m⦌.len + 1)\nhk✝ : ↑k ≤ i\nhk : ↑k < i\n⊢ 0 = ↑(Fin.predAbove 0 ((ConcreteCategory.hom (σ₀Iter i ⋯)) k))",
"ppTerm": "?pos.inl✝",
"assigned": true,
"usedConstants": [
"_private.Mathlib.AlgebraicTopology.SimplexCategory.DeltaZeroI... | [] | grind [Fin.predAbove_of_le_castSucc, Fin.coe_castPred, σ₀Iter_coe_eq_of_lt] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplexCategory.DeltaZeroIter | {
"line": 169,
"column": 6
} | {
"line": 169,
"column": 81
} | {
"line": 170,
"column": 4
} | [
{
"pp": "case pos.inl\ni n m : ℕ\nh : n + (i + 1) = m\nk : Fin (⦋m⦌.len + 1)\nhk✝ : ↑k ≤ i\nhk : ↑k < i\n⊢ 0 = ↑(Fin.predAbove 0 ((ConcreteCategory.hom (σ₀Iter i ⋯)) k))",
"ppTerm": "?pos.inl✝",
"assigned": true,
"usedConstants": [
"_private.Mathlib.AlgebraicTopology.SimplexCategory.DeltaZeroI... | [] | grind [Fin.predAbove_of_le_castSucc, Fin.coe_castPred, σ₀Iter_coe_eq_of_lt] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.Degenerate | {
"line": 273,
"column": 2
} | {
"line": 278,
"column": 30
} | {
"line": 280,
"column": 0
} | [
{
"pp": "case mpr\nX : SSet\nA : X.Subcomplex\nn : ℕ\nx : ↑(A.obj (op ⦋n⦌))\n⊢ (∃ m, ∃ (_ : m < n), ∃ f, ∃ (_ : Epi f), ↑x ∈ Set.range ⇑(ConcreteCategory.hom (X.map f.op))) →\n ∃ m, ∃ (_ : m < n), ∃ f, ∃ (_ : Epi f), x ∈ Set.range ⇑(ConcreteCategory.hom (A.toSSet.map f.op))",
"ppTerm": "?mpr",
"assig... | [] | · obtain ⟨x, hx⟩ := x
rintro ⟨m, hm, f, _, ⟨y, rfl⟩⟩
refine ⟨m, hm, f, inferInstance, ⟨y, ?_⟩, rfl⟩
have := isSplitEpi_of_epi f
simpa [Set.mem_preimage, ← op_comp, ← comp_apply, ← Functor.map_comp] using
A.map (section_ f).op hx | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.AlgebraicTopology.SimplicialSet.Degenerate | {
"line": 283,
"column": 64
} | {
"line": 285,
"column": 64
} | {
"line": 287,
"column": 0
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nn : ℕ\nx : ↑(A.obj (op ⦋n⦌))\n⊢ x ∈ A.toSSet.nonDegenerate n ↔ ↑x ∈ X.nonDegenerate n",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.toSSet",
"Eq.mpr",
"Opposite",
"congrArg",
"Iff.rfl",
"SSet.nonDeg... | [] | by
rw [mem_nonDegenerate_iff_notMem_degenerate,
mem_nonDegenerate_iff_notMem_degenerate, mem_degenerate_iff] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.AlgebraicTopology.SimplicialSet.Finite | {
"line": 94,
"column": 87
} | {
"line": 99,
"column": 65
} | {
"line": 101,
"column": 0
} | [
{
"pp": "X Y : SSet\ninst✝ : Y.Finite\nf : X ⟶ Y\nhf : Mono f\n⊢ X.Finite",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"CategoryTheory.Limits.hasFiniteLimits_of_hasLimits",
"Opposite",
"CategoryTheory.ConcreteCategory.hom",
"Subtype.val_injective",
"SSet.fin... | [] | by
obtain ⟨d, _⟩ := Y.hasDimensionLT_of_finite
have := hasDimensionLT_of_mono f d
exact finite_of_hasDimensionLT _ d
(fun _ _ ↦ Finite.of_injective _
((injective_of_mono (f.app _)).comp Subtype.val_injective)) | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.AlgebraicTopology.SimplicialSet.CompStructTruncated | {
"line": 113,
"column": 4
} | {
"line": 113,
"column": 10
} | {
"line": 115,
"column": 0
} | [
{
"pp": "case refine_1\nX : Truncated 2\ns : X.obj (Opposite.op { obj := ⦋2⦌, property := _proof_1 })\n⊢ δ₂ 1 Edge._proof_1 _proof_3 ≫ δ₂ 2 Edge._proof_2 _proof_2 = Hom.tr (⦋0⦌.const ⦋2⦌ 0) ⋯ ⋯",
"ppTerm": "?refine_1",
"assigned": true,
"usedConstants": [
"CategoryTheory.ObjectProperty.FullSub... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicTopology.SimplicialSet.CompStructTruncated | {
"line": 113,
"column": 4
} | {
"line": 113,
"column": 10
} | {
"line": 115,
"column": 0
} | [
{
"pp": "case refine_2\nX : Truncated 2\ns : X.obj (Opposite.op { obj := ⦋2⦌, property := _proof_1 })\n⊢ δ₂ 0 Edge._proof_1 _proof_3 ≫ δ₂ 2 Edge._proof_2 _proof_2 = Hom.tr (⦋0⦌.const ⦋2⦌ 1) ⋯ ⋯",
"ppTerm": "?refine_2",
"assigned": true,
"usedConstants": [
"CategoryTheory.ObjectProperty.FullSub... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicTopology.SimplicialSet.CompStructTruncated | {
"line": 113,
"column": 4
} | {
"line": 113,
"column": 10
} | {
"line": 115,
"column": 0
} | [
{
"pp": "case refine_3\nX : Truncated 2\ns : X.obj (Opposite.op { obj := ⦋2⦌, property := _proof_1 })\n⊢ δ₂ 1 Edge._proof_1 _proof_3 ≫ δ₂ 0 Edge._proof_2 _proof_2 = Hom.tr (⦋0⦌.const ⦋2⦌ 1) ⋯ ⋯",
"ppTerm": "?refine_3",
"assigned": true,
"usedConstants": [
"CategoryTheory.ObjectProperty.FullSub... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicTopology.SimplicialSet.CompStructTruncated | {
"line": 113,
"column": 4
} | {
"line": 113,
"column": 10
} | {
"line": 115,
"column": 0
} | [
{
"pp": "case refine_4\nX : Truncated 2\ns : X.obj (Opposite.op { obj := ⦋2⦌, property := _proof_1 })\n⊢ δ₂ 0 Edge._proof_1 _proof_3 ≫ δ₂ 0 Edge._proof_2 _proof_2 = Hom.tr (⦋0⦌.const ⦋2⦌ 2) ⋯ ⋯",
"ppTerm": "?refine_4",
"assigned": true,
"usedConstants": [
"CategoryTheory.ObjectProperty.FullSub... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicTopology.SimplicialSet.CompStructTruncated | {
"line": 113,
"column": 4
} | {
"line": 113,
"column": 10
} | {
"line": 115,
"column": 0
} | [
{
"pp": "case refine_5\nX : Truncated 2\ns : X.obj (Opposite.op { obj := ⦋2⦌, property := _proof_1 })\n⊢ δ₂ 1 Edge._proof_1 _proof_3 ≫ δ₂ 1 Edge._proof_2 _proof_2 = Hom.tr (⦋0⦌.const ⦋2⦌ 0) ⋯ ⋯",
"ppTerm": "?refine_5",
"assigned": true,
"usedConstants": [
"CategoryTheory.ObjectProperty.FullSub... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicTopology.SimplicialSet.CompStructTruncated | {
"line": 113,
"column": 4
} | {
"line": 113,
"column": 10
} | {
"line": 115,
"column": 0
} | [
{
"pp": "case refine_6\nX : Truncated 2\ns : X.obj (Opposite.op { obj := ⦋2⦌, property := _proof_1 })\n⊢ δ₂ 0 Edge._proof_1 _proof_3 ≫ δ₂ 1 Edge._proof_2 _proof_2 = Hom.tr (⦋0⦌.const ⦋2⦌ 2) ⋯ ⋯",
"ppTerm": "?refine_6",
"assigned": true,
"usedConstants": [
"CategoryTheory.ObjectProperty.FullSub... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicTopology.SimplexCategory.Truncated | {
"line": 94,
"column": 63
} | {
"line": 94,
"column": 69
} | {
"line": 94,
"column": 69
} | [
{
"pp": "⊢ 2 = Fin.succ 1",
"ppTerm": "?m.36",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Fin.succ",
"instDecidableEqFin",
"id",
"instOfNatNat",
"Bool.true",
"instHAdd",
"HAdd.hAdd",
"SimplexCategory.mk",
"Nat",
"Bool"... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicTopology.SimplexCategory.Truncated | {
"line": 94,
"column": 63
} | {
"line": 94,
"column": 69
} | {
"line": 94,
"column": 69
} | [
{
"pp": "⊢ 2 = Fin.succ 1",
"ppTerm": "?m.36",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Fin.succ",
"instDecidableEqFin",
"id",
"instOfNatNat",
"Bool.true",
"instHAdd",
"HAdd.hAdd",
"SimplexCategory.mk",
"Nat",
"Bool"... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplexCategory.Truncated | {
"line": 94,
"column": 63
} | {
"line": 94,
"column": 69
} | {
"line": 94,
"column": 69
} | [
{
"pp": "⊢ 2 = Fin.succ 1",
"ppTerm": "?m.36",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Fin.succ",
"instDecidableEqFin",
"id",
"instOfNatNat",
"Bool.true",
"instHAdd",
"HAdd.hAdd",
"SimplexCategory.mk",
"Nat",
"Bool"... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplexCategory.Truncated | {
"line": 98,
"column": 64
} | {
"line": 98,
"column": 70
} | {
"line": 98,
"column": 70
} | [
{
"pp": "⊢ Fin.succ 0 < 2",
"ppTerm": "?m.52",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Fin.succ",
"id",
"instOfNatNat",
"Bool.true",
"instHAdd",
"Fin.decLt",
"HAdd.hAdd",
"SimplexCategory.mk",
"Nat",
"LT.lt",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicTopology.SimplexCategory.Truncated | {
"line": 98,
"column": 64
} | {
"line": 98,
"column": 70
} | {
"line": 98,
"column": 70
} | [
{
"pp": "⊢ Fin.succ 0 < 2",
"ppTerm": "?m.52",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Fin.succ",
"id",
"instOfNatNat",
"Bool.true",
"instHAdd",
"Fin.decLt",
"HAdd.hAdd",
"SimplexCategory.mk",
"Nat",
"LT.lt",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplexCategory.Truncated | {
"line": 98,
"column": 64
} | {
"line": 98,
"column": 70
} | {
"line": 98,
"column": 70
} | [
{
"pp": "⊢ Fin.succ 0 < 2",
"ppTerm": "?m.52",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Fin.succ",
"id",
"instOfNatNat",
"Bool.true",
"instHAdd",
"Fin.decLt",
"HAdd.hAdd",
"SimplexCategory.mk",
"Nat",
"LT.lt",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplexCategory.Truncated | {
"line": 100,
"column": 68
} | {
"line": 100,
"column": 74
} | {
"line": 102,
"column": 0
} | [
{
"pp": "⊢ δ₂ 1 δ₂_zero_comp_σ₂_one._proof_4 δ₂_zero_comp_σ₂_one._proof_3 =\n Hom.tr (⦋0⦌.const ⦋0 + 1⦌ 0) δ₂_zero_comp_σ₂_one._proof_4 δ₂_zero_comp_σ₂_one._proof_3",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"CategoryTheory.ObjectProperty.FullSubcategory.mk",
"of_decide... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicTopology.SimplexCategory.Truncated | {
"line": 100,
"column": 68
} | {
"line": 100,
"column": 74
} | {
"line": 102,
"column": 0
} | [
{
"pp": "⊢ δ₂ 1 δ₂_zero_comp_σ₂_one._proof_4 δ₂_zero_comp_σ₂_one._proof_3 =\n Hom.tr (⦋0⦌.const ⦋0 + 1⦌ 0) δ₂_zero_comp_σ₂_one._proof_4 δ₂_zero_comp_σ₂_one._proof_3",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"CategoryTheory.ObjectProperty.FullSubcategory.mk",
"of_decide... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplexCategory.Truncated | {
"line": 100,
"column": 68
} | {
"line": 100,
"column": 74
} | {
"line": 102,
"column": 0
} | [
{
"pp": "⊢ δ₂ 1 δ₂_zero_comp_σ₂_one._proof_4 δ₂_zero_comp_σ₂_one._proof_3 =\n Hom.tr (⦋0⦌.const ⦋0 + 1⦌ 0) δ₂_zero_comp_σ₂_one._proof_4 δ₂_zero_comp_σ₂_one._proof_3",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"CategoryTheory.ObjectProperty.FullSubcategory.mk",
"of_decide... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplexCategory.Truncated | {
"line": 102,
"column": 69
} | {
"line": 102,
"column": 75
} | {
"line": 104,
"column": 0
} | [
{
"pp": "⊢ δ₂ 0 δ₂_zero_comp_σ₂_one._proof_4 δ₂_zero_comp_σ₂_one._proof_3 =\n Hom.tr (⦋0⦌.const ⦋0 + 1⦌ 1) δ₂_zero_comp_σ₂_one._proof_4 δ₂_zero_comp_σ₂_one._proof_3",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"CategoryTheory.ObjectProperty.FullSubcategory.mk",
"of_decide... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicTopology.SimplexCategory.Truncated | {
"line": 102,
"column": 69
} | {
"line": 102,
"column": 75
} | {
"line": 104,
"column": 0
} | [
{
"pp": "⊢ δ₂ 0 δ₂_zero_comp_σ₂_one._proof_4 δ₂_zero_comp_σ₂_one._proof_3 =\n Hom.tr (⦋0⦌.const ⦋0 + 1⦌ 1) δ₂_zero_comp_σ₂_one._proof_4 δ₂_zero_comp_σ₂_one._proof_3",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"CategoryTheory.ObjectProperty.FullSubcategory.mk",
"of_decide... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplexCategory.Truncated | {
"line": 102,
"column": 69
} | {
"line": 102,
"column": 75
} | {
"line": 104,
"column": 0
} | [
{
"pp": "⊢ δ₂ 0 δ₂_zero_comp_σ₂_one._proof_4 δ₂_zero_comp_σ₂_one._proof_3 =\n Hom.tr (⦋0⦌.const ⦋0 + 1⦌ 1) δ₂_zero_comp_σ₂_one._proof_4 δ₂_zero_comp_σ₂_one._proof_3",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"CategoryTheory.ObjectProperty.FullSubcategory.mk",
"of_decide... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplexCategory.Truncated | {
"line": 105,
"column": 70
} | {
"line": 105,
"column": 76
} | {
"line": 107,
"column": 0
} | [
{
"pp": "⊢ δ₂ 0 δ₂_zero_comp_σ₂_one._proof_4 δ₂_zero_comp_σ₂_one._proof_3 ≫\n δ₂ 2 δ₂_zero_comp_σ₂_one._proof_3 δ₂_zero_comp_δ₂_two._proof_1 =\n δ₂ 1 δ₂_zero_comp_σ₂_one._proof_4 δ₂_zero_comp_σ₂_one._proof_3 ≫\n δ₂ 0 δ₂_zero_comp_σ₂_one._proof_3 δ₂_zero_comp_δ₂_two._proof_1",
"ppTerm": "?m.42",... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicTopology.SimplexCategory.Truncated | {
"line": 105,
"column": 70
} | {
"line": 105,
"column": 76
} | {
"line": 107,
"column": 0
} | [
{
"pp": "⊢ δ₂ 0 δ₂_zero_comp_σ₂_one._proof_4 δ₂_zero_comp_σ₂_one._proof_3 ≫\n δ₂ 2 δ₂_zero_comp_σ₂_one._proof_3 δ₂_zero_comp_δ₂_two._proof_1 =\n δ₂ 1 δ₂_zero_comp_σ₂_one._proof_4 δ₂_zero_comp_σ₂_one._proof_3 ≫\n δ₂ 0 δ₂_zero_comp_σ₂_one._proof_3 δ₂_zero_comp_δ₂_two._proof_1",
"ppTerm": "?m.42",... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplexCategory.Truncated | {
"line": 105,
"column": 70
} | {
"line": 105,
"column": 76
} | {
"line": 107,
"column": 0
} | [
{
"pp": "⊢ δ₂ 0 δ₂_zero_comp_σ₂_one._proof_4 δ₂_zero_comp_σ₂_one._proof_3 ≫\n δ₂ 2 δ₂_zero_comp_σ₂_one._proof_3 δ₂_zero_comp_δ₂_two._proof_1 =\n δ₂ 1 δ₂_zero_comp_σ₂_one._proof_4 δ₂_zero_comp_σ₂_one._proof_3 ≫\n δ₂ 0 δ₂_zero_comp_σ₂_one._proof_3 δ₂_zero_comp_δ₂_two._proof_1",
"ppTerm": "?m.42",... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Homology.Augment | {
"line": 101,
"column": 8
} | {
"line": 101,
"column": 24
} | {
"line": 101,
"column": 25
} | [
{
"pp": "V : Type u\ninst✝¹ : Category.{v, u} V\ninst✝ : HasZeroMorphisms V\nC : ChainComplex V ℕ\nX : V\nf : C.X 0 ⟶ X\nw : C.d 1 0 ≫ f = 0\ni j : ℕ\n⊢ (ComplexShape.down ℕ).Rel i j → 𝟙 (C.X i) ≫ (truncate.obj (C.augment f w)).d i j = C.d i j ≫ 𝟙 (C.X j)",
"ppTerm": "?m.79",
"assigned": true,
"us... | [] | cases j <;> simp | Lean.Parser.Tactic.«_aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tactic_<;>__1» | Lean.Parser.Tactic.«tactic_<;>_» |
Mathlib.Algebra.Homology.Augment | {
"line": 101,
"column": 8
} | {
"line": 101,
"column": 24
} | {
"line": 101,
"column": 25
} | [
{
"pp": "V : Type u\ninst✝¹ : Category.{v, u} V\ninst✝ : HasZeroMorphisms V\nC : ChainComplex V ℕ\nX : V\nf : C.X 0 ⟶ X\nw : C.d 1 0 ≫ f = 0\ni j : ℕ\n⊢ (ComplexShape.down ℕ).Rel i j → 𝟙 (C.X i) ≫ (truncate.obj (C.augment f w)).d i j = C.d i j ≫ 𝟙 (C.X j)",
"ppTerm": "?m.79",
"assigned": true,
"us... | [] | cases j <;> simp | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Homology.Augment | {
"line": 101,
"column": 8
} | {
"line": 101,
"column": 24
} | {
"line": 101,
"column": 25
} | [
{
"pp": "V : Type u\ninst✝¹ : Category.{v, u} V\ninst✝ : HasZeroMorphisms V\nC : ChainComplex V ℕ\nX : V\nf : C.X 0 ⟶ X\nw : C.d 1 0 ≫ f = 0\ni j : ℕ\n⊢ (ComplexShape.down ℕ).Rel i j → 𝟙 (C.X i) ≫ (truncate.obj (C.augment f w)).d i j = C.d i j ≫ 𝟙 (C.X j)",
"ppTerm": "?m.79",
"assigned": true,
"us... | [] | cases j <;> simp | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex | {
"line": 240,
"column": 2
} | {
"line": 240,
"column": 8
} | {
"line": 242,
"column": 0
} | [
{
"pp": "⊢ stdSimplex.δ 1 = SSet.const (obj₀Equiv.symm 0)",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"SSet.const",
"Opposite",
"Equiv.instEquivLike",
"of_decide_eq_true",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex | {
"line": 240,
"column": 2
} | {
"line": 240,
"column": 8
} | {
"line": 242,
"column": 0
} | [
{
"pp": "⊢ stdSimplex.δ 1 = SSet.const (obj₀Equiv.symm 0)",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"SSet.const",
"Opposite",
"Equiv.instEquivLike",
"of_decide_eq_true",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex | {
"line": 240,
"column": 2
} | {
"line": 240,
"column": 8
} | {
"line": 242,
"column": 0
} | [
{
"pp": "⊢ stdSimplex.δ 1 = SSet.const (obj₀Equiv.symm 0)",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"SSet.const",
"Opposite",
"Equiv.instEquivLike",
"of_decide_eq_true",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex | {
"line": 243,
"column": 2
} | {
"line": 243,
"column": 8
} | {
"line": 245,
"column": 0
} | [
{
"pp": "⊢ stdSimplex.δ 0 = SSet.const (obj₀Equiv.symm 1)",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"SSet.const",
"Opposite",
"Equiv.instEquivLike",
"of_decide_eq_true",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex | {
"line": 243,
"column": 2
} | {
"line": 243,
"column": 8
} | {
"line": 245,
"column": 0
} | [
{
"pp": "⊢ stdSimplex.δ 0 = SSet.const (obj₀Equiv.symm 1)",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"SSet.const",
"Opposite",
"Equiv.instEquivLike",
"of_decide_eq_true",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex | {
"line": 243,
"column": 2
} | {
"line": 243,
"column": 8
} | {
"line": 245,
"column": 0
} | [
{
"pp": "⊢ stdSimplex.δ 0 = SSet.const (obj₀Equiv.symm 1)",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"SSet.const",
"Opposite",
"Equiv.instEquivLike",
"of_decide_eq_true",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex | {
"line": 577,
"column": 2
} | {
"line": 577,
"column": 8
} | {
"line": 579,
"column": 0
} | [
{
"pp": "⊢ (faceSingletonIso 0).hom ≫ (face {0}).ι = stdSimplex.δ 1",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.toSSet",
"Opposite",
"of_decide_eq_true",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Finset",
"Catego... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex | {
"line": 577,
"column": 2
} | {
"line": 577,
"column": 8
} | {
"line": 579,
"column": 0
} | [
{
"pp": "⊢ (faceSingletonIso 0).hom ≫ (face {0}).ι = stdSimplex.δ 1",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.toSSet",
"Opposite",
"of_decide_eq_true",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Finset",
"Catego... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex | {
"line": 577,
"column": 2
} | {
"line": 577,
"column": 8
} | {
"line": 579,
"column": 0
} | [
{
"pp": "⊢ (faceSingletonIso 0).hom ≫ (face {0}).ι = stdSimplex.δ 1",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.toSSet",
"Opposite",
"of_decide_eq_true",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Finset",
"Catego... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex | {
"line": 582,
"column": 2
} | {
"line": 582,
"column": 8
} | {
"line": 584,
"column": 0
} | [
{
"pp": "⊢ (faceSingletonIso 1).hom ≫ (face {1}).ι = stdSimplex.δ 0",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.toSSet",
"Opposite",
"of_decide_eq_true",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Finset",
"Catego... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex | {
"line": 582,
"column": 2
} | {
"line": 582,
"column": 8
} | {
"line": 584,
"column": 0
} | [
{
"pp": "⊢ (faceSingletonIso 1).hom ≫ (face {1}).ι = stdSimplex.δ 0",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.toSSet",
"Opposite",
"of_decide_eq_true",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Finset",
"Catego... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex | {
"line": 582,
"column": 2
} | {
"line": 582,
"column": 8
} | {
"line": 584,
"column": 0
} | [
{
"pp": "⊢ (faceSingletonIso 1).hom ≫ (face {1}).ι = stdSimplex.δ 0",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.toSSet",
"Opposite",
"of_decide_eq_true",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Finset",
"Catego... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Homology.Augment | {
"line": 258,
"column": 8
} | {
"line": 258,
"column": 24
} | {
"line": 258,
"column": 25
} | [
{
"pp": "V : Type u\ninst✝¹ : Category.{v, u} V\ninst✝ : HasZeroMorphisms V\nC : CochainComplex V ℕ\nX : V\nf : X ⟶ C.X 0\nw : f ≫ C.d 0 1 = 0\ni j : ℕ\n⊢ (ComplexShape.up ℕ).Rel i j → 𝟙 (C.X i) ≫ (truncate.obj (C.augment f w)).d i j = C.d i j ≫ 𝟙 (C.X j)",
"ppTerm": "?m.79",
"assigned": true,
"us... | [] | cases j <;> simp | Lean.Parser.Tactic.«_aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tactic_<;>__1» | Lean.Parser.Tactic.«tactic_<;>_» |
Mathlib.Algebra.Homology.Augment | {
"line": 258,
"column": 8
} | {
"line": 258,
"column": 24
} | {
"line": 258,
"column": 25
} | [
{
"pp": "V : Type u\ninst✝¹ : Category.{v, u} V\ninst✝ : HasZeroMorphisms V\nC : CochainComplex V ℕ\nX : V\nf : X ⟶ C.X 0\nw : f ≫ C.d 0 1 = 0\ni j : ℕ\n⊢ (ComplexShape.up ℕ).Rel i j → 𝟙 (C.X i) ≫ (truncate.obj (C.augment f w)).d i j = C.d i j ≫ 𝟙 (C.X j)",
"ppTerm": "?m.79",
"assigned": true,
"us... | [] | cases j <;> simp | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Homology.Augment | {
"line": 258,
"column": 8
} | {
"line": 258,
"column": 24
} | {
"line": 258,
"column": 25
} | [
{
"pp": "V : Type u\ninst✝¹ : Category.{v, u} V\ninst✝ : HasZeroMorphisms V\nC : CochainComplex V ℕ\nX : V\nf : X ⟶ C.X 0\nw : f ≫ C.d 0 1 = 0\ni j : ℕ\n⊢ (ComplexShape.up ℕ).Rel i j → 𝟙 (C.X i) ≫ (truncate.obj (C.augment f w)).d i j = C.d i j ≫ 𝟙 (C.X j)",
"ppTerm": "?m.79",
"assigned": true,
"us... | [] | cases j <;> simp | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Homology.TotalComplex | {
"line": 218,
"column": 8
} | {
"line": 218,
"column": 62
} | {
"line": 219,
"column": 6
} | [
{
"pp": "case neg\nC : Type u_1\ninst✝⁴ : Category.{v_1, u_1} C\ninst✝³ : Preadditive C\nI₁ : Type u_2\nI₂ : Type u_3\nI₁₂ : Type u_4\nc₁ : ComplexShape I₁\nc₂ : ComplexShape I₂\nK : HomologicalComplex₂ C c₁ c₂\nc₁₂ : ComplexShape I₁₂\ninst✝² : TotalComplexShape c₁ c₂ c₁₂\ninst✝¹ : DecidableEq I₁₂\ninst✝ : K.Ha... | [] | · rw [K.d₂_eq_zero c₁₂ _ _ _ h₄, comp_zero, smul_zero] | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Algebra.Homology.TotalComplex | {
"line": 205,
"column": 2
} | {
"line": 221,
"column": 41
} | {
"line": 223,
"column": 0
} | [
{
"pp": "C : Type u_1\ninst✝⁴ : Category.{v_1, u_1} C\ninst✝³ : Preadditive C\nI₁ : Type u_2\nI₂ : Type u_3\nI₁₂ : Type u_4\nc₁ : ComplexShape I₁\nc₂ : ComplexShape I₂\nK : HomologicalComplex₂ C c₁ c₂\nc₁₂ : ComplexShape I₁₂\ninst✝² : TotalComplexShape c₁ c₂ c₁₂\ninst✝¹ : DecidableEq I₁₂\ninst✝ : K.HasTotal c₁₂... | [] | by_cases h₁ : c₁₂.Rel i₁₂ i₁₂'
· by_cases h₂ : c₁₂.Rel i₁₂' i₁₂''
· ext ⟨i₁, i₂⟩ h
simp only [totalAux.ιMapObj_D₂_assoc, comp_zero]
by_cases h₃ : c₂.Rel i₂ (c₂.next i₂)
· rw [totalAux.d₂_eq K c₁₂ i₁ h₃ i₁₂']; swap
· rw [← ComplexShape.next_π₂ c₁ c₁₂ i₁ h₃, ← c₁₂.next_eq' h₁, h]
s... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Homology.TotalComplex | {
"line": 205,
"column": 2
} | {
"line": 221,
"column": 41
} | {
"line": 223,
"column": 0
} | [
{
"pp": "C : Type u_1\ninst✝⁴ : Category.{v_1, u_1} C\ninst✝³ : Preadditive C\nI₁ : Type u_2\nI₂ : Type u_3\nI₁₂ : Type u_4\nc₁ : ComplexShape I₁\nc₂ : ComplexShape I₂\nK : HomologicalComplex₂ C c₁ c₂\nc₁₂ : ComplexShape I₁₂\ninst✝² : TotalComplexShape c₁ c₂ c₁₂\ninst✝¹ : DecidableEq I₁₂\ninst✝ : K.HasTotal c₁₂... | [] | by_cases h₁ : c₁₂.Rel i₁₂ i₁₂'
· by_cases h₂ : c₁₂.Rel i₁₂' i₁₂''
· ext ⟨i₁, i₂⟩ h
simp only [totalAux.ιMapObj_D₂_assoc, comp_zero]
by_cases h₃ : c₂.Rel i₂ (c₂.next i₂)
· rw [totalAux.d₂_eq K c₁₂ i₁ h₃ i₁₂']; swap
· rw [← ComplexShape.next_π₂ c₁ c₁₂ i₁ h₃, ← c₁₂.next_eq' h₁, h]
s... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Homology.TotalComplex | {
"line": 245,
"column": 6
} | {
"line": 251,
"column": 51
} | {
"line": 252,
"column": 4
} | [
{
"pp": "case neg\nC : Type u_1\ninst✝⁴ : Category.{v_1, u_1} C\ninst✝³ : Preadditive C\nI₁ : Type u_2\nI₂ : Type u_3\nI₁₂ : Type u_4\nc₁ : ComplexShape I₁\nc₂ : ComplexShape I₂\nK : HomologicalComplex₂ C c₁ c₂\nc₁₂ : ComplexShape I₁₂\ninst✝² : TotalComplexShape c₁ c₂ c₁₂\ninst✝¹ : DecidableEq I₁₂\ninst✝ : K.Ha... | [] | · rw [K.d₁_eq_zero c₁₂ _ _ _ h₃, zero_comp, neg_zero]
by_cases h₄ : c₂.Rel i₂ (c₂.next i₂)
· rw [totalAux.d₂_eq K c₁₂ i₁ h₄ i₁₂']; swap
· rw [← ComplexShape.next_π₂ c₁ c₁₂ i₁ h₄, ← c₁₂.next_eq' h₁, h]
simp only [Linear.units_smul_comp, assoc, totalAux.ιMapObj_D₁]
rw [K.d₁_e... | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Algebra.Homology.TotalComplex | {
"line": 278,
"column": 2
} | {
"line": 279,
"column": 6
} | {
"line": 281,
"column": 0
} | [
{
"pp": "C : Type u_1\ninst✝⁴ : Category.{v_1, u_1} C\ninst✝³ : Preadditive C\nI₁ : Type u_2\nI₂ : Type u_3\nI₁₂ : Type u_4\nc₁ : ComplexShape I₁\nc₂ : ComplexShape I₂\nK : HomologicalComplex₂ C c₁ c₂\nc₁₂ : ComplexShape I₁₂\ninst✝² : TotalComplexShape c₁ c₂ c₁₂\ninst✝¹ : DecidableEq I₁₂\ninst✝ : K.HasTotal c₁₂... | [] | subst h₁ h₂
simp | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Homology.TotalComplex | {
"line": 278,
"column": 2
} | {
"line": 279,
"column": 6
} | {
"line": 281,
"column": 0
} | [
{
"pp": "C : Type u_1\ninst✝⁴ : Category.{v_1, u_1} C\ninst✝³ : Preadditive C\nI₁ : Type u_2\nI₂ : Type u_3\nI₁₂ : Type u_4\nc₁ : ComplexShape I₁\nc₂ : ComplexShape I₂\nK : HomologicalComplex₂ C c₁ c₂\nc₁₂ : ComplexShape I₁₂\ninst✝² : TotalComplexShape c₁ c₂ c₁₂\ninst✝¹ : DecidableEq I₁₂\ninst✝ : K.HasTotal c₁₂... | [] | subst h₁ h₂
simp | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Homology.TotalComplex | {
"line": 286,
"column": 2
} | {
"line": 287,
"column": 6
} | {
"line": 289,
"column": 0
} | [
{
"pp": "C : Type u_1\ninst✝⁴ : Category.{v_1, u_1} C\ninst✝³ : Preadditive C\nI₁ : Type u_2\nI₂ : Type u_3\nI₁₂ : Type u_4\nc₁ : ComplexShape I₁\nc₂ : ComplexShape I₂\nK : HomologicalComplex₂ C c₁ c₂\nc₁₂ : ComplexShape I₁₂\ninst✝² : TotalComplexShape c₁ c₂ c₁₂\ninst✝¹ : DecidableEq I₁₂\ninst✝ : K.HasTotal c₁₂... | [] | subst h₁ h₂
simp | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Homology.TotalComplex | {
"line": 286,
"column": 2
} | {
"line": 287,
"column": 6
} | {
"line": 289,
"column": 0
} | [
{
"pp": "C : Type u_1\ninst✝⁴ : Category.{v_1, u_1} C\ninst✝³ : Preadditive C\nI₁ : Type u_2\nI₂ : Type u_3\nI₁₂ : Type u_4\nc₁ : ComplexShape I₁\nc₂ : ComplexShape I₂\nK : HomologicalComplex₂ C c₁ c₂\nc₁₂ : ComplexShape I₁₂\ninst✝² : TotalComplexShape c₁ c₂ c₁₂\ninst✝¹ : DecidableEq I₁₂\ninst✝ : K.HasTotal c₁₂... | [] | subst h₁ h₂
simp | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Shift.Twist | {
"line": 86,
"column": 6
} | {
"line": 86,
"column": 32
} | {
"line": 86,
"column": 33
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\nA : Type w\ninst✝¹ : AddMonoid A\ninst✝ : HasShift C A\nt : TwistShiftData C A\na b c : A\nX : t.Category\n⊢ (↑(t.z (a + b) c)).app ((shiftFunctor C (a + b + c)).obj X) ≫\n (↑(t.z a b)).app ((shiftFunctor C (a + b + c)).obj X) ≫\n ((shiftFunctorAdd C ... | [
"C : Type u\ninst✝² : Category.{v, u} C\nA : Type w\ninst✝¹ : AddMonoid A\ninst✝ : HasShift C A\nt : TwistShiftData C A\na b c : A\nX : t.Category\n⊢ (↑(t.z (a + b) c) * ↑(t.z a b)).app ((shiftFunctor C (a + b + c)).obj X) ≫\n ((shiftFunctorAdd C (a + b) c).app X).hom ≫ (shiftFunctor C c).map ((shiftFunctorAdd... | ← CatCenter.mul_app_assoc, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.CategoryTheory.Shift.Twist | {
"line": 86,
"column": 33
} | {
"line": 86,
"column": 59
} | {
"line": 87,
"column": 6
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\nA : Type w\ninst✝¹ : AddMonoid A\ninst✝ : HasShift C A\nt : TwistShiftData C A\na b c : A\nX : t.Category\n⊢ (↑(t.z (a + b) c) * ↑(t.z a b)).app ((shiftFunctor C (a + b + c)).obj X) ≫\n ((shiftFunctorAdd C (a + b) c).app X).hom ≫ (shiftFunctor C c).map ((shi... | [
"C : Type u\ninst✝² : Category.{v, u} C\nA : Type w\ninst✝¹ : AddMonoid A\ninst✝ : HasShift C A\nt : TwistShiftData C A\na b c : A\nX : t.Category\n⊢ (↑(t.z (a + b) c) * ↑(t.z a b)).app ((shiftFunctor C (a + b + c)).obj X) ≫\n ((shiftFunctorAdd C (a + b) c).app X).hom ≫ (shiftFunctor C c).map ((shiftFunctorAdd... | ← CatCenter.mul_app_assoc, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Homology.BifunctorHomotopy | {
"line": 114,
"column": 4
} | {
"line": 114,
"column": 30
} | {
"line": 114,
"column": 31
} | [
{
"pp": "C₁ : Type u_1\nC₂ : Type u_2\nD : Type u_3\nI₁ : Type u_4\nI₂ : Type u_5\nJ : Type u_6\ninst✝¹¹ : Category.{v_1, u_1} C₁\ninst✝¹⁰ : Category.{v_2, u_2} C₂\ninst✝⁹ : Category.{v_3, u_3} D\ninst✝⁸ : Preadditive C₁\ninst✝⁷ : Preadditive C₂\ninst✝⁶ : Preadditive D\nc₁ : ComplexShape I₁\nc₂ : ComplexShape I... | [
"C₁ : Type u_1\nC₂ : Type u_2\nD : Type u_3\nI₁ : Type u_4\nI₂ : Type u_5\nJ : Type u_6\ninst✝¹¹ : Category.{v_1, u_1} C₁\ninst✝¹⁰ : Category.{v_2, u_2} C₂\ninst✝⁹ : Category.{v_3, u_3} D\ninst✝⁸ : Preadditive C₁\ninst✝⁷ : Preadditive C₂\ninst✝⁶ : Preadditive D\nc₁ : ComplexShape I₁\nc₂ : ComplexShape I₂\nK₁ L₁ : H... | NatTrans.naturality_assoc, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Homology.CochainComplexOpposite | {
"line": 111,
"column": 6
} | {
"line": 111,
"column": 10
} | {
"line": 112,
"column": 6
} | [
{
"pp": "case e_a\nC : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Preadditive C\nK L : CochainComplex C ℤ\nf g : K ⟶ L\nh : Homotopy f g\nn : ℤ\n⊢ (h.hom (-n) (-(n + 1)) ≫ L.d (-(n + 1)) (-n)).op = (dNext n) fun p q ↦ (h.hom (-q) (-p)).op",
"ppTerm": "?e_a✝",
"assigned": true,
"usedConstants"... | [
"case e_a\nC : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Preadditive C\nK L : CochainComplex C ℤ\nf g : K ⟶ L\nh : Homotopy f g\nn : ℤ\n⊢ ((dNext n) fun p q ↦ (h.hom (-q) (-p)).op) = (h.hom (-n) (-(n + 1)) ≫ L.d (-(n + 1)) (-n)).op"
] | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.Algebra.Homology.CochainComplexOpposite | {
"line": 114,
"column": 6
} | {
"line": 114,
"column": 10
} | {
"line": 115,
"column": 6
} | [
{
"pp": "case e_a\nC : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Preadditive C\nK L : CochainComplex C ℤ\nf g : K ⟶ L\nh : Homotopy f g\nn : ℤ\n⊢ (K.d (-n) (-(n - 1)) ≫ h.hom (-(n - 1)) (-n)).op = (prevD n) fun p q ↦ (h.hom (-q) (-p)).op",
"ppTerm": "?e_a✝",
"assigned": true,
"usedConstants"... | [
"case e_a\nC : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Preadditive C\nK L : CochainComplex C ℤ\nf g : K ⟶ L\nh : Homotopy f g\nn : ℤ\n⊢ ((prevD n) fun p q ↦ (h.hom (-q) (-p)).op) = (K.d (-n) (-(n - 1)) ≫ h.hom (-(n - 1)) (-n)).op"
] | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.Algebra.Homology.TotalComplexShift | {
"line": 316,
"column": 6
} | {
"line": 319,
"column": 52
} | {
"line": 319,
"column": 52
} | [
{
"pp": "C : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Preadditive C\nK L : HomologicalComplex₂ C (up ℤ) (up ℤ)\nf : K ⟶ L\nx y : ℤ\ninst✝ : K.HasTotal (up ℤ)\nn n' : ℤ\nx✝ : (up ℤ).Rel n n'\n⊢ (K.totalShift₂XIso y n (n + y) ⋯).hom ≫ ((shiftFunctor (HomologicalComplex C (up ℤ)) y).obj (K.total (up ℤ)))... | [] | dsimp
simp only [total_d, Preadditive.add_comp, Preadditive.comp_add, smul_add,
Linear.comp_units_smul, K.D₁_totalShift₂XIso_hom y n n' _ _ rfl rfl,
K.D₂_totalShift₂XIso_hom y n n' _ _ rfl rfl] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Homology.TotalComplexShift | {
"line": 316,
"column": 6
} | {
"line": 319,
"column": 52
} | {
"line": 319,
"column": 52
} | [
{
"pp": "C : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Preadditive C\nK L : HomologicalComplex₂ C (up ℤ) (up ℤ)\nf : K ⟶ L\nx y : ℤ\ninst✝ : K.HasTotal (up ℤ)\nn n' : ℤ\nx✝ : (up ℤ).Rel n n'\n⊢ (K.totalShift₂XIso y n (n + y) ⋯).hom ≫ ((shiftFunctor (HomologicalComplex C (up ℤ)) y).obj (K.total (up ℤ)))... | [] | dsimp
simp only [total_d, Preadditive.add_comp, Preadditive.comp_add, smul_add,
Linear.comp_units_smul, K.D₁_totalShift₂XIso_hom y n n' _ _ rfl rfl,
K.D₂_totalShift₂XIso_hom y n n' _ _ rfl rfl] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Homology.CommSq | {
"line": 82,
"column": 10
} | {
"line": 82,
"column": 14
} | {
"line": 83,
"column": 10
} | [
{
"pp": "case h₀\nC : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Preadditive C\nX₁ X₂ X₃ X₄ : C\ninst✝ : HasBinaryBiproduct X₂ X₃\nf : X₁ ⟶ X₂\ng : X₁ ⟶ X₃\ninl : X₂ ⟶ X₄\ninr : X₃ ⟶ X₄\nsq : CommSq f g inl inr\nh : IsColimit (PushoutCocone.mk inl inr ⋯)\ns : Cofork (biprod.lift f (-g)) 0\nm : sq.cokern... | [
"case h₀\nC : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Preadditive C\nX₁ X₂ X₃ X₄ : C\ninst✝ : HasBinaryBiproduct X₂ X₃\nf : X₁ ⟶ X₂\ng : X₁ ⟶ X₃\ninl : X₂ ⟶ X₄\ninr : X₃ ⟶ X₄\nsq : CommSq f g inl inr\nh : IsColimit (PushoutCocone.mk inl inr ⋯)\ns : Cofork (biprod.lift f (-g)) 0\nm : sq.cokernelCofork.pt ... | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.Algebra.Homology.CommSq | {
"line": 88,
"column": 10
} | {
"line": 88,
"column": 14
} | {
"line": 89,
"column": 10
} | [
{
"pp": "case h₁\nC : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Preadditive C\nX₁ X₂ X₃ X₄ : C\ninst✝ : HasBinaryBiproduct X₂ X₃\nf : X₁ ⟶ X₂\ng : X₁ ⟶ X₃\ninl : X₂ ⟶ X₄\ninr : X₃ ⟶ X₄\nsq : CommSq f g inl inr\nh : IsColimit (PushoutCocone.mk inl inr ⋯)\ns : Cofork (biprod.lift f (-g)) 0\nm : sq.cokern... | [
"case h₁\nC : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Preadditive C\nX₁ X₂ X₃ X₄ : C\ninst✝ : HasBinaryBiproduct X₂ X₃\nf : X₁ ⟶ X₂\ng : X₁ ⟶ X₃\ninl : X₂ ⟶ X₄\ninr : X₃ ⟶ X₄\nsq : CommSq f g inl inr\nh : IsColimit (PushoutCocone.mk inl inr ⋯)\ns : Cofork (biprod.lift f (-g)) 0\nm : sq.cokernelCofork.pt ... | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.Algebra.Homology.CommSq | {
"line": 163,
"column": 10
} | {
"line": 163,
"column": 14
} | {
"line": 164,
"column": 10
} | [
{
"pp": "case h₀\nC : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Preadditive C\nX₁ X₂ X₃ X₄ : C\ninst✝ : HasBinaryBiproduct X₂ X₃\nfst : X₁ ⟶ X₂\nsnd : X₁ ⟶ X₃\nf : X₂ ⟶ X₄\ng : X₃ ⟶ X₄\nsq : CommSq fst snd f g\nh : IsLimit (PullbackCone.mk fst snd ⋯)\ns : Fork (biprod.desc f (-g)) 0\nm : s.pt ⟶ sq.kern... | [
"case h₀\nC : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Preadditive C\nX₁ X₂ X₃ X₄ : C\ninst✝ : HasBinaryBiproduct X₂ X₃\nfst : X₁ ⟶ X₂\nsnd : X₁ ⟶ X₃\nf : X₂ ⟶ X₄\ng : X₃ ⟶ X₄\nsq : CommSq fst snd f g\nh : IsLimit (PullbackCone.mk fst snd ⋯)\ns : Fork (biprod.desc f (-g)) 0\nm : s.pt ⟶ sq.kernelFork.pt\nh... | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.Algebra.Homology.CommSq | {
"line": 169,
"column": 10
} | {
"line": 169,
"column": 14
} | {
"line": 170,
"column": 10
} | [
{
"pp": "case h₁\nC : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Preadditive C\nX₁ X₂ X₃ X₄ : C\ninst✝ : HasBinaryBiproduct X₂ X₃\nfst : X₁ ⟶ X₂\nsnd : X₁ ⟶ X₃\nf : X₂ ⟶ X₄\ng : X₃ ⟶ X₄\nsq : CommSq fst snd f g\nh : IsLimit (PullbackCone.mk fst snd ⋯)\ns : Fork (biprod.desc f (-g)) 0\nm : s.pt ⟶ sq.kern... | [
"case h₁\nC : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Preadditive C\nX₁ X₂ X₃ X₄ : C\ninst✝ : HasBinaryBiproduct X₂ X₃\nfst : X₁ ⟶ X₂\nsnd : X₁ ⟶ X₃\nf : X₂ ⟶ X₄\ng : X₃ ⟶ X₄\nsq : CommSq fst snd f g\nh : IsLimit (PullbackCone.mk fst snd ⋯)\ns : Fork (biprod.desc f (-g)) 0\nm : s.pt ⟶ sq.kernelFork.pt\nh... | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.Algebra.Homology.DerivedCategory.TStructure | {
"line": 65,
"column": 32
} | {
"line": 80,
"column": 29
} | {
"line": 82,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : Abelian C\ninst✝ : HasDerivedCategory C\nX : DerivedCategory C\n⊢ ∃ X_1 Y,\n ∃ (_ : ∃ K x, K.IsStrictlyLE 0) (_ : ∃ K x, K.IsStrictlyGE 1), ∃ f g h, Triangle.mk f g h ∈ distinguishedTriangles",
"ppTerm": "?m.493",
"assigned": true,
"usedCo... | [] | by
obtain ⟨K, ⟨e₂⟩⟩ : ∃ K, Nonempty (Q.obj K ≅ X) := ⟨_, ⟨Q.objObjPreimageIso X⟩⟩
have h := K.shortComplexTruncLE_shortExact 0
refine ⟨Q.obj (K.truncLE 0), Q.obj (K.truncGE 1),
⟨_, Iso.refl _, inferInstance⟩, ⟨_, Iso.refl _, inferInstance⟩,
Q.map (K.ιTruncLE 0) ≫ e₂.hom, e₂.inv ≫ Q.map (K.πTrunc... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.LiftingProperties.Limits | {
"line": 35,
"column": 40
} | {
"line": 35,
"column": 63
} | {
"line": 35,
"column": 63
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\nX Y Z W : C\nf : X ⟶ Y\ns : X ⟶ Z\ng : Z ⟶ W\nt : Y ⟶ W\nh : IsPushout s f g t\nZ' W' : C\ng' : Z' ⟶ W'\ninst✝ : HasLiftingProperty f g'\nu : Z ⟶ Z'\nv : W ⟶ W'\nsq : CommSq u g g' v\nw : (s ≫ u) ≫ g' = f ≫ t ≫ v\n⊢ s ≫ u = f ≫ ⋯.lift",
"ppTerm": "?m.17... | [] | by rw [CommSq.fac_left] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.AlgebraicTopology.ModelCategory.CategoryWithCofibrations | {
"line": 282,
"column": 2
} | {
"line": 282,
"column": 47
} | {
"line": 284,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\nX✝ Y✝ : C\nf✝ : X✝ ⟶ Y✝\ninst✝¹ : CategoryWithWeakEquivalences C\nP : ObjectProperty C\nX Y : P.FullSubcategory\nf : X ⟶ Y\ninst✝ : WeakEquivalence f\n⊢ WeakEquivalence f.hom",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"Eq.mpr",
... | [] | rwa [← weakEquivalence_iff_of_objectProperty] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticRwa___1 | Lean.Parser.Tactic.tacticRwa__ |
Mathlib.AlgebraicTopology.ModelCategory.CategoryWithCofibrations | {
"line": 282,
"column": 2
} | {
"line": 282,
"column": 47
} | {
"line": 284,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\nX✝ Y✝ : C\nf✝ : X✝ ⟶ Y✝\ninst✝¹ : CategoryWithWeakEquivalences C\nP : ObjectProperty C\nX Y : P.FullSubcategory\nf : X ⟶ Y\ninst✝ : WeakEquivalence f\n⊢ WeakEquivalence f.hom",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"Eq.mpr",
... | [] | rwa [← weakEquivalence_iff_of_objectProperty] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.ModelCategory.CategoryWithCofibrations | {
"line": 282,
"column": 2
} | {
"line": 282,
"column": 47
} | {
"line": 284,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\nX✝ Y✝ : C\nf✝ : X✝ ⟶ Y✝\ninst✝¹ : CategoryWithWeakEquivalences C\nP : ObjectProperty C\nX Y : P.FullSubcategory\nf : X ⟶ Y\ninst✝ : WeakEquivalence f\n⊢ WeakEquivalence f.hom",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"Eq.mpr",
... | [] | rwa [← weakEquivalence_iff_of_objectProperty] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.ModelCategory.IsCofibrant | {
"line": 92,
"column": 2
} | {
"line": 92,
"column": 6
} | {
"line": 93,
"column": 2
} | [
{
"pp": "C : Type u_1\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : CategoryWithFibrations C\ninst✝¹ : HasTerminal C\ninst✝ : (fibrations C).RespectsIso\nX Y : C\np : X ⟶ Y\nhY : IsTerminal Y\n⊢ fibrations C (terminal.from X) ↔ fibrations C p",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
... | [
"C : Type u_1\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : CategoryWithFibrations C\ninst✝¹ : HasTerminal C\ninst✝ : (fibrations C).RespectsIso\nX Y : C\np : X ⟶ Y\nhY : IsTerminal Y\n⊢ fibrations C p ↔ fibrations C (terminal.from X)"
] | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.AlgebraicTopology.ModelCategory.RightHomotopy | {
"line": 263,
"column": 2
} | {
"line": 265,
"column": 37
} | {
"line": 267,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\nX Y : C\ninst✝¹ : ModelCategory C\nf₀ f₁ f₂ : X ⟶ Y\ninst✝ : IsFibrant Y\nh : RightHomotopyRel f₀ f₁\nh' : RightHomotopyRel f₁ f₂\n⊢ RightHomotopyRel f₀ f₂",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"HomotopicalAlgebra.PathObject"... | [] | obtain ⟨P, ⟨h⟩⟩ := h
obtain ⟨P', _, ⟨h'⟩⟩ := h'.exists_good_pathObject
exact (h.trans h').rightHomotopyRel | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
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