module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.AlgebraicTopology.ModelCategory.Instances | {
"line": 375,
"column": 2
} | {
"line": 375,
"column": 40
} | {
"line": 375,
"column": 41
} | [
{
"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⊢ WeakEquivalence h.p",
"ppTerm": "?m.27",
"assigned": t... | [
"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⊢ weakEquivalences C h.p"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.ModelCategory.Instances | {
"line": 384,
"column": 2
} | {
"line": 384,
"column": 36
} | {
"line": 384,
"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 : (trivialCofibrations C).MapFactorizationData (fibrations 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 : (trivialCofibrations C).MapFactorizationData (fibrations C) f\n⊢ cofibrations C h.i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.ModelCategory.Instances | {
"line": 387,
"column": 2
} | {
"line": 387,
"column": 40
} | {
"line": 387,
"column": 41
} | [
{
"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 : (trivialCofibrations C).MapFactorizationData (fibrations C) f\n⊢ WeakEquivalence h.i",
"ppTerm": "?m.27",
"assigned": t... | [
"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 : (trivialCofibrations C).MapFactorizationData (fibrations C) f\n⊢ weakEquivalences C h.i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.ModelCategory.Instances | {
"line": 390,
"column": 2
} | {
"line": 390,
"column": 34
} | {
"line": 390,
"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 : (trivialCofibrations C).MapFactorizationData (fibrations 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 : (trivialCofibrations C).MapFactorizationData (fibrations C) f\n⊢ fibrations C h.p"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.ModelCategory.PathObject | {
"line": 256,
"column": 20
} | {
"line": 256,
"column": 31
} | {
"line": 256,
"column": 32
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : ModelCategory C\nA : C\nP : PathObject A\nh : (trivialCofibrations C).MapFactorizationData (fibrations C) (diag A)\n⊢ Fibration (ofFactorizationData h).p",
"ppTerm": "?m.36",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Category... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : ModelCategory C\nA : C\nP : PathObject A\nh : (trivialCofibrations C).MapFactorizationData (fibrations C) (diag A)\n⊢ Fibration h.p"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.ModelCategory.Cylinder | {
"line": 251,
"column": 22
} | {
"line": 251,
"column": 33
} | {
"line": 251,
"column": 34
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : ModelCategory C\nA : C\nP : Cylinder A\nh : (cofibrations C).MapFactorizationData (trivialFibrations C) (codiag A)\n⊢ Cofibration (ofFactorizationData h).i",
"ppTerm": "?m.36",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Catego... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : ModelCategory C\nA : C\nP : Cylinder A\nh : (cofibrations C).MapFactorizationData (trivialFibrations C) (codiag A)\n⊢ Cofibration h.i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.ModelCategory.PathObject | {
"line": 298,
"column": 6
} | {
"line": 298,
"column": 21
} | {
"line": 298,
"column": 22
} | [
{
"pp": "C : Type u\ninst✝⁴ : Category.{v, u} C\ninst✝³ : ModelCategory C\nA : C\nP✝ : PathObject A\ninst✝² : IsFibrant A\nP P' : PathObject A\ninst✝¹ : P.IsGood\ninst✝ : P'.IsGood\nψ : (P.trans P').P ⟶ P.P ⨯ A := prod.lift (pullback.fst P.p₁ P'.p₀) (pullback.snd P.p₁ P'.p₀ ≫ P'.p₁)\nfac : ψ ≫ prod.map P.p₁ (𝟙... | [
"C : Type u\ninst✝⁴ : Category.{v, u} C\ninst✝³ : ModelCategory C\nA : C\nP✝ : PathObject A\ninst✝² : IsFibrant A\nP P' : PathObject A\ninst✝¹ : P.IsGood\ninst✝ : P'.IsGood\nψ : (P.trans P').P ⟶ P.P ⨯ A := prod.lift (pullback.fst P.p₁ P'.p₀) (pullback.snd P.p₁ P'.p₀ ≫ P'.p₁)\nfac : ψ ≫ prod.map P.p₁ (𝟙 A) = pullba... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.ModelCategory.Cylinder | {
"line": 295,
"column": 6
} | {
"line": 295,
"column": 21
} | {
"line": 295,
"column": 22
} | [
{
"pp": "C : Type u\ninst✝⁴ : Category.{v, u} C\ninst✝³ : ModelCategory C\nA : C\nP✝ : Cylinder A\ninst✝² : IsCofibrant A\nP P' : Cylinder A\ninst✝¹ : P.IsGood\ninst✝ : P'.IsGood\nψ : P.I ⨿ A ⟶ (P.trans P').I := coprod.desc (pushout.inl P.i₁ P'.i₀) (P'.i₁ ≫ pushout.inr P.i₁ P'.i₀)\nfac : coprod.map P.i₁ (𝟙 A) ... | [
"C : Type u\ninst✝⁴ : Category.{v, u} C\ninst✝³ : ModelCategory C\nA : C\nP✝ : Cylinder A\ninst✝² : IsCofibrant A\nP P' : Cylinder A\ninst✝¹ : P.IsGood\ninst✝ : P'.IsGood\nψ : P.I ⨿ A ⟶ (P.trans P').I := coprod.desc (pushout.inl P.i₁ P'.i₀) (P'.i₁ ≫ pushout.inr P.i₁ P'.i₀)\nfac : coprod.map P.i₁ (𝟙 A) ≫ ψ = P'.i ≫... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.HomotopyCategory.Plus | {
"line": 45,
"column": 4
} | {
"line": 45,
"column": 15
} | {
"line": 45,
"column": 16
} | [
{
"pp": "case refine_1\nC : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Preadditive C\ninst✝ : HasBinaryBiproducts C\nK : CochainComplex C ℤ\nn : ℤ\nhn : K.IsStrictlyGE n\ni : ℤ\nhi : autoParam (i < n - 1) isStrictlyGE_iff._auto_1\n⊢ IsZero ((eval C (ComplexShape.up ℤ) i).obj K ⊞ (eval C (ComplexShape.up... | [
"case refine_1\nC : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Preadditive C\ninst✝ : HasBinaryBiproducts C\nK : CochainComplex C ℤ\nn : ℤ\nhn : K.IsStrictlyGE n\ni : ℤ\nhi : autoParam (i < n - 1) isStrictlyGE_iff._auto_1\n⊢ IsZero (K.X i)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.HomotopyCategory.Plus | {
"line": 127,
"column": 6
} | {
"line": 130,
"column": 28
} | {
"line": 131,
"column": 4
} | [
{
"pp": "case refine_1\nC : Type u_1\nD : Type u_2\ninst✝⁷ : Category.{v_1, u_1} C\ninst✝⁶ : Category.{v_2, u_2} D\ninst✝⁵ : Preadditive C\ninst✝⁴ : Preadditive D\nA : Type u_3\ninst✝³ : Category.{v_3, u_3} A\ninst✝² : Abelian A\ninst✝¹ : HasZeroObject C\ninst✝ : HasBinaryBiproducts C\nT : Triangle (HomotopyCat... | [] | dsimp
simp only [plus_quotient_obj_iff]
exact ⟨min (n₁ - 1) n₂, CochainComplex.isStrictlyGE_mappingCone f n₁ n₂ _
(by simp) (by simp)⟩ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Homology.HomotopyCategory.Plus | {
"line": 127,
"column": 6
} | {
"line": 130,
"column": 28
} | {
"line": 131,
"column": 4
} | [
{
"pp": "case refine_1\nC : Type u_1\nD : Type u_2\ninst✝⁷ : Category.{v_1, u_1} C\ninst✝⁶ : Category.{v_2, u_2} D\ninst✝⁵ : Preadditive C\ninst✝⁴ : Preadditive D\nA : Type u_3\ninst✝³ : Category.{v_3, u_3} A\ninst✝² : Abelian A\ninst✝¹ : HasZeroObject C\ninst✝ : HasBinaryBiproducts C\nT : Triangle (HomotopyCat... | [] | dsimp
simp only [plus_quotient_obj_iff]
exact ⟨min (n₁ - 1) n₂, CochainComplex.isStrictlyGE_mappingCone f n₁ n₂ _
(by simp) (by simp)⟩ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Homology.BifunctorAssociator | {
"line": 705,
"column": 8
} | {
"line": 706,
"column": 15
} | {
"line": 706,
"column": 16
} | [
{
"pp": "case e_a.h\nC₁ : Type u_1\nC₂ : Type u_2\nC₂₃ : Type u_4\nC₃ : Type u_5\nC₄ : Type u_6\ninst✝²³ : Category.{v_1, u_1} C₁\ninst✝²² : Category.{v_2, u_2} C₂\ninst✝²¹ : Category.{v_3, u_5} C₃\ninst✝²⁰ : Category.{v_4, u_6} C₄\ninst✝¹⁹ : Category.{v_6, u_4} C₂₃\ninst✝¹⁸ : HasZeroMorphisms C₁\ninst✝¹⁷ : Has... | [
"case e_a.h\nC₁ : Type u_1\nC₂ : Type u_2\nC₂₃ : Type u_4\nC₃ : Type u_5\nC₄ : Type u_6\ninst✝²³ : Category.{v_1, u_1} C₁\ninst✝²² : Category.{v_2, u_2} C₂\ninst✝²¹ : Category.{v_3, u_5} C₃\ninst✝²⁰ : Category.{v_4, u_6} C₄\ninst✝¹⁹ : Category.{v_6, u_4} C₂₃\ninst✝¹⁸ : HasZeroMorphisms C₁\ninst✝¹⁷ : HasZeroMorphism... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.BifunctorAssociator | {
"line": 710,
"column": 8
} | {
"line": 711,
"column": 15
} | {
"line": 711,
"column": 16
} | [
{
"pp": "case e_a.h\nC₁ : Type u_1\nC₂ : Type u_2\nC₂₃ : Type u_4\nC₃ : Type u_5\nC₄ : Type u_6\ninst✝²³ : Category.{v_1, u_1} C₁\ninst✝²² : Category.{v_2, u_2} C₂\ninst✝²¹ : Category.{v_3, u_5} C₃\ninst✝²⁰ : Category.{v_4, u_6} C₄\ninst✝¹⁹ : Category.{v_6, u_4} C₂₃\ninst✝¹⁸ : HasZeroMorphisms C₁\ninst✝¹⁷ : Has... | [
"case e_a.h\nC₁ : Type u_1\nC₂ : Type u_2\nC₂₃ : Type u_4\nC₃ : Type u_5\nC₄ : Type u_6\ninst✝²³ : Category.{v_1, u_1} C₁\ninst✝²² : Category.{v_2, u_2} C₂\ninst✝²¹ : Category.{v_3, u_5} C₃\ninst✝²⁰ : Category.{v_4, u_6} C₄\ninst✝¹⁹ : Category.{v_6, u_4} C₂₃\ninst✝¹⁸ : HasZeroMorphisms C₁\ninst✝¹⁷ : HasZeroMorphism... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.DerivedCategory.Plus | {
"line": 70,
"column": 2
} | {
"line": 70,
"column": 17
} | {
"line": 71,
"column": 2
} | [
{
"pp": "C : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Abelian C\ninst✝ : HasDerivedCategory C\n⊢ Qh.CommShift ℤ",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"HomotopyCategory.Plus",
"CategoryTheory.Abelian.toPreadditive",
"instCategoryDerivedCategory",
... | [
"C : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Abelian C\ninst✝ : HasDerivedCategory C\n⊢ (t.plus.lift (HomotopyCategory.Plus.ι C ⋙ DerivedCategory.Qh) ⋯).CommShift ℤ"
] | dsimp only [Qh] | Lean.Elab.Tactic.evalDSimp | Lean.Parser.Tactic.dsimp |
Mathlib.Algebra.Homology.DerivedCategory.Plus | {
"line": 75,
"column": 2
} | {
"line": 75,
"column": 17
} | {
"line": 76,
"column": 2
} | [
{
"pp": "C : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Abelian C\ninst✝ : HasDerivedCategory C\n⊢ Qh.IsTriangulated",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Int.instAddCommGroup",
"CategoryTheory.Functor.IsTriangulated",
"HomotopyCategory.Plus",
"Ca... | [
"C : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Abelian C\ninst✝ : HasDerivedCategory C\n⊢ (t.plus.lift (HomotopyCategory.Plus.ι C ⋙ DerivedCategory.Qh) ⋯).IsTriangulated"
] | dsimp only [Qh] | Lean.Elab.Tactic.evalDSimp | Lean.Parser.Tactic.dsimp |
Mathlib.CategoryTheory.Triangulated.TStructure.TruncLTGE | {
"line": 267,
"column": 52
} | {
"line": 267,
"column": 67
} | {
"line": 267,
"column": 67
} | [
{
"pp": "C : Type u\ninst✝⁵ : Category.{v, u} 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\nX : C\na b : ℤ\nhn : a ≤ b + 1\n⊢ t.IsLE ((t.truncLT a).obj X) (a - 1)",
"ppTerm": "?m.77",
... | [
"C : Type u\ninst✝⁵ : Category.{v, u} 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\nX : C\na b : ℤ\nhn : a ≤ b + 1\n⊢ t.IsLE (TruncAux.triangle t a X).obj₁ (a - 1)"
] | dsimp [truncLT] | Lean.Elab.Tactic.evalDSimp | Lean.Parser.Tactic.dsimp |
Mathlib.CategoryTheory.Triangulated.TStructure.TruncLTGE | {
"line": 479,
"column": 4
} | {
"line": 479,
"column": 21
} | {
"line": 479,
"column": 22
} | [
{
"pp": "C : Type u\ninst✝⁵ : Category.{v, u} 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\nn₀ : ℤ\nX : C\nx✝ : t.IsLE X n₀\ne : contractibleTriangle X ≅ (t.triangleLTGE (n₀ + 1)).obj X\nh... | [
"C : Type u\ninst✝⁵ : Category.{v, u} 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\nn₀ : ℤ\nX : C\nx✝ : t.IsLE X n₀\ne : contractibleTriangle X ≅ (t.triangleLTGE (n₀ + 1)).obj X\nhe : e.hom.ho... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.TStructure.TruncLTGE | {
"line": 509,
"column": 49
} | {
"line": 511,
"column": 79
} | {
"line": 513,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝⁵ : Category.{v, u} 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\nn : ℤ\nX : C\n⊢ t.IsGE X n ↔ IsZero ((t.truncLT n).obj X)",
"ppTerm": "?m.46",
"assigned... | [] | by
rw [t.isGE_iff_isIso_truncGEπ_app n X]
exact (Triangle.isZero₁_iff_isIso₂ _ (t.triangleLTGE_distinguished n X)).symm | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Triangulated.TStructure.TruncLTGE | {
"line": 619,
"column": 35
} | {
"line": 619,
"column": 46
} | {
"line": 619,
"column": 47
} | [
{
"pp": "C : Type u\ninst✝⁵ : Category.{v, u} 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\nn₀ n₁ : ℤ\nh : n₀ + 1 = n₁\nX : C\nhX : ∀ (Y : C) (f : X ⟶ Y), t.IsGE Y n₁ → f = 0\n⊢ (t.truncGE... | [
"C : Type u\ninst✝⁵ : Category.{v, u} 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\nn₀ n₁ : ℤ\nh : n₀ + 1 = n₁\nX : C\nhX : ∀ (Y : C) (f : X ⟶ Y), t.IsGE Y n₁ → f = 0\n⊢ (t.truncGEπ n₁).app X ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.TStructure.TruncLTGE | {
"line": 625,
"column": 33
} | {
"line": 625,
"column": 44
} | {
"line": 625,
"column": 45
} | [
{
"pp": "C : Type u\ninst✝⁵ : Category.{v, u} 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\nn₀ n₁ : ℤ\nh : n₀ + 1 = n₁\nX : C\nhX : ∀ (Y : C) (f : Y ⟶ X), t.IsLE Y n₀ → f = 0\n⊢ 𝟙 ((t.tru... | [
"C : Type u\ninst✝⁵ : Category.{v, u} 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\nn₀ n₁ : ℤ\nh : n₀ + 1 = n₁\nX : C\nhX : ∀ (Y : C) (f : Y ⟶ X), t.IsLE Y n₀ → f = 0\n⊢ (t.truncLTι n₁).app X ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.ModelCategory.Lifting | {
"line": 171,
"column": 8
} | {
"line": 171,
"column": 29
} | {
"line": 171,
"column": 30
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Abelian C\nA B X Y : CochainComplex C ℤ\nt : A ⟶ X\ni : A ⟶ B\np : X ⟶ Y\nb : B ⟶ Y\nsq : CommSq t i p b\nhsq : (n : ℤ) → ⋯.LiftStruct\nQ : CochainComplex C ℤ\nπ : B ⟶ Q\nhπ : i ≫ π = 0\nhQ : IsColimit (CokernelCofork.ofπ π hπ)\nK : CochainComplex C... | [
"C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Abelian C\nA B X Y : CochainComplex C ℤ\nt : A ⟶ X\ni : A ⟶ B\np : X ⟶ Y\nb : B ⟶ Y\nsq : CommSq t i p b\nhsq : (n : ℤ) → ⋯.LiftStruct\nQ : CochainComplex C ℤ\nπ : B ⟶ Q\nhπ : i ≫ π = 0\nhQ : IsColimit (CokernelCofork.ofπ π hπ)\nK : CochainComplex C ℤ\nι : K ⟶ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.ModelCategory.Homotopy | {
"line": 85,
"column": 6
} | {
"line": 85,
"column": 49
} | {
"line": 86,
"column": 6
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : ModelCategory C\nX Y Z : C\nf g : X ⟶ Y\ninst✝¹ : IsFibrant Y\nh✝ : RightHomotopyRel f g\nQ : Cylinder X\ninst✝ : Q.IsGood\nP : PathObject Y := ⋯.choose\nh : ⋯.choose.RightHomotopy f g\nh' : ⋯.choose.IsGood\nsq : CommSq (coprod.desc (f ≫ P.ι) h.h) Q.i P.... | [
"C : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : ModelCategory C\nX Y Z : C\nf g : X ⟶ Y\ninst✝¹ : IsFibrant Y\nh✝ : RightHomotopyRel f g\nQ : Cylinder X\ninst✝ : Q.IsGood\nP : PathObject Y := ⋯.choose\nh : ⋯.choose.RightHomotopy f g\nh' : ⋯.choose.IsGood\nsq : CommSq (coprod.desc (f ≫ P.ι) h.h) Q.i P.p₀ (Q.π ≫ f)... | rw [Q.inl_i_assoc, coprod.inl_desc] at this | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.CategoryTheory.Triangulated.TStructure.TruncLTGE | {
"line": 886,
"column": 52
} | {
"line": 886,
"column": 63
} | {
"line": 886,
"column": 64
} | [
{
"pp": "C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : Preadditive C\ninst✝⁴ : HasZeroObject C\ninst✝³ : HasShift C ℤ\ninst✝² : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝¹ : Pretriangulated C\nt : TStructure C\ninst✝ : IsTriangulated C\na b : ℤ\nX : C\nh : a ≤ b\nu₁₂ : (t.truncLT a).obj X ⟶ (t.truncLT b).... | [
"C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : Preadditive C\ninst✝⁴ : HasZeroObject C\ninst✝³ : HasShift C ℤ\ninst✝² : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝¹ : Pretriangulated C\nt : TStructure C\ninst✝ : IsTriangulated C\na b : ℤ\nX : C\nh : a ≤ b\nu₁₂ : (t.truncLT a).obj X ⟶ (t.truncLT b).obj X := (t.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.ModelCategory.Homotopy | {
"line": 227,
"column": 2
} | {
"line": 227,
"column": 13
} | {
"line": 227,
"column": 14
} | [
{
"pp": "C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : ModelCategory C\nX Y : C\ninst✝⁴ : IsCofibrant X\ninst✝³ : IsCofibrant Y\ninst✝² : IsFibrant X\ninst✝¹ : IsFibrant Y\nf : X ⟶ Y\ninst✝ : WeakEquivalence f\ng : Y ⟶ X\nhg : LeftHomotopyRel (f ≫ g) (𝟙 X)\n⊢ LeftHomotopyRel (f ≫ g ≫ f) f",
"ppTerm": "?... | [
"C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : ModelCategory C\nX Y : C\ninst✝⁴ : IsCofibrant X\ninst✝³ : IsCofibrant Y\ninst✝² : IsFibrant X\ninst✝¹ : IsFibrant Y\nf : X ⟶ Y\ninst✝ : WeakEquivalence f\ng : Y ⟶ X\nhg : LeftHomotopyRel (f ≫ g) (𝟙 X)\n⊢ LeftHomotopyRel (f ≫ g ≫ f) f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.ModelCategory.Homotopy | {
"line": 234,
"column": 2
} | {
"line": 235,
"column": 36
} | {
"line": 237,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : ModelCategory C\nX Y : C\ninst✝⁴ : IsCofibrant X\ninst✝³ : IsCofibrant Y\ninst✝² : IsFibrant X\ninst✝¹ : IsFibrant Y\nf : X ⟶ Y\ninst✝ : WeakEquivalence f\n⊢ ∃ g, LeftHomotopyRel (f ≫ g) (𝟙 X) ∧ LeftHomotopyRel (g ≫ f) (𝟙 Y)",
"ppTerm": "?m.52",
... | [] | simp only [leftHomotopyRel_iff_rightHomotopyRel]
apply RightHomotopyClass.whitehead | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.ModelCategory.Homotopy | {
"line": 234,
"column": 2
} | {
"line": 235,
"column": 36
} | {
"line": 237,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : ModelCategory C\nX Y : C\ninst✝⁴ : IsCofibrant X\ninst✝³ : IsCofibrant Y\ninst✝² : IsFibrant X\ninst✝¹ : IsFibrant Y\nf : X ⟶ Y\ninst✝ : WeakEquivalence f\n⊢ ∃ g, LeftHomotopyRel (f ≫ g) (𝟙 X) ∧ LeftHomotopyRel (g ≫ f) (𝟙 Y)",
"ppTerm": "?m.52",
... | [] | simp only [leftHomotopyRel_iff_rightHomotopyRel]
apply RightHomotopyClass.whitehead | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Homology.Factorizations.CM5a | {
"line": 193,
"column": 4
} | {
"line": 193,
"column": 68
} | {
"line": 193,
"column": 69
} | [
{
"pp": "C : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Abelian C\nK L : CochainComplex C ℤ\nf : K ⟶ L\ninst✝ : EnoughInjectives C\nn₀✝ n₁ : ℤ\nhn₁ : n₀✝ + 1 = n₁\nhf : ∀ i ≤ n₀✝, QuasiIsoAt f i\nn₀ : ℤ := n₁ - 1\nA : C\nx₁ : A ⟶ K.X n₁\nx✝ : x₁ ≫ K.d n₁ (n₁ + 1) = 0\ny₀ : A ⟶ L.X n₀\nh₁ : x₁ ≫ (i K n₁)... | [
"C : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Abelian C\nK L : CochainComplex C ℤ\nf : K ⟶ L\ninst✝ : EnoughInjectives C\nn₀✝ n₁ : ℤ\nhn₁ : n₀✝ + 1 = n₁\nhf : ∀ i ≤ n₀✝, QuasiIsoAt f i\nn₀ : ℤ := n₁ - 1\nA : C\nx₁ : A ⟶ K.X n₁\nx✝ : x₁ ≫ K.d n₁ (n₁ + 1) = 0\ny₀ : A ⟶ L.X n₀\nh₁ : x₁ ≫ (i K n₁).f n₁ = 0\nh... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.ModelCategory.FibrantObjectHomotopy | {
"line": 201,
"column": 36
} | {
"line": 201,
"column": 47
} | {
"line": 201,
"column": 48
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : ModelCategory C\nX : C\n⊢ RightHomotopyRel (iResolutionObj X ≫ resolutionMap (𝟙 X)) (iResolutionObj X ≫ 𝟙 (mk (resolutionObj X)).obj)",
"ppTerm": "?m.77",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"HomotopicalAlgebra.M... | [
"C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : ModelCategory C\nX : C\n⊢ RightHomotopyRel (iResolutionObj X) (iResolutionObj X)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.ModelCategory.FibrantObjectHomotopy | {
"line": 204,
"column": 36
} | {
"line": 204,
"column": 47
} | {
"line": 204,
"column": 48
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : ModelCategory C\nX₁ X₂ X₃ : C\nf : X₁ ⟶ X₂\ng : X₂ ⟶ X₃\n⊢ RightHomotopyRel (iResolutionObj X₁ ≫ resolutionMap (f ≫ g))\n (iResolutionObj X₁ ≫ (homMk (resolutionMap f)).hom ≫ (homMk (resolutionMap g)).hom)",
"ppTerm": "?m.114",
"assigned"... | [
"C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : ModelCategory C\nX₁ X₂ X₃ : C\nf : X₁ ⟶ X₂\ng : X₂ ⟶ X₃\n⊢ RightHomotopyRel (f ≫ g ≫ iResolutionObj X₃) (f ≫ g ≫ iResolutionObj X₃)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Factorizations.CM5a | {
"line": 331,
"column": 2
} | {
"line": 345,
"column": 40
} | {
"line": 347,
"column": 0
} | [
{
"pp": "C : Type u_1\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : Abelian C\nK L : CochainComplex C ℤ\nf : K ⟶ L\ninst✝¹ : EnoughInjectives C\nn : ℤ\ninst✝ : Mono f\n⊢ (homologyShortComplex f n).Exact",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"CategoryTheory.Abelian.toPreadditive... | [] | let T := ShortComplex.mk (homologyMap f n) (homologyMap (cokernel.π f) n)
(by rw [← homologyMap_comp, cokernel.condition, homologyMap_zero])
let φ : T ⟶ homologyShortComplex f n :=
{ τ₁ := 𝟙 _
τ₂ := 𝟙 _
τ₃ := homologyMap ((cokernel f).πTruncGE n ≫ p f n) n
comm₂₃ := by
dsimp
... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Homology.Factorizations.CM5a | {
"line": 331,
"column": 2
} | {
"line": 345,
"column": 40
} | {
"line": 347,
"column": 0
} | [
{
"pp": "C : Type u_1\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : Abelian C\nK L : CochainComplex C ℤ\nf : K ⟶ L\ninst✝¹ : EnoughInjectives C\nn : ℤ\ninst✝ : Mono f\n⊢ (homologyShortComplex f n).Exact",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"CategoryTheory.Abelian.toPreadditive... | [] | let T := ShortComplex.mk (homologyMap f n) (homologyMap (cokernel.π f) n)
(by rw [← homologyMap_comp, cokernel.condition, homologyMap_zero])
let φ : T ⟶ homologyShortComplex f n :=
{ τ₁ := 𝟙 _
τ₂ := 𝟙 _
τ₃ := homologyMap ((cokernel f).πTruncGE n ≫ p f n) n
comm₂₃ := by
dsimp
... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.ModelCategory.FibrantObjectHomotopy | {
"line": 214,
"column": 4
} | {
"line": 216,
"column": 38
} | {
"line": 216,
"column": 39
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : ModelCategory C\nx✝² x✝¹ : C\nx✝ : x✝² ⟶ x✝¹\nh : weakEquivalences C x✝\n⊢ (weakEquivalences (HoCat C)).inverseImage resolution x✝",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"HomotopicalAlgebra.ModelC... | [
"C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : ModelCategory C\nx✝² x✝¹ : C\nx✝ : x✝² ⟶ x✝¹\nh : weakEquivalences C x✝\n⊢ WeakEquivalence x✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Factorizations.CM5a | {
"line": 434,
"column": 6
} | {
"line": 439,
"column": 41
} | {
"line": 439,
"column": 41
} | [
{
"pp": "C : Type u_1\ninst✝⁵ : Category.{v_1, u_1} C\ninst✝⁴ : Abelian C\nK L : CochainComplex C ℤ\nf : K ⟶ L\ninst✝³ : EnoughInjectives C\ninst✝² : Mono f\nn : ℤ\ninst✝¹ : K.IsStrictlyGE (n + 1)\ninst✝ : L.IsStrictlyGE (n + 1)\ni : ℤ\nhi : i ≤ n + ↑0\n⊢ QuasiIsoAt { obj := { mid := L, ι := f, π := 𝟙 L, ι_π :... | [] | dsimp
rw [quasiIsoAt_iff_isIso_homologyMap]
apply IsZero.isIso
all_goals
· rw [← exactAt_iff_isZero_homology]
exact exactAt_of_isGE _ (n + 1) i | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Homology.Factorizations.CM5a | {
"line": 434,
"column": 6
} | {
"line": 439,
"column": 41
} | {
"line": 439,
"column": 41
} | [
{
"pp": "C : Type u_1\ninst✝⁵ : Category.{v_1, u_1} C\ninst✝⁴ : Abelian C\nK L : CochainComplex C ℤ\nf : K ⟶ L\ninst✝³ : EnoughInjectives C\ninst✝² : Mono f\nn : ℤ\ninst✝¹ : K.IsStrictlyGE (n + 1)\ninst✝ : L.IsStrictlyGE (n + 1)\ni : ℤ\nhi : i ≤ n + ↑0\n⊢ QuasiIsoAt { obj := { mid := L, ι := f, π := 𝟙 L, ι_π :... | [] | dsimp
rw [quasiIsoAt_iff_isIso_homologyMap]
apply IsZero.isIso
all_goals
· rw [← exactAt_iff_isZero_homology]
exact exactAt_of_isGE _ (n + 1) i | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.GuitartExact.Opposite | {
"line": 106,
"column": 2
} | {
"line": 107,
"column": 18
} | {
"line": 109,
"column": 0
} | [
{
"pp": "case mpr\nC₁ : Type u₁\nC₂ : Type u₂\nC₃ : Type u₃\nC₄ : Type u₄\ninst✝³ : Category.{v₁, u₁} C₁\ninst✝² : Category.{v₂, u₂} C₂\ninst✝¹ : Category.{v₃, u₃} C₃\ninst✝ : Category.{v₄, u₄} C₄\nT : C₁ ⥤ C₂\nL : C₁ ⥤ C₃\nR : C₂ ⥤ C₄\nB : C₃ ⥤ C₄\nw : TwoSquare T L R B\n⊢ w.GuitartExact → w.op.GuitartExact",
... | [] | · intro
infer_instance | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.CategoryTheory.GuitartExact.Basic | {
"line": 121,
"column": 33
} | {
"line": 121,
"column": 44
} | {
"line": 121,
"column": 45
} | [
{
"pp": "C₁ : Type u₁\nC₂ : Type u₂\nC₃ : Type u₃\nC₄ : Type u₄\ninst✝³ : Category.{v₁, u₁} C₁\ninst✝² : Category.{v₂, u₂} C₂\ninst✝¹ : Category.{v₃, u₃} C₃\ninst✝ : Category.{v₄, u₄} C₄\nT : C₁ ⥤ C₂\nL : C₁ ⥤ C₃\nR : C₂ ⥤ C₄\nB : C₃ ⥤ C₄\nw : TwoSquare T L R B\nX₂ : C₂\nX₃ : C₃\ng : R.obj X₂ ⟶ B.obj X₃\nX₁ : C... | [
"C₁ : Type u₁\nC₂ : Type u₂\nC₃ : Type u₃\nC₄ : Type u₄\ninst✝³ : Category.{v₁, u₁} C₁\ninst✝² : Category.{v₂, u₂} C₂\ninst✝¹ : Category.{v₃, u₃} C₃\ninst✝ : Category.{v₄, u₄} C₄\nT : C₁ ⥤ C₂\nL : C₁ ⥤ C₃\nR : C₂ ⥤ C₄\nB : C₃ ⥤ C₄\nw : TwoSquare T L R B\nX₂ : C₂\nX₃ : C₃\ng : R.obj X₂ ⟶ B.obj X₃\nX₁ : C₁\na : X₂ ⟶ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.GuitartExact.Basic | {
"line": 132,
"column": 22
} | {
"line": 132,
"column": 33
} | {
"line": 132,
"column": 34
} | [
{
"pp": "C₁ : Type u₁\nC₂ : Type u₂\nC₃ : Type u₃\nC₄ : Type u₄\ninst✝³ : Category.{v₁, u₁} C₁\ninst✝² : Category.{v₂, u₂} C₂\ninst✝¹ : Category.{v₃, u₃} C₃\ninst✝ : Category.{v₄, u₄} C₄\nT : C₁ ⥤ C₂\nL : C₁ ⥤ C₃\nR : C₂ ⥤ C₄\nB : C₃ ⥤ C₄\nw : TwoSquare T L R B\nX₂ : C₂\nX₃ : C₃\ng : R.obj X₂ ⟶ B.obj X₃\nX₁ : C... | [
"C₁ : Type u₁\nC₂ : Type u₂\nC₃ : Type u₃\nC₄ : Type u₄\ninst✝³ : Category.{v₁, u₁} C₁\ninst✝² : Category.{v₂, u₂} C₂\ninst✝¹ : Category.{v₃, u₃} C₃\ninst✝ : Category.{v₄, u₄} C₄\nT : C₁ ⥤ C₂\nL : C₁ ⥤ C₃\nR : C₂ ⥤ C₄\nB : C₃ ⥤ C₄\nw : TwoSquare T L R B\nX₂ : C₂\nX₃ : C₃\ng : R.obj X₂ ⟶ B.obj X₃\nX₁ : C₁\nb : L.obj... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Factorizations.CM5a | {
"line": 509,
"column": 33
} | {
"line": 509,
"column": 44
} | {
"line": 509,
"column": 45
} | [
{
"pp": "C : Type u_1\ninst✝⁵ : Category.{v_1, u_1} C\ninst✝⁴ : Abelian C\nK L : CochainComplex C ℤ\nf : K ⟶ L\ninst✝³ : EnoughInjectives C\ninst✝² : Mono f\nn₀ : ℤ\ninst✝¹ : K.IsStrictlyGE (n₀ + 1)\ninst✝ : L.IsStrictlyGE (n₀ + 1)\ni : ℤ\nthis : ∀ {q₁ q₂ : ℕ} (hq : q₁ ≤ q₂), i ≤ n₀ + ↑q₁ → q₁ + 1 = q₂ → IsIso ... | [
"C : Type u_1\ninst✝⁵ : Category.{v_1, u_1} C\ninst✝⁴ : Abelian C\nK L : CochainComplex C ℤ\nf : K ⟶ L\ninst✝³ : EnoughInjectives C\ninst✝² : Mono f\nn₀ : ℤ\ninst✝¹ : K.IsStrictlyGE (n₀ + 1)\ninst✝ : L.IsStrictlyGE (n₀ + 1)\ni : ℤ\nthis : ∀ {q₁ q₂ : ℕ} (hq : q₁ ≤ q₂), i ≤ n₀ + ↑q₁ → q₁ + 1 = q₂ → IsIso (((functor f... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.GuitartExact.Basic | {
"line": 141,
"column": 22
} | {
"line": 141,
"column": 33
} | {
"line": 141,
"column": 34
} | [
{
"pp": "C₁ : Type u₁\nC₂ : Type u₂\nC₃ : Type u₃\nC₄ : Type u₄\ninst✝³ : Category.{v₁, u₁} C₁\ninst✝² : Category.{v₂, u₂} C₂\ninst✝¹ : Category.{v₃, u₃} C₃\ninst✝ : Category.{v₄, u₄} C₄\nT : C₁ ⥤ C₂\nL : C₁ ⥤ C₃\nR : C₂ ⥤ C₄\nB : C₃ ⥤ C₄\nw : TwoSquare T L R B\nX₂ : C₂\nX₃ : C₃\ng : R.obj X₂ ⟶ B.obj X₃\nX₁ : C... | [
"C₁ : Type u₁\nC₂ : Type u₂\nC₃ : Type u₃\nC₄ : Type u₄\ninst✝³ : Category.{v₁, u₁} C₁\ninst✝² : Category.{v₂, u₂} C₂\ninst✝¹ : Category.{v₃, u₃} C₃\ninst✝ : Category.{v₄, u₄} C₄\nT : C₁ ⥤ C₂\nL : C₁ ⥤ C₃\nR : C₂ ⥤ C₄\nB : C₃ ⥤ C₄\nw : TwoSquare T L R B\nX₂ : C₂\nX₃ : C₃\ng : R.obj X₂ ⟶ B.obj X₃\nX₁ : C₁\na : X₂ ⟶ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.GuitartExact.Basic | {
"line": 152,
"column": 45
} | {
"line": 152,
"column": 56
} | {
"line": 152,
"column": 57
} | [
{
"pp": "C₁ : Type u₁\nC₂ : Type u₂\nC₃ : Type u₃\nC₄ : Type u₄\ninst✝³ : Category.{v₁, u₁} C₁\ninst✝² : Category.{v₂, u₂} C₂\ninst✝¹ : Category.{v₃, u₃} C₃\ninst✝ : Category.{v₄, u₄} C₄\nT : C₁ ⥤ C₂\nL : C₁ ⥤ C₃\nR : C₂ ⥤ C₄\nB : C₃ ⥤ C₄\nw : TwoSquare T L R B\nX₂ : C₂\nX₃ : C₃\ng : R.obj X₂ ⟶ B.obj X₃\nf : w.... | [
"C₁ : Type u₁\nC₂ : Type u₂\nC₃ : Type u₃\nC₄ : Type u₄\ninst✝³ : Category.{v₁, u₁} C₁\ninst✝² : Category.{v₂, u₂} C₂\ninst✝¹ : Category.{v₃, u₃} C₃\ninst✝ : Category.{v₄, u₄} C₄\nT : C₁ ⥤ C₂\nL : C₁ ⥤ C₃\nR : C₂ ⥤ C₄\nB : C₃ ⥤ C₄\nw : TwoSquare T L R B\nX₂ : C₂\nX₃ : C₃\ng : R.obj X₂ ⟶ B.obj X₃\nf : w.StructuredAr... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.GuitartExact.Basic | {
"line": 165,
"column": 46
} | {
"line": 165,
"column": 57
} | {
"line": 165,
"column": 58
} | [
{
"pp": "C₁ : Type u₁\nC₂ : Type u₂\nC₃ : Type u₃\nC₄ : Type u₄\ninst✝³ : Category.{v₁, u₁} C₁\ninst✝² : Category.{v₂, u₂} C₂\ninst✝¹ : Category.{v₃, u₃} C₃\ninst✝ : Category.{v₄, u₄} C₄\nT : C₁ ⥤ C₂\nL : C₁ ⥤ C₃\nR : C₂ ⥤ C₄\nB : C₃ ⥤ C₄\nw : TwoSquare T L R B\nX₂ : C₂\nX₃ : C₃\ng : R.obj X₂ ⟶ B.obj X₃\nf : w.... | [
"C₁ : Type u₁\nC₂ : Type u₂\nC₃ : Type u₃\nC₄ : Type u₄\ninst✝³ : Category.{v₁, u₁} C₁\ninst✝² : Category.{v₂, u₂} C₂\ninst✝¹ : Category.{v₃, u₃} C₃\ninst✝ : Category.{v₄, u₄} C₄\nT : C₁ ⥤ C₂\nL : C₁ ⥤ C₃\nR : C₂ ⥤ C₄\nB : C₃ ⥤ C₄\nw : TwoSquare T L R B\nX₂ : C₂\nX₃ : C₃\ng : R.obj X₂ ⟶ B.obj X₃\nf : w.Costructured... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.GuitartExact.Basic | {
"line": 201,
"column": 8
} | {
"line": 201,
"column": 26
} | {
"line": 201,
"column": 27
} | [
{
"pp": "C₁ : Type u₁\nC₂ : Type u₂\nC₃ : Type u₃\nC₄ : Type u₄\ninst✝³ : Category.{v₁, u₁} C₁\ninst✝² : Category.{v₂, u₂} C₂\ninst✝¹ : Category.{v₃, u₃} C₃\ninst✝ : Category.{v₄, u₄} C₄\nT : C₁ ⥤ C₂\nL : C₁ ⥤ C₃\nR : C₂ ⥤ C₄\nB : C₃ ⥤ C₄\nw : TwoSquare T L R B\nX₂ X₂' : C₂\nX₃ : C₃\ng : R.obj X₂ ⟶ B.obj X₃\ng'... | [
"C₁ : Type u₁\nC₂ : Type u₂\nC₃ : Type u₃\nC₄ : Type u₄\ninst✝³ : Category.{v₁, u₁} C₁\ninst✝² : Category.{v₂, u₂} C₂\ninst✝¹ : Category.{v₃, u₃} C₃\ninst✝ : Category.{v₄, u₄} C₄\nT : C₁ ⥤ C₂\nL : C₁ ⥤ C₃\nR : C₂ ⥤ C₄\nB : C₃ ⥤ C₄\nw : TwoSquare T L R B\nX₂ X₂' : C₂\nX₃ : C₃\ng : R.obj X₂ ⟶ B.obj X₃\ng' : R.obj X₂'... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.ModelCategory.DerivabilityStructureFibrant | {
"line": 38,
"column": 2
} | {
"line": 38,
"column": 40
} | {
"line": 38,
"column": 41
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : ModelCategory C\nX : C\nR : (localizerMorphism C).RightResolution X\n⊢ WeakEquivalence R.w",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"HomotopicalAlgebra.ModelCategory.cm1a",
"CategoryTheory.Loc... | [
"C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : ModelCategory C\nX : C\nR : (localizerMorphism C).RightResolution X\n⊢ weakEquivalences C R.w"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.ModelCategory.DerivabilityStructureFibrant | {
"line": 46,
"column": 15
} | {
"line": 46,
"column": 26
} | {
"line": 46,
"column": 27
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : ModelCategory C\nX : C\n⊢ weakEquivalences C (HoCat.iResolutionObj X)",
"ppTerm": "?m.39",
"assigned": true,
"usedConstants": [
"HomotopicalAlgebra.ModelCategory.cm1a",
"CategoryTheory.Limits.hasFiniteProducts_of_hasFiniteLim... | [
"C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : ModelCategory C\nX : C\n⊢ weakEquivalences C (HoCat.iResolutionObj X)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Localization.DerivabilityStructure.Basic | {
"line": 121,
"column": 2
} | {
"line": 121,
"column": 65
} | {
"line": 121,
"column": 66
} | [
{
"pp": "C₁ : Type u₁\nC₂ : Type u₂\ninst✝⁵ : Category.{v₁, u₁} C₁\ninst✝⁴ : Category.{v₂, u₂} C₂\nW₁ : MorphismProperty C₁\nW₂ : MorphismProperty C₂\nΦ : LocalizerMorphism W₁ W₂\nD₁ : Type u_1\nD₂ : Type u_2\ninst✝³ : Category.{v_1, u_1} D₁\ninst✝² : Category.{v_2, u_2} D₂\nL₁ : C₁ ⥤ D₁\nL₂ : C₂ ⥤ D₂\ninst✝¹ :... | [
"C₁ : Type u₁\nC₂ : Type u₂\ninst✝⁵ : Category.{v₁, u₁} C₁\ninst✝⁴ : Category.{v₂, u₂} C₂\nW₁ : MorphismProperty C₁\nW₂ : MorphismProperty C₂\nΦ : LocalizerMorphism W₁ W₂\nD₁ : Type u_1\nD₂ : Type u_2\ninst✝³ : Category.{v_1, u_1} D₁\ninst✝² : Category.{v_2, u_2} D₂\nL₁ : C₁ ⥤ D₁\nL₂ : C₂ ⥤ D₂\ninst✝¹ : L₁.IsLocali... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Localization.DerivabilityStructure.Basic | {
"line": 178,
"column": 2
} | {
"line": 178,
"column": 64
} | {
"line": 178,
"column": 65
} | [
{
"pp": "C₁ : Type u₁\nC₂ : Type u₂\ninst✝⁵ : Category.{v₁, u₁} C₁\ninst✝⁴ : Category.{v₂, u₂} C₂\nW₁ : MorphismProperty C₁\nW₂ : MorphismProperty C₂\nΦ : LocalizerMorphism W₁ W₂\nD₁ : Type u_1\nD₂ : Type u_2\ninst✝³ : Category.{v_1, u_1} D₁\ninst✝² : Category.{v_2, u_2} D₂\nL₁ : C₁ ⥤ D₁\nL₂ : C₂ ⥤ D₂\ninst✝¹ :... | [
"C₁ : Type u₁\nC₂ : Type u₂\ninst✝⁵ : Category.{v₁, u₁} C₁\ninst✝⁴ : Category.{v₂, u₂} C₂\nW₁ : MorphismProperty C₁\nW₂ : MorphismProperty C₂\nΦ : LocalizerMorphism W₁ W₂\nD₁ : Type u_1\nD₂ : Type u_2\ninst✝³ : Category.{v_1, u_1} D₁\ninst✝² : Category.{v_2, u_2} D₂\nL₁ : C₁ ⥤ D₁\nL₂ : C₂ ⥤ D₂\ninst✝¹ : L₁.IsLocali... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Functor.Derived.RightDerived | {
"line": 187,
"column": 2
} | {
"line": 187,
"column": 53
} | {
"line": 187,
"column": 54
} | [
{
"pp": "C : Type u_1\nD : Type u_2\nH : Type u_3\ninst✝⁴ : Category.{v_1, u_1} C\ninst✝³ : Category.{v_3, u_2} D\ninst✝² : Category.{v_5, u_3} H\nRF : D ⥤ H\nF : C ⥤ H\nL : C ⥤ D\nα : F ⟶ L ⋙ RF\nW : MorphismProperty C\ninst✝¹ : L.IsLocalization W\ninst✝ : RF.IsRightDerivedFunctor α W\nthis : RF.IsLeftKanExten... | [
"C : Type u_1\nD : Type u_2\nH : Type u_3\ninst✝⁴ : Category.{v_1, u_1} C\ninst✝³ : Category.{v_3, u_2} D\ninst✝² : Category.{v_5, u_3} H\nRF : D ⥤ H\nF : C ⥤ H\nL : C ⥤ D\nα : F ⟶ L ⋙ RF\nW : MorphismProperty C\ninst✝¹ : L.IsLocalization W\ninst✝ : RF.IsRightDerivedFunctor α W\nthis : RF.IsLeftKanExtension α\n⊢ L.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Functor.Derived.PointwiseRightDerived | {
"line": 58,
"column": 2
} | {
"line": 60,
"column": 51
} | {
"line": 61,
"column": 2
} | [
{
"pp": "C : Type u₁\nD : Type u₂\nH : Type u₃\ninst✝³ : Category.{v₁, u₁} C\ninst✝² : Category.{v₂, u₂} D\ninst✝¹ : Category.{v₃, u₃} H\nF : C ⥤ H\nL : C ⥤ D\nW : MorphismProperty C\ninst✝ : L.IsLocalization W\nX : C\n⊢ F.HasPointwiseRightDerivedFunctorAt W X ↔ L.HasPointwiseLeftKanExtensionAt F (L.obj X)",
... | [
"C : Type u₁\nD : Type u₂\nH : Type u₃\ninst✝³ : Category.{v₁, u₁} C\ninst✝² : Category.{v₂, u₂} D\ninst✝¹ : Category.{v₃, u₃} H\nF : C ⥤ H\nL : C ⥤ D\nW : MorphismProperty C\ninst✝ : L.IsLocalization W\nX : C\n⊢ F.HasPointwiseRightDerivedFunctorAt W X ↔ W.Q.HasPointwiseLeftKanExtensionAt F (W.Q.obj X)"
] | rw [← hasPointwiseLeftKanExtensionAt_iff_of_equivalence W.Q L F
(Localization.uniq W.Q L W) (Localization.compUniqFunctor W.Q L W) (W.Q.obj X) (L.obj X)
((Localization.compUniqFunctor W.Q L W).app X)] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.CategoryTheory.Localization.DerivabilityStructure.PointwiseRightDerived | {
"line": 83,
"column": 2
} | {
"line": 83,
"column": 13
} | {
"line": 83,
"column": 14
} | [
{
"pp": "C₁ : Type u₁\nC₂ : Type u₂\nH : Type u₃\ninst✝⁷ : Category.{v₁, u₁} C₁\ninst✝⁶ : Category.{v₂, u₂} C₂\ninst✝⁵ : Category.{v₃, u₃} H\nD₁ : Type u₄\nD₂ : Type u₅\ninst✝⁴ : Category.{v₄, u₄} D₁\ninst✝³ : Category.{v₅, u₅} D₂\nW₁ : MorphismProperty C₁\nW₂ : MorphismProperty C₂\nΦ : LocalizerMorphism W₁ W₂\... | [
"C₁ : Type u₁\nC₂ : Type u₂\nH : Type u₃\ninst✝⁷ : Category.{v₁, u₁} C₁\ninst✝⁶ : Category.{v₂, u₂} C₂\ninst✝⁵ : Category.{v₃, u₃} H\nD₁ : Type u₄\nD₂ : Type u₅\ninst✝⁴ : Category.{v₄, u₄} D₁\ninst✝³ : Category.{v₅, u₅} D₂\nW₁ : MorphismProperty C₁\nW₂ : MorphismProperty C₂\nΦ : LocalizerMorphism W₁ W₂\nL₁ : C₁ ⥤ D... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Localization.DerivabilityStructure.PointwiseRightDerived | {
"line": 105,
"column": 4
} | {
"line": 106,
"column": 73
} | {
"line": 106,
"column": 74
} | [
{
"pp": "case mpr\nC₁ : Type u₁\nC₂ : Type u₂\nH : Type u₃\ninst✝³ : Category.{v₁, u₁} C₁\ninst✝² : Category.{v₂, u₂} C₂\ninst✝¹ : Category.{v₃, u₃} H\nW₁ : MorphismProperty C₁\nW₂ : MorphismProperty C₂\nΦ : LocalizerMorphism W₁ W₂\nF : C₂ ⥤ H\ninst✝ : Φ.IsRightDerivabilityStructure\nhF : (Φ.functor ⋙ F).HasPoi... | [
"case mpr\nC₁ : Type u₁\nC₂ : Type u₂\nH : Type u₃\ninst✝³ : Category.{v₁, u₁} C₁\ninst✝² : Category.{v₂, u₂} C₂\ninst✝¹ : Category.{v₃, u₃} H\nW₁ : MorphismProperty C₁\nW₂ : MorphismProperty C₂\nΦ : LocalizerMorphism W₁ W₂\nF : C₂ ⥤ H\ninst✝ : Φ.IsRightDerivabilityStructure\nhF : (Φ.functor ⋙ F).HasPointwiseRightD... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Localization.DerivabilityStructure.OfLocalizedEquivalences | {
"line": 93,
"column": 42
} | {
"line": 105,
"column": 25
} | {
"line": 106,
"column": 2
} | [
{
"pp": "C₁ : Type u_1\nC₂ : Type u_2\nD₁ : Type u_3\nD₂ : Type u_4\ninst✝¹¹ : Category.{v_1, u_1} C₁\ninst✝¹⁰ : Category.{v_2, u_2} C₂\ninst✝⁹ : Category.{v_3, u_3} D₁\ninst✝⁸ : Category.{v_4, u_4} D₂\nW₁ : MorphismProperty C₁\nW₁' : MorphismProperty D₁\nW₂ : MorphismProperty C₂\nW₂' : MorphismProperty D₂\nT :... | [] | by
let ρ : B.LeftResolution (R.functor.obj X₂) := Classical.arbitrary _
exact ⟨{
X₁ := L.functor.objPreimage ρ.X₁
w :=
R.functor.preimage (iso.hom.app _ ≫
B.functor.map (L.functor.objObjPreimageIso ρ.X₁).hom ≫ ρ.w)
hw := by
simp only [← R.inverseImage_eq, Functor.comp... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure | {
"line": 55,
"column": 22
} | {
"line": 55,
"column": 59
} | {
"line": 55,
"column": 60
} | [
{
"pp": "C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : Abelian C\ninst✝⁴ : HasExt C\nK L : CochainComplex C ℤ\na b : ℤ\ninst✝³ : K.IsGE a\ninst✝² : K.IsLE a\ninst✝¹ : L.IsGE b\ninst✝ : L.IsLE b\nthis : (C : Type u) → [inst : Category.{v, u} C] → [inst_1 : Abelian C] → HasDerivedCategory C :=\n HasDerivedCat... | [
"C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : Abelian C\ninst✝⁴ : HasExt C\nK L : CochainComplex C ℤ\na b : ℤ\ninst✝³ : K.IsGE a\ninst✝² : K.IsLE a\ninst✝¹ : L.IsGE b\ninst✝ : L.IsLE b\nthis : (C : Type u) → [inst : Category.{v, u} C] → [inst_1 : Abelian C] → HasDerivedCategory C :=\n HasDerivedCategory.standa... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.DerivedCategory.Ext.MapBijective | {
"line": 47,
"column": 12
} | {
"line": 47,
"column": 46
} | {
"line": 47,
"column": 47
} | [
{
"pp": "case zero\nC : Type u\ninst✝¹² : Category.{v, u} C\ninst✝¹¹ : Abelian C\nD : Type u'\ninst✝¹⁰ : Category.{v', u'} D\ninst✝⁹ : Abelian D\nF : C ⥤ D\ninst✝⁸ : F.Additive\ninst✝⁷ : PreservesFiniteLimits F\ninst✝⁶ : PreservesFiniteColimits F\ninst✝⁵ : F.Full\ninst✝⁴ : F.Faithful\ninst✝³ : HasExt C\ninst✝² ... | [
"case zero\nC : Type u\ninst✝¹² : Category.{v, u} C\ninst✝¹¹ : Abelian C\nD : Type u'\ninst✝¹⁰ : Category.{v', u'} D\ninst✝⁹ : Abelian D\nF : C ⥤ D\ninst✝⁸ : F.Additive\ninst✝⁷ : PreservesFiniteLimits F\ninst✝⁶ : PreservesFiniteColimits F\ninst✝⁵ : F.Full\ninst✝⁴ : F.Faithful\ninst✝³ : HasExt C\ninst✝² : HasExt D\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.DerivedCategory.Ext.MapBijective | {
"line": 69,
"column": 12
} | {
"line": 69,
"column": 46
} | {
"line": 69,
"column": 47
} | [
{
"pp": "case zero\nC : Type u\ninst✝¹² : Category.{v, u} C\ninst✝¹¹ : Abelian C\nD : Type u'\ninst✝¹⁰ : Category.{v', u'} D\ninst✝⁹ : Abelian D\nF : C ⥤ D\ninst✝⁸ : F.Additive\ninst✝⁷ : PreservesFiniteLimits F\ninst✝⁶ : PreservesFiniteColimits F\ninst✝⁵ : F.Full\ninst✝⁴ : F.Faithful\ninst✝³ : HasExt C\ninst✝² ... | [
"case zero\nC : Type u\ninst✝¹² : Category.{v, u} C\ninst✝¹¹ : Abelian C\nD : Type u'\ninst✝¹⁰ : Category.{v', u'} D\ninst✝⁹ : Abelian D\nF : C ⥤ D\ninst✝⁸ : F.Additive\ninst✝⁷ : PreservesFiniteLimits F\ninst✝⁶ : PreservesFiniteColimits F\ninst✝⁵ : F.Full\ninst✝⁴ : F.Faithful\ninst✝³ : HasExt C\ninst✝² : HasExt D\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.DerivedCategory.DerivabilityStructureInjectives | {
"line": 386,
"column": 14
} | {
"line": 386,
"column": 25
} | {
"line": 386,
"column": 26
} | [
{
"pp": "C : Type u_1\nH : Type u_2\ninst✝⁶ : Category.{v_1, u_1} C\ninst✝⁵ : Abelian C\ninst✝⁴ : Category.{v_2, u_2} H\ninst✝³ : EnoughInjectives C\nF : Plus C ⥤ H\ninst✝² : HasDerivedCategory C\nF' : DerivedCategory.Plus C ⥤ H\nα : F ⟶ DerivedCategory.Plus.Qh ⋙ F'\ninst✝¹ : F'.IsRightDerivedFunctor α (quasiIs... | [
"C : Type u_1\nH : Type u_2\ninst✝⁶ : Category.{v_1, u_1} C\ninst✝⁵ : Abelian C\ninst✝⁴ : Category.{v_2, u_2} H\ninst✝³ : EnoughInjectives C\nF : Plus C ⥤ H\ninst✝² : HasDerivedCategory C\nF' : DerivedCategory.Plus C ⥤ H\nα : F ⟶ DerivedCategory.Plus.Qh ⋙ F'\ninst✝¹ : F'.IsRightDerivedFunctor α (quasiIso C)\nthis :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.StupidTrunc | {
"line": 63,
"column": 6
} | {
"line": 63,
"column": 17
} | {
"line": 63,
"column": 18
} | [
{
"pp": "case neg\nι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝⁴ : Category.{v_1, u_3} C\ninst✝³ : HasZeroMorphisms C\ninst✝² : HasZeroObject C\nK L M : HomologicalComplex C c'\nφ : K ⟶ L\nφ' : L ⟶ M\ne : c.Embedding c'\ninst✝¹ : e.IsRelIff\nι'' : Type u_4\nc'' : Co... | [
"case neg\nι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝⁴ : Category.{v_1, u_3} C\ninst✝³ : HasZeroMorphisms C\ninst✝² : HasZeroObject C\nK L M : HomologicalComplex C c'\nφ : K ⟶ L\nφ' : L ⟶ M\ne : c.Embedding c'\ninst✝¹ : e.IsRelIff\nι'' : Type u_4\nc'' : ComplexShape ι... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.Connect | {
"line": 98,
"column": 39
} | {
"line": 98,
"column": 60
} | {
"line": 98,
"column": 60
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : HasZeroMorphisms C\nK : ChainComplex C ℕ\nL : CochainComplex C ℕ\nh : ConnectData K L\nn✝ m✝ : ℤ\nn m : ℕ\nhnm : Int.ofNat n + 1 ≠ Int.ofNat m\n⊢ ¬(ComplexShape.up ℕ).Rel n m",
"ppTerm": "?m.60",
"assigned": true,
"usedConstants": [
"Eq.... | [] | by simp at hnm ⊢; lia | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Homology.Embedding.Connect | {
"line": 100,
"column": 47
} | {
"line": 100,
"column": 68
} | {
"line": 100,
"column": 68
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : HasZeroMorphisms C\nK : ChainComplex C ℕ\nL : CochainComplex C ℕ\nh : ConnectData K L\nn✝ m✝ : ℤ\nn m : ℕ\nhnm : Int.negSucc n + 1 ≠ Int.negSucc m\n⊢ ¬(ComplexShape.down ℕ).Rel n m",
"ppTerm": "?m.167",
"assigned": true,
"usedConstants": [
... | [] | by simp at hnm ⊢; lia | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.DifferentialObject | {
"line": 234,
"column": 52
} | {
"line": 234,
"column": 92
} | {
"line": 234,
"column": 93
} | [
{
"pp": "S : Type u_1\ninst✝⁵ : AddMonoidWithOne S\nC : Type (u + 1)\ninst✝⁴ : LargeCategory C\ninst✝³ : HasZeroMorphisms C\nFC : C → C → Type u_2\nCC : C → Type u_3\ninst✝² : (X Y : C) → FunLike (FC X Y) (CC X) (CC Y)\ninst✝¹ : ConcreteCategory C FC\ninst✝ : HasShift C S\nX✝ Y✝ : DifferentialObject S C\nf : Ho... | [
"S : Type u_1\ninst✝⁵ : AddMonoidWithOne S\nC : Type (u + 1)\ninst✝⁴ : LargeCategory C\ninst✝³ : HasZeroMorphisms C\nFC : C → C → Type u_2\nCC : C → Type u_3\ninst✝² : (X Y : C) → FunLike (FC X Y) (CC X) (CC Y)\ninst✝¹ : ConcreteCategory C FC\ninst✝ : HasShift C S\nX✝ Y✝ : DifferentialObject S C\nf : HomSubtype S C... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.ExactSequenceFour | {
"line": 47,
"column": 35
} | {
"line": 47,
"column": 46
} | {
"line": 47,
"column": 47
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{?u.4, u_1} C\ninst✝ : HasZeroMorphisms C\nn : ℕ\nS : ComposableArrows C (n + 3)\nhS : S.IsComplex\nk : ℕ\nhk : k ≤ n\ncc : CokernelCofork (S.map' k (k + 1) ⋯ ⋯)\nkf : KernelFork (S.map' (k + 2) (k + 3) ⋯ ⋯)\nhcc : IsColimit cc\nhkf : IsLimit kf\n⊢ (S.map' k (k + 1) ⋯ ⋯ ... | [
"C : Type u_1\ninst✝¹ : Category.{?u.4, u_1} C\ninst✝ : HasZeroMorphisms C\nn : ℕ\nS : ComposableArrows C (n + 3)\nhS : S.IsComplex\nk : ℕ\nhk : k ≤ n\ncc : CokernelCofork (S.map' k (k + 1) ⋯ ⋯)\nkf : KernelFork (S.map' (k + 2) (k + 3) ⋯ ⋯)\nhcc : IsColimit cc\nhkf : IsLimit kf\n⊢ S.map (homOfLE ⋯) ≫ S.map (homOfLE... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.GrothendieckAbelian | {
"line": 43,
"column": 6
} | {
"line": 43,
"column": 23
} | {
"line": 43,
"column": 24
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\nι : Type t\nc : ComplexShape ι\ninst✝² : HasZeroMorphisms C\ninst✝¹ : LocallySmall.{w, v, u} C\ninst✝ : Small.{w, t} ι\nK L : HomologicalComplex C c\nemb : (K ⟶ L) → (i : Shrink.{w, t} ι) → Shrink.{w, v} (K.X ((equivShrink ι).symm i) ⟶ L.X ((equivShrink ι).symm i... | [
"C : Type u\ninst✝³ : Category.{v, u} C\nι : Type t\nc : ComplexShape ι\ninst✝² : HasZeroMorphisms C\ninst✝¹ : LocallySmall.{w, v, u} C\ninst✝ : Small.{w, t} ι\nK L : HomologicalComplex C c\nemb : (K ⟶ L) → (i : Shrink.{w, t} ι) → Shrink.{w, v} (K.X ((equivShrink ι).symm i) ⟶ L.X ((equivShrink ι).symm i)) :=\n fun... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle | {
"line": 257,
"column": 15
} | {
"line": 257,
"column": 26
} | {
"line": 257,
"column": 27
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : Preadditive C\ninst✝ : HasZeroObject C\nX : C\nK : CochainComplex C ℤ\np n : ℤ\nα : Cocycle ((singleFunctor C p).obj X) K n\nq : ℤ\nh : p + n = q\nq' : ℤ\nhq' : q + 1 = q'\nf : X ⟶ K.X q\nhf : Cochain.fromSingleMk f h = ↑α\nhα : (Cochain.fromSingleMk (f ... | [
"C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : Preadditive C\ninst✝ : HasZeroObject C\nX : C\nK : CochainComplex C ℤ\np n : ℤ\nα : Cocycle ((singleFunctor C p).obj X) K n\nq : ℤ\nh : p + n = q\nq' : ℤ\nhq' : q + 1 = q'\nf : X ⟶ K.X q\nhf : Cochain.fromSingleMk f h = ↑α\nhα : (Cochain.fromSingleMk (f ≫ K.d q q') ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle | {
"line": 294,
"column": 4
} | {
"line": 294,
"column": 55
} | {
"line": 295,
"column": 2
} | [
{
"pp": "case mp\nC : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : Preadditive C\ninst✝ : HasZeroObject C\nX : C\nK : CochainComplex C ℤ\np q : ℤ\nf : X ⟶ K.X q\nn : ℤ\nh : p + n = q\nq' : ℤ\nhq' : q + 1 = q'\nhf : f ≫ K.d q q' = 0\nq'' : ℤ\nhq'' : q'' + 1 = q\nα : Cochain ((singleFunctor C p).obj X) K (n - 1)\... | [] | exact (Cochain.fromSingleEquiv h).symm.injective hα | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.CategoryTheory.Abelian.Projective.Resolution | {
"line": 184,
"column": 4
} | {
"line": 184,
"column": 25
} | {
"line": 184,
"column": 26
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Abelian C\nX : C\nP Q : ProjectiveResolution X\n⊢ Homotopy (lift (𝟙 X ≫ 𝟙 X) P P) (𝟙 P.complex)",
"ppTerm": "?m.75",
"assigned": true,
"usedConstants": [
"CategoryTheory.Abelian.toPreadditive",
"Eq.mpr",
"ChainComplex",
... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Abelian C\nX : C\nP Q : ProjectiveResolution X\n⊢ Homotopy (lift (𝟙 X) P P) (𝟙 P.complex)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.Projective.Resolution | {
"line": 186,
"column": 4
} | {
"line": 186,
"column": 25
} | {
"line": 186,
"column": 26
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Abelian C\nX : C\nP Q : ProjectiveResolution X\n⊢ Homotopy (lift (𝟙 X ≫ 𝟙 X) Q Q) (𝟙 Q.complex)",
"ppTerm": "?m.105",
"assigned": true,
"usedConstants": [
"CategoryTheory.Abelian.toPreadditive",
"Eq.mpr",
"ChainComplex",
... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Abelian C\nX : C\nP Q : ProjectiveResolution X\n⊢ Homotopy (lift (𝟙 X) Q Q) (𝟙 Q.complex)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.LeftDerived | {
"line": 155,
"column": 2
} | {
"line": 155,
"column": 85
} | {
"line": 156,
"column": 2
} | [
{
"pp": "C : Type u\ninst✝⁶ : Category.{v, u} C\nD : Type u_1\ninst✝⁵ : Category.{v_1, u_1} D\ninst✝⁴ : Abelian C\ninst✝³ : HasProjectiveResolutions C\ninst✝² : Abelian D\nF : C ⥤ D\ninst✝¹ : F.Additive\nn : ℕ\nX : C\ninst✝ : Projective X\n⊢ IsZero ((F.leftDerived (n + 1)).obj X)",
"ppTerm": "?m.36",
"a... | [
"C : Type u\ninst✝⁶ : Category.{v, u} C\nD : Type u_1\ninst✝⁵ : Category.{v_1, u_1} D\ninst✝⁴ : Abelian C\ninst✝³ : HasProjectiveResolutions C\ninst✝² : Abelian D\nF : C ⥤ D\ninst✝¹ : F.Additive\nn : ℕ\nX : C\ninst✝ : Projective X\n⊢ IsZero\n ((HomologicalComplex.homologyFunctor D (ComplexShape.down ℕ) (n + 1)).... | refine IsZero.of_iso ?_ ((ProjectiveResolution.self X).isoLeftDerivedObj F (n + 1)) | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Algebra.Homology.Monoidal | {
"line": 254,
"column": 42
} | {
"line": 262,
"column": 53
} | {
"line": 264,
"column": 0
} | [
{
"pp": "C : Type u_1\ninst✝⁹ : Category.{v_1, u_1} C\ninst✝⁸ : MonoidalCategory C\ninst✝⁷ : Preadditive C\ninst✝⁶ : HasZeroObject C\ninst✝⁵ : (curriedTensor C).Additive\ninst✝⁴ : ∀ (X₁ : C), ((curriedTensor C).obj X₁).Additive\nI : Type u_2\ninst✝³ : AddMonoid I\nc : ComplexShape I\ninst✝² : c.TensorSigns\nK :... | [] | by
by_cases hij : c.Rel i j
· simp only [rightUnitor'_inv, assoc, mapBifunctor.d_eq,
Preadditive.comp_add, mapBifunctor.ι_D₁, mapBifunctor.ι_D₂,
tensor_unit_d₂, comp_zero, add_zero]
rw [mapBifunctor.d₁_eq _ _ _ _ hij _ _ (by simp)]
dsimp
simp only [one_smul, whisker_exchange_assoc, whiskerRi... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.GradedObject.Unitor | {
"line": 345,
"column": 2
} | {
"line": 366,
"column": 60
} | {
"line": 368,
"column": 0
} | [
{
"pp": "C₁ : Type u_1\nC₂ : Type u_2\nC₃ : Type u_3\nD : Type u_4\nI₁ : Type u_5\nI₂ : Type u_6\nI₃ : Type u_7\nJ : Type u_8\ninst✝¹⁵ : Category.{v_1, u_1} C₁\ninst✝¹⁴ : Category.{v_2, u_2} C₂\ninst✝¹³ : Category.{v_3, u_3} C₃\ninst✝¹² : Category.{v_4, u_4} D\ninst✝¹¹ : Zero I₂\ninst✝¹⁰ : DecidableEq I₂\ninst✝... | [] | rw [← cancel_epi ((mapBifunctorMapMap G π
(mapBifunctorRightUnitor F₁ X₂ e₁ τ.p₁₂ τ.h₁ X₁).inv (𝟙 X₃)))]
ext j i₁ i₃ hj
simp only [categoryOfGradedObjects_comp, ι_mapBifunctorMapMap_assoc,
mapBifunctorRightUnitor_inv_apply, Functor.id_obj, Functor.map_comp,
NatTrans.comp_app, categoryOfGradedObjects_id... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.GradedObject.Unitor | {
"line": 345,
"column": 2
} | {
"line": 366,
"column": 60
} | {
"line": 368,
"column": 0
} | [
{
"pp": "C₁ : Type u_1\nC₂ : Type u_2\nC₃ : Type u_3\nD : Type u_4\nI₁ : Type u_5\nI₂ : Type u_6\nI₃ : Type u_7\nJ : Type u_8\ninst✝¹⁵ : Category.{v_1, u_1} C₁\ninst✝¹⁴ : Category.{v_2, u_2} C₂\ninst✝¹³ : Category.{v_3, u_3} C₃\ninst✝¹² : Category.{v_4, u_4} D\ninst✝¹¹ : Zero I₂\ninst✝¹⁰ : DecidableEq I₂\ninst✝... | [] | rw [← cancel_epi ((mapBifunctorMapMap G π
(mapBifunctorRightUnitor F₁ X₂ e₁ τ.p₁₂ τ.h₁ X₁).inv (𝟙 X₃)))]
ext j i₁ i₃ hj
simp only [categoryOfGradedObjects_comp, ι_mapBifunctorMapMap_assoc,
mapBifunctorRightUnitor_inv_apply, Functor.id_obj, Functor.map_comp,
NatTrans.comp_app, categoryOfGradedObjects_id... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.GradedObject.Monoidal | {
"line": 393,
"column": 2
} | {
"line": 393,
"column": 80
} | {
"line": 393,
"column": 81
} | [
{
"pp": "I : Type u\ninst✝⁶ : AddMonoid I\nC : Type u_1\ninst✝⁵ : Category.{v_1, u_1} C\ninst✝⁴ : MonoidalCategory C\nX₁ X₂ X₃ X₄ : GradedObject I C\ninst✝³ : X₃.HasTensor X₄\ninst✝² : X₂.HasTensor (tensorObj X₃ X₄)\ninst✝¹ : X₁.HasTensor (tensorObj X₂ (tensorObj X₃ X₄))\nj : I\nA : C\nf g : tensorObj X₁ (tenso... | [
"I : Type u\ninst✝⁶ : AddMonoid I\nC : Type u_1\ninst✝⁵ : Category.{v_1, u_1} C\ninst✝⁴ : MonoidalCategory C\nX₁ X₂ X₃ X₄ : GradedObject I C\ninst✝³ : X₃.HasTensor X₄\ninst✝² : X₂.HasTensor (tensorObj X₃ X₄)\ninst✝¹ : X₁.HasTensor (tensorObj X₂ (tensorObj X₃ X₄))\nj : I\nA : C\nf g : tensorObj X₁ (tensorObj X₂ (ten... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.GradedObject.Monoidal | {
"line": 607,
"column": 2
} | {
"line": 607,
"column": 13
} | {
"line": 607,
"column": 14
} | [
{
"pp": "I : Type u\ninst✝² : AddMonoid I\nC : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : MonoidalCategory C\nn fst✝¹ snd✝¹ : ℕ\nproperty✝¹ : (fst✝¹, snd✝¹) ∈ (fun i ↦ i.1 + i.2) ⁻¹' {n}\nfst✝ snd✝ : ℕ\nproperty✝ : (fst✝, snd✝) ∈ (fun i ↦ i.1 + i.2) ⁻¹' {n}\nh :\n (fun x ↦\n match x with\n ... | [
"I : Type u\ninst✝² : AddMonoid I\nC : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : MonoidalCategory C\nn fst✝¹ snd✝¹ : ℕ\nproperty✝¹ : (fst✝¹, snd✝¹) ∈ (fun i ↦ i.1 + i.2) ⁻¹' {n}\nfst✝ snd✝ : ℕ\nproperty✝ : (fst✝, snd✝) ∈ (fun i ↦ i.1 + i.2) ⁻¹' {n}\nh :\n (fun x ↦\n match x with\n | ⟨(i₁, i₂)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.SpectralObject.Differentials | {
"line": 214,
"column": 6
} | {
"line": 214,
"column": 47
} | {
"line": 214,
"column": 48
} | [
{
"pp": "C : Type u_1\nι : Type u_2\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Category.{v_2, u_2} ι\ninst✝ : Abelian C\nX : SpectralObject C ι\ni₀ i₁ i₂ i₃ i₄ i₅ : ι\nf₁ : i₀ ⟶ i₁\nf₂ : i₁ ⟶ i₂\nf₃ : i₂ ⟶ i₃\nf₄ : i₃ ⟶ i₄\nf₅ : i₄ ⟶ i₅\nn₀ n₁ n₂ n₃ : ℤ\nhn₁ : n₀ + 1 = n₁\nhn₂ : n₁ + 1 = n₂\nhn₃ : n₂ + 1 = n₃\n⊢... | [
"C : Type u_1\nι : Type u_2\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Category.{v_2, u_2} ι\ninst✝ : Abelian C\nX : SpectralObject C ι\ni₀ i₁ i₂ i₃ i₄ i₅ : ι\nf₁ : i₀ ⟶ i₁\nf₂ : i₁ ⟶ i₂\nf₃ : i₂ ⟶ i₃\nf₄ : i₃ ⟶ i₄\nf₅ : i₄ ⟶ i₅\nn₀ n₁ n₂ n₃ : ℤ\nhn₁ : n₀ + 1 = n₁\nhn₂ : n₁ + 1 = n₂\nhn₃ : n₂ + 1 = n₃\n⊢ X.toCycles ... | ← cancel_epi (X.toCycles f₃ f₄ _ rfl n₁), | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Homology.SpectralObject.FirstPage | {
"line": 122,
"column": 14
} | {
"line": 123,
"column": 17
} | {
"line": 123,
"column": 18
} | [
{
"pp": "C : Type u_1\nι : Type u_2\nκ : Type u_3\ninst✝⁴ : Category.{?u.6, u_1} C\ninst✝³ : Abelian C\ninst✝² : Preorder ι\nX : SpectralObject C ι\nc : ℤ → ComplexShape κ\nr₀ : ℤ\ndata : SpectralSequenceDataCore ι c r₀\ninst✝¹ : data.HasFirstPageComputation\ninst✝ : X.HasSpectralSequence data\npq pq' : κ\nhpq ... | [
"C : Type u_1\nι : Type u_2\nκ : Type u_3\ninst✝⁴ : Category.{?u.6, u_1} C\ninst✝³ : Abelian C\ninst✝² : Preorder ι\nX : SpectralObject C ι\nc : ℤ → ComplexShape κ\nr₀ : ℤ\ndata : SpectralSequenceDataCore ι c r₀\ninst✝¹ : data.HasFirstPageComputation\ninst✝ : X.HasSpectralSequence data\npq pq' : κ\nhpq : (c r₀).Rel... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.SpectralObject.FirstPage | {
"line": 124,
"column": 21
} | {
"line": 124,
"column": 46
} | {
"line": 124,
"column": 47
} | [
{
"pp": "C : Type u_1\nι : Type u_2\nκ : Type u_3\ninst✝⁴ : Category.{?u.6, u_1} C\ninst✝³ : Abelian C\ninst✝² : Preorder ι\nX : SpectralObject C ι\nc : ℤ → ComplexShape κ\nr₀ : ℤ\ndata : SpectralSequenceDataCore ι c r₀\ninst✝¹ : data.HasFirstPageComputation\ninst✝ : X.HasSpectralSequence data\npq pq' : κ\nhpq ... | [
"C : Type u_1\nι : Type u_2\nκ : Type u_3\ninst✝⁴ : Category.{?u.6, u_1} C\ninst✝³ : Abelian C\ninst✝² : Preorder ι\nX : SpectralObject C ι\nc : ℤ → ComplexShape κ\nr₀ : ℤ\ndata : SpectralSequenceDataCore ι c r₀\ninst✝¹ : data.HasFirstPageComputation\ninst✝ : X.HasSpectralSequence data\npq pq' : κ\nhpq : (c r₀).Rel... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.SpectralObject.Page | {
"line": 156,
"column": 2
} | {
"line": 156,
"column": 56
} | {
"line": 156,
"column": 57
} | [
{
"pp": "C : Type u_1\nι : Type u_2\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Category.{v_2, u_2} ι\ninst✝ : Abelian C\nX : SpectralObject C ι\ni j k : ι\nf : i ⟶ j\ng : j ⟶ k\nhf : IsIso f\nn₀ n₁ : ℤ\nhn₁ : n₀ + 1 = n₁\n⊢ X.δ f g n₀ n₁ hn₁ = 0",
"ppTerm": "?m.31",
"assigned": false,
"usedConstants"... | [
"C : Type u_1\nι : Type u_2\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Category.{v_2, u_2} ι\ninst✝ : Abelian C\nX : SpectralObject C ι\ni j k : ι\nf : i ⟶ j\ng : j ⟶ k\nhf : IsIso f\nn₀ n₁ : ℤ\nhn₁ : n₀ + 1 = n₁\n⊢ X.δ f g n₀ n₁ hn₁ = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.SpectralObject.Page | {
"line": 160,
"column": 2
} | {
"line": 160,
"column": 57
} | {
"line": 160,
"column": 58
} | [
{
"pp": "C : Type u_1\nι : Type u_2\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Category.{v_2, u_2} ι\ninst✝ : Abelian C\nX : SpectralObject C ι\ni j k : ι\nf : i ⟶ j\ng : j ⟶ k\nhg : IsIso g\nn₀ n₁ : ℤ\nhn₁ : n₀ + 1 = n₁\n⊢ X.δ f g n₀ n₁ hn₁ = 0",
"ppTerm": "?m.31",
"assigned": false,
"usedConstants"... | [
"C : Type u_1\nι : Type u_2\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Category.{v_2, u_2} ι\ninst✝ : Abelian C\nX : SpectralObject C ι\ni j k : ι\nf : i ⟶ j\ng : j ⟶ k\nhg : IsIso g\nn₀ n₁ : ℤ\nhn₁ : n₀ + 1 = n₁\n⊢ X.δ f g n₀ n₁ hn₁ = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.SpectralObject.FirstPage | {
"line": 128,
"column": 2
} | {
"line": 131,
"column": 9
} | {
"line": 131,
"column": 10
} | [
{
"pp": "C : Type u_1\nι : Type u_2\nκ : Type u_3\ninst✝⁴ : Category.{u_4, u_1} C\ninst✝³ : Abelian C\ninst✝² : Preorder ι\nX : SpectralObject C ι\nc : ℤ → ComplexShape κ\nr₀ : ℤ\ndata : SpectralSequenceDataCore ι c r₀\ninst✝¹ : data.HasFirstPageComputation\ninst✝ : X.HasSpectralSequence data\npq pq' : κ\nhpq :... | [
"C : Type u_1\nι : Type u_2\nκ : Type u_3\ninst✝⁴ : Category.{u_4, u_1} C\ninst✝³ : Abelian C\ninst✝² : Preorder ι\nX : SpectralObject C ι\nc : ℤ → ComplexShape κ\nr₀ : ℤ\ndata : SpectralSequenceDataCore ι c r₀\ninst✝¹ : data.HasFirstPageComputation\ninst✝ : X.HasSpectralSequence data\npq pq' : κ\nhpq : (c r₀).Rel ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.SpectralObject.HasSpectralSequence | {
"line": 118,
"column": 2
} | {
"line": 118,
"column": 29
} | {
"line": 118,
"column": 30
} | [
{
"pp": "ι : Type u_2\nκ : Type u_3\ninst✝ : Preorder ι\nc : ℤ → ComplexShape κ\nr₀ : ℤ\ndata : SpectralSequenceDataCore ι c r₀\nr : ℤ\nhr : r₀ ≤ r\npq' : κ\ni₀ i₁ : ι\nhi₀ : i₀ = data.i₀ r pq' ⋯\nhi₁ : i₁ = data.i₁ pq'\nthis : data.i₀ r pq' ⋯ ≤ data.i₁ pq'\n⊢ i₀ ≤ i₁",
"ppTerm": "?m.31",
"assigned": tr... | [
"ι : Type u_2\nκ : Type u_3\ninst✝ : Preorder ι\nc : ℤ → ComplexShape κ\nr₀ : ℤ\ndata : SpectralSequenceDataCore ι c r₀\nr : ℤ\nhr : r₀ ≤ r\npq' : κ\ni₀ i₁ : ι\nhi₀ : i₀ = data.i₀ r pq' ⋯\nhi₁ : i₁ = data.i₁ pq'\nthis : data.i₀ r pq' ⋯ ≤ data.i₁ pq'\n⊢ data.i₀ r pq' ⋯ ≤ data.i₁ pq'"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.SpectralObject.HasSpectralSequence | {
"line": 122,
"column": 2
} | {
"line": 122,
"column": 29
} | {
"line": 122,
"column": 30
} | [
{
"pp": "ι : Type u_2\nκ : Type u_3\ninst✝ : Preorder ι\nc : ℤ → ComplexShape κ\nr₀ : ℤ\ndata : SpectralSequenceDataCore ι c r₀\npq' : κ\ni₁ i₂ : ι\nhi₁ : i₁ = data.i₁ pq'\nhi₂ : i₂ = data.i₂ pq'\n⊢ i₁ ≤ i₂",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
... | [
"ι : Type u_2\nκ : Type u_3\ninst✝ : Preorder ι\nc : ℤ → ComplexShape κ\nr₀ : ℤ\ndata : SpectralSequenceDataCore ι c r₀\npq' : κ\ni₁ i₂ : ι\nhi₁ : i₁ = data.i₁ pq'\nhi₂ : i₂ = data.i₂ pq'\n⊢ data.i₁ pq' ≤ data.i₂ pq'"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.SpectralObject.HasSpectralSequence | {
"line": 129,
"column": 2
} | {
"line": 129,
"column": 29
} | {
"line": 129,
"column": 30
} | [
{
"pp": "ι : Type u_2\nκ : Type u_3\ninst✝ : Preorder ι\nc : ℤ → ComplexShape κ\nr₀ : ℤ\ndata : SpectralSequenceDataCore ι c r₀\nr : ℤ\nhr : r₀ ≤ r\npq' : κ\ni₂ i₃ : ι\nhi₂ : i₂ = data.i₂ pq'\nhi₃ : i₃ = data.i₃ r pq' ⋯\n⊢ i₂ ≤ i₃",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Eq.m... | [
"ι : Type u_2\nκ : Type u_3\ninst✝ : Preorder ι\nc : ℤ → ComplexShape κ\nr₀ : ℤ\ndata : SpectralSequenceDataCore ι c r₀\nr : ℤ\nhr : r₀ ≤ r\npq' : κ\ni₂ i₃ : ι\nhi₂ : i₂ = data.i₂ pq'\nhi₃ : i₃ = data.i₃ r pq' ⋯\n⊢ data.i₂ pq' ≤ data.i₃ r pq' ⋯"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.SpectralObject.HasSpectralSequence | {
"line": 136,
"column": 2
} | {
"line": 136,
"column": 30
} | {
"line": 136,
"column": 31
} | [
{
"pp": "ι : Type u_2\nκ : Type u_3\ninst✝ : Preorder ι\nc : ℤ → ComplexShape κ\nr₀ : ℤ\ndata : SpectralSequenceDataCore ι c r₀\nr r' : ℤ\nhrr' : r + 1 = r'\nhr : r₀ ≤ r\npq' : κ\ni₃ i₃' : ι\nhi₃ : i₃ = data.i₃ r pq' ⋯\nhi₃' : i₃' = data.i₃ r' pq' ⋯\n⊢ i₃ ≤ i₃'",
"ppTerm": "?m.33",
"assigned": true,
... | [
"ι : Type u_2\nκ : Type u_3\ninst✝ : Preorder ι\nc : ℤ → ComplexShape κ\nr₀ : ℤ\ndata : SpectralSequenceDataCore ι c r₀\nr r' : ℤ\nhrr' : r + 1 = r'\nhr : r₀ ≤ r\npq' : κ\ni₃ i₃' : ι\nhi₃ : i₃ = data.i₃ r pq' ⋯\nhi₃' : i₃' = data.i₃ r' pq' ⋯\n⊢ data.i₃ r pq' ⋯ ≤ data.i₃ r' pq' ⋯"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Square | {
"line": 342,
"column": 12
} | {
"line": 342,
"column": 23
} | {
"line": 342,
"column": 24
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nD : Type u'\ninst✝ : Category.{v', u'} D\nsq : Square C\nF : C ⥤ D\n⊢ F.map sq.f₁₂ ≫ F.map sq.f₂₄ = F.map sq.f₁₃ ≫ F.map sq.f₃₄",
"ppTerm": "?m.44",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"C : Type u\ninst✝¹ : Category.{v, u} C\nD : Type u'\ninst✝ : Category.{v', u'} D\nsq : Square C\nF : C ⥤ D\n⊢ F.map sq.f₁₂ ≫ F.map sq.f₂₄ = F.map sq.f₁₃ ≫ F.map sq.f₃₄"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.SpectralObject.HasSpectralSequence | {
"line": 327,
"column": 6
} | {
"line": 327,
"column": 34
} | {
"line": 327,
"column": 35
} | [
{
"pp": "C : Type u_1\nι : Type u_2\nκ : Type u_3\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : Abelian C\ninst✝¹ : Preorder ι\nc : ℤ → ComplexShape κ\nr₀ : ℤ\nX : SpectralObject C ι\ndata : SpectralSequenceDataCore ι c r₀\ninst✝ : X.HasSpectralSequence data\nr r' : ℤ\nhrr' : r + 1 = r'\nhr : r₀ ≤ r\npq : κ\nhpq : ... | [
"C : Type u_1\nι : Type u_2\nκ : Type u_3\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : Abelian C\ninst✝¹ : Preorder ι\nc : ℤ → ComplexShape κ\nr₀ : ℤ\nX : SpectralObject C ι\ndata : SpectralSequenceDataCore ι c r₀\ninst✝ : X.HasSpectralSequence data\nr r' : ℤ\nhrr' : r + 1 = r'\nhr : r₀ ≤ r\npq : κ\nhpq : ∀ (pq' : κ),... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.SpectralObject.HasSpectralSequence | {
"line": 343,
"column": 6
} | {
"line": 343,
"column": 34
} | {
"line": 343,
"column": 35
} | [
{
"pp": "C : Type u_1\nι : Type u_2\nκ : Type u_3\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : Abelian C\ninst✝¹ : Preorder ι\nc : ℤ → ComplexShape κ\nr₀ : ℤ\nX : SpectralObject C ι\ndata : SpectralSequenceDataCore ι c r₀\ninst✝ : X.HasSpectralSequence data\nr r' : ℤ\nhrr' : r + 1 = r'\nhr : r₀ ≤ r\npq : κ\nhpq : ... | [
"C : Type u_1\nι : Type u_2\nκ : Type u_3\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : Abelian C\ninst✝¹ : Preorder ι\nc : ℤ → ComplexShape κ\nr₀ : ℤ\nX : SpectralObject C ι\ndata : SpectralSequenceDataCore ι c r₀\ninst✝ : X.HasSpectralSequence data\nr r' : ℤ\nhrr' : r + 1 = r'\nhr : r₀ ≤ r\npq : κ\nhpq : ∀ (pq' : κ),... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.SpectralObject.Page | {
"line": 443,
"column": 62
} | {
"line": 446,
"column": 68
} | {
"line": 448,
"column": 0
} | [
{
"pp": "C : Type u_1\nι : Type u_2\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Category.{v_2, u_2} ι\ninst✝ : Abelian C\nX : SpectralObject C ι\ni j k l : ι\nf₁ : i ⟶ j\nf₂ : j ⟶ k\nf₃ : k ⟶ l\nf₁₂ : i ⟶ k\nh₁₂ : f₁ ≫ f₂ = f₁₂\nn₀ n₁ n₂ : ℤ\nA : C\nx : (X.H n₁).obj (mk₁ f₁₂) ⟶ A\nh : (X.H n₁).map (twoδ₂Toδ₁ f₁ f... | [] | by
dsimp only [descE]
rw [← Category.assoc]
apply (X.cokernelSequenceE_exact f₁ f₂ f₃ f₁₂ h₁₂ n₀ n₁ n₂).g_desc | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Homology.SpectralObject.Page | {
"line": 475,
"column": 43
} | {
"line": 475,
"column": 54
} | {
"line": 475,
"column": 55
} | [
{
"pp": "C : Type u_1\nι : Type u_2\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Category.{v_2, u_2} ι\ninst✝ : Abelian C\nX : SpectralObject C ι\ni j k l : ι\nf₁ : i ⟶ j\nf₂ : j ⟶ k\nf₃ : k ⟶ l\nf₂₃ : j ⟶ l\nh₂₃ : f₂ ≫ f₃ = f₂₃\nn₀ n₁ n₂ : ℤ\nhn₁ : n₀ + 1 = n₁\nhn₂ : n₁ + 1 = n₂\nA : C\nx₂ : A ⟶ (X.H n₁).obj (mk₁... | [
"C : Type u_1\nι : Type u_2\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Category.{v_2, u_2} ι\ninst✝ : Abelian C\nX : SpectralObject C ι\ni j k l : ι\nf₁ : i ⟶ j\nf₂ : j ⟶ k\nf₃ : k ⟶ l\nf₂₃ : j ⟶ l\nh₂₃ : f₂ ≫ f₃ = f₂₃\nn₀ n₁ n₂ : ℤ\nhn₁ : n₀ + 1 = n₁\nhn₂ : n₁ + 1 = n₂\nA : C\nx₂ : A ⟶ (X.H n₁).obj (mk₁ f₂₃)\nhx₂ :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.SpectralObject.Page | {
"line": 479,
"column": 8
} | {
"line": 479,
"column": 19
} | {
"line": 479,
"column": 20
} | [
{
"pp": "C : Type u_1\nι : Type u_2\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Category.{v_2, u_2} ι\ninst✝ : Abelian C\nX : SpectralObject C ι\ni j k l : ι\nf₁ : i ⟶ j\nf₂ : j ⟶ k\nf₃ : k ⟶ l\nf₂₃ : j ⟶ l\nh₂₃ : f₂ ≫ f₃ = f₂₃\nn₀ n₁ n₂ : ℤ\nhn₁ : n₀ + 1 = n₁\nhn₂ : n₁ + 1 = n₂\nA : C\nx₂ : A ⟶ (X.H n₁).obj (mk₁... | [
"C : Type u_1\nι : Type u_2\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Category.{v_2, u_2} ι\ninst✝ : Abelian C\nX : SpectralObject C ι\ni j k l : ι\nf₁ : i ⟶ j\nf₂ : j ⟶ k\nf₃ : k ⟶ l\nf₂₃ : j ⟶ l\nh₂₃ : f₂ ≫ f₃ = f₂₃\nn₀ n₁ n₂ : ℤ\nhn₁ : n₀ + 1 = n₁\nhn₂ : n₁ + 1 = n₂\nA : C\nx₂ : A ⟶ (X.H n₁).obj (mk₁ f₂₃)\nhx₂ :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.SpectralObject.Page | {
"line": 589,
"column": 2
} | {
"line": 589,
"column": 52
} | {
"line": 589,
"column": 53
} | [
{
"pp": "C : Type u_1\nι : Type u_2\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Category.{v_2, u_2} ι\ninst✝ : Abelian C\nX : SpectralObject C ι\ni₀ i₁ i₂ i₃ : ι\nf₁ : i₀ ⟶ i₁\nf₂ : i₁ ⟶ i₂\nf₃ : i₂ ⟶ i₃\nf₁₂ : i₀ ⟶ i₂\nh₁₂ : f₁ ≫ f₂ = f₁₂\nn₀ n₁ n₂ : ℤ\nhn₁ : n₀ + 1 = n₁\nhn₂ : n₁ + 1 = n₂\n⊢ X.opcyclesToE f₁ f₂... | [
"C : Type u_1\nι : Type u_2\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Category.{v_2, u_2} ι\ninst✝ : Abelian C\nX : SpectralObject C ι\ni₀ i₁ i₂ i₃ : ι\nf₁ : i₀ ⟶ i₁\nf₂ : i₁ ⟶ i₂\nf₃ : i₂ ⟶ i₃\nf₁₂ : i₀ ⟶ i₂\nh₁₂ : f₁ ≫ f₂ = f₁₂\nn₀ n₁ n₂ : ℤ\nhn₁ : n₀ + 1 = n₁\nhn₂ : n₁ + 1 = n₂\n⊢ (X.H n₁).map (twoδ₁Toδ₀ f₁ f₂ f... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.SpectralObject.SpectralSequence | {
"line": 145,
"column": 11
} | {
"line": 145,
"column": 45
} | {
"line": 145,
"column": 45
} | [
{
"pp": "C : Type u_1\nι : Type u_2\nκ : Type u_3\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Abelian C\ninst✝ : Preorder ι\nX : SpectralObject C ι\nc : ℤ → ComplexShape κ\nr₀ : ℤ\ndata : SpectralSequenceDataCore ι c r₀\nr : ℤ\nhr : r₀ ≤ r\npq pq' : κ\nhpq : (c r).Rel pq pq'\ni₀ i₁ i₂ i₃ i₄ i₅ : ι\nf₁ : i₀ ⟶ i₁\n... | [] | by rw [h₃, data.hc₁₃ r pq pq' hpq] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Homology.SpectralObject.SpectralSequence | {
"line": 146,
"column": 14
} | {
"line": 146,
"column": 44
} | {
"line": 146,
"column": 45
} | [
{
"pp": "C : Type u_1\nι : Type u_2\nκ : Type u_3\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Abelian C\ninst✝ : Preorder ι\nX : SpectralObject C ι\nc : ℤ → ComplexShape κ\nr₀ : ℤ\ndata : SpectralSequenceDataCore ι c r₀\nr : ℤ\nhr : r₀ ≤ r\npq pq' : κ\nhpq : (c r).Rel pq pq'\ni₀ i₁ i₂ i₃ i₄ i₅ : ι\nf₁ : i₀ ⟶ i₁\n... | [
"C : Type u_1\nι : Type u_2\nκ : Type u_3\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Abelian C\ninst✝ : Preorder ι\nX : SpectralObject C ι\nc : ℤ → ComplexShape κ\nr₀ : ℤ\ndata : SpectralSequenceDataCore ι c r₀\nr : ℤ\nhr : r₀ ≤ r\npq pq' : κ\nhpq : (c r).Rel pq pq'\ni₀ i₁ i₂ i₃ i₄ i₅ : ι\nf₁ : i₀ ⟶ i₁\nf₂ : i₁ ⟶ i₂... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.SpectralObject.Page | {
"line": 651,
"column": 2
} | {
"line": 651,
"column": 51
} | {
"line": 651,
"column": 52
} | [
{
"pp": "C : Type u_1\nι : Type u_2\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Category.{v_2, u_2} ι\ninst✝ : Abelian C\nX : SpectralObject C ι\ni₀ i₁ i₂ i₃ : ι\nf₁ : i₀ ⟶ i₁\nf₂ : i₁ ⟶ i₂\nf₃ : i₂ ⟶ i₃\nf₂₃ : i₁ ⟶ i₃\nh₂₃ : f₂ ≫ f₃ = f₂₃\nn₀ n₁ n₂ : ℤ\nhn₁ : n₀ + 1 = n₁\nhn₂ : n₁ + 1 = n₂\n⊢ X.πE f₁ f₂ f₃ n₀ n₁... | [
"C : Type u_1\nι : Type u_2\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Category.{v_2, u_2} ι\ninst✝ : Abelian C\nX : SpectralObject C ι\ni₀ i₁ i₂ i₃ : ι\nf₁ : i₀ ⟶ i₁\nf₂ : i₁ ⟶ i₂\nf₃ : i₂ ⟶ i₃\nf₂₃ : i₁ ⟶ i₃\nh₂₃ : f₂ ≫ f₃ = f₂₃\nn₀ n₁ n₂ : ℤ\nhn₁ : n₀ + 1 = n₁\nhn₂ : n₁ + 1 = n₂\n⊢ X.iCycles f₁ f₂ n₁ ≫ (X.H n₁).m... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.SpectralObject.Page | {
"line": 753,
"column": 2
} | {
"line": 753,
"column": 13
} | {
"line": 753,
"column": 14
} | [
{
"pp": "C : Type u_1\nι : Type u_2\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Category.{v_2, u_2} ι\ninst✝ : Abelian C\nX : SpectralObject C ι\ni₀ i₁ : ι\nf : i₀ ⟶ i₁\nn₀ n₁ : ℤ\nhn₁ : n₀ + 1 = n₁\n⊢ (X.cyclesIsoH f n₀ n₁ hn₁).hom ≫ X.toCycles (𝟙 i₀) f f ⋯ n₀ = 𝟙 (X.cycles (𝟙 i₀) f n₀)",
"ppTerm": "?m.47... | [
"C : Type u_1\nι : Type u_2\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Category.{v_2, u_2} ι\ninst✝ : Abelian C\nX : SpectralObject C ι\ni₀ i₁ : ι\nf : i₀ ⟶ i₁\nn₀ n₁ : ℤ\nhn₁ : n₀ + 1 = n₁\n⊢ (X.cyclesIsoH f n₀ n₁ hn₁).hom ≫ X.toCycles (𝟙 i₀) f f ⋯ n₀ = 𝟙 (X.cycles (𝟙 i₀) f n₀)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.SpectralObject.Page | {
"line": 759,
"column": 2
} | {
"line": 759,
"column": 13
} | {
"line": 759,
"column": 14
} | [
{
"pp": "C : Type u_1\nι : Type u_2\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Category.{v_2, u_2} ι\ninst✝ : Abelian C\nX : SpectralObject C ι\ni₀ i₁ : ι\nf : i₀ ⟶ i₁\nn₀ n₁ : ℤ\nhn₁ : n₀ + 1 = n₁\n⊢ X.toCycles (𝟙 i₀) f f ⋯ n₀ ≫ (X.cyclesIsoH f n₀ n₁ hn₁).hom = 𝟙 ((X.H n₀).obj (mk₁ f))",
"ppTerm": "?m.47"... | [
"C : Type u_1\nι : Type u_2\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Category.{v_2, u_2} ι\ninst✝ : Abelian C\nX : SpectralObject C ι\ni₀ i₁ : ι\nf : i₀ ⟶ i₁\nn₀ n₁ : ℤ\nhn₁ : n₀ + 1 = n₁\n⊢ X.toCycles (𝟙 i₀) f f ⋯ n₀ ≫ (X.cyclesIsoH f n₀ n₁ hn₁).hom = 𝟙 ((X.H n₀).obj (mk₁ f))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.SpectralObject.Page | {
"line": 783,
"column": 2
} | {
"line": 783,
"column": 13
} | {
"line": 783,
"column": 14
} | [
{
"pp": "C : Type u_1\nι : Type u_2\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Category.{v_2, u_2} ι\ninst✝ : Abelian C\nX : SpectralObject C ι\ni₀ i₁ : ι\nf : i₀ ⟶ i₁\nn₀ n₁ : ℤ\nhn₁ : n₀ + 1 = n₁\n⊢ X.fromOpcycles f (𝟙 i₁) f ⋯ n₁ ≫ (X.opcyclesIsoH f n₀ n₁ hn₁).inv = 𝟙 (X.opcycles f (𝟙 i₁) n₁)",
"ppTerm"... | [
"C : Type u_1\nι : Type u_2\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Category.{v_2, u_2} ι\ninst✝ : Abelian C\nX : SpectralObject C ι\ni₀ i₁ : ι\nf : i₀ ⟶ i₁\nn₀ n₁ : ℤ\nhn₁ : n₀ + 1 = n₁\n⊢ X.fromOpcycles f (𝟙 i₁) f ⋯ n₁ ≫ (X.opcyclesIsoH f n₀ n₁ hn₁).inv = 𝟙 (X.opcycles f (𝟙 i₁) n₁)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.SpectralObject.Page | {
"line": 789,
"column": 2
} | {
"line": 789,
"column": 13
} | {
"line": 789,
"column": 14
} | [
{
"pp": "C : Type u_1\nι : Type u_2\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Category.{v_2, u_2} ι\ninst✝ : Abelian C\nX : SpectralObject C ι\ni₀ i₁ : ι\nf : i₀ ⟶ i₁\nn₀ n₁ : ℤ\nhn₁ : n₀ + 1 = n₁\n⊢ (X.opcyclesIsoH f n₀ n₁ hn₁).inv ≫ X.fromOpcycles f (𝟙 i₁) f ⋯ n₁ = 𝟙 ((X.H n₁).obj (mk₁ f))",
"ppTerm": "... | [
"C : Type u_1\nι : Type u_2\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Category.{v_2, u_2} ι\ninst✝ : Abelian C\nX : SpectralObject C ι\ni₀ i₁ : ι\nf : i₀ ⟶ i₁\nn₀ n₁ : ℤ\nhn₁ : n₀ + 1 = n₁\n⊢ (X.opcyclesIsoH f n₀ n₁ hn₁).inv ≫ X.fromOpcycles f (𝟙 i₁) f ⋯ n₁ = 𝟙 ((X.H n₁).obj (mk₁ f))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.SpectralObject.SpectralSequence | {
"line": 202,
"column": 21
} | {
"line": 203,
"column": 15
} | {
"line": 203,
"column": 16
} | [
{
"pp": "C : Type u_1\nι : Type u_2\nκ : Type u_3\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Abelian C\ninst✝ : Preorder ι\nX : SpectralObject C ι\nc : ℤ → ComplexShape κ\nr₀ : ℤ\ndata : SpectralSequenceDataCore ι c r₀\nr : ℤ\nhr : r₀ ≤ r\npq pq' pq'' : κ\nhpq : (c r).Rel pq pq'\nhpq' : (c r).Rel pq' pq''\nn₀ n₁... | [
"C : Type u_1\nι : Type u_2\nκ : Type u_3\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Abelian C\ninst✝ : Preorder ι\nX : SpectralObject C ι\nc : ℤ → ComplexShape κ\nr₀ : ℤ\ndata : SpectralSequenceDataCore ι c r₀\nr : ℤ\nhr : r₀ ≤ r\npq pq' pq'' : κ\nhpq : (c r).Rel pq pq'\nhpq' : (c r).Rel pq' pq''\nn₀ n₁ n₂ n₃ n₄ : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.SpectralObject.Page | {
"line": 884,
"column": 2
} | {
"line": 884,
"column": 88
} | {
"line": 886,
"column": 0
} | [
{
"pp": "C : Type u_1\nι : Type u_2\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Category.{v_2, u_2} ι\ninst✝ : Abelian C\nX : SpectralObject C ι\ni₀ i₁ i₂ i₃ : ι\nf₁ : i₀ ⟶ i₁\nf₂ : i₁ ⟶ i₂\nf₃ : i₂ ⟶ i₃\nf₁₂ : i₀ ⟶ i₂\nf₂₃ : i₁ ⟶ i₃\nh₁₂ : f₁ ≫ f₂ = f₁₂\nh₂₃ : f₂ ≫ f₃ = f₂₃\nn₀ n₁ n₂ : ℤ\nhn₁ : n₀ + 1 = n₁\nhn₂ ... | [] | rw [← cancel_mono (X.fromOpcycles f₁ f₂₃ (f₁₂ ≫ f₃) (by cat_disch) n₁), hx, zero_comp] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Algebra.Homology.SpectralObject.Page | {
"line": 936,
"column": 4
} | {
"line": 936,
"column": 20
} | {
"line": 936,
"column": 21
} | [
{
"pp": "case e_a.h₀\nC : Type u_1\nι : Type u_2\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Category.{v_2, u_2} ι\ninst✝ : Abelian C\nX : SpectralObject C ι\ni₀ i₁ i₂ i₃ : ι\nf₁ : i₀ ⟶ i₁\nf₂ : i₁ ⟶ i₂\nf₃ : i₂ ⟶ i₃\nf₁₂ : i₀ ⟶ i₂\nh₁₂ : f₁ ≫ f₂ = f₁₂\ni₀' i₁' i₂' i₃' : ι\nf₁' : i₀' ⟶ i₁'\nf₂' : i₁' ⟶ i₂'\nf₃' :... | [
"case e_a.h₀\nC : Type u_1\nι : Type u_2\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Category.{v_2, u_2} ι\ninst✝ : Abelian C\nX : SpectralObject C ι\ni₀ i₁ i₂ i₃ : ι\nf₁ : i₀ ⟶ i₁\nf₂ : i₁ ⟶ i₂\nf₃ : i₂ ⟶ i₃\nf₁₂ : i₀ ⟶ i₂\nh₁₂ : f₁ ≫ f₂ = f₁₂\ni₀' i₁' i₂' i₃' : ι\nf₁' : i₀' ⟶ i₁'\nf₂' : i₁' ⟶ i₂'\nf₃' : i₂' ⟶ i₃'\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.SpectralObject.SpectralSequence | {
"line": 215,
"column": 2
} | {
"line": 216,
"column": 72
} | {
"line": 218,
"column": 0
} | [
{
"pp": "case refine_2\nC : Type u_1\nι : Type u_2\nκ : Type u_3\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Abelian C\ninst✝ : Preorder ι\nX : SpectralObject C ι\nc : ℤ → ComplexShape κ\nr₀ : ℤ\ndata : SpectralSequenceDataCore ι c r₀\nr : ℤ\nhr : r₀ ≤ r\npq pq' pq'' : κ\nhpq : (c r).Rel pq pq'\nhpq' : (c r).Rel ... | [] | · simp only [← Iso.comp_inv_eq, Category.assoc]
exact (pageD_eq X data r hr pq' pq'' hpq' _ _ _ _ _ rfl rfl ..).symm | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Algebra.Homology.SpectralObject.SpectralSequence | {
"line": 245,
"column": 19
} | {
"line": 245,
"column": 67
} | {
"line": 245,
"column": 68
} | [
{
"pp": "C : Type u_1\nι : Type u_2\nκ : Type u_3\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Abelian C\ninst✝ : Preorder ι\nX : SpectralObject C ι\nc : ℤ → ComplexShape κ\nr₀ : ℤ\ndata : SpectralSequenceDataCore ι c r₀\nr r' : ℤ\nhrr' : r + 1 = r'\nhr : r₀ ≤ r\npq' pq'' : κ\ni₀' i₀ i₁ i₂ i₃ : ι\nhi₀' : i₀' = dat... | [
"C : Type u_1\nι : Type u_2\nκ : Type u_3\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Abelian C\ninst✝ : Preorder ι\nX : SpectralObject C ι\nc : ℤ → ComplexShape κ\nr₀ : ℤ\ndata : SpectralSequenceDataCore ι c r₀\nr r' : ℤ\nhrr' : r + 1 = r'\nhr : r₀ ≤ r\npq' pq'' : κ\ni₀' i₀ i₁ i₂ i₃ : ι\nhi₀' : i₀' = data.i₀ r' pq' ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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