module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.AlgebraicTopology.SimplicialObject.Homotopy | {
"line": 146,
"column": 4
} | {
"line": 146,
"column": 15
} | {
"line": 146,
"column": 16
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nX Y : SimplicialObject C\nf g : X ⟶ Y\nH : Homotopy f g\nY' : SimplicialObject C\np : Y ⟶ Y'\nn✝ : ℕ\ni j : Fin (n✝ + 1)\nhji : j ≤ i\n⊢ (H.h j ≫ p.app (op ⦋n✝ + 1⦌)) ≫ Y'.σ i.succ = X.σ i ≫ H.h j.castSucc ≫ p.app (op ⦋n✝ + 1 + 1⦌)",
"ppTerm": "?m.278",
"a... | [
"C : Type u\ninst✝ : Category.{v, u} C\nX Y : SimplicialObject C\nf g : X ⟶ Y\nH : Homotopy f g\nY' : SimplicialObject C\np : Y ⟶ Y'\nn✝ : ℕ\ni j : Fin (n✝ + 1)\nhji : j ≤ i\n⊢ H.h j ≫ p.app (op ⦋n✝ + 1⦌) ≫ Y'.σ i.succ = X.σ i ≫ H.h j.castSucc ≫ p.app (op ⦋n✝ + 1 + 1⦌)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialObject.Homotopy | {
"line": 154,
"column": 4
} | {
"line": 154,
"column": 37
} | {
"line": 154,
"column": 38
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nX Y : SimplicialObject C\nf g : X ⟶ Y\nH : Homotopy f g\nX' : SimplicialObject C\np : X' ⟶ X\nn : ℕ\n⊢ (p.app (op ⦋n⦌) ≫ H.h 0) ≫ Y.δ 0 = (p ≫ g).app (op ⦋n⦌)",
"ppTerm": "?m.88",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"CategoryTheo... | [
"C : Type u\ninst✝ : Category.{v, u} C\nX Y : SimplicialObject C\nf g : X ⟶ Y\nH : Homotopy f g\nX' : SimplicialObject C\np : X' ⟶ X\nn : ℕ\n⊢ p.app (op ⦋n⦌) ≫ H.h 0 ≫ Y.δ 0 = p.app (op ⦋n⦌) ≫ g.app (op ⦋n⦌)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialObject.Homotopy | {
"line": 156,
"column": 4
} | {
"line": 156,
"column": 37
} | {
"line": 156,
"column": 38
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nX Y : SimplicialObject C\nf g : X ⟶ Y\nH : Homotopy f g\nX' : SimplicialObject C\np : X' ⟶ X\nn : ℕ\n⊢ (p.app (op ⦋n⦌) ≫ H.h (Fin.last n)) ≫ Y.δ (Fin.last (n + 1)) = (p ≫ f).app (op ⦋n⦌)",
"ppTerm": "?m.115",
"assigned": true,
"usedConstants": [
... | [
"C : Type u\ninst✝ : Category.{v, u} C\nX Y : SimplicialObject C\nf g : X ⟶ Y\nH : Homotopy f g\nX' : SimplicialObject C\np : X' ⟶ X\nn : ℕ\n⊢ p.app (op ⦋n⦌) ≫ H.h (Fin.last n) ≫ Y.δ (Fin.last (n + 1)) = p.app (op ⦋n⦌) ≫ f.app (op ⦋n⦌)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialObject.Homotopy | {
"line": 158,
"column": 4
} | {
"line": 158,
"column": 15
} | {
"line": 158,
"column": 16
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nX Y : SimplicialObject C\nf g : X ⟶ Y\nH : Homotopy f g\nX' : SimplicialObject C\np : X' ⟶ X\nn✝ : ℕ\ni : Fin (n✝ + 2)\nj : Fin (n✝ + 1)\nhij : i ≤ j.castSucc\n⊢ (p.app (op ⦋n✝ + 1⦌) ≫ H.h j.succ) ≫ Y.δ i.castSucc = X'.δ i ≫ p.app (op ⦋n✝⦌) ≫ H.h j",
"ppTerm":... | [
"C : Type u\ninst✝ : Category.{v, u} C\nX Y : SimplicialObject C\nf g : X ⟶ Y\nH : Homotopy f g\nX' : SimplicialObject C\np : X' ⟶ X\nn✝ : ℕ\ni : Fin (n✝ + 2)\nj : Fin (n✝ + 1)\nhij : i ≤ j.castSucc\n⊢ p.app (op ⦋n✝ + 1⦌) ≫ H.h j.succ ≫ Y.δ i.castSucc = p.app (op ⦋n✝ + 1⦌) ≫ X.δ i ≫ H.h j"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialObject.Homotopy | {
"line": 160,
"column": 4
} | {
"line": 160,
"column": 15
} | {
"line": 160,
"column": 16
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nX Y : SimplicialObject C\nf g : X ⟶ Y\nH : Homotopy f g\nX' : SimplicialObject C\np : X' ⟶ X\nn✝ : ℕ\nj : Fin (n✝ + 1)\n⊢ (p.app (op ⦋n✝ + 1⦌) ≫ H.h j.succ) ≫ Y.δ j.castSucc.succ =\n (p.app (op ⦋n✝ + 1⦌) ≫ H.h j.castSucc) ≫ Y.δ j.castSucc.succ",
"ppTerm": "... | [
"C : Type u\ninst✝ : Category.{v, u} C\nX Y : SimplicialObject C\nf g : X ⟶ Y\nH : Homotopy f g\nX' : SimplicialObject C\np : X' ⟶ X\nn✝ : ℕ\nj : Fin (n✝ + 1)\n⊢ p.app (op ⦋n✝ + 1⦌) ≫ H.h j.succ ≫ Y.δ j.castSucc.succ = p.app (op ⦋n✝ + 1⦌) ≫ H.h j.castSucc ≫ Y.δ j.castSucc.succ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialObject.Homotopy | {
"line": 162,
"column": 4
} | {
"line": 162,
"column": 15
} | {
"line": 162,
"column": 16
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nX Y : SimplicialObject C\nf g : X ⟶ Y\nH : Homotopy f g\nX' : SimplicialObject C\np : X' ⟶ X\nn✝ : ℕ\ni : Fin (n✝ + 2)\nj : Fin (n✝ + 1)\nhji : j.castSucc < i\n⊢ (p.app (op ⦋n✝ + 1⦌) ≫ H.h j.castSucc) ≫ Y.δ i.succ = X'.δ i ≫ p.app (op ⦋n✝⦌) ≫ H.h j",
"ppTerm":... | [
"C : Type u\ninst✝ : Category.{v, u} C\nX Y : SimplicialObject C\nf g : X ⟶ Y\nH : Homotopy f g\nX' : SimplicialObject C\np : X' ⟶ X\nn✝ : ℕ\ni : Fin (n✝ + 2)\nj : Fin (n✝ + 1)\nhji : j.castSucc < i\n⊢ p.app (op ⦋n✝ + 1⦌) ≫ H.h j.castSucc ≫ Y.δ i.succ = p.app (op ⦋n✝ + 1⦌) ≫ X.δ i ≫ H.h j"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialObject.Homotopy | {
"line": 164,
"column": 4
} | {
"line": 164,
"column": 15
} | {
"line": 164,
"column": 16
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nX Y : SimplicialObject C\nf g : X ⟶ Y\nH : Homotopy f g\nX' : SimplicialObject C\np : X' ⟶ X\nn✝ : ℕ\ni j : Fin (n✝ + 1)\nhij : i ≤ j\n⊢ (p.app (op ⦋n✝⦌) ≫ H.h j) ≫ Y.σ i.castSucc = X'.σ i ≫ p.app (op ⦋n✝ + 1⦌) ≫ H.h j.succ",
"ppTerm": "?m.226",
"assigned"... | [
"C : Type u\ninst✝ : Category.{v, u} C\nX Y : SimplicialObject C\nf g : X ⟶ Y\nH : Homotopy f g\nX' : SimplicialObject C\np : X' ⟶ X\nn✝ : ℕ\ni j : Fin (n✝ + 1)\nhij : i ≤ j\n⊢ p.app (op ⦋n✝⦌) ≫ H.h j ≫ Y.σ i.castSucc = p.app (op ⦋n✝⦌) ≫ X.σ i ≫ H.h j.succ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialObject.Homotopy | {
"line": 166,
"column": 4
} | {
"line": 166,
"column": 15
} | {
"line": 166,
"column": 16
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nX Y : SimplicialObject C\nf g : X ⟶ Y\nH : Homotopy f g\nX' : SimplicialObject C\np : X' ⟶ X\nn✝ : ℕ\ni j : Fin (n✝ + 1)\nhji : j ≤ i\n⊢ (p.app (op ⦋n✝⦌) ≫ H.h j) ≫ Y.σ i.succ = X'.σ i ≫ p.app (op ⦋n✝ + 1⦌) ≫ H.h j.castSucc",
"ppTerm": "?m.254",
"assigned"... | [
"C : Type u\ninst✝ : Category.{v, u} C\nX Y : SimplicialObject C\nf g : X ⟶ Y\nH : Homotopy f g\nX' : SimplicialObject C\np : X' ⟶ X\nn✝ : ℕ\ni j : Fin (n✝ + 1)\nhji : j ≤ i\n⊢ p.app (op ⦋n✝⦌) ≫ H.h j ≫ Y.σ i.succ = p.app (op ⦋n✝⦌) ≫ X.σ i ≫ H.h j.castSucc"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.CechNerve | {
"line": 127,
"column": 4
} | {
"line": 127,
"column": 15
} | {
"line": 127,
"column": 16
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : ∀ (n : ℕ) (f : Arrow C), HasWidePullback f.right (fun x ↦ f.left) fun x ↦ f.hom\nX : Augmented C\nF : Arrow C\nG : X ⟶ F.augmentedCechNerve\nthis :\n ((𝟭 (SimplicialObject C)).map G.left ≫ F.augmentedCechNerve.hom).app (Opposite.op ⦋0⦌) =\n (X.hom ≫ ... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : ∀ (n : ℕ) (f : Arrow C), HasWidePullback f.right (fun x ↦ f.left) fun x ↦ f.hom\nX : Augmented C\nF : Arrow C\nG : X ⟶ F.augmentedCechNerve\nthis :\n ((𝟭 (SimplicialObject C)).map G.left ≫ F.augmentedCechNerve.hom).app (Opposite.op ⦋0⦌) =\n (X.hom ≫ (const C).ma... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 794,
"column": 2
} | {
"line": 794,
"column": 29
} | {
"line": 794,
"column": 30
} | [
{
"pp": "case h\nn : ℕ\nΔ : SimplexCategory\nθ : Δ ⟶ ⦋n + 1⦌\ni : Fin (n + 2)\nhi : ∀ (x : Fin (Δ.len + 1)), (Hom.toOrderHom θ) x ≠ i\nx : Fin (Δ.len + 1)\nj : Fin (n + 2)\nhj : j ≠ i\n⊢ i.succAbove (((Fin.last n).predAbove i).predAbove j) = j",
"ppTerm": "?h",
"assigned": true,
"usedConstants": [
... | [
"case h.last\nn : ℕ\nΔ : SimplexCategory\nθ : Δ ⟶ ⦋n + 1⦌\nx : Fin (Δ.len + 1)\nj : Fin (n + 2)\nhi : ∀ (x : Fin (Δ.len + 1)), (Hom.toOrderHom θ) x ≠ Fin.last (n + 1)\nhj : j ≠ Fin.last (n + 1)\n⊢ (Fin.last (n + 1)).succAbove (((Fin.last n).predAbove (Fin.last (n + 1))).predAbove j) = j",
"case h.cast\nn : ℕ\nΔ :... | cases i using Fin.lastCases | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalCases | Lean.Parser.Tactic.cases |
Mathlib.AlgebraicTopology.CechNerve | {
"line": 162,
"column": 8
} | {
"line": 162,
"column": 19
} | {
"line": 162,
"column": 20
} | [
{
"pp": "case h₁.refine_2\nC : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : ∀ (n : ℕ) (f : Arrow C), HasWidePullback f.right (fun x ↦ f.left) fun x ↦ f.hom\nX : Augmented C\nF : Arrow C\nA : X ⟶ F.augmentedCechNerve\nx : SimplexCategoryᵒᵖ\n⊢ ((equivalenceLeftToRight X F (equivalenceRightToLeft X F A)).left.app x... | [
"case h₁.refine_2\nC : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : ∀ (n : ℕ) (f : Arrow C), HasWidePullback f.right (fun x ↦ f.left) fun x ↦ f.hom\nX : Augmented C\nF : Arrow C\nA : X ⟶ F.augmentedCechNerve\nx : SimplexCategoryᵒᵖ\n⊢ X.hom.app x ≫ A.right = A.left.app x ≫ WidePullback.base fun x ↦ F.hom"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.CechNerve | {
"line": 312,
"column": 6
} | {
"line": 314,
"column": 29
} | {
"line": 315,
"column": 2
} | [
{
"pp": "case h₂.refine_2\nC : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : ∀ (n : ℕ) (f : Arrow C), HasWidePushout f.left (fun x ↦ f.right) fun x ↦ f.hom\nF : Arrow C\nX : Augmented C\nA : F.augmentedCechConerve ⟶ X\nx : SimplexCategory\n⊢ (WidePushout.head fun x ↦ F.hom) ≫ (equivalenceRightToLeft F X (equivale... | [] | · dsimp
rw [colimit.ι_desc]
exact congr_app A.w x | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.AlgebraicTopology.SimplicialSet.Degenerate | {
"line": 231,
"column": 2
} | {
"line": 231,
"column": 35
} | {
"line": 231,
"column": 36
} | [
{
"pp": "X : SSet\nn : ℕ\nx : X _⦋n⦌\nm : ℕ\nf₁ : ⦋n⦌ ⟶ ⦋m⦌\ninst✝ : Epi f₁\ny₁ : ↑(X.nonDegenerate m)\nhy₁ : x = (ConcreteCategory.hom (X.map f₁.op)) ↑y₁\nf₂ : ⦋n⦌ ⟶ ⦋m⦌\ny₂ : ↑(X.nonDegenerate m)\nhy₂ : x = (ConcreteCategory.hom (X.map f₂.op)) ↑y₂\nhf₁ : SplitEpi f₁\n⊢ ↑y₁ = ↑y₂",
"ppTerm": "?m.71",
"... | [
"X : SSet\nn : ℕ\nx : X _⦋n⦌\nm : ℕ\nf₁ : ⦋n⦌ ⟶ ⦋m⦌\ninst✝ : Epi f₁\ny₁ : ↑(X.nonDegenerate m)\nhy₁ : x = (ConcreteCategory.hom (X.map f₁.op)) ↑y₁\nf₂ : ⦋n⦌ ⟶ ⦋m⦌\ny₂ : ↑(X.nonDegenerate m)\nhy₂ : x = (ConcreteCategory.hom (X.map f₂.op)) ↑y₂\nhf₁ : SplitEpi f₁\n⊢ ↑y₁ = ↑y₂"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.Degenerate | {
"line": 241,
"column": 4
} | {
"line": 241,
"column": 25
} | {
"line": 241,
"column": 26
} | [
{
"pp": "X : SSet\nn : ℕ\nx✝ : X _⦋n⦌\nm : ℕ\nf₁ : ⦋n⦌ ⟶ ⦋m⦌\ninst✝ : Epi f₁\ny₁ : ↑(X.nonDegenerate m)\nhy₁ : x✝ = (ConcreteCategory.hom (X.map f₁.op)) ↑y₁\nf₂ : ⦋n⦌ ⟶ ⦋m⦌\ny₂ : ↑(X.nonDegenerate m)\nhy₂ : x✝ = (ConcreteCategory.hom (X.map f₂.op)) ↑y₂\nx : Fin (⦋n⦌.len + 1)\nhf₁ : SplitEpi f₁\nhf₁' : (SimplexC... | [
"X : SSet\nn : ℕ\nx✝ : X _⦋n⦌\nm : ℕ\nf₁ : ⦋n⦌ ⟶ ⦋m⦌\ninst✝ : Epi f₁\ny₁ : ↑(X.nonDegenerate m)\nhy₁ : x✝ = (ConcreteCategory.hom (X.map f₁.op)) ↑y₁\nf₂ : ⦋n⦌ ⟶ ⦋m⦌\ny₂ : ↑(X.nonDegenerate m)\nhy₂ : x✝ = (ConcreteCategory.hom (X.map f₂.op)) ↑y₂\nx : Fin (⦋n⦌.len + 1)\nhf₁ : SplitEpi f₁\nhf₁' : (SimplexCategory.Hom.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.Degenerate | {
"line": 255,
"column": 4
} | {
"line": 255,
"column": 26
} | {
"line": 255,
"column": 27
} | [
{
"pp": "X : SSet\nn : ℕ\nx✝ : X _⦋n⦌\nm : ℕ\nf₁ : ⦋n⦌ ⟶ ⦋m⦌\ninst✝ : Epi f₁\ny₁✝ : ↑(X.nonDegenerate m)\nhy₁ : x✝ = (ConcreteCategory.hom (X.map f₁.op)) ↑y₁✝\nf₂ : ⦋n⦌ ⟶ ⦋m⦌\ny₂✝ : ↑(X.nonDegenerate m)\nhy₂ : x✝ = (ConcreteCategory.hom (X.map f₂.op)) ↑y₂✝\nx : Fin (⦋n⦌.len + 1)\nhf : SplitEpi f₁\nα : Fin (m + ... | [
"X : SSet\nn : ℕ\nx✝ : X _⦋n⦌\nm : ℕ\nf₁ : ⦋n⦌ ⟶ ⦋m⦌\ninst✝ : Epi f₁\ny₁✝ : ↑(X.nonDegenerate m)\nhy₁ : x✝ = (ConcreteCategory.hom (X.map f₁.op)) ↑y₁✝\nf₂ : ⦋n⦌ ⟶ ⦋m⦌\ny₂✝ : ↑(X.nonDegenerate m)\nhy₂ : x✝ = (ConcreteCategory.hom (X.map f₂.op)) ↑y₂✝\nx : Fin (⦋n⦌.len + 1)\nhf : SplitEpi f₁\nα : Fin (m + 1) → Fin (n ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.Degenerate | {
"line": 277,
"column": 4
} | {
"line": 277,
"column": 79
} | {
"line": 278,
"column": 6
} | [
{
"pp": "case mpr\nX : SSet\nA : X.Subcomplex\nn m : ℕ\nhm : m < n\nf : ⦋n⦌ ⟶ ⦋m⦌\nw✝ : Epi f\ny : X _⦋m⦌\nhx : (ConcreteCategory.hom (X.map f.op)) y ∈ A.obj (op ⦋n⦌)\nthis : IsSplitEpi f\n⊢ y ∈ A.obj (op ⦋m⦌)",
"ppTerm": "?mpr",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"used... | [
"case mpr\nX : SSet\nA : X.Subcomplex\nn m : ℕ\nhm : m < n\nf : ⦋n⦌ ⟶ ⦋m⦌\nw✝ : Epi f\ny : X _⦋m⦌\nhx : (ConcreteCategory.hom (X.map f.op)) y ∈ A.obj (op ⦋n⦌)\nthis : IsSplitEpi f\n⊢ y ∈ A.obj (op ⦋m⦌)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.Finite | {
"line": 51,
"column": 67
} | {
"line": 51,
"column": 78
} | {
"line": 51,
"column": 79
} | [
{
"pp": "X : SSet\nd : ℕ\ninst✝ : X.HasDimensionLT d\nh : ∀ i < d, Finite ↑(X.nonDegenerate i)\nthis✝ : ∀ (i : Fin d), Finite ↑(X.nonDegenerate ↑i)\nx : X.N\nhj : ¬x.dim < d\nthis : x.simplex ∈ X.nonDegenerate x.dim\n⊢ d ≤ x.dim",
"ppTerm": "?m.64",
"assigned": false,
"usedConstants": [],
"usedF... | [
"X : SSet\nd : ℕ\ninst✝ : X.HasDimensionLT d\nh : ∀ i < d, Finite ↑(X.nonDegenerate i)\nthis✝ : ∀ (i : Fin d), Finite ↑(X.nonDegenerate ↑i)\nx : X.N\nhj : ¬x.dim < d\nthis : x.simplex ∈ X.nonDegenerate x.dim\n⊢ d ≤ x.dim"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.Finite | {
"line": 75,
"column": 2
} | {
"line": 83,
"column": 33
} | {
"line": 85,
"column": 0
} | [
{
"pp": "X : SSet\ninst✝ : X.Finite\nn : SimplexCategoryᵒᵖ\n⊢ Finite (X.obj n)",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"SimplexCategory.rec",
"Opposite",
"SimplexCategory.instFiniteHom",
"CategoryTheory.Epi",
"SimplexCategory.instFintypeToTypeOrderHomFi... | [] | obtain ⟨n⟩ := n
induction n using SimplexCategory.rec with | _ n
let φ : (Σ (m : Fin (n + 1)) (f : ⦋n⦌ ⟶ ⦋m.1⦌),
X.nonDegenerate m.1) → X _⦋n⦌ := fun ⟨m, f, x⟩ ↦ X.map f.op x.1
have hφ : Function.Surjective φ := fun x ↦ by
obtain ⟨m, f, hf, y, rfl⟩ := X.exists_nonDegenerate x
have := SimplexCategory.l... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.Finite | {
"line": 75,
"column": 2
} | {
"line": 83,
"column": 33
} | {
"line": 85,
"column": 0
} | [
{
"pp": "X : SSet\ninst✝ : X.Finite\nn : SimplexCategoryᵒᵖ\n⊢ Finite (X.obj n)",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"SimplexCategory.rec",
"Opposite",
"SimplexCategory.instFiniteHom",
"CategoryTheory.Epi",
"SimplexCategory.instFintypeToTypeOrderHomFi... | [] | obtain ⟨n⟩ := n
induction n using SimplexCategory.rec with | _ n
let φ : (Σ (m : Fin (n + 1)) (f : ⦋n⦌ ⟶ ⦋m.1⦌),
X.nonDegenerate m.1) → X _⦋n⦌ := fun ⟨m, f, x⟩ ↦ X.map f.op x.1
have hφ : Function.Surjective φ := fun x ↦ by
obtain ⟨m, f, hf, y, rfl⟩ := X.exists_nonDegenerate x
have := SimplexCategory.l... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.Finite | {
"line": 133,
"column": 10
} | {
"line": 133,
"column": 54
} | {
"line": 133,
"column": 55
} | [
{
"pp": "X : SSet\nι : Type u_1\ninst✝ : Finite ι\nA : ι → X.Subcomplex\nh : ∀ (i : ι), (A i).toSSet.Finite\nx✝ : (i : ι) × (A i).toSSet.N\ni : ι\ns : (A i).toSSet.N\n⊢ (ConcreteCategory.hom ((Subcomplex.homOfLE ⋯).app (Opposite.op ⦋s.dim⦌))) s.simplex ∈\n (⨆ i, A i).toSSet.nonDegenerate s.dim",
"ppTerm"... | [
"X : SSet\nι : Type u_1\ninst✝ : Finite ι\nA : ι → X.Subcomplex\nh : ∀ (i : ι), (A i).toSSet.Finite\nx✝ : (i : ι) × (A i).toSSet.N\ni : ι\ns : (A i).toSSet.N\n⊢ s.simplex ∈ (A i).toSSet.nonDegenerate s.dim"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.NonDegenerateSimplices | {
"line": 103,
"column": 29
} | {
"line": 103,
"column": 40
} | {
"line": 103,
"column": 41
} | [
{
"pp": "X : SSet\nd : ℕ\nx : X _⦋d⦌\nhx : x ∈ X.nonDegenerate d\ny : X _⦋d⦌\nhy : y ∈ X.nonDegenerate d\nh : mk ↑⟨x, hx⟩ ⋯ < mk ↑⟨y, hy⟩ ⋯\nw✝ : Mono (𝟙 ⦋(mk ↑⟨x, hx⟩ ⋯).dim⦌)\nhf : (ConcreteCategory.hom (X.map (𝟙 ⦋(mk ↑⟨x, hx⟩ ⋯).dim⦌).op)) (mk ↑⟨y, hy⟩ ⋯).simplex = (mk ↑⟨x, hx⟩ ⋯).simplex\n⊢ y = x",
"p... | [
"X : SSet\nd : ℕ\nx : X _⦋d⦌\nhx : x ∈ X.nonDegenerate d\ny : X _⦋d⦌\nhy : y ∈ X.nonDegenerate d\nh : mk ↑⟨x, hx⟩ ⋯ < mk ↑⟨y, hy⟩ ⋯\nw✝ : Mono (𝟙 ⦋(mk ↑⟨x, hx⟩ ⋯).dim⦌)\nhf : (ConcreteCategory.hom (X.map (𝟙 ⦋(mk ↑⟨x, hx⟩ ⋯).dim⦌).op)) (mk ↑⟨y, hy⟩ ⋯).simplex = (mk ↑⟨x, hx⟩ ⋯).simplex\n⊢ y = x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.Degenerate | {
"line": 318,
"column": 4
} | {
"line": 318,
"column": 38
} | {
"line": 318,
"column": 39
} | [
{
"pp": "case mpr\nX : SSet\nA : X.Subcomplex\nn : ℕ\nh : A.obj (op ⦋n⦌) ⊆ X.degenerate n\nx : A.toSSet _⦋n⦌\n⊢ x ∈ A.toSSet.degenerate n ↔ x ∈ ⊤",
"ppTerm": "?mpr",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.toSSet",
"Eq.mpr",
"Opposite",
"congrArg",
"Set.me... | [
"case mpr\nX : SSet\nA : X.Subcomplex\nn : ℕ\nh : A.obj (op ⦋n⦌) ⊆ X.degenerate n\nx : A.toSSet _⦋n⦌\n⊢ ↑x ∈ X.degenerate n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.Degenerate | {
"line": 346,
"column": 2
} | {
"line": 346,
"column": 13
} | {
"line": 346,
"column": 14
} | [
{
"pp": "X Y : SSet\nf : X ⟶ Y\nn : ℕ\n⊢ ⇑(ConcreteCategory.hom (f.app (op ⦋n⦌))) '' X.degenerate n ⊆ Y.degenerate n",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Opposite",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"TypeCat.instFunLikeFu... | [
"X Y : SSet\nf : X ⟶ Y\nn : ℕ\n⊢ X.degenerate n ⊆ (fun a ↦ (ConcreteCategory.hom (f.app (op ⦋n⦌))) a) ⁻¹' Y.degenerate n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.Degenerate | {
"line": 352,
"column": 4
} | {
"line": 352,
"column": 51
} | {
"line": 352,
"column": 52
} | [
{
"pp": "case mp\nX Y : SSet\nf : X ⟶ Y\ninst✝ : IsIso f\nn : ℕ\nx : X _⦋n⦌\nhy : (ConcreteCategory.hom (f.app (op ⦋n⦌))) x ∈ Y.degenerate n\n⊢ x ∈ X.degenerate n",
"ppTerm": "?mp",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case mp\nX Y : SSet\nf : X ⟶ Y\ninst✝ : IsIso f\nn : ℕ\nx : X _⦋n⦌\nhy : (ConcreteCategory.hom (f.app (op ⦋n⦌))) x ∈ Y.degenerate n\n⊢ x ∈ X.degenerate n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.NonDegenerateSimplices | {
"line": 175,
"column": 8
} | {
"line": 175,
"column": 59
} | {
"line": 175,
"column": 60
} | [
{
"pp": "X : SSet\nx : X.op.N\n⊢ opObjEquiv x.simplex ∈ X.nonDegenerate x.dim",
"ppTerm": "?m.33",
"assigned": true,
"usedConstants": [
"SSet.S.simplex",
"Eq.mpr",
"SSet.op",
"Opposite",
"Equiv.instEquivLike",
"SSet.nonDegenerate",
"Membership.mem",
"S... | [
"X : SSet\nx : X.op.N\n⊢ x.simplex ∈ X.op.nonDegenerate x.dim"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.NonDegenerateSimplices | {
"line": 177,
"column": 8
} | {
"line": 177,
"column": 56
} | {
"line": 177,
"column": 57
} | [
{
"pp": "X : SSet\ny : X.N\n⊢ opObjEquiv.symm y.simplex ∈ X.op.nonDegenerate y.dim",
"ppTerm": "?m.41",
"assigned": true,
"usedConstants": [
"SSet.S.simplex",
"Eq.mpr",
"SSet.op",
"Equiv.apply_symm_apply",
"Opposite",
"Equiv.instEquivLike",
"congrArg",
... | [
"X : SSet\ny : X.N\n⊢ y.simplex ∈ X.nonDegenerate y.dim"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Fin.SuccAboveOrderIso | {
"line": 31,
"column": 54
} | {
"line": 31,
"column": 65
} | {
"line": 31,
"column": 66
} | [
{
"pp": "n : ℕ\ni : Fin (n + 2)\na b : Fin (n + 1)\nh : (fun a ↦ ⟨i.succAboveOrderEmb a, ⋯⟩) a = (fun a ↦ ⟨i.succAboveOrderEmb a, ⋯⟩) b\n⊢ i.succAboveOrderEmb a = i.succAboveOrderEmb b",
"ppTerm": "?m.64",
"assigned": true,
"usedConstants": [
"Fin.succAbove",
"Eq.mpr",
"congrArg",
... | [
"n : ℕ\ni : Fin (n + 2)\na b : Fin (n + 1)\nh : (fun a ↦ ⟨i.succAboveOrderEmb a, ⋯⟩) a = (fun a ↦ ⟨i.succAboveOrderEmb a, ⋯⟩) b\n⊢ a = b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Fin.SuccAboveOrderIso | {
"line": 37,
"column": 24
} | {
"line": 38,
"column": 83
} | {
"line": 39,
"column": 0
} | [
{
"pp": "n : ℕ\ni : Fin (n + 2)\na b : Fin (n + 1)\n⊢ (Equiv.ofBijective (fun a ↦ ⟨i.succAboveOrderEmb a, ⋯⟩) ⋯) a ≤\n (Equiv.ofBijective (fun a ↦ ⟨i.succAboveOrderEmb a, ⋯⟩) ⋯) b ↔\n a ≤ b",
"ppTerm": "?m.133",
"assigned": true,
"usedConstants": [
"_private.Mathlib.Order.Fin.SuccAbove... | [] | by
simp only [Equiv.ofBijective_apply, Subtype.mk_le_mk, OrderEmbedding.le_iff_le] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.AlgebraicTopology.SimplicialSet.NerveNondegenerate | {
"line": 58,
"column": 4
} | {
"line": 58,
"column": 15
} | {
"line": 58,
"column": 16
} | [
{
"pp": "case zero\nX : Type u_1\ninst✝ : PartialOrder X\ns : nerve X _⦋0⦌\n⊢ s ∈ (nerve X).nonDegenerate 0 ↔ StrictMono s.obj",
"ppTerm": "?zero",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Opposite",
"StrictMono",
"congrArg",
"Set.mem_univ._simp_1",
"Set.un... | [
"case zero\nX : Type u_1\ninst✝ : PartialOrder X\ns : nerve X _⦋0⦌\n⊢ StrictMono s.obj"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.AlternatingConst | {
"line": 115,
"column": 2
} | {
"line": 118,
"column": 9
} | {
"line": 118,
"column": 10
} | [
{
"pp": "C : Type u_1\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : HasZeroMorphisms C\nA : C\nφ ψ : A ⟶ A\nhOdd : φ ≫ ψ = 0\nhEven : ψ ≫ φ = 0\nc : ComplexShape ℕ\ninst✝¹ : DecidableRel c.Rel\nhc : ∀ (i j : ℕ), c.Rel i j → Odd (i + j)\ninst✝ : CategoryWithHomology C\nj : ℕ\nhpj : c.Rel (c.prev j) j\nhnj : c.Rel j ... | [
"C : Type u_1\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : HasZeroMorphisms C\nA : C\nφ ψ : A ⟶ A\nhOdd : φ ≫ ψ = 0\nhEven : ψ ≫ φ = 0\nc : ComplexShape ℕ\ninst✝¹ : DecidableRel c.Rel\nhc : ∀ (i j : ℕ), c.Rel i j → Odd (i + j)\ninst✝ : CategoryWithHomology C\nj : ℕ\nhpj : c.Rel (c.prev j) j\nhnj : c.Rel j (c.next j)\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.AlternatingConst | {
"line": 128,
"column": 2
} | {
"line": 131,
"column": 9
} | {
"line": 131,
"column": 10
} | [
{
"pp": "C : Type u_1\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : HasZeroMorphisms C\nA : C\nφ ψ : A ⟶ A\nhOdd : φ ≫ ψ = 0\nhEven : ψ ≫ φ = 0\nc : ComplexShape ℕ\ninst✝¹ : DecidableRel c.Rel\nhc : ∀ (i j : ℕ), c.Rel i j → Odd (i + j)\ninst✝ : CategoryWithHomology C\nj : ℕ\nhpj : c.Rel (c.prev j) j\nhnj : c.Rel j ... | [
"C : Type u_1\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : HasZeroMorphisms C\nA : C\nφ ψ : A ⟶ A\nhOdd : φ ≫ ψ = 0\nhEven : ψ ≫ φ = 0\nc : ComplexShape ℕ\ninst✝¹ : DecidableRel c.Rel\nhc : ∀ (i j : ℕ), c.Rel i j → Odd (i + j)\ninst✝ : CategoryWithHomology C\nj : ℕ\nhpj : c.Rel (c.prev j) j\nhnj : c.Rel j (c.next j)\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex | {
"line": 292,
"column": 2
} | {
"line": 292,
"column": 13
} | {
"line": 292,
"column": 14
} | [
{
"pp": "n : ℕ\nx✝¹ : SimplexCategoryᵒᵖ\nx✝ : Δ[n].obj x✝¹\n⊢ x✝ ∈ (face ∅).obj x✝¹ ↔ x✝ ∈ ⊥.obj x✝¹",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"False",
"Lattice.toSemilatticeSup",
"Opposite",
"Equiv.instEquivLike",
"SimplexCategory.instFi... | [
"n : ℕ\nx✝¹ : SimplexCategoryᵒᵖ\nx✝ : Δ[n].obj x✝¹\n⊢ ¬univ = ∅"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex | {
"line": 450,
"column": 4
} | {
"line": 450,
"column": 29
} | {
"line": 450,
"column": 30
} | [
{
"pp": "case inr\nn d : ℕ\ns : Δ[n] _⦋d⦌\nh : Function.Injective ⇑(Hom.toOrderHom (objEquiv s))\ni : Fin d\nh' : (fun j ↦ s j) i.castSucc = (fun j ↦ s j) i.succ\n⊢ s i.castSucc < s i.succ",
"ppTerm": "?inr",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case inr\nn d : ℕ\ns : Δ[n] _⦋d⦌\nh : Function.Injective ⇑(Hom.toOrderHom (objEquiv s))\ni : Fin d\nh' : (fun j ↦ s j) i.castSucc = (fun j ↦ s j) i.succ\n⊢ s i.castSucc < s i.succ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex | {
"line": 481,
"column": 36
} | {
"line": 481,
"column": 47
} | {
"line": 481,
"column": 48
} | [
{
"pp": "n : ℕ\ni : Fin (n + 2)\nx✝ : { x // x ≠ i }\nx : Fin (n + 1 + 1)\nhx : x ≠ i\n⊢ x ∈ {i}ᶜ",
"ppTerm": "?m.78",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"SimplexCategory.instFintypeToTypeOrderHomFinHAddNatLenOfNat",
"congrArg",
"Compl.compl",
"Finset",
... | [
"n : ℕ\ni : Fin (n + 2)\nx✝ : { x // x ≠ i }\nx : Fin (n + 1 + 1)\nhx : x ≠ i\n⊢ ¬x = i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex | {
"line": 482,
"column": 37
} | {
"line": 482,
"column": 48
} | {
"line": 482,
"column": 49
} | [
{
"pp": "n : ℕ\ni : Fin (n + 2)\nx✝ : ↥{i}ᶜ\nx : Fin (n + 2)\nhx : x ∈ {i}ᶜ\n⊢ x ≠ i",
"ppTerm": "?m.86",
"assigned": true,
"usedConstants": [
"id",
"Ne",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"instAddNat",
"OfNat.ofNat",
"Fin"
],
... | [
"n : ℕ\ni : Fin (n + 2)\nx✝ : ↥{i}ᶜ\nx : Fin (n + 2)\nhx : x ∈ {i}ᶜ\n⊢ ¬x = i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex | {
"line": 612,
"column": 4
} | {
"line": 612,
"column": 15
} | {
"line": 612,
"column": 16
} | [
{
"pp": "case left\nn m : ℕ\nf₁ : unop (op ⦋m⦌) ⟶ ⦋n⦌\nh₁✝ : objEquiv.symm f₁ ∈ Δ[n].nonDegenerate m\nf₂ : unop (op ⦋m⦌) ⟶ ⦋n⦌\nh₂✝ : objEquiv.symm f₂ ∈ Δ[n].nonDegenerate m\nh₁ : Function.Injective ⇑(Hom.toOrderHom f₁)\nh₂ : Function.Injective ⇑(Hom.toOrderHom f₂)\nh₃ : Finset.image (⇑(Hom.toOrderHom f₁)) univ... | [
"case left\nn m : ℕ\nf₁ : unop (op ⦋m⦌) ⟶ ⦋n⦌\nh₁✝ : objEquiv.symm f₁ ∈ Δ[n].nonDegenerate m\nf₂ : unop (op ⦋m⦌) ⟶ ⦋n⦌\nh₂✝ : objEquiv.symm f₂ ∈ Δ[n].nonDegenerate m\nh₁ : Function.Injective ⇑(Hom.toOrderHom f₁)\nh₂ : Function.Injective ⇑(Hom.toOrderHom f₂)\nh₃ : Finset.image (⇑(Hom.toOrderHom f₁)) univ = Finset.im... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex | {
"line": 615,
"column": 47
} | {
"line": 615,
"column": 58
} | {
"line": 615,
"column": 59
} | [
{
"pp": "n m : ℕ\nS : Finset (Fin (n + 1))\nhS : #S = m + 1\n⊢ Fintype.card ↥S = m + 1",
"ppTerm": "?m.234",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Finset",
"Membership.mem",
"Fintype.card",
"id",
"Subtype",
"instOfNatNat",
"... | [
"n m : ℕ\nS : Finset (Fin (n + 1))\nhS : #S = m + 1\n⊢ #S = m + 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.ExtraDegeneracy | {
"line": 108,
"column": 4
} | {
"line": 108,
"column": 27
} | {
"line": 108,
"column": 28
} | [
{
"pp": "C : Type u_1\ninst✝ : Category.{v_1, u_1} C\nX Y : Augmented C\ne : X ≅ Y\ned : X.ExtraDegeneracy\n⊢ ((point.mapIso e).inv ≫ ed.s' ≫ (drop.mapIso e).hom.app (op ⦋0⦌)) ≫ Y.hom.app (op ⦋0⦌) = 𝟙 Y.right",
"ppTerm": "?m.129",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Category... | [
"C : Type u_1\ninst✝ : Category.{v_1, u_1} C\nX Y : Augmented C\ne : X ≅ Y\ned : X.ExtraDegeneracy\n⊢ e.inv.right ≫ e.hom.right = 𝟙 Y.right"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex | {
"line": 643,
"column": 33
} | {
"line": 643,
"column": 44
} | {
"line": 643,
"column": 45
} | [
{
"pp": "n d : ℕ\nx : ↑(Δ[n].nonDegenerate d)\nthis : Function.Injective ⇑(Hom.toOrderHom (objEquiv ↑x))\nx✝¹ x✝ : Fin (d + 1)\nh : (fun i ↦ ⟨↑x i, ⋯⟩) x✝¹ = (fun i ↦ ⟨↑x i, ⋯⟩) x✝\n⊢ (Hom.toOrderHom (objEquiv ↑x)) x✝¹ = (Hom.toOrderHom (objEquiv ↑x)) x✝",
"ppTerm": "?m.67",
"assigned": true,
"usedC... | [
"n d : ℕ\nx : ↑(Δ[n].nonDegenerate d)\nthis : Function.Injective ⇑(Hom.toOrderHom (objEquiv ↑x))\nx✝¹ x✝ : Fin (d + 1)\nh : (fun i ↦ ⟨↑x i, ⋯⟩) x✝¹ = (fun i ↦ ⟨↑x i, ⋯⟩) x✝\n⊢ ↑x x✝¹ = ↑x x✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.ExtraDegeneracy | {
"line": 112,
"column": 4
} | {
"line": 112,
"column": 49
} | {
"line": 113,
"column": 6
} | [
{
"pp": "C : Type u_1\ninst✝ : Category.{v_1, u_1} C\nX Y : Augmented C\ne : X ≅ Y\ned : X.ExtraDegeneracy\nn : ℕ\n⊢ ((drop.mapIso e).inv.app (op ⦋n⦌) ≫ ed.s n ≫ (drop.mapIso e).hom.app (op ⦋n + 1⦌)) ≫ Y.left.δ 0 = 𝟙 (Y.left _⦋n⦌)",
"ppTerm": "?m.151",
"assigned": true,
"usedConstants": [
"Eq... | [
"C : Type u_1\ninst✝ : Category.{v_1, u_1} C\nX Y : Augmented C\ne : X ≅ Y\ned : X.ExtraDegeneracy\nn : ℕ\n⊢ e.inv.left.app (op ⦋n⦌) ≫ e.hom.left.app (op ⦋n⦌) = 𝟙 (Y.left _⦋n⦌)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex | {
"line": 729,
"column": 24
} | {
"line": 729,
"column": 35
} | {
"line": 729,
"column": 36
} | [
{
"pp": "n : ℕ\nf : unop (op ⦋n⦌) ⟶ ⦋n⦌\nh : objEquiv.symm f ∈ Δ[n].nonDegenerate n\n⊢ Mono f",
"ppTerm": "?m.59",
"assigned": true,
"usedConstants": [
"CategoryTheory.Mono",
"id",
"SimplexCategory.mk",
"Opposite.op",
"SimplexCategory",
"SimplexCategory.smallCateg... | [
"n : ℕ\nf : unop (op ⦋n⦌) ⟶ ⦋n⦌\nh : objEquiv.symm f ∈ Δ[n].nonDegenerate n\n⊢ Mono f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex | {
"line": 730,
"column": 4
} | {
"line": 730,
"column": 52
} | {
"line": 730,
"column": 53
} | [
{
"pp": "case refine_1\nn : ℕ\nf : unop (op ⦋n⦌) ⟶ ⦋n⦌\nh : objEquiv.symm f ∈ Δ[n].nonDegenerate n\nthis : Mono f\n⊢ objEquiv.symm f = objEquiv.symm (𝟙 ⦋n⦌)",
"ppTerm": "?refine_1",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Opposite",
"Equiv.instEquivLike",
"CategoryTh... | [
"case refine_1\nn : ℕ\nf : unop (op ⦋n⦌) ⟶ ⦋n⦌\nh : objEquiv.symm f ∈ Δ[n].nonDegenerate n\nthis : Mono f\n⊢ f = 𝟙 ⦋n⦌"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.ComplexShapeSigns | {
"line": 330,
"column": 46
} | {
"line": 330,
"column": 66
} | {
"line": 330,
"column": 67
} | [
{
"pp": "I₁ : Type u_1\nI₂ : Type u_2\nI₃ : Type u_3\nI₁₂ : Type u_4\nI₂₃ : Type u_5\nJ : Type u_6\nc₁ : ComplexShape I₁\nc₂ : ComplexShape I₂\nc₃ : ComplexShape I₃\nc₁₂ : ComplexShape I₁₂\nc₂₃ : ComplexShape I₂₃\nc : ComplexShape J\ninst✝² : TotalComplexShape c₁ c₂ c₁₂\ninst✝¹ : TotalComplexShape c₂ c₁ c₁₂\nin... | [
"I₁ : Type u_1\nI₂ : Type u_2\nI₃ : Type u_3\nI₁₂ : Type u_4\nI₂₃ : Type u_5\nJ : Type u_6\nc₁ : ComplexShape I₁\nc₂ : ComplexShape I₂\nc₃ : ComplexShape I₃\nc₁₂ : ComplexShape I₁₂\nc₂₃ : ComplexShape I₂₃\nc : ComplexShape J\ninst✝² : TotalComplexShape c₁ c₂ c₁₂\ninst✝¹ : TotalComplexShape c₂ c₁ c₁₂\ninst✝ : TotalC... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.ComplexShapeSigns | {
"line": 331,
"column": 47
} | {
"line": 331,
"column": 67
} | {
"line": 331,
"column": 68
} | [
{
"pp": "I₁ : Type u_1\nI₂ : Type u_2\nI₃ : Type u_3\nI₁₂ : Type u_4\nI₂₃ : Type u_5\nJ : Type u_6\nc₁ : ComplexShape I₁\nc₂ : ComplexShape I₂\nc₃ : ComplexShape I₃\nc₁₂ : ComplexShape I₁₂\nc₂₃ : ComplexShape I₂₃\nc : ComplexShape J\ninst✝² : TotalComplexShape c₁ c₂ c₁₂\ninst✝¹ : TotalComplexShape c₂ c₁ c₁₂\nin... | [
"I₁ : Type u_1\nI₂ : Type u_2\nI₃ : Type u_3\nI₁₂ : Type u_4\nI₂₃ : Type u_5\nJ : Type u_6\nc₁ : ComplexShape I₁\nc₂ : ComplexShape I₂\nc₃ : ComplexShape I₃\nc₁₂ : ComplexShape I₁₂\nc₂₃ : ComplexShape I₂₃\nc : ComplexShape J\ninst✝² : TotalComplexShape c₁ c₂ c₁₂\ninst✝¹ : TotalComplexShape c₂ c₁ c₁₂\ninst✝ : TotalC... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.ExtraDegeneracy | {
"line": 269,
"column": 10
} | {
"line": 269,
"column": 42
} | {
"line": 269,
"column": 43
} | [
{
"pp": "case neg\nn : ℕ\nΔ : SimplexCategory\nf : ⦋n⦌ ⟶ Δ\nj₁ j₂ : Fin ⦋n + 1⦌.len\nh₁ : ¬j₁.succ = 0\nh₂ : j₂.succ ≠ 0\nhi : j₁.succ ≤ j₂.succ\n⊢ shiftFun (⇑(SimplexCategory.Hom.toOrderHom f)) j₁.succ ≤ shiftFun (⇑(SimplexCategory.Hom.toOrderHom f)) j₂.succ",
"ppTerm": "?neg✝",
"assigned": true,
"... | [
"case neg\nn : ℕ\nΔ : SimplexCategory\nf : ⦋n⦌ ⟶ Δ\nj₁ j₂ : Fin ⦋n + 1⦌.len\nh₁ : ¬j₁.succ = 0\nh₂ : j₂.succ ≠ 0\nhi : j₁.succ ≤ j₂.succ\n⊢ (SimplexCategory.Hom.toOrderHom f) j₁ ≤ (SimplexCategory.Hom.toOrderHom f) j₂"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.TotalComplex | {
"line": 168,
"column": 18
} | {
"line": 168,
"column": 46
} | {
"line": 168,
"column": 47
} | [
{
"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... | [
"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\ni₁₂ i₁₂' :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.TotalComplex | {
"line": 178,
"column": 18
} | {
"line": 178,
"column": 46
} | {
"line": 178,
"column": 47
} | [
{
"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... | [
"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\ni₁₂ i₁₂' :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.TotalComplexSymmetry | {
"line": 48,
"column": 2
} | {
"line": 49,
"column": 18
} | {
"line": 51,
"column": 0
} | [
{
"pp": "case mpr\nC : Type u_1\nI₁ : Type u_2\nI₂ : Type u_3\nJ : Type u_4\ninst✝⁴ : Category.{v_1, u_1} C\ninst✝³ : Preadditive C\nc₁ : ComplexShape I₁\nc₂ : ComplexShape I₂\nK : HomologicalComplex₂ C c₁ c₂\nc : ComplexShape J\ninst✝² : TotalComplexShape c₁ c₂ c\ninst✝¹ : TotalComplexShape c₂ c₁ c\ninst✝ : To... | [] | · intro
infer_instance | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.CategoryTheory.GradedObject.Trifunctor | {
"line": 517,
"column": 2
} | {
"line": 522,
"column": 13
} | {
"line": 523,
"column": 2
} | [
{
"pp": "C₁ : Type u_1\nC₂ : Type u_2\nC₃ : Type u_3\nC₄ : Type u_4\nC₁₂ : Type u_5\nC₂₃ : Type u_6\ninst✝⁷ : Category.{v_1, u_1} C₁\ninst✝⁶ : Category.{v_2, u_2} C₂\ninst✝⁵ : Category.{v_3, u_3} C₃\ninst✝⁴ : Category.{v_4, u_4} C₄\ninst✝³ : Category.{v_5, u_5} C₁₂\ninst✝² : Category.{v_6, u_6} C₂₃\nF : C₁ ⥤ C₂... | [
"C₁ : Type u_1\nC₂ : Type u_2\nC₃ : Type u_3\nC₄ : Type u_4\nC₁₂ : Type u_5\nC₂₃ : Type u_6\ninst✝⁷ : Category.{v_1, u_1} C₁\ninst✝⁶ : Category.{v_2, u_2} C₂\ninst✝⁵ : Category.{v_3, u_3} C₃\ninst✝⁴ : Category.{v_4, u_4} C₄\ninst✝³ : Category.{v_5, u_5} C₁₂\ninst✝² : Category.{v_6, u_6} C₂₃\nF : C₁ ⥤ C₂₃ ⥤ C₄\nG₂₃ ... | let e : ∀ (i₁ : I₁) (i₂₃ : ρ₂₃.I₂₃), p' ⁻¹' {(i₁, i₂₃)} ≃ ρ₂₃.p ⁻¹' {i₂₃} := fun i₁ i₂₃ =>
{ toFun := fun ⟨⟨i₁', i₂, i₃⟩, hi⟩ => ⟨⟨i₂, i₃⟩, by cat_disch⟩
invFun := fun ⟨⟨i₂, i₃⟩, hi⟩ => ⟨⟨i₁, i₂, i₃⟩, by cat_disch⟩
left_inv := fun ⟨⟨i₁', i₂, i₃⟩, hi⟩ => by
obtain rfl : i₁ = i₁' := by cat_disch
... | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticLet___1 | Lean.Parser.Tactic.tacticLet__ |
Mathlib.CategoryTheory.Shift.Twist | {
"line": 47,
"column": 47
} | {
"line": 47,
"column": 58
} | {
"line": 47,
"column": 59
} | [
{
"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 : A\n⊢ t.z a 0 = 1",
"ppTerm": "?m.16",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"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 : A\n⊢ t.z a 0 = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Shift.Twist | {
"line": 50,
"column": 46
} | {
"line": 50,
"column": 57
} | {
"line": 50,
"column": 58
} | [
{
"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\nb : A\n⊢ t.z 0 b = 1",
"ppTerm": "?m.16",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"C : Type u\ninst✝² : Category.{v, u} C\nA : Type w\ninst✝¹ : AddMonoid A\ninst✝ : HasShift C A\nt : TwistShiftData C A\nb : A\n⊢ t.z 0 b = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Shift.Twist | {
"line": 58,
"column": 2
} | {
"line": 58,
"column": 13
} | {
"line": 58,
"column": 14
} | [
{
"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 : C\n⊢ (shiftFunctor C c).map ((↑(t.z a b)).app X) = (↑(t.z a b)).app ((shiftFunctor C c).obj X)",
"ppTerm": "?m.45",
"assigned": false,
"usedConstants": [],
... | [
"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 : C\n⊢ (shiftFunctor C c).map ((↑(t.z a b)).app X) = (↑(t.z a b)).app ((shiftFunctor C c).obj X)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.BifunctorHomotopy | {
"line": 170,
"column": 10
} | {
"line": 170,
"column": 46
} | {
"line": 171,
"column": 6
} | [
{
"pp": "case neg\nC₁ : 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 : Comp... | [] | rw [zero₁ _ _ _ _ _ _ h₅, comp_zero] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Algebra.Homology.BifunctorHomotopy | {
"line": 170,
"column": 10
} | {
"line": 170,
"column": 46
} | {
"line": 171,
"column": 6
} | [
{
"pp": "case neg\nC₁ : 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 : Comp... | [] | rw [zero₁ _ _ _ _ _ _ h₅, comp_zero] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Homology.BifunctorHomotopy | {
"line": 170,
"column": 10
} | {
"line": 170,
"column": 46
} | {
"line": 171,
"column": 6
} | [
{
"pp": "case neg\nC₁ : 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 : Comp... | [] | rw [zero₁ _ _ _ _ _ _ h₅, comp_zero] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Homology.BifunctorAssociator | {
"line": 241,
"column": 2
} | {
"line": 242,
"column": 88
} | {
"line": 244,
"column": 0
} | [
{
"pp": "C₁ : Type u_1\nC₂ : Type u_2\nC₁₂ : Type u_3\nC₃ : Type u_5\nC₄ : Type u_6\ninst✝¹⁹ : Category.{v_1, u_1} C₁\ninst✝¹⁸ : Category.{v_2, u_2} C₂\ninst✝¹⁷ : Category.{v_3, u_5} C₃\ninst✝¹⁶ : Category.{v_4, u_6} C₄\ninst✝¹⁵ : Category.{v_5, u_3} C₁₂\ninst✝¹⁴ : HasZeroMorphisms C₁\ninst✝¹³ : HasZeroMorphism... | [] | dsimp [d₂]
rw [shape _ _ _ h, Functor.map_zero, Functor.map_zero, zero_app, zero_comp, smul_zero] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Homology.BifunctorAssociator | {
"line": 241,
"column": 2
} | {
"line": 242,
"column": 88
} | {
"line": 244,
"column": 0
} | [
{
"pp": "C₁ : Type u_1\nC₂ : Type u_2\nC₁₂ : Type u_3\nC₃ : Type u_5\nC₄ : Type u_6\ninst✝¹⁹ : Category.{v_1, u_1} C₁\ninst✝¹⁸ : Category.{v_2, u_2} C₂\ninst✝¹⁷ : Category.{v_3, u_5} C₃\ninst✝¹⁶ : Category.{v_4, u_6} C₄\ninst✝¹⁵ : Category.{v_5, u_3} C₁₂\ninst✝¹⁴ : HasZeroMorphisms C₁\ninst✝¹³ : HasZeroMorphism... | [] | dsimp [d₂]
rw [shape _ _ _ h, Functor.map_zero, Functor.map_zero, zero_app, zero_comp, smul_zero] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Homology.BifunctorHomotopy | {
"line": 226,
"column": 22
} | {
"line": 226,
"column": 48
} | {
"line": 226,
"column": 49
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.BifunctorHomotopy | {
"line": 227,
"column": 17
} | {
"line": 227,
"column": 43
} | {
"line": 227,
"column": 44
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.CochainComplexOpposite | {
"line": 142,
"column": 34
} | {
"line": 142,
"column": 45
} | {
"line": 142,
"column": 46
} | [
{
"pp": "C : 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 ((opEquivalence C).functor.map f.op) ((opEquivalence C).functor.map g.op)\nn p q p' q' : ℤ\nhp : p = p'\nhq : q = q'\n⊢ ComplexShape.embeddingUpIntDownInt.f p' = ComplexShape.embeddi... | [
"C : 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 ((opEquivalence C).functor.map f.op) ((opEquivalence C).functor.map g.op)\nn p q p' q' : ℤ\nhp : p = p'\nhq : q = q'\n⊢ p' = p"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.CommSq | {
"line": 94,
"column": 18
} | {
"line": 94,
"column": 29
} | {
"line": 94,
"column": 30
} | [
{
"pp": "C : 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 sq.cokernelCofork\ns : PushoutCocone f g\n⊢ inl ≫ h.desc (CokernelCofork.ofπ (biprod.de... | [
"C : 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 sq.cokernelCofork\ns : PushoutCocone f g\n⊢ inl ≫ h.desc (CokernelCofork.ofπ (biprod.desc s.inl s.i... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.CommSq | {
"line": 97,
"column": 18
} | {
"line": 97,
"column": 29
} | {
"line": 97,
"column": 30
} | [
{
"pp": "C : 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 sq.cokernelCofork\ns : PushoutCocone f g\n⊢ inr ≫ h.desc (CokernelCofork.ofπ (biprod.de... | [
"C : 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 sq.cokernelCofork\ns : PushoutCocone f g\n⊢ inr ≫ h.desc (CokernelCofork.ofπ (biprod.desc s.inl s.i... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.CommSq | {
"line": 118,
"column": 63
} | {
"line": 118,
"column": 74
} | {
"line": 118,
"column": 75
} | [
{
"pp": "C : 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\nh : IsPushout f g inl inr\nR✝ : C\nb : ⋯.shortComplex.X₃ ⟶ R✝\nhb : ⋯.shortComplex.g ≫ b = 0\n⊢ Cofork.π ⋯.cokernelCofork ≫ b ... | [
"C : 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\nh : IsPushout f g inl inr\nR✝ : C\nb : ⋯.shortComplex.X₃ ⟶ R✝\nhb : ⋯.shortComplex.g ≫ b = 0\n⊢ biprod.desc inl inr ≫ b = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.CommSq | {
"line": 175,
"column": 18
} | {
"line": 175,
"column": 29
} | {
"line": 175,
"column": 30
} | [
{
"pp": "C : 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 sq.kernelFork\ns : PullbackCone f g\n⊢ h.lift (KernelFork.ofι (biprod.lift s.fst s.snd) ⋯... | [
"C : 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 sq.kernelFork\ns : PullbackCone f g\n⊢ h.lift (KernelFork.ofι (biprod.lift s.fst s.snd) ⋯) ≫ fst = s.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.CommSq | {
"line": 177,
"column": 18
} | {
"line": 177,
"column": 29
} | {
"line": 177,
"column": 30
} | [
{
"pp": "C : 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 sq.kernelFork\ns : PullbackCone f g\n⊢ h.lift (KernelFork.ofι (biprod.lift s.fst s.snd) ⋯... | [
"C : 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 sq.kernelFork\ns : PullbackCone f g\n⊢ h.lift (KernelFork.ofι (biprod.lift s.fst s.snd) ⋯) ≫ snd = s.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.ConcreteCategory | {
"line": 113,
"column": 2
} | {
"line": 124,
"column": 91
} | {
"line": 126,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝⁶ : Category.{v, u} C\nFC : C → C → Type u_1\nCC : C → Type v\ninst✝⁵ : (X Y : C) → FunLike (FC X Y) (CC X) (CC Y)\ninst✝⁴ : ConcreteCategory C FC\ninst✝³ : HasForget₂ C Ab\ninst✝² : Abelian C\ninst✝¹ : (forget₂ C Ab).Additive\ninst✝ : (forget₂ C Ab).PreservesHomology\nι : Type u_2\nc ... | [] | refine hS.δ_apply' i j hij _ ((forget₂ C Ab).map (S.X₂.pOpcycles i) x₂) _ ?_ ?_
· rw [← ConcreteCategory.forget₂_comp_apply, ← ConcreteCategory.forget₂_comp_apply,
HomologicalComplex.p_opcyclesMap, Functor.map_comp, ConcreteCategory.comp_apply,
HomologicalComplex.homology_π_ι, ConcreteCategory.forget₂_com... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Homology.ConcreteCategory | {
"line": 113,
"column": 2
} | {
"line": 124,
"column": 91
} | {
"line": 126,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝⁶ : Category.{v, u} C\nFC : C → C → Type u_1\nCC : C → Type v\ninst✝⁵ : (X Y : C) → FunLike (FC X Y) (CC X) (CC Y)\ninst✝⁴ : ConcreteCategory C FC\ninst✝³ : HasForget₂ C Ab\ninst✝² : Abelian C\ninst✝¹ : (forget₂ C Ab).Additive\ninst✝ : (forget₂ C Ab).PreservesHomology\nι : Type u_2\nc ... | [] | refine hS.δ_apply' i j hij _ ((forget₂ C Ab).map (S.X₂.pOpcycles i) x₂) _ ?_ ?_
· rw [← ConcreteCategory.forget₂_comp_apply, ← ConcreteCategory.forget₂_comp_apply,
HomologicalComplex.p_opcyclesMap, Functor.map_comp, ConcreteCategory.comp_apply,
HomologicalComplex.homology_π_ι, ConcreteCategory.forget₂_com... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Homology.CommSq | {
"line": 197,
"column": 53
} | {
"line": 197,
"column": 64
} | {
"line": 197,
"column": 65
} | [
{
"pp": "C : 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\nh : IsPullback fst snd f g\nP✝ : C\nb : P✝ ⟶ ⋯.shortComplex'.X₁\nhb : b ≫ ⋯.shortComplex'.f = 0\n⊢ b ≫ Fork.ι ⋯.kernelFork = 0... | [
"C : 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\nh : IsPullback fst snd f g\nP✝ : C\nb : P✝ ⟶ ⋯.shortComplex'.X₁\nhb : b ≫ ⋯.shortComplex'.f = 0\n⊢ b ≫ biprod.lift fst snd = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.HomotopyCategory.HomComplexCohomology | {
"line": 162,
"column": 33
} | {
"line": 162,
"column": 48
} | {
"line": 162,
"column": 49
} | [
{
"pp": "case refine_1\nC : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Preadditive C\nK L : CochainComplex C ℤ\nn : ℤ\nx y : Cocycle K L n\nh : toHom (mk x) = toHom (mk y)\n⊢ mk (x - y) = 0",
"ppTerm": "?refine_1",
"assigned": true,
"usedConstants": [
"CochainComplex.HomComplex.coboundaries",... | [
"case refine_1\nC : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Preadditive C\nK L : CochainComplex C ℤ\nn : ℤ\nx y : Cocycle K L n\nh : toHom (mk x) = toHom (mk y)\n⊢ x - y ∈ coboundaries K L n"
] | mk_eq_zero_iff, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Homology.HomotopyCategory.HomComplexInduction | {
"line": 56,
"column": 2
} | {
"line": 63,
"column": 20
} | {
"line": 65,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Preadditive C\nK L : CochainComplex C ℤ\nd : ℤ\nX : ℕ → Set (Cochain K L d)\nφ : (n : ℕ) → ↑(X n) → ↑(X (n + 1))\np₀ : ℤ\nhφ : ∀ (n : ℕ) (x : ↑(X n)), (↑(φ n x)).EqUpTo (↑x) (p₀ + ↑n)\nx₀ : ↑(X 0)\nn₁ n₂ : ℕ\nh : n₁ ≤ n₂\n⊢ (↑(sequence φ x₀ n₁)).EqUpTo (↑... | [] | obtain ⟨k, rfl⟩ := Nat.exists_eq_add_of_le h
clear h
induction k generalizing n₁ with
| zero => intro _ _ _ _; simp
| succ k hk =>
intro p q hpq hp
rw [hk n₁ p q hpq hp, ← hφ (n₁ + k) (sequence φ x₀ (n₁ + k)) p q hpq (by lia)]
dsimp [sequence] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Homology.HomotopyCategory.HomComplexInduction | {
"line": 56,
"column": 2
} | {
"line": 63,
"column": 20
} | {
"line": 65,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Preadditive C\nK L : CochainComplex C ℤ\nd : ℤ\nX : ℕ → Set (Cochain K L d)\nφ : (n : ℕ) → ↑(X n) → ↑(X (n + 1))\np₀ : ℤ\nhφ : ∀ (n : ℕ) (x : ↑(X n)), (↑(φ n x)).EqUpTo (↑x) (p₀ + ↑n)\nx₀ : ↑(X 0)\nn₁ n₂ : ℕ\nh : n₁ ≤ n₂\n⊢ (↑(sequence φ x₀ n₁)).EqUpTo (↑... | [] | obtain ⟨k, rfl⟩ := Nat.exists_eq_add_of_le h
clear h
induction k generalizing n₁ with
| zero => intro _ _ _ _; simp
| succ k hk =>
intro p q hpq hp
rw [hk n₁ p q hpq hp, ← hφ (n₁ + k) (sequence φ x₀ (n₁ + k)) p q hpq (by lia)]
dsimp [sequence] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Homology.BifunctorShift | {
"line": 243,
"column": 26
} | {
"line": 254,
"column": 44
} | {
"line": 256,
"column": 0
} | [
{
"pp": "C₁ : Type u_1\nC₂ : Type u_2\nD : Type u_3\ninst✝⁸ : Category.{v_1, u_1} C₁\ninst✝⁷ : Category.{v_2, u_2} C₂\ninst✝⁶ : Category.{v_3, u_3} D\ninst✝⁵ : Preadditive C₁\ninst✝⁴ : Preadditive C₂\ninst✝³ : Preadditive D\nF : C₁ ⥤ C₂ ⥤ D\ninst✝² : F.Additive\ninst✝¹ : ∀ (X₁ : C₁), (F.obj X₁).Additive\ninst✝ ... | [] | by
ext K₂ n
dsimp
ext p q h
dsimp at h
simp [CochainComplex.ι_mapBifunctorShift₂Iso_hom_f _ _ F (a + b) p q n h
(q + a + b) (n + a + b) (by lia) (by lia),
CochainComplex.ι_mapBifunctorShift₂Iso_hom_f_assoc _ _ F b p q n h _ _ rfl rfl,
CochainComplex.ι_mapBifunctorShift₂Iso_hom_f_... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Triangulated.Orthogonal | {
"line": 81,
"column": 6
} | {
"line": 81,
"column": 31
} | {
"line": 81,
"column": 32
} | [
{
"pp": "C : Type u\ninst✝⁶ : Category.{v, u} C\nP : ObjectProperty C\ninst✝⁵ : HasZeroObject C\ninst✝⁴ : HasShift C ℤ\ninst✝³ : Preadditive C\ninst✝² : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝¹ : Pretriangulated C\ninst✝ : P.IsTriangulated\nY : C\nhY : P.rightOrthogonal Y\nX₁ X₂ : C\nf : X₁ ⟶ X₂\nx✝ : P.t... | [
"C : Type u\ninst✝⁶ : Category.{v, u} C\nP : ObjectProperty C\ninst✝⁵ : HasZeroObject C\ninst✝⁴ : HasShift C ℤ\ninst✝³ : Preadditive C\ninst✝² : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝¹ : Pretriangulated C\ninst✝ : P.IsTriangulated\nY : C\nhY : P.rightOrthogonal Y\nX₁ X₂ : C\nf : X₁ ⟶ X₂\nx✝ : P.trW f\nX₃ : C... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.Orthogonal | {
"line": 81,
"column": 51
} | {
"line": 81,
"column": 76
} | {
"line": 81,
"column": 77
} | [
{
"pp": "C : Type u\ninst✝⁶ : Category.{v, u} C\nP : ObjectProperty C\ninst✝⁵ : HasZeroObject C\ninst✝⁴ : HasShift C ℤ\ninst✝³ : Preadditive C\ninst✝² : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝¹ : Pretriangulated C\ninst✝ : P.IsTriangulated\nY : C\nhY : P.rightOrthogonal Y\nX₁ X₂ : C\nf : X₁ ⟶ X₂\nx✝ : P.t... | [
"C : Type u\ninst✝⁶ : Category.{v, u} C\nP : ObjectProperty C\ninst✝⁵ : HasZeroObject C\ninst✝⁴ : HasShift C ℤ\ninst✝³ : Preadditive C\ninst✝² : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝¹ : Pretriangulated C\ninst✝ : P.IsTriangulated\nY : C\nhY : P.rightOrthogonal Y\nX₁ X₂ : C\nf : X₁ ⟶ X₂\nx✝ : P.trW f\nX₃ : C... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.ExtendHomotopy | {
"line": 76,
"column": 10
} | {
"line": 76,
"column": 30
} | {
"line": 76,
"column": 31
} | [
{
"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 : Preadditive C\nK L : HomologicalComplex C c\nf g : K ⟶ L\nh : Homotopy f g\ne : c.Embedding c'\ninst✝ : e.IsRelIff\ni : ι\n⊢ (extendMap f e).... | [
"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 : Preadditive C\nK L : HomologicalComplex C c\nf g : K ⟶ L\nh : Homotopy f g\ne : c.Embedding c'\ninst✝ : e.IsRelIff\ni : ι\n⊢ (K.extendXIso e ⋯).hom ≫ f.f... | extendMap_f _ _ rfl, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Homology.Embedding.ExtendHomotopy | {
"line": 76,
"column": 31
} | {
"line": 76,
"column": 51
} | {
"line": 76,
"column": 52
} | [
{
"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 : Preadditive C\nK L : HomologicalComplex C c\nf g : K ⟶ L\nh : Homotopy f g\ne : c.Embedding c'\ninst✝ : e.IsRelIff\ni : ι\n⊢ (K.extendXIso e ... | [
"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 : Preadditive C\nK L : HomologicalComplex C c\nf g : K ⟶ L\nh : Homotopy f g\ne : c.Embedding c'\ninst✝ : e.IsRelIff\ni : ι\n⊢ (K.extendXIso e ⋯).hom ≫ f.f... | extendMap_f _ _ rfl, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.CategoryTheory.Triangulated.Orthogonal | {
"line": 99,
"column": 8
} | {
"line": 99,
"column": 33
} | {
"line": 99,
"column": 34
} | [
{
"pp": "C : Type u\ninst✝⁶ : Category.{v, u} C\nP : ObjectProperty C\ninst✝⁵ : HasZeroObject C\ninst✝⁴ : HasShift C ℤ\ninst✝³ : Preadditive C\ninst✝² : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝¹ : Pretriangulated C\ninst✝ : P.IsTriangulated\nX : C\nhX : P.leftOrthogonal X\nY₂ Y₃ : C\nh : Y₂ ⟶ Y₃\nY₁ : C\nf... | [
"C : Type u\ninst✝⁶ : Category.{v, u} C\nP : ObjectProperty C\ninst✝⁵ : HasZeroObject C\ninst✝⁴ : HasShift C ℤ\ninst✝³ : Preadditive C\ninst✝² : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝¹ : Pretriangulated C\ninst✝ : P.IsTriangulated\nX : C\nhX : P.leftOrthogonal X\nY₂ Y₃ : C\nh : Y₂ ⟶ Y₃\nY₁ : C\nf : Y₁ ⟶ Y₂\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.Orthogonal | {
"line": 117,
"column": 4
} | {
"line": 117,
"column": 65
} | {
"line": 118,
"column": 4
} | [
{
"pp": "case refine_2\nC : Type u\ninst✝⁹ : Category.{v, u} C\nD : Type u'\ninst✝⁸ : Category.{v', u'} D\nP : ObjectProperty C\ninst✝⁷ : HasZeroObject C\ninst✝⁶ : HasShift C ℤ\ninst✝⁵ : Preadditive C\ninst✝⁴ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝³ : Pretriangulated C\ninst✝² : P.IsTriangulated\ninst✝¹... | [
"case refine_2\nC : Type u\ninst✝⁹ : Category.{v, u} C\nD : Type u'\ninst✝⁸ : Category.{v', u'} D\nP : ObjectProperty C\ninst✝⁷ : HasZeroObject C\ninst✝⁶ : HasShift C ℤ\ninst✝⁵ : Preadditive C\ninst✝⁴ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝³ : Pretriangulated C\ninst✝² : P.IsTriangulated\ninst✝¹ : IsTriangu... | obtain ⟨φ, hφ⟩ := Localization.exists_rightFraction L P.trW g | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.CategoryTheory.Triangulated.Orthogonal | {
"line": 117,
"column": 4
} | {
"line": 121,
"column": 29
} | {
"line": 123,
"column": 0
} | [
{
"pp": "case refine_2\nC : Type u\ninst✝⁹ : Category.{v, u} C\nD : Type u'\ninst✝⁸ : Category.{v', u'} D\nP : ObjectProperty C\ninst✝⁷ : HasZeroObject C\ninst✝⁶ : HasShift C ℤ\ninst✝⁵ : Preadditive C\ninst✝⁴ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝³ : Pretriangulated C\ninst✝² : P.IsTriangulated\ninst✝¹... | [] | obtain ⟨φ, hφ⟩ := Localization.exists_rightFraction L P.trW g
obtain ⟨α, hα⟩ := (hY _ φ.hs).2 φ.f
refine ⟨α, ?_⟩
rw [hφ, ← cancel_epi (L.map φ.s), MorphismProperty.RightFraction.map_s_comp_map,
← hα, Functor.map_comp] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Triangulated.Orthogonal | {
"line": 117,
"column": 4
} | {
"line": 121,
"column": 29
} | {
"line": 123,
"column": 0
} | [
{
"pp": "case refine_2\nC : Type u\ninst✝⁹ : Category.{v, u} C\nD : Type u'\ninst✝⁸ : Category.{v', u'} D\nP : ObjectProperty C\ninst✝⁷ : HasZeroObject C\ninst✝⁶ : HasShift C ℤ\ninst✝⁵ : Preadditive C\ninst✝⁴ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝³ : Pretriangulated C\ninst✝² : P.IsTriangulated\ninst✝¹... | [] | obtain ⟨φ, hφ⟩ := Localization.exists_rightFraction L P.trW g
obtain ⟨α, hα⟩ := (hY _ φ.hs).2 φ.f
refine ⟨α, ?_⟩
rw [hφ, ← cancel_epi (L.map φ.s), MorphismProperty.RightFraction.map_s_comp_map,
← hα, Functor.map_comp] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Homology.Embedding.ExtendHomotopy | {
"line": 141,
"column": 18
} | {
"line": 141,
"column": 79
} | {
"line": 143,
"column": 0
} | [
{
"pp": "ι : 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 : Preadditive C\nK L : HomologicalComplex C c\nf g : K ⟶ L\ne : c.Embedding c'\ninst✝ : e.IsRelIff\nh : Homotopy (extendMap f e) (extendMap g e)\ni j : ι... | [] | by rw [h.zero _ _ (by rwa [e.rel_iff]), zero_comp, comp_zero] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Homology.DerivedCategory.TStructure | {
"line": 101,
"column": 6
} | {
"line": 101,
"column": 28
} | {
"line": 102,
"column": 6
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : Abelian C\ninst✝ : HasDerivedCategory C\nX : DerivedCategory C\nn : ℤ\nhX : ∀ i < n, IsZero ((homologyFunctor C i).obj X)\ni : ℤ\nhi : i < n\n⊢ IsZero (HomologicalComplex.homology (Q.objPreimage X) i)",
"ppTerm": "?m.129",
"assigned": true,
"... | [
"C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : Abelian C\ninst✝ : HasDerivedCategory C\nX : DerivedCategory C\nn : ℤ\nhX : ∀ i < n, IsZero ((homologyFunctor C i).obj X)\ni : ℤ\nhi : i < n\n⊢ HomologicalComplex.homology (Q.objPreimage X) i ≅ (homologyFunctor C i).obj X"
] | apply (hX i hi).of_iso | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.Algebra.Homology.HomotopyFiber | {
"line": 95,
"column": 26
} | {
"line": 95,
"column": 37
} | {
"line": 95,
"column": 38
} | [
{
"pp": "C : Type u_1\ninst✝⁴ : Category.{v_1, u_1} C\ninst✝³ : Preadditive C\nα : Type u_2\nc : ComplexShape α\nK : HomologicalComplex C c\ninst✝² : DecidableRel c.Rel\ninst✝¹ : ∀ (i : α), HasBinaryBiproduct (K.X i) (K.X i)\ninst✝ : K.HasPathObject\ni : α\nh₁ : IsZero (K.X i)\nh₂ : ∀ (j : α), c.Rel j i → IsZer... | [
"C : Type u_1\ninst✝⁴ : Category.{v_1, u_1} C\ninst✝³ : Preadditive C\nα : Type u_2\nc : ComplexShape α\nK : HomologicalComplex C c\ninst✝² : DecidableRel c.Rel\ninst✝¹ : ∀ (i : α), HasBinaryBiproduct (K.X i) (K.X i)\ninst✝ : K.HasPathObject\ni : α\nh₁ : IsZero (K.X i)\nh₂ : ∀ (j : α), c.Rel j i → IsZero (K.X j)\n⊢... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.DerivedCategory.TStructure | {
"line": 118,
"column": 6
} | {
"line": 118,
"column": 28
} | {
"line": 119,
"column": 6
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : Abelian C\ninst✝ : HasDerivedCategory C\nX : DerivedCategory C\nn : ℤ\nhX : ∀ (i : ℤ), n < i → IsZero ((homologyFunctor C i).obj X)\ni : ℤ\nhi : n < i\n⊢ IsZero (HomologicalComplex.homology (Q.objPreimage X) i)",
"ppTerm": "?m.129",
"assigned": t... | [
"C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : Abelian C\ninst✝ : HasDerivedCategory C\nX : DerivedCategory C\nn : ℤ\nhX : ∀ (i : ℤ), n < i → IsZero ((homologyFunctor C i).obj X)\ni : ℤ\nhi : n < i\n⊢ HomologicalComplex.homology (Q.objPreimage X) i ≅ (homologyFunctor C i).obj X"
] | apply (hX i hi).of_iso | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.CategoryTheory.MorphismProperty.LiftingProperty | {
"line": 138,
"column": 4
} | {
"line": 138,
"column": 28
} | {
"line": 139,
"column": 4
} | [
{
"pp": "case a\nC : Type u\ninst✝ : Category.{v, u} C\nT : MorphismProperty C\n⊢ T.rlp ≤ T.pushouts.rlp",
"ppTerm": "?a✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"CategoryTheory.MorphismProperty",
"CategoryTheory.MorphismProperty.pushouts",
"CategoryTheory.MorphismPr... | [
"case a\nC : Type u\ninst✝ : Category.{v, u} C\nT : MorphismProperty C\n⊢ T.pushouts ≤ T.rlp.llp"
] | rw [← le_llp_iff_le_rlp] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.CategoryTheory.MorphismProperty.LiftingProperty | {
"line": 156,
"column": 4
} | {
"line": 156,
"column": 28
} | {
"line": 157,
"column": 4
} | [
{
"pp": "case a\nC : Type u\ninst✝ : Category.{v, u} C\nT : MorphismProperty C\n⊢ T.rlp ≤ (coproducts.{w, v, u} T).rlp",
"ppTerm": "?a✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"CategoryTheory.MorphismProperty",
"CategoryTheory.MorphismProperty.llp",
"CategoryTheory.M... | [
"case a\nC : Type u\ninst✝ : Category.{v, u} C\nT : MorphismProperty C\n⊢ coproducts.{w, v, u} T ≤ T.rlp.llp"
] | rw [← le_llp_iff_le_rlp] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.CategoryTheory.MorphismProperty.LiftingProperty | {
"line": 166,
"column": 4
} | {
"line": 166,
"column": 28
} | {
"line": 167,
"column": 4
} | [
{
"pp": "case a\nC : Type u\ninst✝ : Category.{v, u} C\nT : MorphismProperty C\n⊢ T.rlp ≤ T.retracts.rlp",
"ppTerm": "?a✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"CategoryTheory.MorphismProperty",
"CategoryTheory.MorphismProperty.llp",
"CategoryTheory.MorphismPropert... | [
"case a\nC : Type u\ninst✝ : Category.{v, u} C\nT : MorphismProperty C\n⊢ T.retracts ≤ T.rlp.llp"
] | rw [← le_llp_iff_le_rlp] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Algebra.Homology.HomotopyCategory.KInjective | {
"line": 184,
"column": 4
} | {
"line": 184,
"column": 46
} | {
"line": 184,
"column": 46
} | [
{
"pp": "C : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Abelian C\nK L : CochainComplex C ℤ\nn : ℤ\nz : Cocycle K L n\ninst✝ : L.IsKInjective\nhK : HomologicalComplex.Acyclic K\nm : ℤ\nhm : m + 1 = n\nφ : K ⟶ (CategoryTheory.shiftFunctor (CochainComplex C ℤ) n).obj L\nhφ : Cochain.ofHom φ = (↑z).rightSh... | [
"C : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Abelian C\nK L : CochainComplex C ℤ\nn : ℤ\nz : Cocycle K L n\ninst✝ : L.IsKInjective\nhK : HomologicalComplex.Acyclic K\nm : ℤ\nhm : m + 1 = n\nφ : K ⟶ (CategoryTheory.shiftFunctor (CochainComplex C ℤ) n).obj L\nhφ : Cochain.ofHom φ = (↑z).rightShift n 0 ⋯\nh... | Cochain.δ_rightUnshift _ _ _ _ 0 (by simp) | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.CategoryTheory.MorphismProperty.RetractArgument | {
"line": 63,
"column": 4
} | {
"line": 63,
"column": 15
} | {
"line": 63,
"column": 16
} | [
{
"pp": "C : Type u_1\ninst✝² : Category.{v_1, u_1} C\nW₁ W₂ : MorphismProperty C\ninst✝¹ : W₁.HasFactorization W₂\ninst✝ : W₁.IsStableUnderRetracts\nh₁ : W₁ ≤ W₂.llp\nA B : C\ni : A ⟶ B\nhi : W₂.llp i\nh : W₁.MapFactorizationData W₂ i\nthis : HasLiftingProperty i h.p\n⊢ W₁ i",
"ppTerm": "?m.49",
"assig... | [
"C : Type u_1\ninst✝² : Category.{v_1, u_1} C\nW₁ W₂ : MorphismProperty C\ninst✝¹ : W₁.HasFactorization W₂\ninst✝ : W₁.IsStableUnderRetracts\nh₁ : W₁ ≤ W₂.llp\nA B : C\ni : A ⟶ B\nhi : W₂.llp i\nh : W₁.MapFactorizationData W₂ i\nthis : HasLiftingProperty i h.p\n⊢ W₁ i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.MorphismProperty.RetractArgument | {
"line": 71,
"column": 4
} | {
"line": 71,
"column": 15
} | {
"line": 71,
"column": 16
} | [
{
"pp": "C : Type u_1\ninst✝² : Category.{v_1, u_1} C\nW₁ W₂ : MorphismProperty C\ninst✝¹ : W₁.HasFactorization W₂\ninst✝ : W₂.IsStableUnderRetracts\nh₂ : W₂ ≤ W₁.rlp\nX Y : C\np : X ⟶ Y\nhp : W₁.rlp p\nh : W₁.MapFactorizationData W₂ p\nthis : HasLiftingProperty h.i p\n⊢ W₂ p",
"ppTerm": "?m.49",
"assig... | [
"C : Type u_1\ninst✝² : Category.{v_1, u_1} C\nW₁ W₂ : MorphismProperty C\ninst✝¹ : W₁.HasFactorization W₂\ninst✝ : W₂.IsStableUnderRetracts\nh₂ : W₂ ≤ W₁.rlp\nX Y : C\np : X ⟶ Y\nhp : W₁.rlp p\nh : W₁.MapFactorizationData W₂ p\nthis : HasLiftingProperty h.i p\n⊢ W₂ p"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.ModelCategory.CategoryWithCofibrations | {
"line": 205,
"column": 71
} | {
"line": 206,
"column": 26
} | {
"line": 208,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\nX✝ Y✝ : C\nf✝ : X✝ ⟶ Y✝\ninst✝¹ : CategoryWithFibrations C\nX Y : Cᵒᵖ\nf : X ⟶ Y\ninst✝ : Cofibration f\n⊢ Fibration f.unop",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Opposite",
"CategoryTheory.CategoryStruc... | [] | by
rwa [fibration_unop_iff] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.AlgebraicTopology.ModelCategory.Basic | {
"line": 120,
"column": 2
} | {
"line": 120,
"column": 40
} | {
"line": 120,
"column": 41
} | [
{
"pp": "C : Type u\ninst✝⁸ : Category.{v, u} C\ninst✝⁷ : CategoryWithFibrations C\ninst✝⁶ : CategoryWithCofibrations C\ninst✝⁵ : CategoryWithWeakEquivalences C\ninst✝⁴ : (weakEquivalences C).HasTwoOutOfThreeProperty\ninst✝³ : (trivialCofibrations C).IsWeakFactorizationSystem (fibrations C)\ninst✝² : (cofibrati... | [
"C : Type u\ninst✝⁸ : Category.{v, u} C\ninst✝⁷ : CategoryWithFibrations C\ninst✝⁶ : CategoryWithCofibrations C\ninst✝⁵ : CategoryWithWeakEquivalences C\ninst✝⁴ : (weakEquivalences C).HasTwoOutOfThreeProperty\ninst✝³ : (trivialCofibrations C).IsWeakFactorizationSystem (fibrations C)\ninst✝² : (cofibrations C).IsWea... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.ModelCategory.Basic | {
"line": 137,
"column": 6
} | {
"line": 137,
"column": 40
} | {
"line": 137,
"column": 41
} | [
{
"pp": "C : Type u\ninst✝⁸ : Category.{v, u} C\ninst✝⁷ : CategoryWithFibrations C\ninst✝⁶ : CategoryWithCofibrations C\ninst✝⁵ : CategoryWithWeakEquivalences C\ninst✝⁴ : HasFiniteLimits C\ninst✝³ : HasFiniteColimits C\ninst✝² : (weakEquivalences C).HasTwoOutOfThreeProperty\ninst✝¹ : (cofibrations C).IsWeakFact... | [
"C : Type u\ninst✝⁸ : Category.{v, u} C\ninst✝⁷ : CategoryWithFibrations C\ninst✝⁶ : CategoryWithCofibrations C\ninst✝⁵ : CategoryWithWeakEquivalences C\ninst✝⁴ : HasFiniteLimits C\ninst✝³ : HasFiniteColimits C\ninst✝² : (weakEquivalences C).HasTwoOutOfThreeProperty\ninst✝¹ : (cofibrations C).IsWeakFactorizationSys... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.ModelCategory.Basic | {
"line": 139,
"column": 6
} | {
"line": 139,
"column": 44
} | {
"line": 139,
"column": 45
} | [
{
"pp": "C : Type u\ninst✝⁸ : Category.{v, u} C\ninst✝⁷ : CategoryWithFibrations C\ninst✝⁶ : CategoryWithCofibrations C\ninst✝⁵ : CategoryWithWeakEquivalences C\ninst✝⁴ : HasFiniteLimits C\ninst✝³ : HasFiniteColimits C\ninst✝² : (weakEquivalences C).HasTwoOutOfThreeProperty\ninst✝¹ : (cofibrations C).IsWeakFact... | [
"C : Type u\ninst✝⁸ : Category.{v, u} C\ninst✝⁷ : CategoryWithFibrations C\ninst✝⁶ : CategoryWithCofibrations C\ninst✝⁵ : CategoryWithWeakEquivalences C\ninst✝⁴ : HasFiniteLimits C\ninst✝³ : HasFiniteColimits C\ninst✝² : (weakEquivalences C).HasTwoOutOfThreeProperty\ninst✝¹ : (cofibrations C).IsWeakFactorizationSys... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.ModelCategory.Basic | {
"line": 142,
"column": 32
} | {
"line": 142,
"column": 64
} | {
"line": 142,
"column": 65
} | [
{
"pp": "C : Type u\ninst✝⁸ : Category.{v, u} C\ninst✝⁷ : CategoryWithFibrations C\ninst✝⁶ : CategoryWithCofibrations C\ninst✝⁵ : CategoryWithWeakEquivalences C\ninst✝⁴ : HasFiniteLimits C\ninst✝³ : HasFiniteColimits C\ninst✝² : (weakEquivalences C).HasTwoOutOfThreeProperty\ninst✝¹ : (cofibrations C).IsWeakFact... | [
"C : Type u\ninst✝⁸ : Category.{v, u} C\ninst✝⁷ : CategoryWithFibrations C\ninst✝⁶ : CategoryWithCofibrations C\ninst✝⁵ : CategoryWithWeakEquivalences C\ninst✝⁴ : HasFiniteLimits C\ninst✝³ : HasFiniteColimits C\ninst✝² : (weakEquivalences C).HasTwoOutOfThreeProperty\ninst✝¹ : (cofibrations C).IsWeakFactorizationSys... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.ModelCategory.Instances | {
"line": 267,
"column": 44
} | {
"line": 270,
"column": 48
} | {
"line": 272,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝⁷ : Category.{v, u} C\ninst✝⁶ : CategoryWithWeakEquivalences C\ninst✝⁵ : CategoryWithCofibrations C\ninst✝⁴ : CategoryWithFibrations C\nJ✝ : Type w\nJ : Type u_1\nX Y : J → C\nf : (i : J) → X i ⟶ Y i\ninst✝³ : HasCoproduct X\ninst✝² : HasCoproduct Y\nh : ∀ (i : J), Cofibration (f i)\ni... | [] | by
rw [weakEquivalence_iff]
exact (MorphismProperty.colimMap (W := (trivialCofibrations C)) _
(fun ⟨i⟩ ↦ mem_trivialCofibrations (f i))).2 | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.AlgebraicTopology.ModelCategory.Instances | {
"line": 322,
"column": 2
} | {
"line": 322,
"column": 36
} | {
"line": 322,
"column": 37
} | [
{
"pp": "C : Type u\ninst✝⁵ : Category.{v, u} C\ninst✝⁴ : CategoryWithWeakEquivalences C\ninst✝³ : CategoryWithCofibrations C\ninst✝² : CategoryWithFibrations C\nX Y : C\nf : X ⟶ Y\ninst✝¹ : (trivialCofibrations C).IsWeakFactorizationSystem (fibrations C)\ninst✝ : IsIso f\nthis : trivialCofibrations C f\n⊢ Cofi... | [
"C : Type u\ninst✝⁵ : Category.{v, u} C\ninst✝⁴ : CategoryWithWeakEquivalences C\ninst✝³ : CategoryWithCofibrations C\ninst✝² : CategoryWithFibrations C\nX Y : C\nf : X ⟶ Y\ninst✝¹ : (trivialCofibrations C).IsWeakFactorizationSystem (fibrations C)\ninst✝ : IsIso f\nthis : trivialCofibrations C f\n⊢ cofibrations C f... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.ModelCategory.Instances | {
"line": 328,
"column": 2
} | {
"line": 328,
"column": 34
} | {
"line": 328,
"column": 35
} | [
{
"pp": "C : Type u\ninst✝⁵ : Category.{v, u} C\ninst✝⁴ : CategoryWithWeakEquivalences C\ninst✝³ : CategoryWithCofibrations C\ninst✝² : CategoryWithFibrations C\nX Y : C\nf : X ⟶ Y\ninst✝¹ : (cofibrations C).IsWeakFactorizationSystem (trivialFibrations C)\ninst✝ : IsIso f\nthis : trivialFibrations C f\n⊢ Fibrat... | [
"C : Type u\ninst✝⁵ : Category.{v, u} C\ninst✝⁴ : CategoryWithWeakEquivalences C\ninst✝³ : CategoryWithCofibrations C\ninst✝² : CategoryWithFibrations C\nX Y : C\nf : X ⟶ Y\ninst✝¹ : (cofibrations C).IsWeakFactorizationSystem (trivialFibrations C)\ninst✝ : IsIso f\nthis : trivialFibrations C f\n⊢ fibrations C f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.ModelCategory.Instances | {
"line": 369,
"column": 2
} | {
"line": 369,
"column": 36
} | {
"line": 369,
"column": 37
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : CategoryWithWeakEquivalences C\ninst✝¹ : CategoryWithCofibrations C\ninst✝ : CategoryWithFibrations C\nX Y : C\nf : X ⟶ Y\nh : (cofibrations C).MapFactorizationData (trivialFibrations C) f\n⊢ Cofibration h.i",
"ppTerm": "?m.27",
"assigned": true,... | [
"C : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : CategoryWithWeakEquivalences C\ninst✝¹ : CategoryWithCofibrations C\ninst✝ : CategoryWithFibrations C\nX Y : C\nf : X ⟶ Y\nh : (cofibrations C).MapFactorizationData (trivialFibrations C) f\n⊢ cofibrations C h.i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.ModelCategory.Instances | {
"line": 372,
"column": 2
} | {
"line": 372,
"column": 34
} | {
"line": 372,
"column": 35
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : CategoryWithWeakEquivalences C\ninst✝¹ : CategoryWithCofibrations C\ninst✝ : CategoryWithFibrations C\nX Y : C\nf : X ⟶ Y\nh : (cofibrations C).MapFactorizationData (trivialFibrations C) f\n⊢ Fibration h.p",
"ppTerm": "?m.27",
"assigned": true,
... | [
"C : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : CategoryWithWeakEquivalences C\ninst✝¹ : CategoryWithCofibrations C\ninst✝ : CategoryWithFibrations C\nX Y : C\nf : X ⟶ Y\nh : (cofibrations C).MapFactorizationData (trivialFibrations C) f\n⊢ fibrations C h.p"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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