module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.AlgebraicTopology.SimplicialSet.Degenerate | {
"line": 368,
"column": 19
} | {
"line": 368,
"column": 24
} | {
"line": 369,
"column": 2
} | [
{
"pp": "X : SSet\nn✝ : ℕ\nY : SSet\ne : X ≅ Y\nn : ℕ\nx✝ : ↑(X.nonDegenerate n)\n⊢ (fun x ↦\n match x with\n | ⟨y, hy⟩ => ⟨(ConcreteCategory.hom (e.inv.app (op ⦋n⦌))) y, ⋯⟩)\n ((fun x ↦\n match x with\n | ⟨x, hx⟩ => ⟨(ConcreteCategory.hom (e.hom.app (op ⦋n⦌))) x, ⋯⟩)\n ... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.Degenerate | {
"line": 368,
"column": 19
} | {
"line": 368,
"column": 24
} | {
"line": 369,
"column": 2
} | [
{
"pp": "X : SSet\nn✝ : ℕ\nY : SSet\ne : X ≅ Y\nn : ℕ\nx✝ : ↑(X.nonDegenerate n)\n⊢ (fun x ↦\n match x with\n | ⟨y, hy⟩ => ⟨(ConcreteCategory.hom (e.inv.app (op ⦋n⦌))) y, ⋯⟩)\n ((fun x ↦\n match x with\n | ⟨x, hx⟩ => ⟨(ConcreteCategory.hom (e.hom.app (op ⦋n⦌))) x, ⋯⟩)\n ... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.Degenerate | {
"line": 369,
"column": 20
} | {
"line": 369,
"column": 25
} | {
"line": 371,
"column": 0
} | [
{
"pp": "X : SSet\nn✝ : ℕ\nY : SSet\ne : X ≅ Y\nn : ℕ\nx✝ : ↑(Y.nonDegenerate n)\n⊢ (fun x ↦\n match x with\n | ⟨x, hx⟩ => ⟨(ConcreteCategory.hom (e.hom.app (op ⦋n⦌))) x, ⋯⟩)\n ((fun x ↦\n match x with\n | ⟨y, hy⟩ => ⟨(ConcreteCategory.hom (e.inv.app (op ⦋n⦌))) y, ⋯⟩)\n ... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialSet.Degenerate | {
"line": 369,
"column": 20
} | {
"line": 369,
"column": 25
} | {
"line": 371,
"column": 0
} | [
{
"pp": "X : SSet\nn✝ : ℕ\nY : SSet\ne : X ≅ Y\nn : ℕ\nx✝ : ↑(Y.nonDegenerate n)\n⊢ (fun x ↦\n match x with\n | ⟨x, hx⟩ => ⟨(ConcreteCategory.hom (e.hom.app (op ⦋n⦌))) x, ⋯⟩)\n ((fun x ↦\n match x with\n | ⟨y, hy⟩ => ⟨(ConcreteCategory.hom (e.inv.app (op ⦋n⦌))) y, ⋯⟩)\n ... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.Degenerate | {
"line": 369,
"column": 20
} | {
"line": 369,
"column": 25
} | {
"line": 371,
"column": 0
} | [
{
"pp": "X : SSet\nn✝ : ℕ\nY : SSet\ne : X ≅ Y\nn : ℕ\nx✝ : ↑(Y.nonDegenerate n)\n⊢ (fun x ↦\n match x with\n | ⟨x, hx⟩ => ⟨(ConcreteCategory.hom (e.hom.app (op ⦋n⦌))) x, ⋯⟩)\n ((fun x ↦\n match x with\n | ⟨y, hy⟩ => ⟨(ConcreteCategory.hom (e.inv.app (op ⦋n⦌))) y, ⋯⟩)\n ... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Fin.SuccAboveOrderIso | {
"line": 36,
"column": 35
} | {
"line": 36,
"column": 40
} | {
"line": 36,
"column": 40
} | [
{
"pp": "n : ℕ\nj : Fin (n + 2)\ni : Fin (n + 1)\nhj✝ : j ∈ {i.succ}ᶜ\nhj : ¬j = i.succ\n⊢ (fun a ↦ ⟨i.succ.succAboveOrderEmb a, ⋯⟩) (i.predAbove j) = ⟨j, hj✝⟩",
"ppTerm": "?m.132",
"assigned": true,
"usedConstants": [
"Fin.succAbove",
"False",
"Subtype.mk.congr_simp",
"eq_fa... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Order.Fin.SuccAboveOrderIso | {
"line": 36,
"column": 35
} | {
"line": 36,
"column": 40
} | {
"line": 36,
"column": 40
} | [
{
"pp": "n : ℕ\nj : Fin (n + 2)\ni : Fin (n + 1)\nhj✝ : j ∈ {i.succ}ᶜ\nhj : ¬j = i.succ\n⊢ (fun a ↦ ⟨i.succ.succAboveOrderEmb a, ⋯⟩) (i.predAbove j) = ⟨j, hj✝⟩",
"ppTerm": "?m.132",
"assigned": true,
"usedConstants": [
"Fin.succAbove",
"False",
"Subtype.mk.congr_simp",
"eq_fa... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Fin.SuccAboveOrderIso | {
"line": 36,
"column": 35
} | {
"line": 36,
"column": 40
} | {
"line": 36,
"column": 40
} | [
{
"pp": "n : ℕ\nj : Fin (n + 2)\ni : Fin (n + 1)\nhj✝ : j ∈ {i.succ}ᶜ\nhj : ¬j = i.succ\n⊢ (fun a ↦ ⟨i.succ.succAboveOrderEmb a, ⋯⟩) (i.predAbove j) = ⟨j, hj✝⟩",
"ppTerm": "?m.132",
"assigned": true,
"usedConstants": [
"Fin.succAbove",
"False",
"Subtype.mk.congr_simp",
"eq_fa... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.Nerve | {
"line": 132,
"column": 38
} | {
"line": 132,
"column": 53
} | {
"line": 132,
"column": 53
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Quiver.IsThin C\nn : SimplexCategoryᵒᵖ\nx y : (nerve C).obj n\nh : x.obj = y.obj\n⊢ ∀ (i : ℕ) (hi : i < (unop n).len),\n ComposableArrows.map' x i (i + 1) ⋯ hi = eqToHom ⋯ ≫ ComposableArrows.map' y i (i + 1) ⋯ hi ≫ eqToHom ⋯",
"ppTerm": "?m.28",
... | [] | by subsingleton | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.AlgebraicTopology.SimplicialSet.Nerve | {
"line": 218,
"column": 2
} | {
"line": 218,
"column": 50
} | {
"line": 219,
"column": 2
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nx₀ x₁ x₂ : C\nf₀₁ : x₀ ⟶ x₁\nf₁₂ : x₁ ⟶ x₂\nf₀₂ : x₀ ⟶ x₂\nh' : (edgeMk f₀₁).CompStruct (edgeMk f₁₂) (edgeMk (f₀₁ ≫ f₁₂)) :=\n Edge.CompStruct.mk (ComposableArrows.mk₂ f₀₁ f₁₂) ⋯ ⋯ ⋯\nx✝ : Nonempty ((edgeMk f₀₁).CompStruct (edgeMk f₁₂) (edgeMk f₀₂))\nh : (edgeMk ... | [
"C : Type u\ninst✝ : Category.{v, u} C\nx₀ x₁ x₂ : C\nf₀₁ : x₀ ⟶ x₁\nf₁₂ : x₁ ⟶ x₂\nf₀₂ : x₀ ⟶ x₂\nh' : (edgeMk f₀₁).CompStruct (edgeMk f₁₂) (edgeMk (f₀₁ ≫ f₁₂)) := ⋯\nx✝ : Nonempty ((edgeMk f₀₁).CompStruct (edgeMk f₁₂) (edgeMk f₀₂))\nh : (edgeMk f₀₁).CompStruct (edgeMk f₁₂) (edgeMk f₀₂)\n⊢ ComposableArrows.arrowEq... | apply ComposableArrows.arrowEquiv.symm.injective | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.Algebra.Homology.AlternatingConst | {
"line": 64,
"column": 18
} | {
"line": 64,
"column": 23
} | {
"line": 65,
"column": 2
} | [
{
"pp": "C : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : HasZeroMorphisms C\nA : C\nφ ψ : A ⟶ A\nhOdd : φ ≫ ψ = 0\nhEven : ψ ≫ φ = 0\nc : ComplexShape ℕ\ninst✝ : DecidableRel c.Rel\nhc : ∀ (i j : ℕ), c.Rel i j → Odd (i + j)\ni j : ℕ\n⊢ ¬c.Rel i j → (if hij : c.Rel i j then if hi : Even i then φ else ψ el... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Algebra.Homology.AlternatingConst | {
"line": 64,
"column": 18
} | {
"line": 64,
"column": 23
} | {
"line": 65,
"column": 2
} | [
{
"pp": "C : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : HasZeroMorphisms C\nA : C\nφ ψ : A ⟶ A\nhOdd : φ ≫ ψ = 0\nhEven : ψ ≫ φ = 0\nc : ComplexShape ℕ\ninst✝ : DecidableRel c.Rel\nhc : ∀ (i j : ℕ), c.Rel i j → Odd (i + j)\ni j : ℕ\n⊢ ¬c.Rel i j → (if hij : c.Rel i j then if hi : Even i then φ else ψ el... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Homology.AlternatingConst | {
"line": 64,
"column": 18
} | {
"line": 64,
"column": 23
} | {
"line": 65,
"column": 2
} | [
{
"pp": "C : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : HasZeroMorphisms C\nA : C\nφ ψ : A ⟶ A\nhOdd : φ ≫ ψ = 0\nhEven : ψ ≫ φ = 0\nc : ComplexShape ℕ\ninst✝ : DecidableRel c.Rel\nhc : ∀ (i j : ℕ), c.Rel i j → Odd (i + j)\ni j : ℕ\n⊢ ¬c.Rel i j → (if hij : c.Rel i j then if hi : Even i then φ else ψ el... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Homology.Augment | {
"line": 222,
"column": 8
} | {
"line": 222,
"column": 15
} | {
"line": 223,
"column": 6
} | [
{
"pp": "case zero\nV : 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 k : ℕ\nhij : (ComplexShape.up ℕ).Rel i j\nhjk : (ComplexShape.up ℕ).Rel j k\n⊢ f ≫ C.d 0 (0 + 1) = 0",
"ppTerm": "?zero",
"assigned": true,
"... | [] | exact w | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Algebra.Homology.Augment | {
"line": 222,
"column": 8
} | {
"line": 222,
"column": 15
} | {
"line": 223,
"column": 6
} | [
{
"pp": "case zero\nV : 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 k : ℕ\nhij : (ComplexShape.up ℕ).Rel i j\nhjk : (ComplexShape.up ℕ).Rel j k\n⊢ f ≫ C.d 0 (0 + 1) = 0",
"ppTerm": "?zero",
"assigned": true,
"... | [] | exact w | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Homology.Augment | {
"line": 222,
"column": 8
} | {
"line": 222,
"column": 15
} | {
"line": 223,
"column": 6
} | [
{
"pp": "case zero\nV : 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 k : ℕ\nhij : (ComplexShape.up ℕ).Rel i j\nhjk : (ComplexShape.up ℕ).Rel j k\n⊢ f ≫ C.d 0 (0 + 1) = 0",
"ppTerm": "?zero",
"assigned": true,
"... | [] | exact w | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Homology.Augment | {
"line": 223,
"column": 12
} | {
"line": 223,
"column": 20
} | {
"line": 223,
"column": 21
} | [
{
"pp": "case succ\nV : 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 k : ℕ\nhij : (ComplexShape.up ℕ).Rel i j\nhjk : (ComplexShape.up ℕ).Rel j k\nn✝ : ℕ\n⊢ f ≫ C.d 0 (n✝ + 1 + 1) = 0",
"ppTerm": "?succ",
"assigned"... | [
"case succ\nV : 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 k : ℕ\nhij : (ComplexShape.up ℕ).Rel i j\nhjk : (ComplexShape.up ℕ).Rel j k\nn✝ : ℕ\n⊢ f ≫ 0 = 0",
"case succ.a\nV : Type u\ninst✝¹ : Category.{v, u} V\ninst✝ : Ha... | C.shape, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex | {
"line": 275,
"column": 20
} | {
"line": 275,
"column": 25
} | {
"line": 277,
"column": 0
} | [
{
"pp": "n : ℕ\nS : Finset (Fin (n + 1))\nU V : SimplexCategoryᵒᵖ\ni : U ⟶ V\n⊢ {f | Finset.image ⇑(Hom.toOrderHom (objEquiv f)) ⊤ ⊆ S} ⊆\n ⇑(ConcreteCategory.hom (Δ[n].map i)) ⁻¹' {f | Finset.image ⇑(Hom.toOrderHom (objEquiv f)) ⊤ ⊆ S}",
"ppTerm": "?m.35",
"assigned": true,
"usedConstants": [
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex | {
"line": 275,
"column": 20
} | {
"line": 275,
"column": 25
} | {
"line": 277,
"column": 0
} | [
{
"pp": "n : ℕ\nS : Finset (Fin (n + 1))\nU V : SimplexCategoryᵒᵖ\ni : U ⟶ V\n⊢ {f | Finset.image ⇑(Hom.toOrderHom (objEquiv f)) ⊤ ⊆ S} ⊆\n ⇑(ConcreteCategory.hom (Δ[n].map i)) ⁻¹' {f | Finset.image ⇑(Hom.toOrderHom (objEquiv f)) ⊤ ⊆ S}",
"ppTerm": "?m.35",
"assigned": true,
"usedConstants": [
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex | {
"line": 275,
"column": 20
} | {
"line": 275,
"column": 25
} | {
"line": 277,
"column": 0
} | [
{
"pp": "n : ℕ\nS : Finset (Fin (n + 1))\nU V : SimplexCategoryᵒᵖ\ni : U ⟶ V\n⊢ {f | Finset.image ⇑(Hom.toOrderHom (objEquiv f)) ⊤ ⊆ S} ⊆\n ⇑(ConcreteCategory.hom (Δ[n].map i)) ⁻¹' {f | Finset.image ⇑(Hom.toOrderHom (objEquiv f)) ⊤ ⊆ S}",
"ppTerm": "?m.35",
"assigned": true,
"usedConstants": [
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex | {
"line": 286,
"column": 2
} | {
"line": 286,
"column": 7
} | {
"line": 288,
"column": 0
} | [
{
"pp": "n : ℕ\nS₁ S₂ : Finset (Fin (n + 1))\n⊢ face S₁ ⊓ face S₂ = face (S₁ ⊓ S₂)",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"Opposite",
"Equiv.instEquivLike",
"SimplexCategory.instFintypeToTypeOrderHomFinHAddNatLenOfNat",
"Fin... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex | {
"line": 286,
"column": 2
} | {
"line": 286,
"column": 7
} | {
"line": 288,
"column": 0
} | [
{
"pp": "n : ℕ\nS₁ S₂ : Finset (Fin (n + 1))\n⊢ face S₁ ⊓ face S₂ = face (S₁ ⊓ S₂)",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"Opposite",
"Equiv.instEquivLike",
"SimplexCategory.instFintypeToTypeOrderHomFinHAddNatLenOfNat",
"Fin... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex | {
"line": 286,
"column": 2
} | {
"line": 286,
"column": 7
} | {
"line": 288,
"column": 0
} | [
{
"pp": "n : ℕ\nS₁ S₂ : Finset (Fin (n + 1))\n⊢ face S₁ ⊓ face S₂ = face (S₁ ⊓ S₂)",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"Opposite",
"Equiv.instEquivLike",
"SimplexCategory.instFintypeToTypeOrderHomFinHAddNatLenOfNat",
"Fin... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex | {
"line": 344,
"column": 33
} | {
"line": 344,
"column": 38
} | {
"line": 344,
"column": 38
} | [
{
"pp": "n : ℕ\nS : Finset (Fin (n + 1))\ni : Fin (n + 1)\n⊢ i ∈ S → obj₀Equiv.symm i ∈ (face S).obj (op ⦋0⦌)",
"ppTerm": "?m.35",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"SSet.stdSimplex.const",
"SSet.stdSimplex.obj₀Equiv_symm_apply",
"Opposite",
"Equiv.instEqui... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex | {
"line": 344,
"column": 33
} | {
"line": 344,
"column": 38
} | {
"line": 344,
"column": 38
} | [
{
"pp": "n : ℕ\nS : Finset (Fin (n + 1))\ni : Fin (n + 1)\n⊢ i ∈ S → obj₀Equiv.symm i ∈ (face S).obj (op ⦋0⦌)",
"ppTerm": "?m.35",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"SSet.stdSimplex.const",
"SSet.stdSimplex.obj₀Equiv_symm_apply",
"Opposite",
"Equiv.instEqui... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex | {
"line": 344,
"column": 33
} | {
"line": 344,
"column": 38
} | {
"line": 344,
"column": 38
} | [
{
"pp": "n : ℕ\nS : Finset (Fin (n + 1))\ni : Fin (n + 1)\n⊢ i ∈ S → obj₀Equiv.symm i ∈ (face S).obj (op ⦋0⦌)",
"ppTerm": "?m.35",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"SSet.stdSimplex.const",
"SSet.stdSimplex.obj₀Equiv_symm_apply",
"Opposite",
"Equiv.instEqui... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex | {
"line": 379,
"column": 73
} | {
"line": 379,
"column": 78
} | {
"line": 379,
"column": 78
} | [
{
"pp": "n : ℕ\nS : Finset (Fin (n + 1))\nm : ℕ\ne : Fin (m + 1) ≃o ↥S\nj : SimplexCategory\nf : j ⟶ ⦋m⦌\nx✝ : Fin (⦋n⦌.len + 1)\n⊢ x✝ ∈\n Finset.image\n ⇑(Hom.toOrderHom\n (objEquiv\n (objMk\n ((OrderHom.Subtype.val fun x ↦ x ∈ S).comp (e.toOrderEmbedding.toOr... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex | {
"line": 379,
"column": 73
} | {
"line": 379,
"column": 78
} | {
"line": 379,
"column": 78
} | [
{
"pp": "n : ℕ\nS : Finset (Fin (n + 1))\nm : ℕ\ne : Fin (m + 1) ≃o ↥S\nj : SimplexCategory\nf : j ⟶ ⦋m⦌\nx✝ : Fin (⦋n⦌.len + 1)\n⊢ x✝ ∈\n Finset.image\n ⇑(Hom.toOrderHom\n (objEquiv\n (objMk\n ((OrderHom.Subtype.val fun x ↦ x ∈ S).comp (e.toOrderEmbedding.toOr... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex | {
"line": 379,
"column": 73
} | {
"line": 379,
"column": 78
} | {
"line": 379,
"column": 78
} | [
{
"pp": "n : ℕ\nS : Finset (Fin (n + 1))\nm : ℕ\ne : Fin (m + 1) ≃o ↥S\nj : SimplexCategory\nf : j ⟶ ⦋m⦌\nx✝ : Fin (⦋n⦌.len + 1)\n⊢ x✝ ∈\n Finset.image\n ⇑(Hom.toOrderHom\n (objEquiv\n (objMk\n ((OrderHom.Subtype.val fun x ↦ x ∈ S).comp (e.toOrderEmbedding.toOr... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex | {
"line": 394,
"column": 26
} | {
"line": 394,
"column": 31
} | {
"line": 396,
"column": 0
} | [
{
"pp": "n : ℕ\nS : Finset (Fin (n + 1))\nm : ℕ\ne : Fin (m + 1) ≃o ↥S\nX✝ X'✝ : SimplexCategory\nf : X✝ ⟶ X'✝\ng : X'✝ ⟶ ⦋m⦌\n⊢ {\n toFun := fun f ↦\n ⟨objMk ((OrderHom.Subtype.val fun x ↦ x ∈ S).comp (e.toOrderEmbedding.toOrderHom.comp (Hom.toOrderHom f))),\n ⋯⟩,\n invFun := ... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex | {
"line": 394,
"column": 26
} | {
"line": 394,
"column": 31
} | {
"line": 396,
"column": 0
} | [
{
"pp": "n : ℕ\nS : Finset (Fin (n + 1))\nm : ℕ\ne : Fin (m + 1) ≃o ↥S\nX✝ X'✝ : SimplexCategory\nf : X✝ ⟶ X'✝\ng : X'✝ ⟶ ⦋m⦌\n⊢ {\n toFun := fun f ↦\n ⟨objMk ((OrderHom.Subtype.val fun x ↦ x ∈ S).comp (e.toOrderEmbedding.toOrderHom.comp (Hom.toOrderHom f))),\n ⋯⟩,\n invFun := ... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex | {
"line": 394,
"column": 26
} | {
"line": 394,
"column": 31
} | {
"line": 396,
"column": 0
} | [
{
"pp": "n : ℕ\nS : Finset (Fin (n + 1))\nm : ℕ\ne : Fin (m + 1) ≃o ↥S\nX✝ X'✝ : SimplexCategory\nf : X✝ ⟶ X'✝\ng : X'✝ ⟶ ⦋m⦌\n⊢ {\n toFun := fun f ↦\n ⟨objMk ((OrderHom.Subtype.val fun x ↦ x ∈ S).comp (e.toOrderEmbedding.toOrderHom.comp (Hom.toOrderHom f))),\n ⋯⟩,\n invFun := ... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex | {
"line": 423,
"column": 23
} | {
"line": 423,
"column": 28
} | {
"line": 423,
"column": 29
} | [
{
"pp": "n : ℕ\nd : SimplexCategoryᵒᵖ\nx✝ : unop d ⟶ ⦋n⦌\n⊢ (fun f ↦ Hom.mk (ULift.orderIso.{u, 0}.toOrderEmbedding.toOrderHom.comp (Functor.toOrderHom f)))\n ((fun f ↦ ⋯.functor) x✝) =\n x✝",
"ppTerm": "?m.100",
"assigned": true,
"usedConstants": [
"CategoryTheory.Functor.toOrderHom_c... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex | {
"line": 423,
"column": 23
} | {
"line": 423,
"column": 28
} | {
"line": 423,
"column": 29
} | [
{
"pp": "n : ℕ\nd : SimplexCategoryᵒᵖ\nx✝ : unop d ⟶ ⦋n⦌\n⊢ (fun f ↦ Hom.mk (ULift.orderIso.{u, 0}.toOrderEmbedding.toOrderHom.comp (Functor.toOrderHom f)))\n ((fun f ↦ ⋯.functor) x✝) =\n x✝",
"ppTerm": "?m.100",
"assigned": true,
"usedConstants": [
"CategoryTheory.Functor.toOrderHom_c... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex | {
"line": 423,
"column": 23
} | {
"line": 423,
"column": 28
} | {
"line": 423,
"column": 29
} | [
{
"pp": "n : ℕ\nd : SimplexCategoryᵒᵖ\nx✝ : unop d ⟶ ⦋n⦌\n⊢ (fun f ↦ Hom.mk (ULift.orderIso.{u, 0}.toOrderEmbedding.toOrderHom.comp (Functor.toOrderHom f)))\n ((fun f ↦ ⋯.functor) x✝) =\n x✝",
"ppTerm": "?m.100",
"assigned": true,
"usedConstants": [
"CategoryTheory.Functor.toOrderHom_c... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex | {
"line": 464,
"column": 19
} | {
"line": 464,
"column": 24
} | {
"line": 466,
"column": 0
} | [
{
"pp": "n d : ℕ\nx✝ : ↑(Δ[n].nonDegenerate d)\n⊢ (fun s ↦ ⟨objEquiv.symm (Hom.mk s.toOrderHom), ⋯⟩) ((fun s ↦ OrderEmbedding.ofStrictMono ⇑↑s ⋯) x✝) = x✝",
"ppTerm": "?m.65",
"assigned": true,
"usedConstants": [
"SSet.stdSimplex.mem_nonDegenerate_iff_strictMono",
"Eq.mpr",
"SSet.s... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex | {
"line": 464,
"column": 19
} | {
"line": 464,
"column": 24
} | {
"line": 466,
"column": 0
} | [
{
"pp": "n d : ℕ\nx✝ : ↑(Δ[n].nonDegenerate d)\n⊢ (fun s ↦ ⟨objEquiv.symm (Hom.mk s.toOrderHom), ⋯⟩) ((fun s ↦ OrderEmbedding.ofStrictMono ⇑↑s ⋯) x✝) = x✝",
"ppTerm": "?m.65",
"assigned": true,
"usedConstants": [
"SSet.stdSimplex.mem_nonDegenerate_iff_strictMono",
"Eq.mpr",
"SSet.s... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex | {
"line": 464,
"column": 19
} | {
"line": 464,
"column": 24
} | {
"line": 466,
"column": 0
} | [
{
"pp": "n d : ℕ\nx✝ : ↑(Δ[n].nonDegenerate d)\n⊢ (fun s ↦ ⟨objEquiv.symm (Hom.mk s.toOrderHom), ⋯⟩) ((fun s ↦ OrderEmbedding.ofStrictMono ⇑↑s ⋯) x✝) = x✝",
"ppTerm": "?m.65",
"assigned": true,
"usedConstants": [
"SSet.stdSimplex.mem_nonDegenerate_iff_strictMono",
"Eq.mpr",
"SSet.s... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex | {
"line": 511,
"column": 46
} | {
"line": 511,
"column": 76
} | {
"line": 511,
"column": 76
} | [
{
"pp": "n : ℕ\ni j : Fin (n + 2)\nh : i < j\nx✝¹ x✝ : Fin n\nhk :\n (fun k ↦ ⟨j.succAbove ((i.castPred ⋯).succAbove k), ⋯⟩) x✝¹ =\n (fun k ↦ ⟨j.succAbove ((i.castPred ⋯).succAbove k), ⋯⟩) x✝\n⊢ (RelEmbedding.trans (i.castPred ⋯).succAboveOrderEmb j.succAboveOrderEmb) x✝¹ =\n (RelEmbedding.trans (i.castP... | [] | by rwa [Subtype.ext_iff] at hk | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex | {
"line": 516,
"column": 6
} | {
"line": 516,
"column": 29
} | {
"line": 517,
"column": 2
} | [
{
"pp": "case refine_3\nn : ℕ\ni j : Fin (n + 2)\nh : i < j\nx✝ : ↥{i, j}ᶜ\nm : Fin (n + 1)\nhl : j.succAbove m ∈ {i, j}ᶜ\nk : Fin n\nhk : (i.castPred ⋯).succAbove k = m\n⊢ ∃ a, (fun k ↦ ⟨j.succAbove ((i.castPred ⋯).succAbove k), ⋯⟩) a = ⟨j.succAbove m, hl⟩",
"ppTerm": "?refine_3",
"assigned": true,
... | [] | exact ⟨k, by simp [hk]⟩ | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex | {
"line": 646,
"column": 6
} | {
"line": 646,
"column": 11
} | {
"line": 646,
"column": 11
} | [
{
"pp": "case right\nn d : ℕ\nx : ↑(Δ[n].nonDegenerate d)\nj : Fin (n + 1)\nhj✝ : j ∈ ↑(nonDegenerateEquiv' x)\nhj : ∃ i, ↑x i = j\n⊢ ∃ a, (fun i ↦ ⟨↑x i, ⋯⟩) a = ⟨j, hj✝⟩",
"ppTerm": "?right",
"assigned": true,
"usedConstants": [
"Opposite",
"Equiv.instEquivLike",
"SimplexCategory... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.GradedObject.Trifunctor | {
"line": 165,
"column": 2
} | {
"line": 165,
"column": 56
} | {
"line": 166,
"column": 2
} | [
{
"pp": "C₁ : Type u_1\nC₂ : Type u_2\nC₃ : Type u_3\nC₄ : Type u_4\ninst✝⁵ : Category.{v_1, u_1} C₁\ninst✝⁴ : Category.{v_2, u_2} C₂\ninst✝³ : Category.{v_3, u_3} C₃\ninst✝² : Category.{v_4, u_4} C₄\nF : C₁ ⥤ C₂ ⥤ C₃ ⥤ C₄\nI₁ : Type u_7\nI₂ : Type u_8\nI₃ : Type u_9\nJ : Type u_10\np : I₁ × I₂ × I₃ → J\nX₁ Y₁ ... | [
"C₁ : Type u_1\nC₂ : Type u_2\nC₃ : Type u_3\nC₄ : Type u_4\ninst✝⁵ : Category.{v_1, u_1} C₁\ninst✝⁴ : Category.{v_2, u_2} C₂\ninst✝³ : Category.{v_3, u_3} C₃\ninst✝² : Category.{v_4, u_4} C₄\nF : C₁ ⥤ C₂ ⥤ C₃ ⥤ C₄\nI₁ : Type u_7\nI₂ : Type u_8\nI₃ : Type u_9\nJ : Type u_10\np : I₁ × I₂ × I₃ → J\nX₁ Y₁ : GradedObje... | dsimp only [ιMapTrifunctorMapObj, mapTrifunctorMapMap] | Lean.Elab.Tactic.evalDSimp | Lean.Parser.Tactic.dsimp |
Mathlib.Algebra.Homology.Augment | {
"line": 292,
"column": 50
} | {
"line": 292,
"column": 55
} | {
"line": 292,
"column": 56
} | [
{
"pp": "case zero.zero\nV : Type u\ninst✝¹ : Category.{v, u} V\ninst✝ : HasZeroMorphisms V\nC : CochainComplex V ℕ\n⊢ (ComplexShape.up ℕ).Rel 0 0 →\n (match 0 with\n | 0 => 𝟙 (((truncate.obj C).augment (C.d 0 1) ⋯).X 0)\n | n.succ => 𝟙 (((truncate.obj C).augment (C.d 0 1) ⋯).X (n + 1))) ≫\n ... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Algebra.Homology.Augment | {
"line": 292,
"column": 50
} | {
"line": 292,
"column": 55
} | {
"line": 292,
"column": 56
} | [
{
"pp": "case zero.succ\nV : Type u\ninst✝¹ : Category.{v, u} V\ninst✝ : HasZeroMorphisms V\nC : CochainComplex V ℕ\nn✝ : ℕ\n⊢ (ComplexShape.up ℕ).Rel (n✝ + 1) 0 →\n (match n✝ + 1 with\n | 0 => 𝟙 (((truncate.obj C).augment (C.d 0 1) ⋯).X 0)\n | n.succ => 𝟙 (((truncate.obj C).augment (C.d 0 1)... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Algebra.Homology.Augment | {
"line": 292,
"column": 50
} | {
"line": 292,
"column": 55
} | {
"line": 292,
"column": 56
} | [
{
"pp": "case succ.zero.zero\nV : Type u\ninst✝¹ : Category.{v, u} V\ninst✝ : HasZeroMorphisms V\nC : CochainComplex V ℕ\n⊢ (ComplexShape.up ℕ).Rel 0 (0 + 1) →\n (match 0 with\n | 0 => 𝟙 (((truncate.obj C).augment (C.d 0 1) ⋯).X 0)\n | n.succ => 𝟙 (((truncate.obj C).augment (C.d 0 1) ⋯).X (n ... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Algebra.Homology.Augment | {
"line": 292,
"column": 50
} | {
"line": 292,
"column": 55
} | {
"line": 292,
"column": 56
} | [
{
"pp": "case succ.zero.succ\nV : Type u\ninst✝¹ : Category.{v, u} V\ninst✝ : HasZeroMorphisms V\nC : CochainComplex V ℕ\nn✝ : ℕ\n⊢ (ComplexShape.up ℕ).Rel (n✝ + 1) (0 + 1) →\n (match n✝ + 1 with\n | 0 => 𝟙 (((truncate.obj C).augment (C.d 0 1) ⋯).X 0)\n | n.succ => 𝟙 (((truncate.obj C).augmen... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Algebra.Homology.Augment | {
"line": 292,
"column": 50
} | {
"line": 292,
"column": 55
} | {
"line": 292,
"column": 56
} | [
{
"pp": "case succ.succ.zero\nV : Type u\ninst✝¹ : Category.{v, u} V\ninst✝ : HasZeroMorphisms V\nC : CochainComplex V ℕ\nj : ℕ\n⊢ (ComplexShape.up ℕ).Rel 0 (j + 1 + 1) →\n (match 0 with\n | 0 => 𝟙 (((truncate.obj C).augment (C.d 0 1) ⋯).X 0)\n | n.succ => 𝟙 (((truncate.obj C).augment (C.d 0 ... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Algebra.Homology.Augment | {
"line": 292,
"column": 50
} | {
"line": 292,
"column": 55
} | {
"line": 292,
"column": 56
} | [
{
"pp": "case succ.succ.succ\nV : Type u\ninst✝¹ : Category.{v, u} V\ninst✝ : HasZeroMorphisms V\nC : CochainComplex V ℕ\nj n✝ : ℕ\n⊢ (ComplexShape.up ℕ).Rel (n✝ + 1) (j + 1 + 1) →\n (match n✝ + 1 with\n | 0 => 𝟙 (((truncate.obj C).augment (C.d 0 1) ⋯).X 0)\n | n.succ => 𝟙 (((truncate.obj C).... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex | {
"line": 771,
"column": 4
} | {
"line": 771,
"column": 9
} | {
"line": 771,
"column": 9
} | [
{
"pp": "n : SimplexCategory\nd d' : SimplexCategoryᵒᵖ\nf : d ⟶ d'\ng : (stdSimplex.obj n).op.obj d\ni : Fin (d'.1.len + 1)\n⊢ ((opObjEquiv g) ((ConcreteCategory.hom f.unop) i.rev.rev).rev).rev =\n ((ConcreteCategory.hom ((stdSimplex.obj n).map f)) (stdSimplex.opObjEquiv g)) i",
"ppTerm": "?m.82",
"a... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex | {
"line": 831,
"column": 2
} | {
"line": 831,
"column": 7
} | {
"line": 833,
"column": 0
} | [
{
"pp": "X : SSet\nn : ℕ\nx : X _⦋n⦌\nm : SimplexCategoryᵒᵖ\nu : op ⦋n⦌ ⟶ m\n⊢ ↑({ toFun := fun x_1 ↦ ⟨(ConcreteCategory.hom (X.map u)) ↑x_1, ⋯⟩ } ⟨yonedaEquiv.toFun (yonedaEquiv.invFun x), ⋯⟩) =\n ↑⟨(ConcreteCategory.hom (X.map u)) (yonedaEquiv.toFun (yonedaEquiv.invFun x)), ⋯⟩",
"ppTerm": "?m.72",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Algebra.Homology.Augment | {
"line": 296,
"column": 62
} | {
"line": 296,
"column": 67
} | {
"line": 296,
"column": 68
} | [
{
"pp": "case zero.zero\nV : Type u\ninst✝¹ : Category.{v, u} V\ninst✝ : HasZeroMorphisms V\nC : CochainComplex V ℕ\n⊢ (ComplexShape.up ℕ).Rel 0 0 →\n (match 0 with\n | 0 => 𝟙 (C.X 0)\n | n.succ => 𝟙 (C.X (n + 1))) ≫\n ((truncate.obj C).augment (C.d 0 1) ⋯).d 0 0 =\n C.d 0 0 ≫\n ... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Algebra.Homology.Augment | {
"line": 296,
"column": 62
} | {
"line": 296,
"column": 67
} | {
"line": 296,
"column": 68
} | [
{
"pp": "case zero.succ\nV : Type u\ninst✝¹ : Category.{v, u} V\ninst✝ : HasZeroMorphisms V\nC : CochainComplex V ℕ\ni : ℕ\n⊢ (ComplexShape.up ℕ).Rel (i + 1) 0 →\n (match i + 1 with\n | 0 => 𝟙 (C.X 0)\n | n.succ => 𝟙 (C.X (n + 1))) ≫\n ((truncate.obj C).augment (C.d 0 1) ⋯).d (i + 1) 0... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Algebra.Homology.Augment | {
"line": 296,
"column": 62
} | {
"line": 296,
"column": 67
} | {
"line": 296,
"column": 68
} | [
{
"pp": "case succ.zero.zero\nV : Type u\ninst✝¹ : Category.{v, u} V\ninst✝ : HasZeroMorphisms V\nC : CochainComplex V ℕ\n⊢ (ComplexShape.up ℕ).Rel 0 (0 + 1) →\n (match 0 with\n | 0 => 𝟙 (C.X 0)\n | n.succ => 𝟙 (C.X (n + 1))) ≫\n ((truncate.obj C).augment (C.d 0 1) ⋯).d 0 (0 + 1) =\n ... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Algebra.Homology.Augment | {
"line": 296,
"column": 62
} | {
"line": 296,
"column": 67
} | {
"line": 296,
"column": 68
} | [
{
"pp": "case succ.zero.succ\nV : Type u\ninst✝¹ : Category.{v, u} V\ninst✝ : HasZeroMorphisms V\nC : CochainComplex V ℕ\ni : ℕ\n⊢ (ComplexShape.up ℕ).Rel (i + 1) (0 + 1) →\n (match i + 1 with\n | 0 => 𝟙 (C.X 0)\n | n.succ => 𝟙 (C.X (n + 1))) ≫\n ((truncate.obj C).augment (C.d 0 1) ⋯).... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Algebra.Homology.Augment | {
"line": 296,
"column": 62
} | {
"line": 296,
"column": 67
} | {
"line": 296,
"column": 68
} | [
{
"pp": "case succ.succ.zero\nV : Type u\ninst✝¹ : Category.{v, u} V\ninst✝ : HasZeroMorphisms V\nC : CochainComplex V ℕ\nj : ℕ\n⊢ (ComplexShape.up ℕ).Rel 0 (j + 1 + 1) →\n (match 0 with\n | 0 => 𝟙 (C.X 0)\n | n.succ => 𝟙 (C.X (n + 1))) ≫\n ((truncate.obj C).augment (C.d 0 1) ⋯).d 0 (j... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Algebra.Homology.Augment | {
"line": 296,
"column": 62
} | {
"line": 296,
"column": 67
} | {
"line": 296,
"column": 68
} | [
{
"pp": "case succ.succ.succ\nV : Type u\ninst✝¹ : Category.{v, u} V\ninst✝ : HasZeroMorphisms V\nC : CochainComplex V ℕ\nj i : ℕ\n⊢ (ComplexShape.up ℕ).Rel (i + 1) (j + 1 + 1) →\n (match i + 1 with\n | 0 => 𝟙 (C.X 0)\n | n.succ => 𝟙 (C.X (n + 1))) ≫\n ((truncate.obj C).augment (C.d 0 ... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Algebra.Homology.ComplexShapeSigns | {
"line": 311,
"column": 19
} | {
"line": 311,
"column": 24
} | {
"line": 312,
"column": 4
} | [
{
"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✝ : TotalComplexShape c₁ c₂ c₁₂\nthis : TotalComplexShape c₂ c₁ c₁₂ := sym... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Algebra.Homology.ComplexShapeSigns | {
"line": 311,
"column": 19
} | {
"line": 311,
"column": 24
} | {
"line": 312,
"column": 4
} | [
{
"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✝ : TotalComplexShape c₁ c₂ c₁₂\nthis : TotalComplexShape c₂ c₁ c₁₂ := sym... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Homology.ComplexShapeSigns | {
"line": 311,
"column": 19
} | {
"line": 311,
"column": 24
} | {
"line": 312,
"column": 4
} | [
{
"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✝ : TotalComplexShape c₁ c₂ c₁₂\nthis : TotalComplexShape c₂ c₁ c₁₂ := sym... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Homology.ComplexShapeSigns | {
"line": 312,
"column": 19
} | {
"line": 312,
"column": 24
} | {
"line": 312,
"column": 25
} | [
{
"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✝ : TotalComplexShape c₁ c₂ c₁₂\nthis : TotalComplexShape c₂ c₁ c₁₂ := sym... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Algebra.Homology.ComplexShapeSigns | {
"line": 312,
"column": 19
} | {
"line": 312,
"column": 24
} | {
"line": 312,
"column": 25
} | [
{
"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✝ : TotalComplexShape c₁ c₂ c₁₂\nthis : TotalComplexShape c₂ c₁ c₁₂ := sym... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Homology.ComplexShapeSigns | {
"line": 312,
"column": 19
} | {
"line": 312,
"column": 24
} | {
"line": 312,
"column": 25
} | [
{
"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✝ : TotalComplexShape c₁ c₂ c₁₂\nthis : TotalComplexShape c₂ c₁ c₁₂ := sym... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.ExtraDegeneracy | {
"line": 372,
"column": 4
} | {
"line": 376,
"column": 10
} | {
"line": 377,
"column": 2
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\nf : Arrow C\ninst✝ : ∀ (n : ℕ), HasWidePullback f.right (fun x ↦ f.left) fun x ↦ f.hom\nS : SplitEpi f.hom\n⊢ ExtraDegeneracy.s f S 0 ≫ f.augmentedCechNerve.left.δ 1 =\n f.augmentedCechNerve.hom.app (op ⦋0⦌) ≫ S.section_ ≫ WidePullback.lift f.hom (fun x ... | [] | dsimp [SimplicialObject.δ, SimplexCategory.δ]
ext j
· fin_cases j
simp
· simp | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Homology.TotalComplex | {
"line": 192,
"column": 8
} | {
"line": 192,
"column": 64
} | {
"line": 193,
"column": 8
} | [
{
"pp": "case pos\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... | [
"case pos\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.HasTotal c₁₂\n... | by_cases h₄ : c₁.Rel (c₁.next i₁) (c₁.next (c₁.next i₁)) | «_aux_Init_ByCases___macroRules_tacticBy_cases_:__2» | «tacticBy_cases_:_» |
Mathlib.AlgebraicTopology.ExtraDegeneracy | {
"line": 372,
"column": 4
} | {
"line": 376,
"column": 10
} | {
"line": 377,
"column": 2
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\nf : Arrow C\ninst✝ : ∀ (n : ℕ), HasWidePullback f.right (fun x ↦ f.left) fun x ↦ f.hom\nS : SplitEpi f.hom\n⊢ ExtraDegeneracy.s f S 0 ≫ f.augmentedCechNerve.left.δ 1 =\n f.augmentedCechNerve.hom.app (op ⦋0⦌) ≫ S.section_ ≫ WidePullback.lift f.hom (fun x ... | [] | dsimp [SimplicialObject.δ, SimplexCategory.δ]
ext j
· fin_cases j
simp
· simp | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.GradedObject.Associator | {
"line": 73,
"column": 6
} | {
"line": 73,
"column": 46
} | {
"line": 73,
"column": 47
} | [
{
"pp": "C₁ : Type u_1\nC₂ : Type u_2\nC₁₂ : Type u_3\nC₂₃ : Type u_4\nC₃ : Type u_5\nC₄ : Type u_6\ninst✝⁹ : Category.{v_1, u_1} C₁\ninst✝⁸ : Category.{v_2, u_2} C₂\ninst✝⁷ : Category.{v_3, u_5} C₃\ninst✝⁶ : Category.{v_4, u_6} C₄\ninst✝⁵ : Category.{v_5, u_3} C₁₂\ninst✝⁴ : Category.{v_6, u_4} C₂₃\nF₁₂ : C₁ ⥤ ... | [
"C₁ : Type u_1\nC₂ : Type u_2\nC₁₂ : Type u_3\nC₂₃ : Type u_4\nC₃ : Type u_5\nC₄ : Type u_6\ninst✝⁹ : Category.{v_1, u_1} C₁\ninst✝⁸ : Category.{v_2, u_2} C₂\ninst✝⁷ : Category.{v_3, u_5} C₃\ninst✝⁶ : Category.{v_4, u_6} C₄\ninst✝⁵ : Category.{v_5, u_3} C₁₂\ninst✝⁴ : Category.{v_6, u_4} C₂₃\nF₁₂ : C₁ ⥤ C₂ ⥤ C₁₂\nG ... | ι_mapBifunctorComp₁₂MapObjIso_inv_assoc, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Homology.TotalComplex | {
"line": 429,
"column": 2
} | {
"line": 429,
"column": 78
} | {
"line": 431,
"column": 0
} | [
{
"pp": "C : Type u_1\ninst✝⁶ : Category.{v_1, u_1} C\ninst✝⁵ : Preadditive C\nI₁ : Type u_2\nI₂ : Type u_3\nI₁₂ : Type u_4\nc₁ : ComplexShape I₁\nc₂ : ComplexShape I₂\nK L M : HomologicalComplex₂ C c₁ c₂\nφ : K ⟶ L\nψ : L ⟶ M\nc₁₂ : ComplexShape I₁₂\ninst✝⁴ : TotalComplexShape c₁ c₂ c₁₂\ninst✝³ : DecidableEq I... | [] | exact GradedObject.mapMap_comp (toGradedObjectMap φ) (toGradedObjectMap ψ) _ | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Algebra.Homology.TotalComplexShift | {
"line": 233,
"column": 6
} | {
"line": 233,
"column": 23
} | {
"line": 233,
"column": 24
} | [
{
"pp": "C : Type u_1\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : Preadditive C\nK L : HomologicalComplex₂ C (up ℤ) (up ℤ)\nf : K ⟶ L\nx : ℤ\ninst✝¹ : K.HasTotal (up ℤ)\ninst✝ : L.HasTotal (up ℤ)\nn i₁ i₂ : ℤ\nh : i₁ + i₂ = n\n⊢ ((shiftFunctor₁ C x).obj K).ιTotal (up ℤ) i₁ i₂ n h ≫\n (total.map ((shiftFuncto... | [
"C : Type u_1\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : Preadditive C\nK L : HomologicalComplex₂ C (up ℤ) (up ℤ)\nf : K ⟶ L\nx : ℤ\ninst✝¹ : K.HasTotal (up ℤ)\ninst✝ : L.HasTotal (up ℤ)\nn i₁ i₂ : ℤ\nh : i₁ + i₂ = n\n⊢ (((shiftFunctor₁ C x).map f).f i₁).f i₂ ≫\n ((shiftFunctor₁ C x).obj L).ιTotal (up ℤ) i₁ i₂ ... | ιTotal_map_assoc, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Homology.TotalComplexShift | {
"line": 236,
"column": 42
} | {
"line": 236,
"column": 52
} | {
"line": 236,
"column": 52
} | [
{
"pp": "C : Type u_1\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : Preadditive C\nK L : HomologicalComplex₂ C (up ℤ) (up ℤ)\nf : K ⟶ L\nx : ℤ\ninst✝¹ : K.HasTotal (up ℤ)\ninst✝ : L.HasTotal (up ℤ)\nn i₁ i₂ : ℤ\nh : i₁ + i₂ = n\n⊢ (f.f (i₁ + x)).f i₂ ≫ L.ιTotal (up ℤ) (i₁ + x) i₂ (n + x) ⋯ =\n K.ιTotal (up ℤ) (i... | [
"C : Type u_1\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : Preadditive C\nK L : HomologicalComplex₂ C (up ℤ) (up ℤ)\nf : K ⟶ L\nx : ℤ\ninst✝¹ : K.HasTotal (up ℤ)\ninst✝ : L.HasTotal (up ℤ)\nn i₁ i₂ : ℤ\nh : i₁ + i₂ = n\n⊢ (f.f (i₁ + x)).f i₂ ≫ L.ιTotal (up ℤ) (i₁ + x) i₂ (n + x) ⋯ =\n (f.f (i₁ + x)).f i₂ ≫ L.ιTotal... | ιTotal_map | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Homology.TotalComplexShift | {
"line": 357,
"column": 6
} | {
"line": 357,
"column": 23
} | {
"line": 357,
"column": 24
} | [
{
"pp": "C : Type u_1\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : Preadditive C\nK L : HomologicalComplex₂ C (up ℤ) (up ℤ)\nf : K ⟶ L\ny : ℤ\ninst✝¹ : K.HasTotal (up ℤ)\ninst✝ : L.HasTotal (up ℤ)\nn i₁ i₂ : ℤ\nh : i₁ + i₂ = n\n⊢ ((shiftFunctor₂ C y).obj K).ιTotal (up ℤ) i₁ i₂ n h ≫\n (total.map ((shiftFuncto... | [
"C : Type u_1\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : Preadditive C\nK L : HomologicalComplex₂ C (up ℤ) (up ℤ)\nf : K ⟶ L\ny : ℤ\ninst✝¹ : K.HasTotal (up ℤ)\ninst✝ : L.HasTotal (up ℤ)\nn i₁ i₂ : ℤ\nh : i₁ + i₂ = n\n⊢ (((shiftFunctor₂ C y).map f).f i₁).f i₂ ≫\n ((shiftFunctor₂ C y).obj L).ιTotal (up ℤ) i₁ i₂ ... | ιTotal_map_assoc, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Homology.TotalComplexShift | {
"line": 361,
"column": 28
} | {
"line": 361,
"column": 38
} | {
"line": 361,
"column": 38
} | [
{
"pp": "C : Type u_1\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : Preadditive C\nK L : HomologicalComplex₂ C (up ℤ) (up ℤ)\nf : K ⟶ L\ny : ℤ\ninst✝¹ : K.HasTotal (up ℤ)\ninst✝ : L.HasTotal (up ℤ)\nn i₁ i₂ : ℤ\nh : i₁ + i₂ = n\n⊢ (i₁ * y).negOnePow • (f.f i₁).f (i₂ + y) ≫ L.ιTotal (up ℤ) i₁ (i₂ + y) (n + y) ⋯ =\n ... | [
"C : Type u_1\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : Preadditive C\nK L : HomologicalComplex₂ C (up ℤ) (up ℤ)\nf : K ⟶ L\ny : ℤ\ninst✝¹ : K.HasTotal (up ℤ)\ninst✝ : L.HasTotal (up ℤ)\nn i₁ i₂ : ℤ\nh : i₁ + i₂ = n\n⊢ (i₁ * y).negOnePow • (f.f i₁).f (i₂ + y) ≫ L.ιTotal (up ℤ) i₁ (i₂ + y) (n + y) ⋯ =\n (i₁ * y).... | ιTotal_map | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Homology.TotalComplexShift | {
"line": 384,
"column": 4
} | {
"line": 384,
"column": 21
} | {
"line": 384,
"column": 22
} | [
{
"pp": "C : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Preadditive C\nK : HomologicalComplex₂ C (up ℤ) (up ℤ)\nx y : ℤ\ninst✝ : K.HasTotal (up ℤ)\nn n₁ n₂ : ℤ\nh : n₁ + n₂ = n\n⊢ (((shiftFunctor₂ C y).obj K).shiftFunctor₁XXIso n₁ x (n₁ + x) ⋯ n₂).hom ≫\n ((shiftFunctor₂ C y).obj K).ιTotal (up ℤ) (... | [
"C : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Preadditive C\nK : HomologicalComplex₂ C (up ℤ) (up ℤ)\nx y : ℤ\ninst✝ : K.HasTotal (up ℤ)\nn n₁ n₂ : ℤ\nh : n₁ + n₂ = n\n⊢ (((shiftFunctor₂ C y).obj K).shiftFunctor₁XXIso n₁ x (n₁ + x) ⋯ n₂).hom ≫\n ((shiftFunctor₂ C y).obj K).ιTotal (up ℤ) (n₁ + x) n₂ (... | ιTotal_map_assoc, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Homology.HomotopyCategory.HomComplexCohomology | {
"line": 51,
"column": 30
} | {
"line": 51,
"column": 35
} | {
"line": 51,
"column": 35
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : Preadditive C\nR : Type u_1\ninst✝¹ : Ring R\ninst✝ : Linear R C\nK L : CochainComplex C ℤ\nn m✝ p : ℤ\nα₁ α₂ : Cocycle K L n\nm : ℤ\nhm : m + 1 = n\nβ₁ : Cochain K L m\nhβ₁ : δ m n β₁ = ↑α₁\nhm' : m + 1 = n\nβ₂ : Cochain K L m\nhβ₂ : δ m n β₂ = ↑α₂\n⊢ δ... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Algebra.Homology.HomotopyCategory.HomComplexCohomology | {
"line": 51,
"column": 30
} | {
"line": 51,
"column": 35
} | {
"line": 51,
"column": 35
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : Preadditive C\nR : Type u_1\ninst✝¹ : Ring R\ninst✝ : Linear R C\nK L : CochainComplex C ℤ\nn m✝ p : ℤ\nα₁ α₂ : Cocycle K L n\nm : ℤ\nhm : m + 1 = n\nβ₁ : Cochain K L m\nhβ₁ : δ m n β₁ = ↑α₁\nhm' : m + 1 = n\nβ₂ : Cochain K L m\nhβ₂ : δ m n β₂ = ↑α₂\n⊢ δ... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Homology.HomotopyCategory.HomComplexCohomology | {
"line": 51,
"column": 30
} | {
"line": 51,
"column": 35
} | {
"line": 51,
"column": 35
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : Preadditive C\nR : Type u_1\ninst✝¹ : Ring R\ninst✝ : Linear R C\nK L : CochainComplex C ℤ\nn m✝ p : ℤ\nα₁ α₂ : Cocycle K L n\nm : ℤ\nhm : m + 1 = n\nβ₁ : Cochain K L m\nhβ₁ : δ m n β₁ = ↑α₁\nhm' : m + 1 = n\nβ₂ : Cochain K L m\nhβ₂ : δ m n β₂ = ↑α₂\n⊢ δ... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Homology.HomotopyCategory.HomComplexCohomology | {
"line": 54,
"column": 25
} | {
"line": 54,
"column": 30
} | {
"line": 54,
"column": 30
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : Preadditive C\nR : Type u_1\ninst✝¹ : Ring R\ninst✝ : Linear R C\nK L : CochainComplex C ℤ\nn m✝ p : ℤ\nα : Cocycle K L n\nm : ℤ\nhm : m + 1 = n\nβ : Cochain K L m\nhβ : δ m n β = ↑α\n⊢ δ m n (-β) = ↑(-α)",
"ppTerm": "?m.171",
"assigned": true,
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Algebra.Homology.HomotopyCategory.HomComplexCohomology | {
"line": 54,
"column": 25
} | {
"line": 54,
"column": 30
} | {
"line": 54,
"column": 30
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : Preadditive C\nR : Type u_1\ninst✝¹ : Ring R\ninst✝ : Linear R C\nK L : CochainComplex C ℤ\nn m✝ p : ℤ\nα : Cocycle K L n\nm : ℤ\nhm : m + 1 = n\nβ : Cochain K L m\nhβ : δ m n β = ↑α\n⊢ δ m n (-β) = ↑(-α)",
"ppTerm": "?m.171",
"assigned": true,
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Homology.HomotopyCategory.HomComplexCohomology | {
"line": 54,
"column": 25
} | {
"line": 54,
"column": 30
} | {
"line": 54,
"column": 30
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : Preadditive C\nR : Type u_1\ninst✝¹ : Ring R\ninst✝ : Linear R C\nK L : CochainComplex C ℤ\nn m✝ p : ℤ\nα : Cocycle K L n\nm : ℤ\nhm : m + 1 = n\nβ : Cochain K L m\nhβ : δ m n β = ↑α\n⊢ δ m n (-β) = ↑(-α)",
"ppTerm": "?m.171",
"assigned": true,
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Homology.Embedding.ExtendHomotopy | {
"line": 87,
"column": 6
} | {
"line": 94,
"column": 40
} | {
"line": 95,
"column": 4
} | [
{
"pp": "case pos.e_a\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.extendXIs... | [] | · by_cases hi : c.Rel (c.prev i) i
· have hi' : c'.Rel (e.f (c.prev i)) (e.f i) := by rwa [e.rel_iff]
simp [prevD_eq _ hi, prevD_eq _ hi', extend.hom_eq _ _ rfl rfl,
extend_d_eq _ _ rfl rfl]
· rw [prevD_eq_zero _ _ hi]
by_cases hi' : c'.Rel (c'.prev (e.f i)) (e.f i)
... | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Algebra.Homology.HomotopyCategory.KInjective | {
"line": 79,
"column": 8
} | {
"line": 79,
"column": 77
} | {
"line": 79,
"column": 78
} | [
{
"pp": "case refine_1\nC : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Abelian C\nL : CochainComplex C ℤ\nx✝ : L.IsKInjective\nK : HomologicalComplex C (ComplexShape.up ℤ)\nhK : K.Acyclic\nf : K ⟶ L\n⊢ (HomotopyCategory.quotient C (ComplexShape.up ℤ)).map f = 0",
"ppTerm": "?refine_1",
"assigned"... | [
"case refine_1\nC : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Abelian C\nL : CochainComplex C ℤ\nx✝ : L.IsKInjective\nK : HomologicalComplex C (ComplexShape.up ℤ)\nhK : K.Acyclic\nf : K ⟶ L\n⊢ (HomotopyCategory.quotient C (ComplexShape.up ℤ)).map 0 = 0"
] | HomotopyCategory.eq_of_homotopy f 0 (IsKInjective.homotopyZero f hK), | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.CategoryTheory.Triangulated.TStructure.Basic | {
"line": 128,
"column": 4
} | {
"line": 128,
"column": 35
} | {
"line": 129,
"column": 2
} | [
{
"pp": "C : Type u_1\ninst✝⁵ : Category.{v_1, u_1} C\ninst✝⁴ : Preadditive C\ninst✝³ : HasZeroObject C\ninst✝² : HasShift C ℤ\ninst✝¹ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝ : Pretriangulated C\nt : TStructure C\nH : ℕ → Prop := fun a ↦ ∀ (n : ℤ), t.le n ≤ t.le (n + ↑a)\nH_zero : H 0\nH_one : H 1\na b ... | [] | exact (ha n).trans (hb (n + a)) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.CategoryTheory.Triangulated.TStructure.Basic | {
"line": 130,
"column": 2
} | {
"line": 130,
"column": 18
} | {
"line": 131,
"column": 2
} | [
{
"pp": "C : Type u_1\ninst✝⁵ : Category.{v_1, u_1} C\ninst✝⁴ : Preadditive C\ninst✝³ : HasZeroObject C\ninst✝² : HasShift C ℤ\ninst✝¹ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝ : Pretriangulated C\nt : TStructure C\nH : ℕ → Prop := fun a ↦ ∀ (n : ℤ), t.le n ≤ t.le (n + ↑a)\nH_zero : H 0\nH_one : H 1\nH_ad... | [] | induction a with | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | null |
Mathlib.Algebra.Homology.Embedding.ExtendHomotopy | {
"line": 205,
"column": 4
} | {
"line": 205,
"column": 54
} | {
"line": 207,
"column": 0
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\ninst✝³ : e.IsRelIff\nC : Type u_3\ninst✝² : Category.{v_1, u_3} C\ninst✝¹ : HasZeroObject C\ninst✝ : Preadditive C\nK L : HomologicalComplex C c\nφ : K ⟶ L\n⊢ ∃ a, (e.extendHomotopyFunctor C).map a = (HomotopyCat... | [] | exact ⟨(HomotopyCategory.quotient _ _).map φ, rfl⟩ | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.CategoryTheory.Triangulated.TStructure.Basic | {
"line": 153,
"column": 2
} | {
"line": 153,
"column": 18
} | {
"line": 154,
"column": 2
} | [
{
"pp": "C : Type u_1\ninst✝⁵ : Category.{v_1, u_1} C\ninst✝⁴ : Preadditive C\ninst✝³ : HasZeroObject C\ninst✝² : HasShift C ℤ\ninst✝¹ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝ : Pretriangulated C\nt : TStructure C\nH : ℕ → Prop := fun a ↦ ∀ (n : ℤ), t.ge (n + ↑a) ≤ t.ge n\nH_zero : H 0\nH_one : H 1\nH_ad... | [] | induction a with | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | null |
Mathlib.CategoryTheory.Triangulated.TStructure.Basic | {
"line": 246,
"column": 4
} | {
"line": 246,
"column": 22
} | {
"line": 247,
"column": 2
} | [
{
"pp": "case hX\nC : Type u_1\ninst✝⁷ : Category.{v_1, u_1} C\ninst✝⁶ : Preadditive C\ninst✝⁵ : HasZeroObject C\ninst✝⁴ : HasShift C ℤ\ninst✝³ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝² : Pretriangulated C\nt : TStructure C\nX Y : C\nf : X ⟶ Y\nn₀ n₁ : ℤ\nh : n₀ < n₁\ninst✝¹ : t.IsLE X n₀\ninst✝ : t.IsGE... | [] | apply t.le_of_isLE | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.CategoryTheory.Triangulated.TStructure.Basic | {
"line": 246,
"column": 4
} | {
"line": 246,
"column": 22
} | {
"line": 247,
"column": 2
} | [
{
"pp": "case hX\nC : Type u_1\ninst✝⁷ : Category.{v_1, u_1} C\ninst✝⁶ : Preadditive C\ninst✝⁵ : HasZeroObject C\ninst✝⁴ : HasShift C ℤ\ninst✝³ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝² : Pretriangulated C\nt : TStructure C\nX Y : C\nf : X ⟶ Y\nn₀ n₁ : ℤ\nh : n₀ < n₁\ninst✝¹ : t.IsLE X n₀\ninst✝ : t.IsGE... | [] | apply t.le_of_isLE | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Triangulated.TStructure.Basic | {
"line": 246,
"column": 4
} | {
"line": 246,
"column": 22
} | {
"line": 247,
"column": 2
} | [
{
"pp": "case hX\nC : Type u_1\ninst✝⁷ : Category.{v_1, u_1} C\ninst✝⁶ : Preadditive C\ninst✝⁵ : HasZeroObject C\ninst✝⁴ : HasShift C ℤ\ninst✝³ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝² : Pretriangulated C\nt : TStructure C\nX Y : C\nf : X ⟶ Y\nn₀ n₁ : ℤ\nh : n₀ < n₁\ninst✝¹ : t.IsLE X n₀\ninst✝ : t.IsGE... | [] | apply t.le_of_isLE | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.LiftingProperties.Limits | {
"line": 72,
"column": 4
} | {
"line": 72,
"column": 53
} | {
"line": 74,
"column": 0
} | [
{
"pp": "C : Type u_1\ninst✝³ : Category.{v_1, u_1} C\nX✝ Y✝ Z W : C\nf✝ : X✝ ⟶ Y✝\ns : X✝ ⟶ Z\ng : Z ⟶ W\nt✝ : Y✝ ⟶ W\nJ : Type u_2\nA B : J → C\ninst✝² : HasProduct A\ninst✝¹ : HasProduct B\nf : (j : J) → A j ⟶ B j\nX Y : C\np : X ⟶ Y\ninst✝ : ∀ (j : J), HasLiftingProperty p (f j)\nt : X ⟶ ∏ᶜ A\nb : Y ⟶ ∏ᶜ B\... | [] | exact ⟨⟨{ l := Pi.lift (fun j ↦ (sq' j).lift) }⟩⟩ | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.AlgebraicTopology.ModelCategory.LeftHomotopy | {
"line": 173,
"column": 8
} | {
"line": 173,
"column": 13
} | {
"line": 173,
"column": 13
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nX Y : C\ninst✝ : ModelCategory C\nP : Cylinder X\nf g : X ⟶ Y\nh : P.LeftHomotopy f g\nd : (cofibrations C).MapFactorizationData (trivialFibrations C) P.i :=\n (cofibrations C).factorizationData (trivialFibrations C) P.i\n⊢ { I := d.Z, i₀ := coprod.inl ≫ d.i, i₁... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.Localization.OfQuotient | {
"line": 63,
"column": 6
} | {
"line": 63,
"column": 33
} | {
"line": 64,
"column": 4
} | [
{
"pp": "case h_obj\nC : Type u_1\nD : Type u_2\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Category.{v_2, u_2} D\nr : HomRel C\nW : MorphismProperty C\nhW : W.IsInvertedBy (functor r)\nhr : ∀ ⦃X Y : C⦄ (f₀ f₁ : X ⟶ Y), r f₀ f₁ → ∃ P x, W P.π\nE : Type u_3\ninst✝ : Category.{v_3, u_3} E\nF₁ F₂ : Quotient r ⥤ E\nh... | [] | exact Functor.congr_obj h X | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.AlgebraicTopology.ModelCategory.RightHomotopy | {
"line": 176,
"column": 8
} | {
"line": 176,
"column": 13
} | {
"line": 176,
"column": 13
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nX Y : C\ninst✝ : ModelCategory C\nP : PathObject Y\nf g : X ⟶ Y\nh : P.RightHomotopy f g\nd : (trivialCofibrations C).MapFactorizationData (fibrations C) P.p :=\n (trivialCofibrations C).factorizationData (fibrations C) P.p\n⊢ { P := d.Z, p₀ := d.p ≫ prod.fst, p... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.Triangulated.Opposite.Triangulated | {
"line": 40,
"column": 46
} | {
"line": 40,
"column": 51
} | {
"line": 40,
"column": 51
} | [
{
"pp": "C : Type u_1\ninst✝⁶ : Category.{v_1, u_1} C\ninst✝⁵ : HasShift C ℤ\ninst✝⁴ : HasZeroObject C\ninst✝³ : Preadditive C\ninst✝² : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝¹ : Pretriangulated C\ninst✝ : IsTriangulated C\nX₁ X₂ X₃ Z₁₂ Z₂₃ Z₁₃ : Cᵒᵖ\nu₁₂ : X₁ ⟶ X₂\nu₂₃ : X₂ ⟶ X₃\nu₁₃ : X₁ ⟶ X₃\ncomm : u... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.Triangulated.Opposite.Triangulated | {
"line": 40,
"column": 46
} | {
"line": 40,
"column": 51
} | {
"line": 40,
"column": 51
} | [
{
"pp": "C : Type u_1\ninst✝⁶ : Category.{v_1, u_1} C\ninst✝⁵ : HasShift C ℤ\ninst✝⁴ : HasZeroObject C\ninst✝³ : Preadditive C\ninst✝² : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝¹ : Pretriangulated C\ninst✝ : IsTriangulated C\nX₁ X₂ X₃ Z₁₂ Z₂₃ Z₁₃ : Cᵒᵖ\nu₁₂ : X₁ ⟶ X₂\nu₂₃ : X₂ ⟶ X₃\nu₁₃ : X₁ ⟶ X₃\ncomm : u... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Triangulated.Opposite.Triangulated | {
"line": 40,
"column": 46
} | {
"line": 40,
"column": 51
} | {
"line": 40,
"column": 51
} | [
{
"pp": "C : Type u_1\ninst✝⁶ : Category.{v_1, u_1} C\ninst✝⁵ : HasShift C ℤ\ninst✝⁴ : HasZeroObject C\ninst✝³ : Preadditive C\ninst✝² : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝¹ : Pretriangulated C\ninst✝ : IsTriangulated C\nX₁ X₂ X₃ Z₁₂ Z₂₃ Z₁₃ : Cᵒᵖ\nu₁₂ : X₁ ⟶ X₂\nu₂₃ : X₂ ⟶ X₃\nu₁₃ : X₁ ⟶ X₃\ncomm : u... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Triangulated.Opposite.Triangulated | {
"line": 44,
"column": 6
} | {
"line": 44,
"column": 18
} | {
"line": 45,
"column": 6
} | [
{
"pp": "case refine_1\nC : Type u_1\ninst✝⁶ : Category.{v_1, u_1} C\ninst✝⁵ : HasShift C ℤ\ninst✝⁴ : HasZeroObject C\ninst✝³ : Preadditive C\ninst✝² : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝¹ : Pretriangulated C\ninst✝ : IsTriangulated C\nX₁ X₂ X₃ Z₁₂ Z₂₃ Z₁₃ : Cᵒᵖ\nu₁₂ : X₁ ⟶ X₂\nu₂₃ : X₂ ⟶ X₃\nu₁₃ : X₁... | [
"case refine_1\nC : Type u_1\ninst✝⁶ : Category.{v_1, u_1} C\ninst✝⁵ : HasShift C ℤ\ninst✝⁴ : HasZeroObject C\ninst✝³ : Preadditive C\ninst✝² : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝¹ : Pretriangulated C\ninst✝ : IsTriangulated C\nX₁ X₂ X₃ Z₁₂ Z₂₃ Z₁₃ : Cᵒᵖ\nu₁₂ : X₁ ⟶ X₂\nu₂₃ : X₂ ⟶ X₃\nu₁₃ : X₁ ⟶ X₃\ncomm ... | dsimp at eq₃ | Lean.Elab.Tactic.evalDSimp | Lean.Parser.Tactic.dsimp |
Mathlib.CategoryTheory.Triangulated.Opposite.Triangulated | {
"line": 55,
"column": 6
} | {
"line": 60,
"column": 93
} | {
"line": 62,
"column": 0
} | [
{
"pp": "case refine_3\nC : Type u_1\ninst✝⁶ : Category.{v_1, u_1} C\ninst✝⁵ : HasShift C ℤ\ninst✝⁴ : HasZeroObject C\ninst✝³ : Preadditive C\ninst✝² : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝¹ : Pretriangulated C\ninst✝ : IsTriangulated C\nX₁ X₂ X₃ Z₁₂ Z₂₃ Z₁₃ : Cᵒᵖ\nu₁₂ : X₁ ⟶ X₂\nu₂₃ : X₂ ⟶ X₃\nu₁₃ : X₁... | [] | have := op_distinguished _ o.mem
dsimp at this
convert! this using 2
rw [Category.assoc, Functor.map_comp, Functor.map_comp,
← opShiftFunctorEquivalence_counitIso_hom_app_shift,
← opShiftFunctorEquivalence_counitIso_inv_naturality_assoc, Iso.inv_hom_id_app_assoc] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Triangulated.Opposite.Triangulated | {
"line": 55,
"column": 6
} | {
"line": 60,
"column": 93
} | {
"line": 62,
"column": 0
} | [
{
"pp": "case refine_3\nC : Type u_1\ninst✝⁶ : Category.{v_1, u_1} C\ninst✝⁵ : HasShift C ℤ\ninst✝⁴ : HasZeroObject C\ninst✝³ : Preadditive C\ninst✝² : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝¹ : Pretriangulated C\ninst✝ : IsTriangulated C\nX₁ X₂ X₃ Z₁₂ Z₂₃ Z₁₃ : Cᵒᵖ\nu₁₂ : X₁ ⟶ X₂\nu₂₃ : X₂ ⟶ X₃\nu₁₃ : X₁... | [] | have := op_distinguished _ o.mem
dsimp at this
convert! this using 2
rw [Category.assoc, Functor.map_comp, Functor.map_comp,
← opShiftFunctorEquivalence_counitIso_hom_app_shift,
← opShiftFunctorEquivalence_counitIso_inv_naturality_assoc, Iso.inv_hom_id_app_assoc] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Triangulated.LocalizingSubcategory | {
"line": 107,
"column": 2
} | {
"line": 115,
"column": 32
} | {
"line": 116,
"column": 2
} | [
{
"pp": "case refine_1\nC : Type u_1\ninst✝⁸ : Category.{v_1, u_1} C\nA B : 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 : A.IsTriangulated\ninst✝¹ : B.IsTriangulated\ninst✝ : B.IsCl... | [
"case refine_2\nC : Type u_1\ninst✝⁸ : Category.{v_1, u_1} C\nA B : 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 : A.IsTriangulated\ninst✝¹ : B.IsTriangulated\ninst✝ : B.IsClosedUnderIso... | · rw [ObjectProperty.trW_iff'] at hs
obtain ⟨W, a, b, hT, hW⟩ := hs
obtain ⟨W', c, d, h₁, h₂, fac⟩ := IsVerdierRightLocalizing.fac a hW hX
obtain ⟨U, hU, e, f, hT'⟩ := A.distinguished_cocone_triangle d h₁ hX
obtain ⟨g, hg, _⟩ := Pretriangulated.complete_distinguished_triangle_morphism _ _ hT hT'
c... | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.CategoryTheory.Abelian.EpiWithInjectiveKernel | {
"line": 91,
"column": 20
} | {
"line": 91,
"column": 53
} | {
"line": 92,
"column": 10
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Abelian C\nX Y Z : C\ng₁ : X ⟶ Y\ng₂ : Y ⟶ Z\nI₁ : C\nw✝¹ : Injective I₁\nf₁ : I₁ ⟶ X\nw₁ : f₁ ≫ g₁ = 0\nσ₁ : { X₁ := I₁, X₂ := X, X₃ := Y, f := f₁, g := g₁, zero := w₁ }.Splitting\nI₂ : C\nw✝ : Injective I₂\nf₂ : I₂ ⟶ Y\nw₂ : f₂ ≫ g₂ = 0\nσ₂ : { X₁... | [] | simp [reassoc_of% σ₁.s_g, σ₂.s_g] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.CategoryTheory.Abelian.EpiWithInjectiveKernel | {
"line": 91,
"column": 20
} | {
"line": 91,
"column": 53
} | {
"line": 92,
"column": 10
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Abelian C\nX Y Z : C\ng₁ : X ⟶ Y\ng₂ : Y ⟶ Z\nI₁ : C\nw✝¹ : Injective I₁\nf₁ : I₁ ⟶ X\nw₁ : f₁ ≫ g₁ = 0\nσ₁ : { X₁ := I₁, X₂ := X, X₃ := Y, f := f₁, g := g₁, zero := w₁ }.Splitting\nI₂ : C\nw✝ : Injective I₂\nf₂ : I₂ ⟶ Y\nw₂ : f₂ ≫ g₂ = 0\nσ₂ : { X₁... | [] | simp [reassoc_of% σ₁.s_g, σ₂.s_g] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
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