module stringlengths 16 90 | startPos dict | endPos dict | goals listlengths 0 96 | ppTac stringlengths 1 14.5k | elaborator stringclasses 366
values | kind stringclasses 370
values |
|---|---|---|---|---|---|---|
Mathlib.CategoryTheory.GuitartExact.Basic | {
"line": 119,
"column": 33
} | {
"line": 119,
"column": 44
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.GuitartExact.Basic | {
"line": 130,
"column": 22
} | {
"line": 130,
"column": 33
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.GuitartExact.Basic | {
"line": 139,
"column": 22
} | {
"line": 139,
"column": 33
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.GuitartExact.Basic | {
"line": 150,
"column": 45
} | {
"line": 150,
"column": 56
} | [
{
"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.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.ModelCategory.DerivabilityStructureFibrant | {
"line": 38,
"column": 2
} | {
"line": 38,
"column": 40
} | [
{
"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",
"usedConstants": [
"Eq.mpr",
"HomotopicalAlgebra.ModelCategory.cm1a",
"CategoryTheory.LocalizerMorphism.RightResolution.w",
"Cat... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.ModelCategory.DerivabilityStructureFibrant | {
"line": 45,
"column": 15
} | {
"line": 45,
"column": 26
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : ModelCategory C\nX : C\n⊢ weakEquivalences C (HoCat.iResolutionObj X)",
"usedConstants": [
"HomotopicalAlgebra.ModelCategory.cm1a",
"CategoryTheory.Limits.hasFiniteProducts_of_hasFiniteLimits",
"HomotopicalAlgebra.ModelCategory... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.GuitartExact.Basic | {
"line": 163,
"column": 46
} | {
"line": 163,
"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.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.GuitartExact.Basic | {
"line": 199,
"column": 8
} | {
"line": 199,
"column": 26
} | [
{
"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'... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.ModelCategory.FundamentalLemma | {
"line": 84,
"column": 2
} | {
"line": 84,
"column": 37
} | [
{
"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... | wlog _ : IsFibrant X generalizing X | Mathlib.Tactic._aux_Mathlib_Tactic_WLOG___elabRules_Mathlib_Tactic_wlog_1 | Mathlib.Tactic.wlog |
Mathlib.CategoryTheory.GuitartExact.Basic | {
"line": 304,
"column": 10
} | {
"line": 304,
"column": 21
} | [
{
"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\nF : C₁ ⥤ C₂\nX₂ : C₁\nX₃ : C₂\ng : F.obj X₂ ⟶ X₃\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.ModelCategory.JoyalTrick | {
"line": 65,
"column": 16
} | {
"line": 65,
"column": 74
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.ModelCategory.JoyalTrick | {
"line": 86,
"column": 4
} | {
"line": 87,
"column": 57
} | [
{
"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... | 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.Transport | {
"line": 52,
"column": 4
} | {
"line": 52,
"column": 37
} | [
{
"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\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.ModelCategory.Transport | {
"line": 54,
"column": 4
} | {
"line": 54,
"column": 35
} | [
{
"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\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.ModelCategory.Transport | {
"line": 56,
"column": 4
} | {
"line": 56,
"column": 41
} | [
{
"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\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.ModelCategory.Transport | {
"line": 60,
"column": 14
} | {
"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\... | 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
} | [
{
"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\... | rw [h₃] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.AlgebraicTopology.SimplicialSet.Boundary | {
"line": 69,
"column": 2
} | {
"line": 69,
"column": 13
} | [
{
"pp": "n : ℕ\ni : Fin (n + 1)\nhi : objMk OrderHom.id ∈ (face {i}ᶜ).obj (op ⦋n⦌)\n⊢ False",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Subfunctor.Equalizer | {
"line": 96,
"column": 32
} | {
"line": 96,
"column": 73
} | [
{
"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",
"usedConstants": [
"Eq.mpr",
"CategoryTheory.Functor",
"CategoryTheory.Categ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.MultiequalizerPullback | {
"line": 50,
"column": 6
} | {
"line": 50,
"column": 27
} | [
{
"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 ≫ (fun k ↦ if hk : k = J... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.MultiequalizerPullback | {
"line": 73,
"column": 16
} | {
"line": 73,
"column": 27
} | [
{
"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\nhc : IsColimit c\ns : PushoutCocone (I.fst default) (I.snd default)\n⊢ c.π (J.fst default) ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.Horn | {
"line": 95,
"column": 4
} | {
"line": 95,
"column": 86
} | [
{
"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",
"usedConstants": [
"False",
"SimplexCategory.instFintypeToTypeOrderHomFinHAddNatLenOfNat",
"Finset.univ",
"... | 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.CategoryTheory.Limits.Shapes.MultiequalizerPullback | {
"line": 74,
"column": 16
} | {
"line": 74,
"column": 27
} | [
{
"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\nhc : IsColimit c\ns : PushoutCocone (I.fst default) (I.snd default)\n⊢ c.π (J.snd default) ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.Horn | {
"line": 99,
"column": 27
} | {
"line": 99,
"column": 38
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.Horn | {
"line": 103,
"column": 2
} | {
"line": 103,
"column": 28
} | [
{
"pp": "case h\nn : 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⦌) ↔ stdSi... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.MultiequalizerPullback | {
"line": 81,
"column": 8
} | {
"line": 81,
"column": 24
} | [
{
"pp": "case inl\nC : 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\nhc : IsColimit c\ns : PushoutCocone (I.fst default) (I.snd default)\nm : c.pt ⟶ s... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.MultiequalizerPullback | {
"line": 82,
"column": 8
} | {
"line": 82,
"column": 24
} | [
{
"pp": "case inr\nC : 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\nhc : IsColimit c\ns : PushoutCocone (I.fst default) (I.snd default)\nm : c.pt ⟶ s... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.Horn | {
"line": 150,
"column": 2
} | {
"line": 150,
"column": 13
} | [
{
"pp": "case h\nn : 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",
"usedConstants": [
"Eq.mpr",
"Opposite",
"Equiv.instEquivLike",
"CategoryTheory.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Types.Multicoequalizer | {
"line": 88,
"column": 31
} | {
"line": 88,
"column": 42
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.Horn | {
"line": 290,
"column": 4
} | {
"line": 290,
"column": 15
} | [
{
"pp": "n : ℕ\ni j : Fin (n + 2)\nh : j ≠ i\n⊢ Subfunctor.range (stdSimplex.δ j) ≤ Λ[n + 1, i]",
"usedConstants": [
"Eq.mpr",
"Opposite",
"SimplexCategory.instFintypeToTypeOrderHomFinHAddNatLenOfNat",
"congrArg",
"Compl.compl",
"Finset",
"PartialOrder.toPreorder",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.CategoryWithFibrations | {
"line": 122,
"column": 34
} | {
"line": 122,
"column": 45
} | [
{
"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 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.KanComplex | {
"line": 100,
"column": 34
} | {
"line": 100,
"column": 45
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.Path | {
"line": 153,
"column": 4
} | {
"line": 154,
"column": 7
} | [
{
"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
} | [
{
"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.CategoryTheory.Monoidal.Types.Coyoneda | {
"line": 40,
"column": 6
} | {
"line": 40,
"column": 30
} | [
{
"pp": "case h.toFun.h\nC : 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) ... | simp [unitors_inv_equal] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal | {
"line": 86,
"column": 4
} | {
"line": 88,
"column": 57
} | [
{
"pp": "case w.h.toFun.h.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\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal | {
"line": 463,
"column": 8
} | {
"line": 465,
"column": 70
} | [
{
"pp": "case succ.refine_2.h.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",
"usedConstants": [
"SSet.Stric... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | {
"line": 160,
"column": 2
} | {
"line": 160,
"column": 54
} | [
{
"pp": "n : ℕ\nX : SSet\ni : Fin (n + 2)\nf g : Λ[n + 1, i].toSSet ⟶ X\nh : ∀ (j : Fin (n + 2)) (hj : j ≠ i), ι i j hj ≫ f = ι i j hj ≫ g\nx✝ : (MultispanShape.ofLinearOrder ↑{i}ᶜ).R\nj : Fin (n + 1 + 1)\nhj : j ∈ {i}ᶜ\n⊢ ((CompleteLattice.MulticoequalizerDiagram.multicofork ⋯).toLinearOrder.map Subcomplex.toS... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | {
"line": 230,
"column": 4
} | {
"line": 230,
"column": 15
} | [
{
"pp": "n : ℕ\nX : SSet\ni : Fin (n + 2)\nf : (j : Fin (n + 2)) → j ≠ i → (Δ[n] ⟶ X)\nhf : horn.IsCompatible f\nj : Fin (n + 2)\nhj : j ≠ i\n⊢ (stdSimplex.faceSingletonComplIso j).inv ≫ ι i j hj ≫ (isColimit i).desc hf.multicofork =\n (stdSimplex.faceSingletonComplIso j).inv ≫ f j hj",
"usedConstants": ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Enriched.Ordinary.Basic | {
"line": 80,
"column": 2
} | {
"line": 85,
"column": 73
} | [
{
"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.Ordinary.Basic | {
"line": 241,
"column": 24
} | {
"line": 241,
"column": 35
} | [
{
"pp": "V : Type u'\ninst✝⁶ : Category.{v', u'} V\ninst✝⁵ : MonoidalCategory V\nC : Type u\ninst✝⁴ : Category.{v, u} C\ninst✝³ : EnrichedOrdinaryCategory V C\nW : Type u''\ninst✝² : Category.{v'', u''} W\ninst✝¹ : MonoidalCategory W\nF : V ⥤ W\ninst✝ : F.LaxMonoidal\ne : (v : V) → (𝟙_ V ⟶ v) ≃ (𝟙_ W ⟶ F.obj ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Enriched.Basic | {
"line": 331,
"column": 4
} | {
"line": 331,
"column": 15
} | [
{
"pp": "case e_map.h.h\nV : 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 ≫ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Functor.FunctorHom | {
"line": 52,
"column": 4
} | {
"line": 52,
"column": 15
} | [
{
"pp": "case h.toFun.h\nC : Type u\ninst✝¹ : Category.{v, u} C\nD : Type u'\ninst✝ : Category.{v', u'} D\nF✝ G✝ : C ⥤ D\nF G A : C ⥤ Type w\na : F.HomObj G A\nX Y : C\nf : X ⟶ Y\nx : F.obj X\ny : A.obj X\n⊢ (ConcreteCategory.hom\n ((F ⊗ A).map f ≫\n (fun X ↦\n ↾fun x ↦\n ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Functor.FunctorHom | {
"line": 55,
"column": 4
} | {
"line": 55,
"column": 15
} | [
{
"pp": "case h.toFun.h\nC : Type u\ninst✝¹ : Category.{v, u} C\nD : Type u'\ninst✝ : Category.{v', u'} D\nF✝ G✝ : C ⥤ D\nF G A : C ⥤ Type w\na : F ⊗ A ⟶ G\nc✝ d✝ : C\nφ : c✝ ⟶ d✝\ny : A.obj c✝\nx : F.obj c✝\n⊢ (ConcreteCategory.hom\n (F.map φ ≫\n (fun X y ↦ ↾fun x ↦ (ConcreteCategory.hom (a... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Enriched.Basic | {
"line": 357,
"column": 60
} | {
"line": 357,
"column": 71
} | [
{
"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✝... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Quiver.ReflQuiver | {
"line": 77,
"column": 2
} | {
"line": 77,
"column": 13
} | [
{
"pp": "case e_toPrefunctor.e_map.h.h.h\nV : Type u\ninst✝¹ : ReflQuiver V\nW : Type u₂\ninst✝ : ReflQuiver W\nF_obj : V → W\nmap✝¹ : {X Y : V} → (X ⟶ Y) → (F_obj X ⟶ F_obj Y)\nmap_id✝¹ : ∀ (X : V), { obj := F_obj, map := map✝¹ }.map (𝟙rq X) = 𝟙rq ({ obj := F_obj, map := map✝¹ }.obj X)\nmap✝ : {X Y : V} → (X... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Category.ReflQuiv | {
"line": 215,
"column": 13
} | {
"line": 215,
"column": 24
} | [
{
"pp": "case mk.mk.nil\nV : Type u_1\ninst✝ : ReflQuiver V\nmotive : {x y : FreeRefl V} → (x ⟶ y) → Prop\nid : ∀ (x : V), motive (homMk (𝟙rq x))\ncomp_homMk : ∀ {x y z : V} (f : mk x ⟶ mk y) (g : y ⟶ z), motive f → motive (f ≫ homMk g)\nx y : V\n⊢ motive ((quotientFunctor V).map Quiver.Path.nil)",
"usedCo... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Category.ReflQuiv | {
"line": 216,
"column": 20
} | {
"line": 216,
"column": 31
} | [
{
"pp": "case mk.mk.cons\nV : Type u_1\ninst✝ : ReflQuiver V\nmotive : {x y : FreeRefl V} → (x ⟶ y) → Prop\nid : ∀ (x : V), motive (homMk (𝟙rq x))\ncomp_homMk : ∀ {x y z : V} (f : mk x ⟶ mk y) (g : y ⟶ z), motive f → motive (f ≫ homMk g)\nx y b✝ c✝ : V\na✝ : Quiver.Path x b✝\nf : b✝ ⟶ c✝\nh : motive ((quotient... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat | {
"line": 130,
"column": 4
} | {
"line": 130,
"column": 15
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat | {
"line": 301,
"column": 2
} | {
"line": 301,
"column": 21
} | [
{
"pp": "V : Truncated 2\nx₀ x₁ x₂ : V.obj (op { obj := ⦋0⦌, property := OneTruncation₂._proof_1 })\ne₀₁ : Edge x₀ x₁\ne₁₂ : Edge x₁ x₂\ne₀₂ : Edge x₀ x₂\nh : e₀₁.CompStruct e₁₂ e₀₂\n⊢ homMk e₀₁ ≫ homMk e₁₂ = homMk e₀₂",
"usedConstants": [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.Basic | {
"line": 148,
"column": 6
} | {
"line": 148,
"column": 17
} | [
{
"pp": "case of.inl\nP : MorphismProperty SimplexCategoryGenRel\nid : ∀ {n : ℕ}, P (𝟙 (mk n))\ncomp_δ : ∀ {n m : ℕ} (u : mk n ⟶ mk m) (i : Fin (m + 2)), P u → P (u ≫ δ i)\ncomp_σ : ∀ {n m : ℕ} (u : mk n ⟶ mk (m + 1)) (i : Fin (m + 1)), P u → P (u ≫ σ i)\na b : SimplexCategoryGenRel\nf✝ : a ⟶ b\nX✝ Y✝ : Simple... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.Basic | {
"line": 149,
"column": 6
} | {
"line": 149,
"column": 17
} | [
{
"pp": "case of.inr\nP : MorphismProperty SimplexCategoryGenRel\nid : ∀ {n : ℕ}, P (𝟙 (mk n))\ncomp_δ : ∀ {n m : ℕ} (u : mk n ⟶ mk m) (i : Fin (m + 2)), P u → P (u ≫ δ i)\ncomp_σ : ∀ {n m : ℕ} (u : mk n ⟶ mk (m + 1)) (i : Fin (m + 1)), P u → P (u ≫ σ i)\na b : SimplexCategoryGenRel\nf✝ : a ⟶ b\nX✝ Y✝ : Simple... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.Basic | {
"line": 153,
"column": 6
} | {
"line": 153,
"column": 17
} | [
{
"pp": "case comp_of.inl\nP : MorphismProperty SimplexCategoryGenRel\nid : ∀ {n : ℕ}, P (𝟙 (mk n))\ncomp_δ : ∀ {n m : ℕ} (u : mk n ⟶ mk m) (i : Fin (m + 2)), P u → P (u ≫ δ i)\ncomp_σ : ∀ {n m : ℕ} (u : mk n ⟶ mk (m + 1)) (i : Fin (m + 1)), P u → P (u ≫ σ i)\na b : SimplexCategoryGenRel\nf✝¹ : a ⟶ b\nX✝ Y✝ : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.Basic | {
"line": 154,
"column": 6
} | {
"line": 154,
"column": 17
} | [
{
"pp": "case comp_of.inr\nP : MorphismProperty SimplexCategoryGenRel\nid : ∀ {n : ℕ}, P (𝟙 (mk n))\ncomp_δ : ∀ {n m : ℕ} (u : mk n ⟶ mk m) (i : Fin (m + 2)), P u → P (u ≫ δ i)\ncomp_σ : ∀ {n m : ℕ} (u : mk n ⟶ mk (m + 1)) (i : Fin (m + 1)), P u → P (u ≫ σ i)\na b : SimplexCategoryGenRel\nf✝¹ : a ⟶ b\nX✝ Y✝ : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.Basic | {
"line": 174,
"column": 6
} | {
"line": 174,
"column": 17
} | [
{
"pp": "case of.inl\nP : MorphismProperty SimplexCategoryGenRel\nid : ∀ {n : ℕ}, P (𝟙 (mk n))\nδ_comp : ∀ {n m : ℕ} (u : mk (m + 1) ⟶ mk n) (i : Fin (m + 2)), P u → P (δ i ≫ u)\nσ_comp : ∀ {n m : ℕ} (u : mk m ⟶ mk n) (i : Fin (m + 1)), P u → P (σ i ≫ u)\na b : SimplexCategoryGenRel\nf✝ : a ⟶ b\nX✝ Y✝ : Simple... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.Basic | {
"line": 175,
"column": 6
} | {
"line": 175,
"column": 17
} | [
{
"pp": "case of.inr\nP : MorphismProperty SimplexCategoryGenRel\nid : ∀ {n : ℕ}, P (𝟙 (mk n))\nδ_comp : ∀ {n m : ℕ} (u : mk (m + 1) ⟶ mk n) (i : Fin (m + 2)), P u → P (δ i ≫ u)\nσ_comp : ∀ {n m : ℕ} (u : mk m ⟶ mk n) (i : Fin (m + 1)), P u → P (σ i ≫ u)\na b : SimplexCategoryGenRel\nf✝ : a ⟶ b\nX✝ Y✝ : Simple... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.Basic | {
"line": 179,
"column": 6
} | {
"line": 179,
"column": 17
} | [
{
"pp": "case of_comp.inl\nP : MorphismProperty SimplexCategoryGenRel\nid : ∀ {n : ℕ}, P (𝟙 (mk n))\nδ_comp : ∀ {n m : ℕ} (u : mk (m + 1) ⟶ mk n) (i : Fin (m + 2)), P u → P (δ i ≫ u)\nσ_comp : ∀ {n m : ℕ} (u : mk m ⟶ mk n) (i : Fin (m + 1)), P u → P (σ i ≫ u)\na b : SimplexCategoryGenRel\nf✝ : a ⟶ b\nX✝ Y✝ : S... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.Basic | {
"line": 180,
"column": 6
} | {
"line": 180,
"column": 17
} | [
{
"pp": "case of_comp.inr\nP : MorphismProperty SimplexCategoryGenRel\nid : ∀ {n : ℕ}, P (𝟙 (mk n))\nδ_comp : ∀ {n m : ℕ} (u : mk (m + 1) ⟶ mk n) (i : Fin (m + 2)), P u → P (δ i ≫ u)\nσ_comp : ∀ {n m : ℕ} (u : mk m ⟶ mk n) (i : Fin (m + 1)), P u → P (σ i ≫ u)\na b : SimplexCategoryGenRel\nf✝ : a ⟶ b\nX✝ Y✝ : S... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.EpiMono | {
"line": 34,
"column": 4
} | {
"line": 34,
"column": 31
} | [
{
"pp": "n : ℕ\ni : Fin (n + 2)\n⊢ δ i ≫ Fin.lastCases (σ (Fin.last n)) (fun i ↦ σ i) i = 𝟙 (mk n)",
"usedConstants": [
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"instAddNat",
"Eq.refl",
"OfNat.ofNat",
"Fin"
]
}
] | 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
} | [
{
"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",
"usedConstants": [
"Eq.mpr",
"CategoryTheory.CategoryStruct.toQuiver",
"Quive... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.EpiMono | {
"line": 163,
"column": 8
} | {
"line": 163,
"column": 19
} | [
{
"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, ∃... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.EpiMono | {
"line": 204,
"column": 4
} | {
"line": 204,
"column": 67
} | [
{
"pp": "X✝ Y✝ : SimplexCategoryGenRel\nf : X✝ ⟶ Y✝\n⊢ Nonempty (P_σ.MapFactorizationData P_δ f)",
"usedConstants": [
"SimplexCategoryGenRel.exists_P_σ_P_δ_factorization"
]
}
] | 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.SimplexCategory.GeneratorsRelations.NormalForms | {
"line": 259,
"column": 52
} | {
"line": 259,
"column": 68
} | [
{
"pp": "case h\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)\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.NormalForms | {
"line": 260,
"column": 4
} | {
"line": 263,
"column": 89
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.UpperLower.Relative | {
"line": 150,
"column": 4
} | {
"line": 150,
"column": 66
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.UpperLower.Relative | {
"line": 158,
"column": 4
} | {
"line": 158,
"column": 66
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal | {
"line": 153,
"column": 6
} | {
"line": 153,
"column": 17
} | [
{
"pp": "case w.h\nX 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⊢ ((fun {x₀ x₁} e ↦ mkN... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialComplex.Basic | {
"line": 94,
"column": 49
} | {
"line": 95,
"column": 72
} | [
{
"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}",
"usedConstants": ... | 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
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialObject.II | {
"line": 100,
"column": 35
} | {
"line": 100,
"column": 46
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialObject.II | {
"line": 133,
"column": 31
} | {
"line": 133,
"column": 42
} | [
{
"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",
"usedConstants"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialObject.II | {
"line": 135,
"column": 31
} | {
"line": 135,
"column": 42
} | [
{
"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⊢ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialObject.II | {
"line": 139,
"column": 29
} | {
"line": 139,
"column": 40
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialObject.II | {
"line": 159,
"column": 12
} | {
"line": 159,
"column": 58
} | [
{
"pp": "case pos.inl.left.inr\nn : ℕ\nx : Fin (n + 1)\nhx : x.castSucc ≤ x.castSucc\n⊢ x.castSucc ≤ x.castSucc.succAbove x",
"usedConstants": [
"Fin.succAbove",
"Eq.mpr",
"Fin.succ",
"Fin.succAbove_castSucc_self",
"congrArg",
"id",
"instOfNatNat",
"LE.le",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialObject.II | {
"line": 173,
"column": 8
} | {
"line": 173,
"column": 56
} | [
{
"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",
"usedConstants": [
"Fin.succAbove",
"Eq.mpr",
"Fin.succ",
"congrArg",
"id",
"instOfNatNat",
"LE.le",
"instL... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialNerve | {
"line": 107,
"column": 23
} | {
"line": 107,
"column": 34
} | [
{
"pp": "case h\nJ : Type u_1\ninst✝ : LinearOrder J\nX✝ Y✝ : SimplicialThickening J\nf : X✝ ⟶ Y✝\nt✝ : J\n⊢ t✝ ∈ (𝟙 X✝ ≫ f).I ↔ t✝ ∈ f.I",
"usedConstants": [
"Eq.mpr",
"CategoryTheory.SimplicialThickening",
"congrArg",
"CategoryTheory.SimplicialThickening.Path.I",
"Membership... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialNerve | {
"line": 108,
"column": 23
} | {
"line": 108,
"column": 34
} | [
{
"pp": "case h\nJ : Type u_1\ninst✝ : LinearOrder J\nX✝ Y✝ : SimplicialThickening J\nf : X✝ ⟶ Y✝\nt✝ : J\n⊢ t✝ ∈ (f ≫ 𝟙 Y✝).I ↔ t✝ ∈ f.I",
"usedConstants": [
"Eq.mpr",
"CategoryTheory.SimplicialThickening",
"congrArg",
"CategoryTheory.SimplicialThickening.Path.I",
"Membership... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialObject.II | {
"line": 187,
"column": 14
} | {
"line": 187,
"column": 57
} | [
{
"pp": "n : ℕ\ni x : Fin (n + 1)\nhi : i < x\n⊢ i.castSucc < x.succ",
"usedConstants": [
"Eq.mpr",
"_private.Mathlib.AlgebraicTopology.SimplicialObject.II.0.SimplexCategory.II.map'_predAbove._simp_1_3",
"Fin.succ",
"id",
"instOfNatNat",
"LE.le",
"instLEFin",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Monoidal | {
"line": 207,
"column": 6
} | {
"line": 207,
"column": 66
} | [
{
"pp": "case h.h.h.h.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 + ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Monoidal | {
"line": 210,
"column": 6
} | {
"line": 210,
"column": 66
} | [
{
"pp": "case h.h.h.h.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 +... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Monoidal | {
"line": 214,
"column": 6
} | {
"line": 214,
"column": 58
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialObject.II | {
"line": 202,
"column": 8
} | {
"line": 203,
"column": 43
} | [
{
"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",
"usedConstants": [
"Eq.mpr",
"Fin.ne_zero_of_lt",
"Fin.succ",
"Fin.pred",
"congrArg",
"Fin.succ_lt_succ_iff",
"Fin.predAbove_... | · 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.SimplexCategory.Augmented.Monoidal | {
"line": 218,
"column": 6
} | {
"line": 218,
"column": 58
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialObject.II | {
"line": 209,
"column": 25
} | {
"line": 215,
"column": 11
} | [
{
"pp": "n m : ℕ\nf : Fin (n + 1) →o Fin (m + 1)\n⊢ Monotone (map' f)",
"usedConstants": [
"Eq.mpr",
"SimplexCategory.II.finset",
"SimplexCategory.II.castSucc_mem_finset_iff._simp_1",
"Finset",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"Exi... | 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.SimplicialSet.NonDegenerateSimplicesSubcomplex | {
"line": 69,
"column": 29
} | {
"line": 69,
"column": 40
} | [
{
"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⦌)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.IsUniquelyCodimOneFace | {
"line": 70,
"column": 2
} | {
"line": 70,
"column": 32
} | [
{
"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",
"usedConstants": [
"SSet.S.simplex",
"Opposite",
"CategoryTheory.ConcreteCategory.hom",
"TypeCat.i... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.NonDegenerateSimplicesSubcomplex | {
"line": 131,
"column": 2
} | {
"line": 131,
"column": 13
} | [
{
"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",
"usedConstants": [
"Eq.mpr",
"SSet.Subcomplex.ofSimplex",
"Opposite",
"PartialOrder.toPreorder",
"Preorder.toL... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.IsUniquelyCodimOneFace | {
"line": 112,
"column": 34
} | {
"line": 112,
"column": 45
} | [
{
"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",
"usedConstants": [
"SSet.op_δ",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.IsUniquelyCodimOneFace | {
"line": 114,
"column": 2
} | {
"line": 114,
"column": 34
} | [
{
"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",
"usedConstants": [... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.Pairing | {
"line": 101,
"column": 2
} | {
"line": 101,
"column": 73
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.IsUniquelyCodimOneFace | {
"line": 128,
"column": 17
} | {
"line": 128,
"column": 28
} | [
{
"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",
"us... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.Pairing | {
"line": 189,
"column": 4
} | {
"line": 189,
"column": 49
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Monoidal | {
"line": 341,
"column": 4
} | {
"line": 341,
"column": 94
} | [
{
"pp": "case h₁\nx y : AugmentedSimplexCategory\n⊢ x.inl y ≫ (𝟙 x ⊗ₘ 𝟙 y) = x.inl y ≫ 𝟙 (x ⊗ y)",
"usedConstants": [
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.MonoidalCategoryStruct.r... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Monoidal | {
"line": 343,
"column": 4
} | {
"line": 343,
"column": 94
} | [
{
"pp": "case h₂\nx y : AugmentedSimplexCategory\n⊢ x.inr y ≫ (𝟙 x ⊗ₘ 𝟙 y) = x.inr y ≫ 𝟙 (x ⊗ y)",
"usedConstants": [
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Iso.cancel_iso_inv_left.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.PairingCore | {
"line": 119,
"column": 2
} | {
"line": 119,
"column": 53
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nh : A.PairingCore\ns t : h.ι\n⊢ h.type₁ s ≠ h.type₂ t",
"usedConstants": [
"Eq.mpr",
"SSet.S",
"SSet.Subcomplex.PairingCore.type₂",
"congrArg",
"_private.Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.PairingCore.0.SSet.Subcomplex... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.PairingCore | {
"line": 171,
"column": 2
} | {
"line": 171,
"column": 17
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nh : A.PairingCore\nx : h.ι\n⊢ h.type₁ x = ↑(h.pairing.p (h.equivII x))",
"usedConstants": [
"SSet.Subcomplex.PairingCore.ι",
"SSet.Subcomplex.PairingCore.II",
"SSet.Subcomplex.PairingCore.equivII",
"Equiv.instEquivLike",
"congrArg",
"S... | simp +instances | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.PairingCore | {
"line": 171,
"column": 2
} | {
"line": 171,
"column": 17
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nh : A.PairingCore\nx : h.ι\n⊢ h.type₁ x = ↑(h.pairing.p (h.equivII x))",
"usedConstants": [
"SSet.Subcomplex.PairingCore.ι",
"SSet.Subcomplex.PairingCore.II",
"SSet.Subcomplex.PairingCore.equivII",
"Equiv.instEquivLike",
"congrArg",
"S... | simp +instances | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.PairingCore | {
"line": 171,
"column": 2
} | {
"line": 171,
"column": 17
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nh : A.PairingCore\nx : h.ι\n⊢ h.type₁ x = ↑(h.pairing.p (h.equivII x))",
"usedConstants": [
"SSet.Subcomplex.PairingCore.ι",
"SSet.Subcomplex.PairingCore.II",
"SSet.Subcomplex.PairingCore.equivII",
"Equiv.instEquivLike",
"congrArg",
"S... | simp +instances | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.PairingCore | {
"line": 188,
"column": 4
} | {
"line": 188,
"column": 15
} | [
{
"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",
"usedConstants": [
"SSet.Subcomplex.PairingCore.ι",
"SSet.Subcomplex.PairingCore.II",
"Eq.mpr",
"SSet.S",
"SSet.Su... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.PairingCore | {
"line": 193,
"column": 2
} | {
"line": 193,
"column": 29
} | [
{
"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",
"usedConstants": [
"SSet.Subcomplex.PairingCore.ι",
"SSet.Subcomplex.PairingCore.II",
"Eq.mpr",
"SSet.S",
"SSet.Subcomplex.PairingCor... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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