module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.AlgebraicTopology.ModelCategory.DerivabilityStructureCofibrant | {
"line": 46,
"column": 15
} | {
"line": 46,
"column": 26
} | {
"line": 46,
"column": 27
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{u_2, u_1} C\ninst✝ : ModelCategory C\nX : C\n⊢ weakEquivalences C (HoCat.pResolutionObj X)",
"ppTerm": "?m.39",
"assigned": true,
"usedConstants": [
"CategoryTheory.Limits.hasFiniteCoproducts_of_hasFiniteColimits",
"HomotopicalAlgebra.CofibrantOb... | [
"C : Type u_1\ninst✝¹ : Category.{u_2, u_1} C\ninst✝ : ModelCategory C\nX : C\n⊢ weakEquivalences C (HoCat.pResolutionObj X)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.ModelCategory.JoyalTrick | {
"line": 65,
"column": 16
} | {
"line": 65,
"column": 74
} | {
"line": 66,
"column": 18
} | [
{
"pp": "C : Type u_1\ninst✝¹¹ : Category.{v_1, u_1} C\ninst✝¹⁰ : CategoryWithCofibrations C\ninst✝⁹ : CategoryWithFibrations C\ninst✝⁸ : CategoryWithWeakEquivalences C\ninst✝⁷ : (weakEquivalences C).HasTwoOutOfThreeProperty\ninst✝⁶ : (cofibrations C).HasFactorization (trivialFibrations C)\ninst✝⁵ : HasPushouts... | [
"C : Type u_1\ninst✝¹¹ : Category.{v_1, u_1} C\ninst✝¹⁰ : CategoryWithCofibrations C\ninst✝⁹ : CategoryWithFibrations C\ninst✝⁸ : CategoryWithWeakEquivalences C\ninst✝⁷ : (weakEquivalences C).HasTwoOutOfThreeProperty\ninst✝⁶ : (cofibrations C).HasFactorization (trivialFibrations C)\ninst✝⁵ : HasPushouts C\ninst✝⁴ :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.ModelCategory.FundamentalLemma | {
"line": 84,
"column": 2
} | {
"line": 84,
"column": 37
} | {
"line": 85,
"column": 2
} | [
{
"pp": "C : Type u_1\ninst✝⁵ : Category.{v_1, u_1} C\ninst✝⁴ : ModelCategory C\nH : Type u_2\ninst✝³ : Category.{v_2, u_2} H\nL : C ⥤ H\ninst✝² : L.IsLocalization (weakEquivalences C)\nX Y✝ : C\ninst✝¹ : IsCofibrant X\nY : C\ninst✝ : IsFibrant Y\nh✝ : IsCofibrant Y\n⊢ Function.Bijective (rightHomotopyClassToHo... | [
"case inr\nC : Type u_1\ninst✝⁵ : Category.{v_1, u_1} C\ninst✝⁴ : ModelCategory C\nH : Type u_2\ninst✝³ : Category.{v_2, u_2} H\nL : C ⥤ H\ninst✝² : L.IsLocalization (weakEquivalences C)\nX Y✝ : C\ninst✝¹ : IsCofibrant X\nY : C\ninst✝ : IsFibrant Y\nh✝¹ : IsCofibrant Y\nthis : ∀ (X : C) [IsCofibrant X], IsFibrant X... | wlog _ : IsFibrant X generalizing X | Mathlib.Tactic._aux_Mathlib_Tactic_WLOG___elabRules_Mathlib_Tactic_wlog_1 | Mathlib.Tactic.wlog |
Mathlib.AlgebraicTopology.ModelCategory.JoyalTrick | {
"line": 86,
"column": 4
} | {
"line": 87,
"column": 57
} | {
"line": 88,
"column": 4
} | [
{
"pp": "C : Type u_1\ninst✝¹¹ : Category.{v_1, u_1} C\ninst✝¹⁰ : CategoryWithCofibrations C\ninst✝⁹ : CategoryWithFibrations C\ninst✝⁸ : CategoryWithWeakEquivalences C\ninst✝⁷ : (weakEquivalences C).HasTwoOutOfThreeProperty\ninst✝⁶ : (trivialCofibrations C).HasFactorization (fibrations C)\ninst✝⁵ : HasPullback... | [
"C : Type u_1\ninst✝¹¹ : Category.{v_1, u_1} C\ninst✝¹⁰ : CategoryWithCofibrations C\ninst✝⁹ : CategoryWithFibrations C\ninst✝⁸ : CategoryWithWeakEquivalences C\ninst✝⁷ : (weakEquivalences C).HasTwoOutOfThreeProperty\ninst✝⁶ : (trivialCofibrations C).HasFactorization (fibrations C)\ninst✝⁵ : HasPullbacks C\ninst✝⁴ ... | have h₂ := comp_mem _ _ _ h.hp ((fibrations C).of_isPullback
(IsPullback.of_hasPullback p g) (mem_fibrations p)) | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.AlgebraicTopology.ModelCategory.BifibrantObjectHomotopy | {
"line": 184,
"column": 6
} | {
"line": 185,
"column": 41
} | {
"line": 185,
"column": 42
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : ModelCategory C\nx✝³ x✝² : BifibrantObject C\nx✝¹ x✝ : x✝³ ⟶ x✝²\nh : homRel C x✝¹ x✝\n⊢ (BifibrantObject.ιFibrantObject ⋙ FibrantObject.toHoCat).map x✝¹ =\n (BifibrantObject.ιFibrantObject ⋙ FibrantObject.toHoCat).map x✝",
"ppTerm": "?m.35",
"... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : ModelCategory C\nx✝³ x✝² : BifibrantObject C\nx✝¹ x✝ : x✝³ ⟶ x✝²\nh : homRel C x✝¹ x✝\n⊢ LeftHomotopyRel x✝¹.hom x✝.hom"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic | {
"line": 199,
"column": 2
} | {
"line": 199,
"column": 41
} | {
"line": 199,
"column": 42
} | [
{
"pp": "case mk\nX : Type u_1\ninst✝ : TopologicalSpace X\nx₀ x₁ : X\nγ : Path x₀ x₁\n⊢ (refl x₀).trans (mk γ) = mk γ",
"ppTerm": "?mk",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Path.trans",
"id",
"_private.Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic.0.Path.Ho... | [
"case mk\nX : Type u_1\ninst✝ : TopologicalSpace X\nx₀ x₁ : X\nγ : Path x₀ x₁\n⊢ ((Path.refl x₀).trans γ).Homotopic γ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic | {
"line": 205,
"column": 2
} | {
"line": 205,
"column": 41
} | {
"line": 205,
"column": 42
} | [
{
"pp": "case mk\nX : Type u_1\ninst✝ : TopologicalSpace X\nx₀ x₁ : X\nγ : Path x₀ x₁\n⊢ (mk γ).trans (refl x₁) = mk γ",
"ppTerm": "?mk",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Path.trans",
"_private.Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic.0.Path.Homotopic.Quot... | [
"case mk\nX : Type u_1\ninst✝ : TopologicalSpace X\nx₀ x₁ : X\nγ : Path x₀ x₁\n⊢ (γ.trans (Path.refl x₁)).Homotopic γ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic | {
"line": 211,
"column": 2
} | {
"line": 211,
"column": 52
} | {
"line": 211,
"column": 53
} | [
{
"pp": "case mk\nX : Type u_1\ninst✝ : TopologicalSpace X\nx₀ x₁ : X\nγ : Path x₀ x₁\n⊢ (mk γ).trans (mk γ).symm = refl x₀",
"ppTerm": "?mk",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Path.symm",
"Path.trans",
"id",
"Path.Homotopic.Quotient",
"Path.Homotopi... | [
"case mk\nX : Type u_1\ninst✝ : TopologicalSpace X\nx₀ x₁ : X\nγ : Path x₀ x₁\n⊢ (γ.trans γ.symm).Homotopic (Path.refl x₀)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic | {
"line": 217,
"column": 2
} | {
"line": 217,
"column": 52
} | {
"line": 217,
"column": 53
} | [
{
"pp": "case mk\nX : Type u_1\ninst✝ : TopologicalSpace X\nx₀ x₁ : X\nγ : Path x₀ x₁\n⊢ (mk γ).symm.trans (mk γ) = refl x₁",
"ppTerm": "?mk",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Path.symm",
"Path.trans",
"_private.Mathlib.AlgebraicTopology.FundamentalGroupoid.Bas... | [
"case mk\nX : Type u_1\ninst✝ : TopologicalSpace X\nx₀ x₁ : X\nγ : Path x₀ x₁\n⊢ (γ.symm.trans γ).Homotopic (Path.refl x₁)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic | {
"line": 228,
"column": 2
} | {
"line": 228,
"column": 30
} | {
"line": 228,
"column": 31
} | [
{
"pp": "case mk.mk.mk\nX : Type u_1\ninst✝ : TopologicalSpace X\nx₀ x₁ x₂ x₃ : X\nγ₀ : Path x₀ x₁\nγ₁ : Path x₁ x₂\nγ₂ : Path x₂ x₃\n⊢ ((mk γ₀).trans (mk γ₁)).trans (mk γ₂) = (mk γ₀).trans ((mk γ₁).trans (mk γ₂))",
"ppTerm": "?mk.mk.mk",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"P... | [
"case mk.mk.mk\nX : Type u_1\ninst✝ : TopologicalSpace X\nx₀ x₁ x₂ x₃ : X\nγ₀ : Path x₀ x₁\nγ₁ : Path x₁ x₂\nγ₂ : Path x₂ x₃\n⊢ ((γ₀.trans γ₁).trans γ₂).Homotopic (γ₀.trans (γ₁.trans γ₂))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.ModelCategory.Transport | {
"line": 52,
"column": 4
} | {
"line": 52,
"column": 37
} | {
"line": 52,
"column": 38
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝⁵ : Category.{v_1, u_1} C\ninst✝⁴ : Category.{v_2, u_2} D\ninst✝³ : ModelCategory D\ninst✝² : CategoryWithCofibrations C\ninst✝¹ : CategoryWithFibrations C\ninst✝ : CategoryWithWeakEquivalences C\ne : C ≌ D\nh₁ : cofibrations C = (cofibrations D).inverseImage e.functor\... | [
"C : Type u_1\nD : Type u_2\ninst✝⁵ : Category.{v_1, u_1} C\ninst✝⁴ : Category.{v_2, u_2} D\ninst✝³ : ModelCategory D\ninst✝² : CategoryWithCofibrations C\ninst✝¹ : CategoryWithFibrations C\ninst✝ : CategoryWithWeakEquivalences C\ne : C ≌ D\nh₁ : cofibrations C = (cofibrations D).inverseImage e.functor\nh₂ : fibrat... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.ModelCategory.Transport | {
"line": 54,
"column": 4
} | {
"line": 54,
"column": 35
} | {
"line": 54,
"column": 36
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝⁵ : Category.{v_1, u_1} C\ninst✝⁴ : Category.{v_2, u_2} D\ninst✝³ : ModelCategory D\ninst✝² : CategoryWithCofibrations C\ninst✝¹ : CategoryWithFibrations C\ninst✝ : CategoryWithWeakEquivalences C\ne : C ≌ D\nh₁ : cofibrations C = (cofibrations D).inverseImage e.functor\... | [
"C : Type u_1\nD : Type u_2\ninst✝⁵ : Category.{v_1, u_1} C\ninst✝⁴ : Category.{v_2, u_2} D\ninst✝³ : ModelCategory D\ninst✝² : CategoryWithCofibrations C\ninst✝¹ : CategoryWithFibrations C\ninst✝ : CategoryWithWeakEquivalences C\ne : C ≌ D\nh₁ : cofibrations C = (cofibrations D).inverseImage e.functor\nh₂ : fibrat... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.ModelCategory.Transport | {
"line": 56,
"column": 4
} | {
"line": 56,
"column": 41
} | {
"line": 56,
"column": 42
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝⁵ : Category.{v_1, u_1} C\ninst✝⁴ : Category.{v_2, u_2} D\ninst✝³ : ModelCategory D\ninst✝² : CategoryWithCofibrations C\ninst✝¹ : CategoryWithFibrations C\ninst✝ : CategoryWithWeakEquivalences C\ne : C ≌ D\nh₁ : cofibrations C = (cofibrations D).inverseImage e.functor\... | [
"C : Type u_1\nD : Type u_2\ninst✝⁵ : Category.{v_1, u_1} C\ninst✝⁴ : Category.{v_2, u_2} D\ninst✝³ : ModelCategory D\ninst✝² : CategoryWithCofibrations C\ninst✝¹ : CategoryWithFibrations C\ninst✝ : CategoryWithWeakEquivalences C\ne : C ≌ D\nh₁ : cofibrations C = (cofibrations D).inverseImage e.functor\nh₂ : fibrat... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.ModelCategory.Transport | {
"line": 60,
"column": 14
} | {
"line": 60,
"column": 21
} | {
"line": 60,
"column": 21
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝⁵ : Category.{v_1, u_1} C\ninst✝⁴ : Category.{v_2, u_2} D\ninst✝³ : ModelCategory D\ninst✝² : CategoryWithCofibrations C\ninst✝¹ : CategoryWithFibrations C\ninst✝ : CategoryWithWeakEquivalences C\ne : C ≌ D\nh₁ : cofibrations C = (cofibrations D).inverseImage e.functor\... | [
"C : Type u_1\nD : Type u_2\ninst✝⁵ : Category.{v_1, u_1} C\ninst✝⁴ : Category.{v_2, u_2} D\ninst✝³ : ModelCategory D\ninst✝² : CategoryWithCofibrations C\ninst✝¹ : CategoryWithFibrations C\ninst✝ : CategoryWithWeakEquivalences C\ne : C ≌ D\nh₁ : cofibrations C = (cofibrations D).inverseImage e.functor\nh₂ : fibrat... | rw [h₃] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.AlgebraicTopology.ModelCategory.Transport | {
"line": 61,
"column": 15
} | {
"line": 61,
"column": 22
} | {
"line": 61,
"column": 22
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝⁵ : Category.{v_1, u_1} C\ninst✝⁴ : Category.{v_2, u_2} D\ninst✝³ : ModelCategory D\ninst✝² : CategoryWithCofibrations C\ninst✝¹ : CategoryWithFibrations C\ninst✝ : CategoryWithWeakEquivalences C\ne : C ≌ D\nh₁ : cofibrations C = (cofibrations D).inverseImage e.functor\... | [
"C : Type u_1\nD : Type u_2\ninst✝⁵ : Category.{v_1, u_1} C\ninst✝⁴ : Category.{v_2, u_2} D\ninst✝³ : ModelCategory D\ninst✝² : CategoryWithCofibrations C\ninst✝¹ : CategoryWithFibrations C\ninst✝ : CategoryWithWeakEquivalences C\ne : C ≌ D\nh₁ : cofibrations C = (cofibrations D).inverseImage e.functor\nh₂ : fibrat... | rw [h₃] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.CategoryTheory.Limits.Shapes.MultiequalizerPullback | {
"line": 50,
"column": 6
} | {
"line": 50,
"column": 27
} | {
"line": 50,
"column": 28
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\nJ : MultispanShape\ninst✝ : Unique J.L\nI : MultispanIndex J C\nc : Multicofork I\nh : {J.fst default, J.snd default} = Set.univ\nh' : J.fst default ≠ J.snd default\ns : PushoutCocone (I.fst default) (I.snd default)\n⊢ (I.fst default ≫ if hk : J.fst default... | [
"C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\nJ : MultispanShape\ninst✝ : Unique J.L\nI : MultispanIndex J C\nc : Multicofork I\nh : {J.fst default, J.snd default} = Set.univ\nh' : J.fst default ≠ J.snd default\ns : PushoutCocone (I.fst default) (I.snd default)\n⊢ I.fst default ≫ s.inl = I.snd default ≫ s.inr"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Subfunctor.Equalizer | {
"line": 95,
"column": 32
} | {
"line": 95,
"column": 73
} | {
"line": 95,
"column": 74
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF₁ F₂ : C ⥤ Type w\nA : Subfunctor F₁\nf g : A.toFunctor ⟶ F₂\nG : C ⥤ Type w\nφ : G ⟶ A.toFunctor\nw : φ ≫ f = φ ≫ g\n⊢ range (φ ≫ A.ι) ≤ Subfunctor.equalizer f g",
"ppTerm": "?m.59",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Categor... | [
"C : Type u\ninst✝ : Category.{v, u} C\nF₁ F₂ : C ⥤ Type w\nA : Subfunctor F₁\nf g : A.toFunctor ⟶ F₂\nG : C ⥤ Type w\nφ : G ⟶ A.toFunctor\nw : φ ≫ f = φ ≫ g\n⊢ φ ≫ f = φ ≫ g"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Types.Multicoequalizer | {
"line": 89,
"column": 31
} | {
"line": 89,
"column": 42
} | {
"line": 89,
"column": 43
} | [
{
"pp": "X : Type u\nι : Type w\nA : Set X\nU : ι → Set X\nV : ι → ι → Set X\nc : MulticoequalizerDiagram A U V\ne : WalkingMultispan (MultispanShape.prod ι) ⥤ Type u := (c.multispanIndex.map Set.functorToTypes).multispan\ni₁ i₂ : ι\nx✝¹ : (c.multispanIndex.map Set.functorToTypes).right i₁\nx✝ : (c.multispanInd... | [
"X : Type u\nι : Type w\nA : Set X\nU : ι → Set X\nV : ι → ι → Set X\nc : MulticoequalizerDiagram A U V\ne : WalkingMultispan (MultispanShape.prod ι) ⥤ Type u := (c.multispanIndex.map Set.functorToTypes).multispan\ni₁ i₂ : ι\nx✝¹ : (c.multispanIndex.map Set.functorToTypes).right i₁\nx✝ : (c.multispanIndex.map Set.f... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.Horn | {
"line": 95,
"column": 4
} | {
"line": 95,
"column": 86
} | {
"line": 96,
"column": 4
} | [
{
"pp": "n : ℕ\ni : Fin (n + 1)\nm : ℕ\nh : m + 1 < n\nf : unop (op ⦋m⦌) ⟶ ⦋n⦌\nthis : ∀ (j : Fin (n + 1)), j ≠ i → j ∈ Set.range ⇑(SimplexCategory.Hom.toOrderHom f)\n⊢ False",
"ppTerm": "?m.83",
"assigned": true,
"usedConstants": [
"False",
"SimplexCategory.instFintypeToTypeOrderHomFinH... | [
"n : ℕ\ni : Fin (n + 1)\nm : ℕ\nh : m + 1 < n\nf : unop (op ⦋m⦌) ⟶ ⦋n⦌\nthis✝ : ∀ (j : Fin (n + 1)), j ≠ i → j ∈ Set.range ⇑(SimplexCategory.Hom.toOrderHom f)\nthis : Finset.image ⇑(SimplexCategory.Hom.toOrderHom f) ⊤ ∪ {i} = ⊤\n⊢ False"
] | have : Finset.image f.toOrderHom ⊤ ∪ {i} = ⊤ := by ext k; by_cases k = i <;> aesop | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.AlgebraicTopology.SimplicialSet.Horn | {
"line": 99,
"column": 27
} | {
"line": 99,
"column": 38
} | {
"line": 99,
"column": 39
} | [
{
"pp": "n : ℕ\ni : Fin (n + 1)\nm : ℕ\nh : m + 1 < n\nf : unop (op ⦋m⦌) ⟶ ⦋n⦌\nthis✝¹ : ∀ (j : Fin (n + 1)), j ≠ i → j ∈ Set.range ⇑(SimplexCategory.Hom.toOrderHom f)\nthis✝ : Finset.image ⇑(SimplexCategory.Hom.toOrderHom f) ⊤ ∪ {i} = ⊤\nthis : n ≤ (Finset.image (⇑(SimplexCategory.Hom.toOrderHom f)) Finset.uni... | [
"n : ℕ\ni : Fin (n + 1)\nm : ℕ\nh : m + 1 < n\nf : unop (op ⦋m⦌) ⟶ ⦋n⦌\nthis✝¹ : ∀ (j : Fin (n + 1)), j ≠ i → j ∈ Set.range ⇑(SimplexCategory.Hom.toOrderHom f)\nthis✝ : Finset.image ⇑(SimplexCategory.Hom.toOrderHom f) ⊤ ∪ {i} = ⊤\nthis : n ≤ (Finset.image (⇑(SimplexCategory.Hom.toOrderHom f)) Finset.univ).card\n⊢ n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.Horn | {
"line": 103,
"column": 2
} | {
"line": 103,
"column": 28
} | {
"line": 103,
"column": 29
} | [
{
"pp": "n : ℕ\ni : Fin (n + 1)\nm : ℕ\nh : m + 1 < n\nf : unop (op ⦋m⦌) ⟶ ⦋n⦌\nj : Fin (n + 1)\nhij : j ≠ i\nhj : j ∉ Set.range ⇑(SimplexCategory.Hom.toOrderHom f)\nthis : ∃ j, ¬j = i ∧ ∀ (i : Fin (m + 1)), ¬(stdSimplex.objEquiv.symm f) i = j\n⊢ stdSimplex.objEquiv.symm f ∈ Λ[n, i].obj (op ⦋m⦌) ↔ stdSimplex.ob... | [
"n : ℕ\ni : Fin (n + 1)\nm : ℕ\nh : m + 1 < n\nf : unop (op ⦋m⦌) ⟶ ⦋n⦌\nj : Fin (n + 1)\nhij : j ≠ i\nhj : j ∉ Set.range ⇑(SimplexCategory.Hom.toOrderHom f)\nthis : ∃ j, ¬j = i ∧ ∀ (i : Fin (m + 1)), ¬(stdSimplex.objEquiv.symm f) i = j\n⊢ ∃ i_1, ¬i_1 = i ∧ ∀ (i : Fin (m + 1)), ¬(stdSimplex.objEquiv.symm f) i = i_1"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Set | {
"line": 42,
"column": 31
} | {
"line": 42,
"column": 42
} | {
"line": 42,
"column": 43
} | [
{
"pp": "J : Type w\ninst✝¹ : Category.{w', w} J\nX : Type u\ninst✝ : IsFilteredOrEmpty J\nF : J ⥤ Set X\ni j : J\nx : X\nhx : x ∈ F.obj i\ny : X\nhy : y ∈ F.obj j\nh :\n (ConcreteCategory.hom ((functorToTypes.mapCocone (colimitCocone F).cocone).ι.app i)) ⟨x, hx⟩ =\n (ConcreteCategory.hom ((functorToTypes.m... | [
"J : Type w\ninst✝¹ : Category.{w', w} J\nX : Type u\ninst✝ : IsFilteredOrEmpty J\nF : J ⥤ Set X\ni j : J\nx : X\nhx : x ∈ F.obj i\ny : X\nhy : y ∈ F.obj j\nh :\n (ConcreteCategory.hom ((functorToTypes.mapCocone (colimitCocone F).cocone).ι.app i)) ⟨x, hx⟩ =\n (ConcreteCategory.hom ((functorToTypes.mapCocone (co... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.Boundary | {
"line": 69,
"column": 2
} | {
"line": 69,
"column": 13
} | {
"line": 69,
"column": 14
} | [
{
"pp": "n : ℕ\ni : Fin (n + 1)\nhi : objMk OrderHom.id ∈ (face {i}ᶜ).obj (op ⦋n⦌)\n⊢ False",
"ppTerm": "?m.32",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"n : ℕ\ni : Fin (n + 1)\nhi : objMk OrderHom.id ∈ (face {i}ᶜ).obj (op ⦋n⦌)\n⊢ False"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.Horn | {
"line": 150,
"column": 2
} | {
"line": 150,
"column": 13
} | {
"line": 150,
"column": 14
} | [
{
"pp": "n : ℕ\ni✝ : Fin (n + 1)\nd : SimplexCategory\nf : d ⟶ ⦋n⦌\ninst✝ : IsIso f\ni : Fin (n + 1)\n⊢ i ∈ Set.range ⇑(stdSimplex.asOrderHom (stdSimplex.objEquiv.symm f)) ∪ {i✝} ↔ i ∈ Set.univ",
"ppTerm": "?m.41",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Opposite",
"Equiv.i... | [
"n : ℕ\ni✝ : Fin (n + 1)\nd : SimplexCategory\nf : d ⟶ ⦋n⦌\ninst✝ : IsIso f\ni : Fin (n + 1)\n⊢ i = i✝ ∨ ∃ y, (stdSimplex.asOrderHom (stdSimplex.objEquiv.symm f)) y = i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.Horn | {
"line": 290,
"column": 4
} | {
"line": 290,
"column": 15
} | {
"line": 290,
"column": 16
} | [
{
"pp": "n : ℕ\ni j : Fin (n + 2)\nh : j ≠ i\n⊢ Subfunctor.range (stdSimplex.δ j) ≤ Λ[n + 1, i]",
"ppTerm": "?m.39",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Opposite",
"SimplexCategory.instFintypeToTypeOrderHomFinHAddNatLenOfNat",
"congrArg",
"Compl.compl",
... | [
"n : ℕ\ni j : Fin (n + 2)\nh : j ≠ i\n⊢ stdSimplex.face {j}ᶜ ≤ Λ[n + 1, i]"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.CategoryWithFibrations | {
"line": 150,
"column": 34
} | {
"line": 150,
"column": 45
} | {
"line": 150,
"column": 46
} | [
{
"pp": "X : SSet\nn : ℕ\ni : Fin (n + 2)\nf : (j : Fin (n + 2)) → j ≠ i → (Δ[n] ⟶ X)\nhf : horn.IsCompatible f\nY : SSet\np : X ⟶ Y\ninst✝ : Fibration p\nb : Δ[n + 1] ⟶ Y\ncomm : ∀ (j : Fin (n + 2)) (hj : j ≠ i), f j hj ≫ p = stdSimplex.δ j ≫ b\nj : Fin (n + 2)\nhj : j ≠ i\n⊢ ι i j hj ≫ hf.desc ≫ p = ι i j hj ... | [
"X : SSet\nn : ℕ\ni : Fin (n + 2)\nf : (j : Fin (n + 2)) → j ≠ i → (Δ[n] ⟶ X)\nhf : horn.IsCompatible f\nY : SSet\np : X ⟶ Y\ninst✝ : Fibration p\nb : Δ[n + 1] ⟶ Y\ncomm : ∀ (j : Fin (n + 2)) (hj : j ≠ i), f j hj ≫ p = stdSimplex.δ j ≫ b\nj : Fin (n + 2)\nhj : j ≠ i\n⊢ f j hj ≫ p = stdSimplex.δ j ≫ b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.KanComplex | {
"line": 99,
"column": 34
} | {
"line": 99,
"column": 45
} | {
"line": 99,
"column": 46
} | [
{
"pp": "Z : SSet\nh :\n ∀ ⦃n : ℕ⦄ ⦃i : Fin (n + 2)⦄ (f : (j : Fin (n + 2)) → j ≠ i → (Δ[n] ⟶ Z)),\n horn.IsCompatible f → ∃ φ, ∀ (j : Fin (n + 2)) (hj : j ≠ i), stdSimplex.δ j ≫ φ = f j hj\nn : ℕ\nX Y : SSet\ni : Fin (n + 2)\nt : Λ[n + 1, i].toSSet ⟶ Z\nx✝¹ : Δ[n + 1] ⟶ ⊤_ SSet\nx✝ : CommSq t Λ[n + 1, i].ι... | [
"Z : SSet\nh :\n ∀ ⦃n : ℕ⦄ ⦃i : Fin (n + 2)⦄ (f : (j : Fin (n + 2)) → j ≠ i → (Δ[n] ⟶ Z)),\n horn.IsCompatible f → ∃ φ, ∀ (j : Fin (n + 2)) (hj : j ≠ i), stdSimplex.δ j ≫ φ = f j hj\nn : ℕ\nX Y : SSet\ni : Fin (n + 2)\nt : Λ[n + 1, i].toSSet ⟶ Z\nx✝¹ : Δ[n + 1] ⟶ ⊤_ SSet\nx✝ : CommSq t Λ[n + 1, i].ι (terminal.f... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.Skeleton | {
"line": 71,
"column": 2
} | {
"line": 71,
"column": 13
} | {
"line": 71,
"column": 14
} | [
{
"pp": "X : SSet\ni : ℕ\nx : X _⦋i⦌\nn : ℕ\nhi : i < n\n⊢ Subcomplex.ofSimplex x ≤ X.skeleton n",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"SSet.Subcomplex.ofSimplex",
"Opposite",
"PartialOrder.toPreorder",
"SSet.skeleton",
"Preorder.toLE... | [
"X : SSet\ni : ℕ\nx : X _⦋i⦌\nn : ℕ\nhi : i < n\n⊢ x ∈ (X.skeleton n).obj (op ⦋i⦌)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Types.Pushouts | {
"line": 204,
"column": 2
} | {
"line": 204,
"column": 13
} | {
"line": 204,
"column": 14
} | [
{
"pp": "S X₁ X₂ : Type u\nf : S ⟶ X₁\ng : S ⟶ X₂\ninst✝ : Mono f\nx₂ y₂ : X₂\nh : (ConcreteCategory.hom (inr f g)) x₂ = (ConcreteCategory.hom (inr f g)) y₂\n⊢ x₂ = y₂",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"id",
"Eq"
],
"usedFVars": [
"X₂",
"x₂",
... | [
"S X₁ X₂ : Type u\nf : S ⟶ X₁\ng : S ⟶ X₂\ninst✝ : Mono f\nx₂ y₂ : X₂\nh : (ConcreteCategory.hom (inr f g)) x₂ = (ConcreteCategory.hom (inr f g)) y₂\n⊢ x₂ = y₂"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.Path | {
"line": 153,
"column": 4
} | {
"line": 154,
"column": 7
} | {
"line": 155,
"column": 2
} | [
{
"pp": "n : ℕ\nX : Truncated (n + 1)\nm : ℕ\nh : m ≤ n + 1\nΔ : X.obj (op { obj := ⦋m⦌, property := h })\ni : Fin m\n⊢ (ConcreteCategory.hom (((trunc (n + 1) 1 ⋯).obj X).map (tr (SimplexCategory.δ 1) Path₁._proof_1 Path₁._proof_5).op))\n ((ConcreteCategory.hom (X.map (tr (mkOfSucc i) ⋯ h).op)) Δ) =\n (... | [] | simp [← δ_one_mkOfSucc, tr_comp]
rfl | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.Path | {
"line": 153,
"column": 4
} | {
"line": 154,
"column": 7
} | {
"line": 155,
"column": 2
} | [
{
"pp": "n : ℕ\nX : Truncated (n + 1)\nm : ℕ\nh : m ≤ n + 1\nΔ : X.obj (op { obj := ⦋m⦌, property := h })\ni : Fin m\n⊢ (ConcreteCategory.hom (((trunc (n + 1) 1 ⋯).obj X).map (tr (SimplexCategory.δ 1) Path₁._proof_1 Path₁._proof_5).op))\n ((ConcreteCategory.hom (X.map (tr (mkOfSucc i) ⋯ h).op)) Δ) =\n (... | [] | simp [← δ_one_mkOfSucc, tr_comp]
rfl | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal | {
"line": 86,
"column": 4
} | {
"line": 88,
"column": 57
} | {
"line": 89,
"column": 6
} | [
{
"pp": "case mk.zero\nn : ℕ\nX Y : Truncated (n + 1)\ninst✝ : Y.IsStrictSegal\nf g : X ⟶ Y\nh :\n ∀ (x : X.obj (op { obj := ⦋1⦌, property := ⋯ })),\n (ConcreteCategory.hom (f.app (op { obj := ⦋1⦌, property := ⋯ }))) x =\n (ConcreteCategory.hom (g.app (op { obj := ⦋1⦌, property := ⋯ }))) x\nhm : ⦋0⦌.le... | [
"case mk.zero\nn : ℕ\nX Y : Truncated (n + 1)\ninst✝ : Y.IsStrictSegal\nf g : X ⟶ Y\nh :\n ∀ (x : X.obj (op { obj := ⦋1⦌, property := ⋯ })),\n (ConcreteCategory.hom (f.app (op { obj := ⦋1⦌, property := ⋯ }))) x =\n (ConcreteCategory.hom (g.app (op { obj := ⦋1⦌, property := ⋯ }))) x\nhm : ⦋0⦌.len ≤ n + 1\nx... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.Types.Coyoneda | {
"line": 41,
"column": 6
} | {
"line": 41,
"column": 30
} | {
"line": 41,
"column": 30
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : MonoidalCategory C\nX : C\nf : (coyoneda.obj (op (𝟙_ C))).obj X\n⊢ (ConcreteCategory.hom (ρ_ ((coyoneda.obj (op (𝟙_ C))).obj X)).hom).toFun (f, PUnit.unit) =\n (ConcreteCategory.hom\n ((𝟙 ((coyoneda.obj (op (𝟙_ C))).obj X) ⊗ₘ ↾fun x ↦ 𝟙 (... | [] | simp [unitors_inv_equal] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal | {
"line": 465,
"column": 8
} | {
"line": 467,
"column": 70
} | {
"line": 468,
"column": 12
} | [
{
"pp": "case succ.refine_2.inr\nX : SSet\nh : (n : ℕ) → X.StrictSegalCore n\nn : ℕ\nhn : (p : X.Path n) → { s // X.spine n s = p }\np : X.Path (n + 1)\ni : Fin n\n⊢ (X.spine (n + 1) ((h n).concat (p.arrow 0) ↑(hn (p.interval 1 n ⋯)) ⋯)).arrow i.succ = p.arrow i.succ",
"ppTerm": "?succ.refine_2.inr",
"a... | [
"case succ.refine_2.inr\nX : SSet\nh : (n : ℕ) → X.StrictSegalCore n\nn : ℕ\nhn : (p : X.Path n) → { s // X.spine n s = p }\np : X.Path (n + 1)\ni : Fin n\n⊢ (ConcreteCategory.hom (X.map (mkOfSucc i).op)) ↑(hn (p.interval 1 n ⋯)) = (p.interval 1 n ⋯).arrow i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Enriched.Ordinary.Basic | {
"line": 80,
"column": 2
} | {
"line": 85,
"column": 73
} | {
"line": 87,
"column": 0
} | [
{
"pp": "V : Type u'\ninst✝³ : Category.{v', u'} V\ninst✝² : MonoidalCategory V\nC : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : EnrichedOrdinaryCategory V C\nX X' X'' : C\nf : X ⟶ X'\nf' : X' ⟶ X''\nY : C\n⊢ (λ_ (X'' ⟶[V] Y)).inv ≫ ((eHomEquiv V) (f ≫ f') ▷ X'' ⟶[V] Y) ≫ eComp V X X'' Y =\n ((λ_ (X'' ⟶[V] Y... | [] | rw [assoc, assoc, eHomEquiv_comp, comp_whiskerRight_assoc, comp_whiskerRight_assoc, ← e_assoc',
tensorHom_def', comp_whiskerRight_assoc, id_whiskerLeft, comp_whiskerRight_assoc,
← comp_whiskerRight_assoc, Iso.inv_hom_id, id_whiskerRight_assoc,
comp_whiskerRight_assoc, leftUnitor_inv_whiskerRight_assoc,
... | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.CategoryTheory.Enriched.Basic | {
"line": 331,
"column": 4
} | {
"line": 331,
"column": 15
} | {
"line": 331,
"column": 16
} | [
{
"pp": "V : Type v\ninst✝³ : Category.{w, v} V\ninst✝² : MonoidalCategory V\nC : Type u₁\nD : Type u₂\ninst✝¹ : EnrichedCategory V C\ninst✝ : EnrichedCategory V D\nF G : EnrichedFunctor V C D\nF_obj : C → D\nF_map : (X Y : C) → (X ⟶[V] Y) ⟶ F_obj X ⟶[V] F_obj Y\nmap_id✝¹ : ∀ (X : C), eId V X ≫ F_map X X = eId ... | [
"V : Type v\ninst✝³ : Category.{w, v} V\ninst✝² : MonoidalCategory V\nC : Type u₁\nD : Type u₂\ninst✝¹ : EnrichedCategory V C\ninst✝ : EnrichedCategory V D\nF G : EnrichedFunctor V C D\nF_obj : C → D\nF_map : (X Y : C) → (X ⟶[V] Y) ⟶ F_obj X ⟶[V] F_obj Y\nmap_id✝¹ : ∀ (X : C), eId V X ≫ F_map X X = eId V (F_obj X)\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Enriched.Basic | {
"line": 357,
"column": 60
} | {
"line": 357,
"column": 71
} | {
"line": 357,
"column": 72
} | [
{
"pp": "case inj\nV : Type v\ninst✝⁷ : Category.{w, v} V\ninst✝⁶ : MonoidalCategory V\nC✝ : Type u₁\ninst✝⁵ : EnrichedCategory V C✝\nW : Type v'\ninst✝⁴ : Category.{w', v'} W\ninst✝³ : MonoidalCategory W\nC : Type u₁\ninst✝² : EnrichedCategory W C\nD : Type u₂\ninst✝¹ : EnrichedCategory W D\nE : Type u₃\ninst✝... | [
"case inj\nV : Type v\ninst✝⁷ : Category.{w, v} V\ninst✝⁶ : MonoidalCategory V\nC✝ : Type u₁\ninst✝⁵ : EnrichedCategory V C✝\nW : Type v'\ninst✝⁴ : Category.{w', v'} W\ninst✝³ : MonoidalCategory W\nC : Type u₁\ninst✝² : EnrichedCategory W C\nD : Type u₂\ninst✝¹ : EnrichedCategory W D\nE : Type u₃\ninst✝ : EnrichedC... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat | {
"line": 130,
"column": 4
} | {
"line": 130,
"column": 15
} | {
"line": 130,
"column": 16
} | [
{
"pp": "X : Truncated 2\nC : Type u\ninst✝ : Category.{u, u} C\nF G : X ⟶ (truncation 2).obj (nerve C)\nh : map F = map G\nx₀ x₁ : X.obj (op { obj := ⦋0⦌, property := Truncated.Edge._proof_1 })\nf : Truncated.Edge x₀ x₁\n⊢ (ConcreteCategory.hom (F.app (op { obj := ⦋1⦌, property := ⋯ }))) f.edge =\n (Concret... | [
"X : Truncated 2\nC : Type u\ninst✝ : Category.{u, u} C\nF G : X ⟶ (truncation 2).obj (nerve C)\nh : map F = map G\nx₀ x₁ : X.obj (op { obj := ⦋0⦌, property := Truncated.Edge._proof_1 })\nf : Truncated.Edge x₀ x₁\n⊢ (ConcreteCategory.hom (F.app (op { obj := ⦋1⦌, property := ⋯ }))) f.edge =\n (ConcreteCategory.ho... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.Reedy.Basic | {
"line": 69,
"column": 4
} | {
"line": 69,
"column": 52
} | {
"line": 69,
"column": 53
} | [
{
"pp": "C : Type u_1\ninst✝⁶ : Category.{v_1, u_1} C\nW₁ W₂ : MorphismProperty C\ninst✝⁵ : W₁.IsMultiplicative\ninst✝⁴ : W₂.IsMultiplicative\nα : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : OrderBot α\ninst✝¹ : SuccOrder α\ninst✝ : WellFoundedLT α\nr : ReedyStructure W₁ W₂ α\nX✝ Y✝ : Cᵒᵖ\nf : X✝ ⟶ Y✝\nhf : W₂.o... | [
"C : Type u_1\ninst✝⁶ : Category.{v_1, u_1} C\nW₁ W₂ : MorphismProperty C\ninst✝⁵ : W₁.IsMultiplicative\ninst✝⁴ : W₂.IsMultiplicative\nα : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : OrderBot α\ninst✝¹ : SuccOrder α\ninst✝ : WellFoundedLT α\nr : ReedyStructure W₁ W₂ α\nX✝ Y✝ : Cᵒᵖ\nf : X✝ ⟶ Y✝\nhf : W₂.op f\nhf' : ¬... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.Reedy.Basic | {
"line": 71,
"column": 4
} | {
"line": 71,
"column": 52
} | {
"line": 71,
"column": 53
} | [
{
"pp": "C : Type u_1\ninst✝⁶ : Category.{v_1, u_1} C\nW₁ W₂ : MorphismProperty C\ninst✝⁵ : W₁.IsMultiplicative\ninst✝⁴ : W₂.IsMultiplicative\nα : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : OrderBot α\ninst✝¹ : SuccOrder α\ninst✝ : WellFoundedLT α\nr : ReedyStructure W₁ W₂ α\nX✝ Y✝ : Cᵒᵖ\nf : X✝ ⟶ Y✝\nhf : W₁.o... | [
"C : Type u_1\ninst✝⁶ : Category.{v_1, u_1} C\nW₁ W₂ : MorphismProperty C\ninst✝⁵ : W₁.IsMultiplicative\ninst✝⁴ : W₂.IsMultiplicative\nα : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : OrderBot α\ninst✝¹ : SuccOrder α\ninst✝ : WellFoundedLT α\nr : ReedyStructure W₁ W₂ α\nX✝ Y✝ : Cᵒᵖ\nf : X✝ ⟶ Y✝\nhf : W₁.op f\nhf' : ¬... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.Reedy.Basic | {
"line": 156,
"column": 2
} | {
"line": 156,
"column": 13
} | {
"line": 156,
"column": 14
} | [
{
"pp": "C : Type u_1\ninst✝⁶ : Category.{v_1, u_1} C\nW₁ W₂ : MorphismProperty C\ninst✝⁵ : W₁.IsMultiplicative\ninst✝⁴ : W₂.IsMultiplicative\nα : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : OrderBot α\ninst✝¹ : SuccOrder α\ninst✝ : WellFoundedLT α\nr : ReedyStructure W₁ W₂ α\nX Y : C\nf : X ⟶ Y\n⊢ r.degHom f ≤ ... | [
"C : Type u_1\ninst✝⁶ : Category.{v_1, u_1} C\nW₁ W₂ : MorphismProperty C\ninst✝⁵ : W₁.IsMultiplicative\ninst✝⁴ : W₂.IsMultiplicative\nα : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : OrderBot α\ninst✝¹ : SuccOrder α\ninst✝ : WellFoundedLT α\nr : ReedyStructure W₁ W₂ α\nX Y : C\nf : X ⟶ Y\n⊢ r.degHom f ≤ r.deg X"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.Reedy.Basic | {
"line": 160,
"column": 2
} | {
"line": 160,
"column": 13
} | {
"line": 160,
"column": 14
} | [
{
"pp": "C : Type u_1\ninst✝⁶ : Category.{v_1, u_1} C\nW₁ W₂ : MorphismProperty C\ninst✝⁵ : W₁.IsMultiplicative\ninst✝⁴ : W₂.IsMultiplicative\nα : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : OrderBot α\ninst✝¹ : SuccOrder α\ninst✝ : WellFoundedLT α\nr : ReedyStructure W₁ W₂ α\nX Y : C\nf : X ⟶ Y\n⊢ r.degHom f ≤ ... | [
"C : Type u_1\ninst✝⁶ : Category.{v_1, u_1} C\nW₁ W₂ : MorphismProperty C\ninst✝⁵ : W₁.IsMultiplicative\ninst✝⁴ : W₂.IsMultiplicative\nα : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : OrderBot α\ninst✝¹ : SuccOrder α\ninst✝ : WellFoundedLT α\nr : ReedyStructure W₁ W₂ α\nX Y : C\nf : X ⟶ Y\n⊢ r.degHom f ≤ r.deg Y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.Reedy.Basic | {
"line": 178,
"column": 27
} | {
"line": 178,
"column": 38
} | {
"line": 178,
"column": 39
} | [
{
"pp": "C : Type u_1\ninst✝⁶ : Category.{v_1, u_1} C\nW₁ W₂ : MorphismProperty C\ninst✝⁵ : W₁.IsMultiplicative\ninst✝⁴ : W₂.IsMultiplicative\nα : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : OrderBot α\ninst✝¹ : SuccOrder α\ninst✝ : WellFoundedLT α\nr : ReedyStructure W₁ W₂ α\nX✝ Y✝ : C\nf : X✝ ⟶ Y✝\nhf : r.degH... | [
"C : Type u_1\ninst✝⁶ : Category.{v_1, u_1} C\nW₁ W₂ : MorphismProperty C\ninst✝⁵ : W₁.IsMultiplicative\ninst✝⁴ : W₂.IsMultiplicative\nα : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : OrderBot α\ninst✝¹ : SuccOrder α\ninst✝ : WellFoundedLT α\nr : ReedyStructure W₁ W₂ α\nX✝ Y✝ : C\nf : X✝ ⟶ Y✝\nhf : r.degHom f = r.deg... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.Reedy.Basic | {
"line": 185,
"column": 27
} | {
"line": 185,
"column": 38
} | {
"line": 185,
"column": 39
} | [
{
"pp": "C : Type u_1\ninst✝⁶ : Category.{v_1, u_1} C\nW₁ W₂ : MorphismProperty C\ninst✝⁵ : W₁.IsMultiplicative\ninst✝⁴ : W₂.IsMultiplicative\nα : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : OrderBot α\ninst✝¹ : SuccOrder α\ninst✝ : WellFoundedLT α\nr : ReedyStructure W₁ W₂ α\nX✝ Y✝ : C\nf : X✝ ⟶ Y✝\nhf : r.degH... | [
"C : Type u_1\ninst✝⁶ : Category.{v_1, u_1} C\nW₁ W₂ : MorphismProperty C\ninst✝⁵ : W₁.IsMultiplicative\ninst✝⁴ : W₂.IsMultiplicative\nα : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : OrderBot α\ninst✝¹ : SuccOrder α\ninst✝ : WellFoundedLT α\nr : ReedyStructure W₁ W₂ α\nX✝ Y✝ : C\nf : X✝ ⟶ Y✝\nhf : r.degHom f = r.deg... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.Reedy.Basic | {
"line": 212,
"column": 6
} | {
"line": 212,
"column": 17
} | {
"line": 212,
"column": 18
} | [
{
"pp": "case refine_1\nC : Type u_1\ninst✝⁶ : Category.{v_1, u_1} C\nW₁ W₂ : MorphismProperty C\ninst✝⁵ : W₁.IsMultiplicative\ninst✝⁴ : W₂.IsMultiplicative\nα : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : OrderBot α\ninst✝¹ : SuccOrder α\ninst✝ : WellFoundedLT α\nr : ReedyStructure W₁ W₂ α\nX Y : C\ne : X ≅ Y\n... | [
"case refine_1\nC : Type u_1\ninst✝⁶ : Category.{v_1, u_1} C\nW₁ W₂ : MorphismProperty C\ninst✝⁵ : W₁.IsMultiplicative\ninst✝⁴ : W₂.IsMultiplicative\nα : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : OrderBot α\ninst✝¹ : SuccOrder α\ninst✝ : WellFoundedLT α\nr : ReedyStructure W₁ W₂ α\nX Y : C\ne : X ≅ Y\n⊢ r.degHom e... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.Reedy.Basic | {
"line": 213,
"column": 6
} | {
"line": 213,
"column": 17
} | {
"line": 213,
"column": 18
} | [
{
"pp": "case refine_2\nC : Type u_1\ninst✝⁶ : Category.{v_1, u_1} C\nW₁ W₂ : MorphismProperty C\ninst✝⁵ : W₁.IsMultiplicative\ninst✝⁴ : W₂.IsMultiplicative\nα : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : OrderBot α\ninst✝¹ : SuccOrder α\ninst✝ : WellFoundedLT α\nr : ReedyStructure W₁ W₂ α\nX Y : C\ne : X ≅ Y\n... | [
"case refine_2\nC : Type u_1\ninst✝⁶ : Category.{v_1, u_1} C\nW₁ W₂ : MorphismProperty C\ninst✝⁵ : W₁.IsMultiplicative\ninst✝⁴ : W₂.IsMultiplicative\nα : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : OrderBot α\ninst✝¹ : SuccOrder α\ninst✝ : WellFoundedLT α\nr : ReedyStructure W₁ W₂ α\nX Y : C\ne : X ≅ Y\n⊢ r.deg Y ≤ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.EpiMono | {
"line": 34,
"column": 4
} | {
"line": 34,
"column": 31
} | {
"line": 35,
"column": 4
} | [
{
"pp": "n : ℕ\ni : Fin (n + 2)\n⊢ δ i ≫ Fin.lastCases (σ (Fin.last n)) (fun i ↦ σ i) i = 𝟙 (mk n)",
"ppTerm": "?m.33",
"assigned": true,
"usedConstants": [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"SimplexCategoryGenRel.mk",
"CategoryTheory.CategoryStruct.id"... | [
"case last\nn : ℕ\n⊢ δ (Fin.last (n + 1)) ≫ Fin.lastCases (σ (Fin.last n)) (fun i ↦ σ i) (Fin.last (n + 1)) = 𝟙 (mk n)",
"case cast\nn : ℕ\ni✝ : Fin (n + 1)\n⊢ δ i✝.castSucc ≫ Fin.lastCases (σ (Fin.last n)) (fun i ↦ σ i) i✝.castSucc = 𝟙 (mk n)"
] | cases i using Fin.lastCases | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalCases | Lean.Parser.Tactic.cases |
Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.EpiMono | {
"line": 154,
"column": 8
} | {
"line": 154,
"column": 19
} | {
"line": 154,
"column": 20
} | [
{
"pp": "case zero.comp_of.inl\ni : Fin (0 + 1)\nX Y : SimplexCategoryGenRel\nk : Fin (0 + 2)\nhf : faces.multiplicativeClosure (eqToHom ⋯)\n⊢ ∃ z e m, ∃ (_ : P_σ e) (_ : P_δ m), (eqToHom ⋯ ≫ δ k) ≫ σ i = e ≫ m",
"ppTerm": "?zero.comp_of.inl",
"assigned": true,
"usedConstants": [
"Eq.mpr",
... | [
"case zero.comp_of.inl\ni : Fin (0 + 1)\nX Y : SimplexCategoryGenRel\nk : Fin (0 + 2)\nhf : faces.multiplicativeClosure (eqToHom ⋯)\n⊢ ∃ z e m, P_δ m ∧ P_σ e ∧ δ k ≫ σ i = e ≫ m"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.EpiMono | {
"line": 163,
"column": 8
} | {
"line": 163,
"column": 19
} | {
"line": 163,
"column": 20
} | [
{
"pp": "case succ.comp_of.inl\nn : ℕ\nhn :\n ∀ (i : Fin (n + 1)) {x : SimplexCategoryGenRel} (f : x ⟶ mk (n + 1)),\n P_δ f → ∃ z e m, ∃ (_ : P_σ e) (_ : P_δ m), f ≫ σ i = e ≫ m\ni : Fin (n + 1 + 1)\nX Y : SimplexCategoryGenRel\nk : Fin (n + 1 + 2)\nhf : faces.multiplicativeClosure (eqToHom ⋯)\n⊢ ∃ z e m, ∃... | [
"case succ.comp_of.inl\nn : ℕ\nhn :\n ∀ (i : Fin (n + 1)) {x : SimplexCategoryGenRel} (f : x ⟶ mk (n + 1)),\n P_δ f → ∃ z e m, ∃ (_ : P_σ e) (_ : P_δ m), f ≫ σ i = e ≫ m\ni : Fin (n + 1 + 1)\nX Y : SimplexCategoryGenRel\nk : Fin (n + 1 + 2)\nhf : faces.multiplicativeClosure (eqToHom ⋯)\n⊢ ∃ z e m, P_δ m ∧ P_σ e... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.EpiMono | {
"line": 204,
"column": 4
} | {
"line": 204,
"column": 67
} | {
"line": 205,
"column": 4
} | [
{
"pp": "X✝ Y✝ : SimplexCategoryGenRel\nf : X✝ ⟶ Y✝\n⊢ Nonempty (P_σ.MapFactorizationData P_δ f)",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Exists",
"SimplexCategoryGenRel.exists_P_σ_P_δ_factorization",
... | [
"X✝ Y✝ : SimplexCategoryGenRel\nf : X✝ ⟶ Y✝\nz : SimplexCategoryGenRel\ne : X✝ ⟶ z\nm : z ⟶ Y✝\nhe : P_σ e\nhm : P_δ m\nfac : f = e ≫ m\n⊢ Nonempty (P_σ.MapFactorizationData P_δ f)"
] | obtain ⟨z, e, m, he, hm, fac⟩ := exists_P_σ_P_δ_factorization f | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal | {
"line": 153,
"column": 6
} | {
"line": 153,
"column": 17
} | {
"line": 153,
"column": 18
} | [
{
"pp": "X X' Y Y' Z : Truncated 2\nx₀ x₁ x₂ : X.obj (Opposite.op { obj := ⦋0⦌, property := OneTruncation₂._proof_1 })\ne₀₁ : Edge x₀ x₁\ne₁₂ : Edge x₁ x₂\ne₀₂ : Edge x₀ x₂\nh : e₀₁.CompStruct e₁₂ e₀₂\ny : Y.obj (Opposite.op { obj := ⦋0⦌, property := OneTruncation₂._proof_1 })\n⊢ (mkNatTrans (fun y ↦ homMk (e₀₁... | [
"X X' Y Y' Z : Truncated 2\nx₀ x₁ x₂ : X.obj (Opposite.op { obj := ⦋0⦌, property := OneTruncation₂._proof_1 })\ne₀₁ : Edge x₀ x₁\ne₁₂ : Edge x₁ x₂\ne₀₂ : Edge x₀ x₂\nh : e₀₁.CompStruct e₁₂ e₀₂\ny : Y.obj (Opposite.op { obj := ⦋0⦌, property := OneTruncation₂._proof_1 })\n⊢ homMk (e₀₁.tensor (Edge.id y)) ≫ homMk (e₁₂... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.NormalForms | {
"line": 259,
"column": 52
} | {
"line": 259,
"column": 68
} | {
"line": 259,
"column": 69
} | [
{
"pp": "L✝ : List ℕ\nj a : ℕ\nL : List ℕ\nh_rec :\n ∀ (m₁ m₂ : ℕ),\n IsAdmissible m₂ L →\n ∀ (hk : m₂ + L.length = m₁) (hj : j < m₁ + 1),\n ↑((SimplexCategory.Hom.toOrderHom (toSimplexCategory.map (standardσ L hk))) ⟨j, hj⟩) = simplicialEvalσ L j\nm₂ : ℕ\nhL : IsAdmissible m₂ (a :: L)\nhj : j <... | [
"L✝ : List ℕ\nj a : ℕ\nL : List ℕ\nh_rec :\n ∀ (m₁ m₂ : ℕ),\n IsAdmissible m₂ L →\n ∀ (hk : m₂ + L.length = m₁) (hj : j < m₁ + 1),\n ↑((SimplexCategory.Hom.toOrderHom (toSimplexCategory.map (standardσ L hk))) ⟨j, hj⟩) = simplicialEvalσ L j\nm₂ : ℕ\nhL : IsAdmissible m₂ (a :: L)\nhj : j < m₂ + (L.len... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.NormalForms | {
"line": 260,
"column": 4
} | {
"line": 263,
"column": 89
} | {
"line": 263,
"column": 90
} | [
{
"pp": "case cons\nL✝ : List ℕ\nj a : ℕ\nL : List ℕ\nh_rec :\n ∀ (m₁ m₂ : ℕ),\n IsAdmissible m₂ L →\n ∀ (hk : m₂ + L.length = m₁) (hj : j < m₁ + 1),\n ↑((SimplexCategory.Hom.toOrderHom (toSimplexCategory.map (standardσ L hk))) ⟨j, hj⟩) = simplicialEvalσ L j\nm₂ : ℕ\nhL : IsAdmissible m₂ (a :: L... | [
"case cons\nL✝ : List ℕ\nj a : ℕ\nL : List ℕ\nh_rec :\n ∀ (m₁ m₂ : ℕ),\n IsAdmissible m₂ L →\n ∀ (hk : m₂ + L.length = m₁) (hj : j < m₁ + 1),\n ↑((SimplexCategory.Hom.toOrderHom (toSimplexCategory.map (standardσ L hk))) ⟨j, hj⟩) = simplicialEvalσ L j\nm₂ : ℕ\nhL : IsAdmissible m₂ (a :: L)\nhj : j < ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.UpperLower.Relative | {
"line": 150,
"column": 4
} | {
"line": 150,
"column": 66
} | {
"line": 150,
"column": 67
} | [
{
"pp": "case refine_2\nα : Type u_1\nP : α → Prop\ninst✝ : LE α\ns : Set { x // P x }\nh : IsRelUpperSet (Subtype.val '' s) P\na b : { x // P x }\nx : a ≤ b\ny : a ∈ s\nma : ↑a ∈ Subtype.val '' s\n⊢ b ∈ s",
"ppTerm": "?refine_2",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"use... | [
"case refine_2\nα : Type u_1\nP : α → Prop\ninst✝ : LE α\ns : Set { x // P x }\nh : IsRelUpperSet (Subtype.val '' s) P\na b : { x // P x }\nx : a ≤ b\ny : a ∈ s\nma : ↑a ∈ Subtype.val '' s\n⊢ b ∈ s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.UpperLower.Relative | {
"line": 158,
"column": 4
} | {
"line": 158,
"column": 66
} | {
"line": 158,
"column": 67
} | [
{
"pp": "case refine_2\nα : Type u_1\nP : α → Prop\ninst✝ : LE α\ns : Set { x // P x }\nh : IsRelLowerSet (Subtype.val '' s) P\na b : { x // P x }\nx : b ≤ a\ny : a ∈ s\nma : ↑a ∈ Subtype.val '' s\n⊢ b ∈ s",
"ppTerm": "?refine_2",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"use... | [
"case refine_2\nα : Type u_1\nP : α → Prop\ninst✝ : LE α\ns : Set { x // P x }\nh : IsRelLowerSet (Subtype.val '' s) P\na b : { x // P x }\nx : b ≤ a\ny : a ∈ s\nma : ↑a ∈ Subtype.val '' s\n⊢ b ∈ s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialComplex.Basic | {
"line": 94,
"column": 49
} | {
"line": 95,
"column": 72
} | {
"line": 95,
"column": 73
} | [
{
"pp": "ι : Type u_1\ns : Set (PreAbstractSimplicialComplex ι)\nx✝¹ : Finset ι\nx✝ : x✝¹ ∈ (⋂ K ∈ s, K.faces) ∩ {t | t.Nonempty}\nhx : x✝¹ ∈ ⋂ K ∈ s, K.faces\nhn : x✝¹ ∈ {t | t.Nonempty}\n⊢ x✝¹.Nonempty ∧ ∀ ⦃b : Finset ι⦄, b ⊆ x✝¹ → b.Nonempty → b ∈ (⋂ K ∈ s, K.faces) ∩ {t | t.Nonempty}",
"ppTerm": "?m.37"... | [] | by
grind [IsRelLowerSet.mem_of_le, isRelLowerSet_faces, mem_iInter] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.AlgebraicTopology.SimplicialObject.II | {
"line": 95,
"column": 24
} | {
"line": 95,
"column": 35
} | {
"line": 95,
"column": 36
} | [
{
"pp": "n m : ℕ\nf : Fin (n + 1) →o Fin (m + 1)\nx : Fin (m + 2)\ny : Fin (n + 1)\nh : x ≤ (f y).castSucc\nh' : ∀ b ∈ finset f x, y.castSucc ≤ b\ni : Fin (n + 1)\nhi : i < y\nthis : x ≤ (f i).castSucc\n⊢ y ≤ i",
"ppTerm": "?m.77",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"us... | [
"n m : ℕ\nf : Fin (n + 1) →o Fin (m + 1)\nx : Fin (m + 2)\ny : Fin (n + 1)\nh : x ≤ (f y).castSucc\nh' : ∀ b ∈ finset f x, y.castSucc ≤ b\ni : Fin (n + 1)\nhi : i < y\nthis : x ≤ (f i).castSucc\n⊢ y ≤ i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialObject.II | {
"line": 100,
"column": 35
} | {
"line": 100,
"column": 46
} | {
"line": 100,
"column": 47
} | [
{
"pp": "n m : ℕ\nf : Fin (n + 1) →o Fin (m + 1)\nx : Fin (m + 2)\ny : Fin (n + 1)\nh : x ≤ (f y).castSucc\nh' : ∀ i < y, (f i).castSucc < x\ni : Fin (n + 1)\nhi : i.castSucc ∈ finset f x\nthis : i < y\n⊢ x ≤ (f i).castSucc",
"ppTerm": "?m.151",
"assigned": false,
"usedConstants": [],
"usedFVars... | [
"n m : ℕ\nf : Fin (n + 1) →o Fin (m + 1)\nx : Fin (m + 2)\ny : Fin (n + 1)\nh : x ≤ (f y).castSucc\nh' : ∀ i < y, (f i).castSucc < x\ni : Fin (n + 1)\nhi : i.castSucc ∈ finset f x\nthis : i < y\n⊢ x ≤ (f i).castSucc"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Monoidal | {
"line": 208,
"column": 6
} | {
"line": 208,
"column": 66
} | {
"line": 208,
"column": 67
} | [
{
"pp": "case left\nx✝ y✝ z✝ : AugmentedSimplexCategory\nf✝ g✝ : x✝ ⊗ y✝ ⟶ z✝\nx y z : SimplexCategory\nf g : tensorObjOf x y ⟶ z\nh₁ : ⇑(SimplexCategory.Hom.toOrderHom (inl' x y ≫ f)) = ⇑(SimplexCategory.Hom.toOrderHom (inl' x y ≫ g))\nh₂ : inr' x y ≫ f = inr' x y ≫ g\ni : Fin ((tensorObjOf x y).len + 1)\nj✝ :... | [
"case left\nx✝ y✝ z✝ : AugmentedSimplexCategory\nf✝ g✝ : x✝ ⊗ y✝ ⟶ z✝\nx y z : SimplexCategory\nf g : tensorObjOf x y ⟶ z\nh₁ : ⇑(SimplexCategory.Hom.toOrderHom (inl' x y ≫ f)) = ⇑(SimplexCategory.Hom.toOrderHom (inl' x y ≫ g))\nh₂ : inr' x y ≫ f = inr' x y ≫ g\ni : Fin ((tensorObjOf x y).len + 1)\nj✝ : Fin (x.len ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Monoidal | {
"line": 211,
"column": 6
} | {
"line": 211,
"column": 66
} | {
"line": 211,
"column": 67
} | [
{
"pp": "case right\nx✝ y✝ z✝ : AugmentedSimplexCategory\nf✝ g✝ : x✝ ⊗ y✝ ⟶ z✝\nx y z : SimplexCategory\nf g : tensorObjOf x y ⟶ z\nh₁ : inl' x y ≫ f = inl' x y ≫ g\nh₂ : ⇑(SimplexCategory.Hom.toOrderHom (inr' x y ≫ f)) = ⇑(SimplexCategory.Hom.toOrderHom (inr' x y ≫ g))\ni : Fin ((tensorObjOf x y).len + 1)\nj✝ ... | [
"case right\nx✝ y✝ z✝ : AugmentedSimplexCategory\nf✝ g✝ : x✝ ⊗ y✝ ⟶ z✝\nx y z : SimplexCategory\nf g : tensorObjOf x y ⟶ z\nh₁ : inl' x y ≫ f = inl' x y ≫ g\nh₂ : ⇑(SimplexCategory.Hom.toOrderHom (inr' x y ≫ f)) = ⇑(SimplexCategory.Hom.toOrderHom (inr' x y ≫ g))\ni : Fin ((tensorObjOf x y).len + 1)\nj✝ : Fin (x.len... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Monoidal | {
"line": 215,
"column": 6
} | {
"line": 215,
"column": 58
} | {
"line": 215,
"column": 59
} | [
{
"pp": "x✝ y z✝ : AugmentedSimplexCategory\nf✝ g✝ : x✝ ⊗ y ⟶ z✝\nx z : SimplexCategory\nf g : WithInitial.of x ⊗ WithInitial.star ⟶ WithInitial.of z\nh₂ : inr (WithInitial.of x) WithInitial.star ≫ f = inr (WithInitial.of x) WithInitial.star ≫ g\nh₁ : 𝟙 (WithInitial.of x ⊗ WithInitial.star) ≫ f = 𝟙 (WithIniti... | [
"x✝ y z✝ : AugmentedSimplexCategory\nf✝ g✝ : x✝ ⊗ y ⟶ z✝\nx z : SimplexCategory\nf g : WithInitial.of x ⊗ WithInitial.star ⟶ WithInitial.of z\nh₂ : inr (WithInitial.of x) WithInitial.star ≫ f = inr (WithInitial.of x) WithInitial.star ≫ g\nh₁ : 𝟙 (WithInitial.of x ⊗ WithInitial.star) ≫ f = 𝟙 (WithInitial.of x ⊗ Wi... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialObject.II | {
"line": 133,
"column": 31
} | {
"line": 133,
"column": 42
} | {
"line": 133,
"column": 43
} | [
{
"pp": "n m p : ℕ\nf : Fin (n + 1) →o Fin (m + 1)\ng : Fin (m + 1) →o Fin (p + 1)\nx : Fin (p + 1)\ny : Fin (m + 1)\nhy : x.castSucc ≤ (g y).castSucc ∧ ∀ i < y, (g i).castSucc < x.castSucc\nz : Fin (n + 1)\nhz : y.castSucc ≤ (f z).castSucc ∧ ∀ i < z, (f i).castSucc < y.castSucc\n⊢ y ≤ f z",
"ppTerm": "?m.1... | [
"n m p : ℕ\nf : Fin (n + 1) →o Fin (m + 1)\ng : Fin (m + 1) →o Fin (p + 1)\nx : Fin (p + 1)\ny : Fin (m + 1)\nhy : x.castSucc ≤ (g y).castSucc ∧ ∀ i < y, (g i).castSucc < x.castSucc\nz : Fin (n + 1)\nhz : y.castSucc ≤ (f z).castSucc ∧ ∀ i < z, (f i).castSucc < y.castSucc\n⊢ y ≤ f z"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Monoidal | {
"line": 219,
"column": 6
} | {
"line": 219,
"column": 58
} | {
"line": 219,
"column": 59
} | [
{
"pp": "x y✝ z✝ : AugmentedSimplexCategory\nf✝ g✝ : x ⊗ y✝ ⟶ z✝\ny z : SimplexCategory\nf g : WithInitial.star ⊗ WithInitial.of y ⟶ WithInitial.of z\nh₁ : inl WithInitial.star (WithInitial.of y) ≫ f = inl WithInitial.star (WithInitial.of y) ≫ g\nh₂ : 𝟙 (WithInitial.star ⊗ WithInitial.of y) ≫ f = 𝟙 (WithIniti... | [
"x y✝ z✝ : AugmentedSimplexCategory\nf✝ g✝ : x ⊗ y✝ ⟶ z✝\ny z : SimplexCategory\nf g : WithInitial.star ⊗ WithInitial.of y ⟶ WithInitial.of z\nh₁ : inl WithInitial.star (WithInitial.of y) ≫ f = inl WithInitial.star (WithInitial.of y) ≫ g\nh₂ : 𝟙 (WithInitial.star ⊗ WithInitial.of y) ≫ f = 𝟙 (WithInitial.star ⊗ Wi... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialObject.II | {
"line": 135,
"column": 31
} | {
"line": 135,
"column": 42
} | {
"line": 135,
"column": 43
} | [
{
"pp": "n m p : ℕ\nf : Fin (n + 1) →o Fin (m + 1)\ng : Fin (m + 1) →o Fin (p + 1)\nx : Fin (p + 1)\ny : Fin (m + 1)\nhy : x.castSucc ≤ (g y).castSucc ∧ ∀ i < y, (g i).castSucc < x.castSucc\nz : Fin (n + 1)\nhz : y.castSucc ≤ (f z).castSucc ∧ ∀ i < z, (f i).castSucc < y.castSucc\ni : Fin (n + 1)\nhi : i < z\n⊢ ... | [
"n m p : ℕ\nf : Fin (n + 1) →o Fin (m + 1)\ng : Fin (m + 1) →o Fin (p + 1)\nx : Fin (p + 1)\ny : Fin (m + 1)\nhy : x.castSucc ≤ (g y).castSucc ∧ ∀ i < y, (g i).castSucc < x.castSucc\nz : Fin (n + 1)\nhz : y.castSucc ≤ (f z).castSucc ∧ ∀ i < z, (f i).castSucc < y.castSucc\ni : Fin (n + 1)\nhi : i < z\n⊢ f i < y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialObject.II | {
"line": 139,
"column": 29
} | {
"line": 139,
"column": 40
} | {
"line": 139,
"column": 41
} | [
{
"pp": "n m p : ℕ\nf : Fin (n + 1) →o Fin (m + 1)\ng : Fin (m + 1) →o Fin (p + 1)\nx : Fin (p + 1)\ny : Fin (m + 1)\nhy : x.castSucc ≤ (g y).castSucc ∧ ∀ i < y, (g i).castSucc < x.castSucc\nhz : ∀ (i : Fin (n + 1)), (f i).castSucc < y.castSucc\ni : Fin (n + 1)\n⊢ f i < y",
"ppTerm": "?m.236",
"assigned... | [
"n m p : ℕ\nf : Fin (n + 1) →o Fin (m + 1)\ng : Fin (m + 1) →o Fin (p + 1)\nx : Fin (p + 1)\ny : Fin (m + 1)\nhy : x.castSucc ≤ (g y).castSucc ∧ ∀ i < y, (g i).castSucc < x.castSucc\nhz : ∀ (i : Fin (n + 1)), (f i).castSucc < y.castSucc\ni : Fin (n + 1)\n⊢ f i < y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialObject.II | {
"line": 159,
"column": 12
} | {
"line": 159,
"column": 58
} | {
"line": 159,
"column": 59
} | [
{
"pp": "case pos.inl.left.inr\nn : ℕ\nx : Fin (n + 1)\nhx : x.castSucc ≤ x.castSucc\n⊢ x.castSucc ≤ x.castSucc.succAbove x",
"ppTerm": "?pos.inl.left.inr✝",
"assigned": true,
"usedConstants": [
"Fin.succAbove",
"Eq.mpr",
"Fin.succ",
"Fin.succAbove_castSucc_self",
"cong... | [
"case pos.inl.left.inr\nn : ℕ\nx : Fin (n + 1)\nhx : x.castSucc ≤ x.castSucc\n⊢ x.castSucc ≤ x.succ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialObject.II | {
"line": 173,
"column": 8
} | {
"line": 173,
"column": 56
} | {
"line": 173,
"column": 57
} | [
{
"pp": "case pos\nn : ℕ\ni : Fin (n + 2)\nx : Fin (n + 1)\nhx : i < x.succ\nj : Fin (n + 1)\nhj : j < x\nh : j.castSucc < i\n⊢ i.succAbove j < x.succ",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstants": [
"Fin.succAbove",
"Eq.mpr",
"Fin.succ",
"congrArg",
"id",
... | [
"case pos\nn : ℕ\ni : Fin (n + 2)\nx : Fin (n + 1)\nhx : i < x.succ\nj : Fin (n + 1)\nhj : j < x\nh : j.castSucc < i\n⊢ j ≤ x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialObject.II | {
"line": 187,
"column": 14
} | {
"line": 187,
"column": 57
} | {
"line": 187,
"column": 58
} | [
{
"pp": "n : ℕ\ni x : Fin (n + 1)\nhi : i < x\n⊢ i.castSucc < x.succ",
"ppTerm": "?m.98",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"_private.Mathlib.AlgebraicTopology.SimplicialObject.II.0.SimplexCategory.II.map'_predAbove._simp_1_3",
"Fin.succ",
"id",
"instOfNatN... | [
"n : ℕ\ni x : Fin (n + 1)\nhi : i < x\n⊢ i ≤ x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialObject.II | {
"line": 202,
"column": 8
} | {
"line": 203,
"column": 43
} | {
"line": 204,
"column": 8
} | [
{
"pp": "case pos\nn : ℕ\ni x : Fin (n + 1)\nhi : x ≤ i\nj : Fin (n + 1 + 1)\nhj : j < x.castSucc\nh : i.castSucc < j\n⊢ i.predAbove j < x",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Fin.ne_zero_of_lt",
"Fin.succ",
"Fin.pred",
"congrArg",
... | [
"case neg\nn : ℕ\ni x : Fin (n + 1)\nhi : x ≤ i\nj : Fin (n + 1 + 1)\nhj : j < x.castSucc\nh : j ≤ i.castSucc\n⊢ i.predAbove j < x"
] | · rw [Fin.predAbove_of_castSucc_lt _ _ h, ← Fin.succ_lt_succ_iff, Fin.succ_pred]
exact hj.trans x.castSucc_lt_succ | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.AlgebraicTopology.SimplicialObject.II | {
"line": 209,
"column": 25
} | {
"line": 215,
"column": 11
} | {
"line": 217,
"column": 0
} | [
{
"pp": "n m : ℕ\nf : Fin (n + 1) →o Fin (m + 1)\n⊢ Monotone (map' f)",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"SimplexCategory.II.finset",
"SimplexCategory.II.castSucc_mem_finset_iff._simp_1",
"Finset",
"PartialOrder.toPreorder",
"Preor... | [] | by
intro x y hxy
exact Finset.min'_subset _ (fun z hz ↦ by
obtain ⟨z, rfl⟩ | rfl := z.eq_castSucc_or_eq_last
· simp only [castSucc_mem_finset_iff] at hz ⊢
exact hxy.trans hz
· simp) | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.AlgebraicTopology.SimplicialNerve | {
"line": 107,
"column": 23
} | {
"line": 107,
"column": 34
} | {
"line": 107,
"column": 35
} | [
{
"pp": "J : Type u_1\ninst✝ : LinearOrder J\nX✝ Y✝ : SimplicialThickening J\nf : X✝ ⟶ Y✝\nt✝ : J\n⊢ t✝ ∈ (𝟙 X✝ ≫ f).I ↔ t✝ ∈ f.I",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"CategoryTheory.SimplicialThickening",
"congrArg",
"CategoryTheory.Simplicial... | [
"J : Type u_1\ninst✝ : LinearOrder J\nX✝ Y✝ : SimplicialThickening J\nf : X✝ ⟶ Y✝\nt✝ : J\n⊢ t✝ = X✝.as → t✝ ∈ f.I"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialNerve | {
"line": 108,
"column": 23
} | {
"line": 108,
"column": 34
} | {
"line": 108,
"column": 35
} | [
{
"pp": "J : Type u_1\ninst✝ : LinearOrder J\nX✝ Y✝ : SimplicialThickening J\nf : X✝ ⟶ Y✝\nt✝ : J\n⊢ t✝ ∈ (f ≫ 𝟙 Y✝).I ↔ t✝ ∈ f.I",
"ppTerm": "?m.53",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"CategoryTheory.SimplicialThickening",
"congrArg",
"CategoryTheory.Simplicial... | [
"J : Type u_1\ninst✝ : LinearOrder J\nX✝ Y✝ : SimplicialThickening J\nf : X✝ ⟶ Y✝\nt✝ : J\n⊢ t✝ = Y✝.as → t✝ ∈ f.I"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.NonDegenerateSimplicesSubcomplex | {
"line": 74,
"column": 29
} | {
"line": 74,
"column": 40
} | {
"line": 74,
"column": 41
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nmotive : X.N → Prop\nmem : ∀ (s : X.N), s.subcomplex ≤ A → motive s\nnotMem : ∀ (s : A.N), motive s.toN\ns : X.N\nhs : ¬s.subcomplex ≤ A\n⊢ s.simplex ∉ A.obj (Opposite.op ⦋s.dim⦌)",
"ppTerm": "?m.22",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
... | [
"X : SSet\nA : X.Subcomplex\nmotive : X.N → Prop\nmem : ∀ (s : X.N), s.subcomplex ≤ A → motive s\nnotMem : ∀ (s : A.N), motive s.toN\ns : X.N\nhs : ¬s.subcomplex ≤ A\n⊢ s.simplex ∉ A.obj (Opposite.op ⦋s.dim⦌)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.NonDegenerateSimplicesSubcomplex | {
"line": 141,
"column": 2
} | {
"line": 141,
"column": 13
} | {
"line": 141,
"column": 14
} | [
{
"pp": "X : SSet\nn : ℕ\ns : X _⦋n⦌\nA : X.Subcomplex\nhs : s ∉ A.obj (Opposite.op ⦋n⦌)\nh : ofSimplex { dim := n, simplex := s }.toN.simplex ≤ A\n⊢ ofSimplex s ≤ A",
"ppTerm": "?m.64",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"SSet.Subcomplex.ofSimplex",
"Opposite",
"... | [
"X : SSet\nn : ℕ\ns : X _⦋n⦌\nA : X.Subcomplex\nhs : s ∉ A.obj (Opposite.op ⦋n⦌)\nh : ofSimplex { dim := n, simplex := s }.toN.simplex ≤ A\n⊢ s ∈ A.obj (Opposite.op ⦋n⦌)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Monoidal | {
"line": 347,
"column": 4
} | {
"line": 347,
"column": 94
} | {
"line": 348,
"column": 6
} | [
{
"pp": "case h₁\nx y : AugmentedSimplexCategory\n⊢ x.inl y ≫ (𝟙 x ⊗ₘ 𝟙 y) = x.inl y ≫ 𝟙 (x ⊗ y)",
"ppTerm": "?h₁",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
... | [
"case h₁\nx y : AugmentedSimplexCategory\n⊢ tensorHom (𝟙 x) (WithInitial.starInitial.to y) ≫ tensorHom (𝟙 x) (𝟙 y) =\n tensorHom (𝟙 x) (WithInitial.starInitial.to y)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Monoidal | {
"line": 349,
"column": 4
} | {
"line": 349,
"column": 94
} | {
"line": 350,
"column": 6
} | [
{
"pp": "case h₂\nx y : AugmentedSimplexCategory\n⊢ x.inr y ≫ (𝟙 x ⊗ₘ 𝟙 y) = x.inr y ≫ 𝟙 (x ⊗ y)",
"ppTerm": "?h₂",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
... | [
"case h₂\nx y : AugmentedSimplexCategory\n⊢ tensorHom (WithInitial.starInitial.to x) (𝟙 y) ≫ tensorHom (𝟙 x) (𝟙 y) =\n tensorHom (WithInitial.starInitial.to x) (𝟙 y)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.IsUniquelyCodimOneFace | {
"line": 70,
"column": 2
} | {
"line": 70,
"column": 32
} | {
"line": 70,
"column": 33
} | [
{
"pp": "X : SSet\nx y : X.S\nhxy : x.IsUniquelyCodimOneFace y\nd : ℕ\nhd : x.dim = d\n⊢ ∃! i, (ConcreteCategory.hom (SimplicialObject.δ X i)) (y.cast ⋯).simplex = (x.cast hd).simplex",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"SSet.S.simplex",
"Opposite",
"CategoryT... | [
"X : SSet\nx y : X.S\nhxy : x.IsUniquelyCodimOneFace y\nd : ℕ\nhd : x.dim = d\n⊢ ∃! i, (ConcreteCategory.hom (SimplicialObject.δ X i)) (_root_.cast ⋯ y.simplex) = _root_.cast ⋯ x.simplex"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.Pairing | {
"line": 101,
"column": 2
} | {
"line": 101,
"column": 73
} | {
"line": 102,
"column": 4
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nP : A.Pairing\ninst✝ : P.IsProper\nx y : ↑P.II\nhxy : P.AncestralRel x y\n⊢ (↑x).dim ≤ (↑y).dim",
"ppTerm": "?m.20",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"X : SSet\nA : X.Subcomplex\nP : A.Pairing\ninst✝ : P.IsProper\nx y : ↑P.II\nhxy : P.AncestralRel x y\n⊢ (↑x).dim ≤ (↑y).dim"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.IsUniquelyCodimOneFace | {
"line": 113,
"column": 34
} | {
"line": 113,
"column": 45
} | {
"line": 113,
"column": 46
} | [
{
"pp": "X : SSet\nd : ℕ\nx : X _⦋d⦌\ny : X _⦋d + 1⦌\nhxy : { dim := d, simplex := x }.IsUniquelyCodimOneFace { dim := d + 1, simplex := y }\n⊢ (fun i ↦ (ConcreteCategory.hom (SimplicialObject.δ X.op i)) (opObjEquiv.symm y) = opObjEquiv.symm x) (hxy.index ⋯).rev",
"ppTerm": "?m.100",
"assigned": true,
... | [
"X : SSet\nd : ℕ\nx : X _⦋d⦌\ny : X _⦋d + 1⦌\nhxy : { dim := d, simplex := x }.IsUniquelyCodimOneFace { dim := d + 1, simplex := y }\n⊢ (ConcreteCategory.hom (SimplicialObject.δ X (hxy.index ⋯))) y = x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.IsUniquelyCodimOneFace | {
"line": 115,
"column": 2
} | {
"line": 115,
"column": 34
} | {
"line": 115,
"column": 35
} | [
{
"pp": "X : SSet\nd : ℕ\nx : X _⦋d⦌\ny : X _⦋d + 1⦌\nhxy : { dim := d, simplex := x }.IsUniquelyCodimOneFace { dim := d + 1, simplex := y }\ni : Fin (d + 2)\nhi : (ConcreteCategory.hom (SimplicialObject.δ X.op i.rev)) (opObjEquiv.symm y) = opObjEquiv.symm x\n⊢ i.rev = (hxy.index ⋯).rev",
"ppTerm": "?m.135"... | [
"X : SSet\nd : ℕ\nx : X _⦋d⦌\ny : X _⦋d + 1⦌\nhxy : { dim := d, simplex := x }.IsUniquelyCodimOneFace { dim := d + 1, simplex := y }\ni : Fin (d + 2)\nhi : (ConcreteCategory.hom (SimplicialObject.δ X.op i.rev)) (opObjEquiv.symm y) = opObjEquiv.symm x\n⊢ (ConcreteCategory.hom (SimplicialObject.δ X i)) y = x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.IsUniquelyCodimOneFace | {
"line": 130,
"column": 17
} | {
"line": 130,
"column": 28
} | {
"line": 130,
"column": 29
} | [
{
"pp": "X Y : SSet\ne : X ≅ Y\nx y : X.S\nhxy' :\n { dim := x.dim, simplex := (ConcreteCategory.hom (e.hom.app (Opposite.op ⦋x.dim⦌))) x.simplex }.IsUniquelyCodimOneFace\n { dim := y.dim, simplex := (ConcreteCategory.hom (e.hom.app (Opposite.op ⦋y.dim⦌))) y.simplex }\n⊢ x.IsUniquelyCodimOneFace y",
"pp... | [
"X Y : SSet\ne : X ≅ Y\nx y : X.S\nhxy' :\n { dim := x.dim, simplex := (ConcreteCategory.hom (e.hom.app (Opposite.op ⦋x.dim⦌))) x.simplex }.IsUniquelyCodimOneFace\n { dim := y.dim, simplex := (ConcreteCategory.hom (e.hom.app (Opposite.op ⦋y.dim⦌))) y.simplex }\n⊢ x.IsUniquelyCodimOneFace y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.Pairing | {
"line": 202,
"column": 4
} | {
"line": 202,
"column": 49
} | {
"line": 202,
"column": 50
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nP : A.Pairing\nY : SSet\nB : Y.Subcomplex\ne : Y ≅ X\nhA : A.preimage e.hom = B\ninst✝ : P.IsRegular\nhP : IsEmpty { f // ∀ (n : ℕ), P.AncestralRel (f (n + 1)) (f n) }\nf : ℕ → ↑(P.ofIso e hA).II\nhf : ∀ (n : ℕ), (P.ofIso e hA).AncestralRel (f (n + 1)) (f n)\nn : ℕ\n⊢ P.Ance... | [
"X : SSet\nA : X.Subcomplex\nP : A.Pairing\nY : SSet\nB : Y.Subcomplex\ne : Y ≅ X\nhA : A.preimage e.hom = B\ninst✝ : P.IsRegular\nhP : IsEmpty { f // ∀ (n : ℕ), P.AncestralRel (f (n + 1)) (f n) }\nf : ℕ → ↑(P.ofIso e hA).II\nhf : ∀ (n : ℕ), (P.ofIso e hA).AncestralRel (f (n + 1)) (f n)\nn : ℕ\n⊢ (P.ofIso e hA).Anc... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.Pairing | {
"line": 218,
"column": 4
} | {
"line": 218,
"column": 52
} | {
"line": 218,
"column": 53
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nP : A.Pairing\nY : SSet\nB : Y.Subcomplex\ne : Y ≅ X\nhA : A.preimage e.hom = B\ninst✝¹ : P.IsProper\ninst✝ : P.IsInner\nd : ℕ\na : A.N\nhb✝ : (N.orderIsoOfIso e hA).symm a ∈ (P.ofIso e hA).II\nhd : (↑⟨(N.orderIsoOfIso e hA).symm a, hb✝⟩).dim = d\nhb : a ∈ P.II\n⊢ ⋯.index hd... | [
"X : SSet\nA : X.Subcomplex\nP : A.Pairing\nY : SSet\nB : Y.Subcomplex\ne : Y ≅ X\nhA : A.preimage e.hom = B\ninst✝¹ : P.IsProper\ninst✝ : P.IsInner\nd : ℕ\na : A.N\nhb✝ : (N.orderIsoOfIso e hA).symm a ∈ (P.ofIso e hA).II\nhd : (↑⟨(N.orderIsoOfIso e hA).symm a, hb✝⟩).dim = d\nhb : a ∈ P.II\n⊢ ⋯.index hd ≠ 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.Pairing | {
"line": 223,
"column": 4
} | {
"line": 223,
"column": 52
} | {
"line": 223,
"column": 53
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nP : A.Pairing\nY : SSet\nB : Y.Subcomplex\ne : Y ≅ X\nhA : A.preimage e.hom = B\ninst✝¹ : P.IsProper\ninst✝ : P.IsInner\nd : ℕ\na : A.N\nhb✝ : (N.orderIsoOfIso e hA).symm a ∈ (P.ofIso e hA).II\nhd : (↑⟨(N.orderIsoOfIso e hA).symm a, hb✝⟩).dim = d\nhb : a ∈ P.II\n⊢ ⋯.index hd... | [
"X : SSet\nA : X.Subcomplex\nP : A.Pairing\nY : SSet\nB : Y.Subcomplex\ne : Y ≅ X\nhA : A.preimage e.hom = B\ninst✝¹ : P.IsProper\ninst✝ : P.IsInner\nd : ℕ\na : A.N\nhb✝ : (N.orderIsoOfIso e hA).symm a ∈ (P.ofIso e hA).II\nhd : (↑⟨(N.orderIsoOfIso e hA).symm a, hb✝⟩).dim = d\nhb : a ∈ P.II\n⊢ ⋯.index hd ≠ Fin.last ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.ProdStdSimplex | {
"line": 123,
"column": 2
} | {
"line": 123,
"column": 94
} | {
"line": 123,
"column": 95
} | [
{
"pp": "p q n : ℕ\nx : ↑((Δ[p] ⊗ Δ[q]).nonDegenerate n)\nm : ℕ\nhm : p + q = m\n⊢ StrictMono ⇑(orderHomOfSimplex (↑x) hm)",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"_private.Mathlib.AlgebraicTopology.SimplicialSet.ProdStdSimplex.0.SSet.prodStdSimplex.strictMono_orderHomOfSimpl... | [
"p q n : ℕ\nx : ↑((Δ[p] ⊗ Δ[q]).nonDegenerate n)\nm : ℕ\nhm : p + q = m\n⊢ ↑x ∈ (Δ[p] ⊗ Δ[q]).nonDegenerate n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.Rank | {
"line": 139,
"column": 8
} | {
"line": 139,
"column": 49
} | {
"line": 140,
"column": 8
} | [
{
"pp": "X✝ : SSet\nA✝ : X✝.Subcomplex\nX : SSet\nA : X.Subcomplex\nh : A.PairingCore\nα : Type v\ninst✝ : PartialOrder α\nf : h.RankFunction α\ny : ↑h.pairing.II\nx : h.ι\nhxy : h.pairing.AncestralRel (h.equivII x) y\n⊢ f.rank (h.equivII.symm (h.equivII x)) < f.rank (h.equivII.symm y)",
"ppTerm": "?m.82",
... | [
"X✝ : SSet\nA✝ : X✝.Subcomplex\nX : SSet\nA : X.Subcomplex\nh : A.PairingCore\nα : Type v\ninst✝ : PartialOrder α\nf : h.RankFunction α\nx y : h.ι\nhxy : h.pairing.AncestralRel (h.equivII x) (h.equivII y)\n⊢ f.rank (h.equivII.symm (h.equivII x)) < f.rank (h.equivII.symm (h.equivII y))"
] | obtain ⟨y, rfl⟩ := h.equivII.surjective y | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.Rank | {
"line": 141,
"column": 8
} | {
"line": 141,
"column": 19
} | {
"line": 141,
"column": 20
} | [
{
"pp": "X✝ : SSet\nA✝ : X✝.Subcomplex\nX : SSet\nA : X.Subcomplex\nh : A.PairingCore\nα : Type v\ninst✝ : PartialOrder α\nf : h.RankFunction α\nx y : h.ι\nhxy : h.AncestralRel x y\n⊢ f.rank (h.equivII.symm (h.equivII x)) < f.rank (h.equivII.symm (h.equivII y))",
"ppTerm": "?m.114",
"assigned": true,
... | [
"X✝ : SSet\nA✝ : X✝.Subcomplex\nX : SSet\nA : X.Subcomplex\nh : A.PairingCore\nα : Type v\ninst✝ : PartialOrder α\nf : h.RankFunction α\nx y : h.ι\nhxy : h.AncestralRel x y\n⊢ f.rank x < f.rank y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.Rank | {
"line": 158,
"column": 8
} | {
"line": 158,
"column": 49
} | {
"line": 159,
"column": 8
} | [
{
"pp": "X✝ : SSet\nA✝ : X✝.Subcomplex\nX : SSet\nA : X.Subcomplex\nh : A.PairingCore\nα : Type v\ninst✝ : PartialOrder α\nf : h.WeakRankFunction α\ny : ↑h.pairing.II\nx : h.ι\nhxy : h.pairing.AncestralRel (h.equivII x) y\n⊢ (↑(h.equivII x)).dim = (↑y).dim → f.rank (h.equivII.symm (h.equivII x)) < f.rank (h.equ... | [
"X✝ : SSet\nA✝ : X✝.Subcomplex\nX : SSet\nA : X.Subcomplex\nh : A.PairingCore\nα : Type v\ninst✝ : PartialOrder α\nf : h.WeakRankFunction α\nx y : h.ι\nhxy : h.pairing.AncestralRel (h.equivII x) (h.equivII y)\n⊢ (↑(h.equivII x)).dim = (↑(h.equivII y)).dim →\n f.rank (h.equivII.symm (h.equivII x)) < f.rank (h.equ... | obtain ⟨y, rfl⟩ := h.equivII.surjective y | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.Rank | {
"line": 160,
"column": 8
} | {
"line": 160,
"column": 19
} | {
"line": 160,
"column": 20
} | [
{
"pp": "X✝ : SSet\nA✝ : X✝.Subcomplex\nX : SSet\nA : X.Subcomplex\nh : A.PairingCore\nα : Type v\ninst✝ : PartialOrder α\nf : h.WeakRankFunction α\nx y : h.ι\nhxy : h.AncestralRel x y\n⊢ (↑(h.equivII x)).dim = (↑(h.equivII y)).dim →\n f.rank (h.equivII.symm (h.equivII x)) < f.rank (h.equivII.symm (h.equivII... | [
"X✝ : SSet\nA✝ : X✝.Subcomplex\nX : SSet\nA : X.Subcomplex\nh : A.PairingCore\nα : Type v\ninst✝ : PartialOrder α\nf : h.WeakRankFunction α\nx y : h.ι\nhxy : h.AncestralRel x y\n⊢ h.dim x = h.dim y → f.rank x < f.rank y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RankNat | {
"line": 41,
"column": 6
} | {
"line": 41,
"column": 17
} | {
"line": 41,
"column": 18
} | [
{
"pp": "case refine_1\nX : SSet\nA : X.Subcomplex\nP : A.Pairing\ny : ↑P.II\nT : Type (max 0 u) := { x // P.AncestralRel x y }\nU : Type := (d : Fin (↑(P.p y)).dim) × (⦋↑d⦌ ⟶ ⦋(↑(P.p y)).dim⦌)\nψ : U → X.S :=\n fun x ↦\n match x with\n | ⟨d, f⟩ => { dim := ↑d, simplex := (CategoryTheory.ConcreteCategory... | [
"case refine_1\nX : SSet\nA : X.Subcomplex\nP : A.Pairing\ny : ↑P.II\nT : Type (max 0 u) := { x // P.AncestralRel x y }\nU : Type := (d : Fin (↑(P.p y)).dim) × (⦋↑d⦌ ⟶ ⦋(↑(P.p y)).dim⦌)\nψ : U → X.S :=\n fun x ↦\n match x with\n | ⟨d, f⟩ => { dim := ↑d, simplex := (CategoryTheory.ConcreteCategory.hom (X.map ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.FiniteColimits | {
"line": 91,
"column": 4
} | {
"line": 91,
"column": 43
} | {
"line": 93,
"column": 0
} | [
{
"pp": "case refine_2\nι : Type v\ninst✝¹ : HasColimitsOfShape (Discrete ι) (Type u)\nX : ι → SSet\nY : SSet\ninst✝ : HasCoproduct X\nf : ∐ X ⟶ Y\ni : ι\n⊢ Subcomplex.range (Sigma.ι X i ≫ f) ≤ ⨆ j, Subcomplex.range ((Cofan.mk (∐ X) (Sigma.ι X)).ι.app j ≫ f)",
"ppTerm": "?refine_2",
"assigned": true,
... | [] | exact le_trans (by rfl) (le_iSup _ ⟨i⟩) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.PairingCore | {
"line": 173,
"column": 2
} | {
"line": 173,
"column": 17
} | {
"line": 175,
"column": 0
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nh : A.PairingCore\nx : h.ι\n⊢ h.type₁ x = ↑(h.pairing.p (h.equivII x))",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.PairingCore.ι",
"SSet.Subcomplex.PairingCore.II",
"SSet.Subcomplex.PairingCore.equivII",
"Equ... | [] | simp +instances | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.PairingCore | {
"line": 173,
"column": 2
} | {
"line": 173,
"column": 17
} | {
"line": 175,
"column": 0
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nh : A.PairingCore\nx : h.ι\n⊢ h.type₁ x = ↑(h.pairing.p (h.equivII x))",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.PairingCore.ι",
"SSet.Subcomplex.PairingCore.II",
"SSet.Subcomplex.PairingCore.equivII",
"Equ... | [] | simp +instances | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.PairingCore | {
"line": 173,
"column": 2
} | {
"line": 173,
"column": 17
} | {
"line": 175,
"column": 0
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nh : A.PairingCore\nx : h.ι\n⊢ h.type₁ x = ↑(h.pairing.p (h.equivII x))",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.PairingCore.ι",
"SSet.Subcomplex.PairingCore.II",
"SSet.Subcomplex.PairingCore.equivII",
"Equ... | [] | simp +instances | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.PairingCore | {
"line": 198,
"column": 4
} | {
"line": 198,
"column": 15
} | {
"line": 198,
"column": 16
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nh : A.PairingCore\ninst✝ : h.IsProper\ns : h.ι\n⊢ (↑(h.equivII s)).IsUniquelyCodimOneFace (↑(h.pairing.p (h.equivII s))).toS",
"ppTerm": "?m.33",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.PairingCore.ι",
"SSet.Subcomplex.PairingCore.II",
... | [
"X : SSet\nA : X.Subcomplex\nh : A.PairingCore\ninst✝ : h.IsProper\ns : h.ι\n⊢ (h.type₂ s).IsUniquelyCodimOneFace (h.type₁ s).toS"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.PairingCore | {
"line": 203,
"column": 2
} | {
"line": 203,
"column": 29
} | {
"line": 203,
"column": 30
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nh : A.PairingCore\nx✝ : h.pairing.IsProper\ns : h.ι\n⊢ (h.type₂ s).IsUniquelyCodimOneFace (h.type₁ s).toS",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.PairingCore.ι",
"SSet.Subcomplex.PairingCore.II",
"Eq.mpr",
... | [
"X : SSet\nA : X.Subcomplex\nh : A.PairingCore\nx✝ : h.pairing.IsProper\ns : h.ι\n⊢ (h.type₂ s).IsUniquelyCodimOneFace (↑(h.pairing.p (h.equivII s))).toS"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.PairingCore | {
"line": 230,
"column": 4
} | {
"line": 230,
"column": 15
} | {
"line": 230,
"column": 16
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nh : A.PairingCore\ninst✝¹ : h.IsInner\ninst✝ : h.IsProper\ns : h.ι\n⊢ ⋯.index ⋯ ≠ 0",
"ppTerm": "?m.50",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.PairingCore.ι",
"SSet.Subcomplex.PairingCore.II",
"Eq.mpr",
"SSet.S",
"SSe... | [
"X : SSet\nA : X.Subcomplex\nh : A.PairingCore\ninst✝¹ : h.IsInner\ninst✝ : h.IsProper\ns : h.ι\n⊢ ¬h.index s = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.PairingCore | {
"line": 234,
"column": 4
} | {
"line": 234,
"column": 15
} | {
"line": 234,
"column": 16
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nh : A.PairingCore\ninst✝¹ : h.IsInner\ninst✝ : h.IsProper\ns : h.ι\n⊢ ⋯.index ⋯ ≠ Fin.last ((↑(h.equivII s)).dim + 1)",
"ppTerm": "?m.91",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.PairingCore.ι",
"SSet.Subcomplex.PairingCore.II",
"E... | [
"X : SSet\nA : X.Subcomplex\nh : A.PairingCore\ninst✝¹ : h.IsInner\ninst✝ : h.IsProper\ns : h.ι\n⊢ ¬h.index s = Fin.last (h.dim s + 1)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.PairingCore | {
"line": 256,
"column": 48
} | {
"line": 256,
"column": 78
} | {
"line": 256,
"column": 79
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nh : A.PairingCore\ninst✝ : h.IsRegular\nthis : IsEmpty { f // ∀ (n : ℕ), h.AncestralRel (f (n + 1)) (f n) }\nx✝ : { f // ∀ (n : ℕ), h.pairing.AncestralRel (f (n + 1)) (f n) }\nf : ℕ → ↑h.pairing.II\nhf : ∀ (n : ℕ), h.pairing.AncestralRel (f (n + 1)) (f n)\nn : ℕ\n⊢ h.Ancestr... | [
"X : SSet\nA : X.Subcomplex\nh : A.PairingCore\ninst✝ : h.IsRegular\nthis : IsEmpty { f // ∀ (n : ℕ), h.AncestralRel (f (n + 1)) (f n) }\nx✝ : { f // ∀ (n : ℕ), h.pairing.AncestralRel (f (n + 1)) (f n) }\nf : ℕ → ↑h.pairing.II\nhf : ∀ (n : ℕ), h.pairing.AncestralRel (f (n + 1)) (f n)\nn : ℕ\n⊢ h.pairing.AncestralRe... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.PairingCore | {
"line": 268,
"column": 41
} | {
"line": 268,
"column": 71
} | {
"line": 268,
"column": 72
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nh : A.PairingCore\nx✝¹ : h.pairing.IsRegular\nthis✝ : h.IsProper\nthis : IsEmpty { f // ∀ (n : ℕ), h.pairing.AncestralRel (f (n + 1)) (f n) }\nx✝ : { f // ∀ (n : ℕ), h.AncestralRel (f (n + 1)) (f n) }\nf : ℕ → h.ι\nhf : ∀ (n : ℕ), h.AncestralRel (f (n + 1)) (f n)\nn : ℕ\n⊢ h... | [
"X : SSet\nA : X.Subcomplex\nh : A.PairingCore\nx✝¹ : h.pairing.IsRegular\nthis✝ : h.IsProper\nthis : IsEmpty { f // ∀ (n : ℕ), h.pairing.AncestralRel (f (n + 1)) (f n) }\nx✝ : { f // ∀ (n : ℕ), h.AncestralRel (f (n + 1)) (f n) }\nf : ℕ → h.ι\nhf : ∀ (n : ℕ), h.AncestralRel (f (n + 1)) (f n)\nn : ℕ\n⊢ h.pairing.Anc... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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