module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.CategoryTheory.Limits.Types.Multicoequalizer | {
"line": 49,
"column": 6
} | {
"line": 49,
"column": 27
} | {
"line": 50,
"column": 2
} | [
{
"pp": "case right\nJ : MultispanShape\nd : MultispanIndex J (Type u)\nc : d.multispan.CoconeTypes\nr : J.R\nz : d.multispan.obj (WalkingMultispan.right r)\n⊢ ∃ i a, d.multispan.ιColimitType (WalkingMultispan.right i) a = d.multispan.ιColimitType (WalkingMultispan.right r) z",
"ppTerm": "?right",
"assi... | [] | exact ⟨r, z, by simp⟩ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Limits.Types.Multicoequalizer | {
"line": 49,
"column": 6
} | {
"line": 49,
"column": 27
} | {
"line": 50,
"column": 2
} | [
{
"pp": "case right\nJ : MultispanShape\nd : MultispanIndex J (Type u)\nc : d.multispan.CoconeTypes\nr : J.R\nz : d.multispan.obj (WalkingMultispan.right r)\n⊢ ∃ i a, d.multispan.ιColimitType (WalkingMultispan.right i) a = d.multispan.ιColimitType (WalkingMultispan.right r) z",
"ppTerm": "?right",
"assi... | [] | exact ⟨r, z, by simp⟩ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.SubcomplexColimits | {
"line": 59,
"column": 19
} | {
"line": 59,
"column": 40
} | {
"line": 59,
"column": 41
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nι : Type u_1\nU : ι → X.Subcomplex\nV : ι → ι → X.Subcomplex\nh : A.MulticoequalizerDiagram U V\nn : SimplexCategoryᵒᵖ\n⊢ ⨆ i, (U i).obj n = A.obj n",
"ppTerm": "?m.57",
"assigned": true,
"usedConstants": [
"Opposite",
"congrArg",
"iSup",
... | [] | by simp [← h.iSup_eq] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.AlgebraicTopology.SimplicialSet.Horn | {
"line": 95,
"column": 81
} | {
"line": 95,
"column": 86
} | {
"line": 96,
"column": 4
} | [
{
"pp": "case pos\nn : 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)\nk : Fin (⦋n⦌.len + 1)\nh✝ : k = i\n⊢ k ∈ Finset.image ⇑(SimplexCategory.Hom.toOrderHom f) ⊤ ∪ {i} ↔ k ∈ ⊤",
"ppTerm": "?pos✝",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialSet.Horn | {
"line": 95,
"column": 81
} | {
"line": 95,
"column": 86
} | {
"line": 96,
"column": 4
} | [
{
"pp": "case neg\nn : 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)\nk : Fin (⦋n⦌.len + 1)\nh✝ : ¬k = i\n⊢ k ∈ Finset.image ⇑(SimplexCategory.Hom.toOrderHom f) ⊤ ∪ {i} ↔ k ∈ ⊤",
"ppTerm": "?neg✝",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialSet.Boundary | {
"line": 69,
"column": 24
} | {
"line": 69,
"column": 29
} | {
"line": 69,
"column": 29
} | [
{
"pp": "n : ℕ\ni : Fin (n + 1)\nhi : objMk OrderHom.id ∈ (face {i}ᶜ).obj (op ⦋n⦌)\n⊢ i ∈ Finset.image ⇑(SimplexCategory.Hom.toOrderHom (objEquiv (objMk OrderHom.id))) ⊤",
"ppTerm": "?m.34",
"assigned": true,
"usedConstants": [
"SSet.stdSimplex.objMk",
"OrderHom.id",
"False",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialSet.Boundary | {
"line": 69,
"column": 24
} | {
"line": 69,
"column": 29
} | {
"line": 69,
"column": 29
} | [
{
"pp": "n : ℕ\ni : Fin (n + 1)\nhi : objMk OrderHom.id ∈ (face {i}ᶜ).obj (op ⦋n⦌)\n⊢ i ∈ Finset.image ⇑(SimplexCategory.Hom.toOrderHom (objEquiv (objMk OrderHom.id))) ⊤",
"ppTerm": "?m.34",
"assigned": true,
"usedConstants": [
"SSet.stdSimplex.objMk",
"OrderHom.id",
"False",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.Boundary | {
"line": 69,
"column": 24
} | {
"line": 69,
"column": 29
} | {
"line": 69,
"column": 29
} | [
{
"pp": "n : ℕ\ni : Fin (n + 1)\nhi : objMk OrderHom.id ∈ (face {i}ᶜ).obj (op ⦋n⦌)\n⊢ i ∈ Finset.image ⇑(SimplexCategory.Hom.toOrderHom (objEquiv (objMk OrderHom.id))) ⊤",
"ppTerm": "?m.34",
"assigned": true,
"usedConstants": [
"SSet.stdSimplex.objMk",
"OrderHom.id",
"False",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.Boundary | {
"line": 97,
"column": 12
} | {
"line": 97,
"column": 27
} | {
"line": 97,
"column": 27
} | [
{
"pp": "m : SimplexCategoryᵒᵖ\nx✝ : Δ[0].obj m\nx : Fin 1\n⊢ (stdSimplex.asOrderHom x✝) 0 = x",
"ppTerm": "?m.33",
"assigned": true,
"usedConstants": [
"PartialOrder.toPreorder",
"SSet.stdSimplex.asOrderHom",
"instOfNatNat",
"Fin.subsingleton_one",
"instHAdd",
"O... | [] | by subsingleton | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.AlgebraicTopology.SimplicialSet.Boundary | {
"line": 108,
"column": 41
} | {
"line": 108,
"column": 46
} | {
"line": 108,
"column": 46
} | [
{
"pp": "n d : ℕ\nj : Δ[n] _⦋d⦌\nk : Fin (n + 1)\nhk : ∀ (x : Fin (d + 1)), ¬(j x.rev).rev = k\nl : Fin (d + 1)\nx✝ : j l = k.rev\n⊢ (j l.rev.rev).rev = k",
"ppTerm": "?m.63",
"assigned": true,
"usedConstants": [
"Opposite",
"congrArg",
"CategoryTheory.Functor.category",
"ins... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialSet.Boundary | {
"line": 108,
"column": 41
} | {
"line": 108,
"column": 46
} | {
"line": 108,
"column": 46
} | [
{
"pp": "n d : ℕ\nj : Δ[n] _⦋d⦌\nk : Fin (n + 1)\nhk : ∀ (x : Fin (d + 1)), ¬(j x.rev).rev = k\nl : Fin (d + 1)\nx✝ : j l = k.rev\n⊢ (j l.rev.rev).rev = k",
"ppTerm": "?m.63",
"assigned": true,
"usedConstants": [
"Opposite",
"congrArg",
"CategoryTheory.Functor.category",
"ins... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.Boundary | {
"line": 108,
"column": 41
} | {
"line": 108,
"column": 46
} | {
"line": 108,
"column": 46
} | [
{
"pp": "n d : ℕ\nj : Δ[n] _⦋d⦌\nk : Fin (n + 1)\nhk : ∀ (x : Fin (d + 1)), ¬(j x.rev).rev = k\nl : Fin (d + 1)\nx✝ : j l = k.rev\n⊢ (j l.rev.rev).rev = k",
"ppTerm": "?m.63",
"assigned": true,
"usedConstants": [
"Opposite",
"congrArg",
"CategoryTheory.Functor.category",
"ins... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.Boundary | {
"line": 108,
"column": 41
} | {
"line": 108,
"column": 46
} | {
"line": 108,
"column": 46
} | [
{
"pp": "n d : ℕ\nj : Δ[n] _⦋d⦌\nk : Fin (n + 1)\nhk : ∀ (x : Fin (d + 1)), ¬j x = k\nl : Fin (d + 1)\nx✝ : (j l.rev).rev = k.rev\n⊢ j l.rev = k",
"ppTerm": "?m.80",
"assigned": true,
"usedConstants": [
"False",
"Opposite",
"eq_false",
"Fin.rev_inj._simp_1",
"False.elim... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialSet.Boundary | {
"line": 108,
"column": 41
} | {
"line": 108,
"column": 46
} | {
"line": 108,
"column": 46
} | [
{
"pp": "n d : ℕ\nj : Δ[n] _⦋d⦌\nk : Fin (n + 1)\nhk : ∀ (x : Fin (d + 1)), ¬j x = k\nl : Fin (d + 1)\nx✝ : (j l.rev).rev = k.rev\n⊢ j l.rev = k",
"ppTerm": "?m.80",
"assigned": true,
"usedConstants": [
"False",
"Opposite",
"eq_false",
"Fin.rev_inj._simp_1",
"False.elim... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.Boundary | {
"line": 108,
"column": 41
} | {
"line": 108,
"column": 46
} | {
"line": 108,
"column": 46
} | [
{
"pp": "n d : ℕ\nj : Δ[n] _⦋d⦌\nk : Fin (n + 1)\nhk : ∀ (x : Fin (d + 1)), ¬j x = k\nl : Fin (d + 1)\nx✝ : (j l.rev).rev = k.rev\n⊢ j l.rev = k",
"ppTerm": "?m.80",
"assigned": true,
"usedConstants": [
"False",
"Opposite",
"eq_false",
"Fin.rev_inj._simp_1",
"False.elim... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.Horn | {
"line": 140,
"column": 25
} | {
"line": 140,
"column": 30
} | {
"line": 140,
"column": 30
} | [
{
"pp": "n : ℕ\nS : Finset (Fin (n + 2))\nj : Fin (n + 2)\n⊢ S = Finset.univ ∨ S = {j}ᶜ → {j}ᶜ ⊆ S",
"ppTerm": "?m.52",
"assigned": true,
"usedConstants": [
"SimplexCategory.instFintypeToTypeOrderHomFinHAddNatLenOfNat",
"Finset.univ",
"instReflLe",
"Finset.subset_univ._simp_1... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialSet.Horn | {
"line": 140,
"column": 25
} | {
"line": 140,
"column": 30
} | {
"line": 140,
"column": 30
} | [
{
"pp": "n : ℕ\nS : Finset (Fin (n + 2))\nj : Fin (n + 2)\n⊢ S = Finset.univ ∨ S = {j}ᶜ → {j}ᶜ ⊆ S",
"ppTerm": "?m.52",
"assigned": true,
"usedConstants": [
"SimplexCategory.instFintypeToTypeOrderHomFinHAddNatLenOfNat",
"Finset.univ",
"instReflLe",
"Finset.subset_univ._simp_1... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.Horn | {
"line": 140,
"column": 25
} | {
"line": 140,
"column": 30
} | {
"line": 140,
"column": 30
} | [
{
"pp": "n : ℕ\nS : Finset (Fin (n + 2))\nj : Fin (n + 2)\n⊢ S = Finset.univ ∨ S = {j}ᶜ → {j}ᶜ ⊆ S",
"ppTerm": "?m.52",
"assigned": true,
"usedConstants": [
"SimplexCategory.instFintypeToTypeOrderHomFinHAddNatLenOfNat",
"Finset.univ",
"instReflLe",
"Finset.subset_univ._simp_1... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Limits.Types.Pushouts | {
"line": 108,
"column": 2
} | {
"line": 112,
"column": 19
} | {
"line": 114,
"column": 0
} | [
{
"pp": "S X₁ X₂ : Type u\nf : S ⟶ X₁\ng : S ⟶ X₂\nx₂ y₂ : X₂\n⊢ Rel' f g (Sum.inr x₂) (Sum.inr y₂) ↔ x₂ = y₂",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"CategoryTheory.Limits.Types.Pushout.Rel'.inl_inr",
"Sum.ctorIdx",
"CategoryTheory.ConcreteCategory.hom",
"H... | [] | constructor
· rintro ⟨_⟩
rfl
· rintro rfl
apply Rel'.refl | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Limits.Types.Pushouts | {
"line": 108,
"column": 2
} | {
"line": 112,
"column": 19
} | {
"line": 114,
"column": 0
} | [
{
"pp": "S X₁ X₂ : Type u\nf : S ⟶ X₁\ng : S ⟶ X₂\nx₂ y₂ : X₂\n⊢ Rel' f g (Sum.inr x₂) (Sum.inr y₂) ↔ x₂ = y₂",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"CategoryTheory.Limits.Types.Pushout.Rel'.inl_inr",
"Sum.ctorIdx",
"CategoryTheory.ConcreteCategory.hom",
"H... | [] | constructor
· rintro ⟨_⟩
rfl
· rintro rfl
apply Rel'.refl | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.KanComplex | {
"line": 100,
"column": 17
} | {
"line": 100,
"column": 32
} | {
"line": 100,
"column": 33
} | [
{
"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... | [] | by subsingleton | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Limits.Types.Pushouts | {
"line": 149,
"column": 8
} | {
"line": 149,
"column": 17
} | {
"line": 150,
"column": 8
} | [
{
"pp": "case inl_inr.inr\nS X₁ X₂ : Type u\nf : S ⟶ X₁\ng : S ⟶ X₂\ninst✝ : Mono f\ns : S\nz₂ : X₂\nhyz : (ConcreteCategory.hom g) s = z₂\n⊢ Rel' f g (Sum.inl ((ConcreteCategory.hom f) s)) (Sum.inr z₂)",
"ppTerm": "?inl_inr.inr",
"assigned": true,
"usedConstants": [
"CategoryTheory.ConcreteCa... | [
"case inl_inr.inr\nS X₁ X₂ : Type u\nf : S ⟶ X₁\ng : S ⟶ X₂\ninst✝ : Mono f\ns : S\n⊢ Rel' f g (Sum.inl ((ConcreteCategory.hom f) s)) (Sum.inr ((ConcreteCategory.hom g) s))"
] | subst hyz | Lean.Elab.Tactic.evalSubst | Lean.Parser.Tactic.subst |
Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | {
"line": 145,
"column": 4
} | {
"line": 145,
"column": 9
} | {
"line": 147,
"column": 0
} | [
{
"pp": "n : ℕ\ni : Fin (n + 1)\nj k : ↑{i}ᶜ\n⊢ {↑j, ↑k}ᶜ = {↑j}ᶜ ⊓ {↑k}ᶜ",
"ppTerm": "?m.68",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"SimplexCategory.instFintypeToTypeOrderHomFinHAddNatLenOfNat",
"congrArg",
"Compl.compl",
"Finset",
"instDecidableEqFin",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.Quasicategory.StrictSegal | {
"line": 52,
"column": 6
} | {
"line": 52,
"column": 25
} | {
"line": 52,
"column": 26
} | [
{
"pp": "case h.inl\nX : SSet\nsx : X.StrictSegal\nn : ℕ\ni : Fin (n + 3)\nσ₀ : Λ[n + 2, i].toSSet ⟶ X\nh₀ : 0 < i\nhₙ : i < Fin.last (n + 2)\nj : Fin (n + 3)\nhj : j ≠ i\nk : Fin (n + 1)\nksucc : Fin (n + 1 + 1 + 1) := k.succ.castSucc\nhlt : ksucc < j\n⊢ (stdSimplex.spineId (n + 2)).arrow k.castSucc =\n std... | [
"case h.inl\nX : SSet\nsx : X.StrictSegal\nn : ℕ\ni : Fin (n + 3)\nσ₀ : Λ[n + 2, i].toSSet ⟶ X\nh₀ : 0 < i\nhₙ : i < Fin.last (n + 2)\nj : Fin (n + 3)\nhj : j ≠ i\nk : Fin (n + 1)\nksucc : Fin (n + 1 + 1 + 1) := k.succ.castSucc\nhlt : ksucc < j\n⊢ (stdSimplex.spineId (n + 2)).arrow k.castSucc =\n stdSimplex.objE... | Quiver.Hom.unop_op, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.AlgebraicTopology.Quasicategory.StrictSegal | {
"line": 61,
"column": 6
} | {
"line": 61,
"column": 25
} | {
"line": 61,
"column": 26
} | [
{
"pp": "case h.inr.inl\nX : SSet\nsx : X.StrictSegal\nn : ℕ\ni : Fin (n + 3)\nσ₀ : Λ[n + 2, i].toSSet ⟶ X\nh₀ : 0 < i\nhₙ : i < Fin.last (n + 2)\nj : Fin (n + 3)\nhj : j ≠ i\nk : Fin (n + 1)\nksucc : Fin (n + 1 + 1 + 1) := k.succ.castSucc\nhgt : j < ksucc\n⊢ (stdSimplex.spineId (n + 2)).arrow k.succ =\n std... | [
"case h.inr.inl\nX : SSet\nsx : X.StrictSegal\nn : ℕ\ni : Fin (n + 3)\nσ₀ : Λ[n + 2, i].toSSet ⟶ X\nh₀ : 0 < i\nhₙ : i < Fin.last (n + 2)\nj : Fin (n + 3)\nhj : j ≠ i\nk : Fin (n + 1)\nksucc : Fin (n + 1 + 1 + 1) := k.succ.castSucc\nhgt : j < ksucc\n⊢ (stdSimplex.spineId (n + 2)).arrow k.succ =\n stdSimplex.objE... | Quiver.Hom.unop_op, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal | {
"line": 456,
"column": 34
} | {
"line": 456,
"column": 39
} | {
"line": 456,
"column": 39
} | [
{
"pp": "X : SSet\nh : (n : ℕ) → X.StrictSegalCore n\np : X.Path 0\n⊢ X.spine 0 (p.vertex 0) = p",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"SimplexCategory.const_eq_id",
"Opposite",
"Quiver.opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal | {
"line": 456,
"column": 34
} | {
"line": 456,
"column": 39
} | {
"line": 456,
"column": 39
} | [
{
"pp": "X : SSet\nh : (n : ℕ) → X.StrictSegalCore n\np : X.Path 0\n⊢ X.spine 0 (p.vertex 0) = p",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"SimplexCategory.const_eq_id",
"Opposite",
"Quiver.opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal | {
"line": 456,
"column": 34
} | {
"line": 456,
"column": 39
} | {
"line": 456,
"column": 39
} | [
{
"pp": "X : SSet\nh : (n : ℕ) → X.StrictSegalCore n\np : X.Path 0\n⊢ X.spine 0 (p.vertex 0) = p",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"SimplexCategory.const_eq_id",
"Opposite",
"Quiver.opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal | {
"line": 507,
"column": 29
} | {
"line": 507,
"column": 34
} | {
"line": 508,
"column": 2
} | [
{
"pp": "X : SSet\nh : (n : ℕ) → X.StrictSegalCore n\n⊢ ∀ (n : ℕ), X.spine n ∘ StrictSegalCore.spineToSimplex h = id",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"SSet.Path",
"Opposite",
"congrArg",
"Function.comp",
"id",
"SSet.Path.ext",
"instOf... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal | {
"line": 507,
"column": 29
} | {
"line": 507,
"column": 34
} | {
"line": 508,
"column": 2
} | [
{
"pp": "X : SSet\nh : (n : ℕ) → X.StrictSegalCore n\n⊢ ∀ (n : ℕ), X.spine n ∘ StrictSegalCore.spineToSimplex h = id",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"SSet.Path",
"Opposite",
"congrArg",
"Function.comp",
"id",
"SSet.Path.ext",
"instOf... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal | {
"line": 507,
"column": 29
} | {
"line": 507,
"column": 34
} | {
"line": 508,
"column": 2
} | [
{
"pp": "X : SSet\nh : (n : ℕ) → X.StrictSegalCore n\n⊢ ∀ (n : ℕ), X.spine n ∘ StrictSegalCore.spineToSimplex h = id",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"SSet.Path",
"Opposite",
"congrArg",
"Function.comp",
"id",
"SSet.Path.ext",
"instOf... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal | {
"line": 508,
"column": 31
} | {
"line": 508,
"column": 36
} | {
"line": 510,
"column": 0
} | [
{
"pp": "X : SSet\nh : (n : ℕ) → X.StrictSegalCore n\nn : ℕ\n⊢ StrictSegalCore.spineToSimplex h ∘ X.spine n = id",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"SSet.Path",
"Opposite",
"congrArg",
"Function.comp",
"id",
"funext",
"SSet.StrictSegal... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal | {
"line": 508,
"column": 31
} | {
"line": 508,
"column": 36
} | {
"line": 510,
"column": 0
} | [
{
"pp": "X : SSet\nh : (n : ℕ) → X.StrictSegalCore n\nn : ℕ\n⊢ StrictSegalCore.spineToSimplex h ∘ X.spine n = id",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"SSet.Path",
"Opposite",
"congrArg",
"Function.comp",
"id",
"funext",
"SSet.StrictSegal... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal | {
"line": 508,
"column": 31
} | {
"line": 508,
"column": 36
} | {
"line": 510,
"column": 0
} | [
{
"pp": "X : SSet\nh : (n : ℕ) → X.StrictSegalCore n\nn : ℕ\n⊢ StrictSegalCore.spineToSimplex h ∘ X.spine n = id",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"SSet.Path",
"Opposite",
"congrArg",
"Function.comp",
"id",
"funext",
"SSet.StrictSegal... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.Quasicategory.StrictSegal | {
"line": 93,
"column": 8
} | {
"line": 93,
"column": 27
} | {
"line": 93,
"column": 28
} | [
{
"pp": "case h.inr.inr.succ\nX : SSet\nsx : X.StrictSegal\nn : ℕ\ni : Fin (n + 1 + 3)\nσ₀ : Λ[n + 1 + 2, i].toSSet ⟶ X\nh₀ : 0 < i\nhₙ : i < Fin.last (n + 1 + 2)\nj : Fin (n + 1 + 3)\nhj : j ≠ i\nk : Fin (n + 1 + 1)\nksucc : Fin (n + 1 + 1 + 1 + 1) := k.succ.castSucc\nheq : j = ksucc\ntriangle : Λ[n + 3, i].to... | [
"case h.inr.inr.succ\nX : SSet\nsx : X.StrictSegal\nn : ℕ\ni : Fin (n + 1 + 3)\nσ₀ : Λ[n + 1 + 2, i].toSSet ⟶ X\nh₀ : 0 < i\nhₙ : i < Fin.last (n + 1 + 2)\nj : Fin (n + 1 + 3)\nhj : j ≠ i\nk : Fin (n + 1 + 1)\nksucc : Fin (n + 1 + 1 + 1 + 1) := k.succ.castSucc\nheq : j = ksucc\ntriangle : Λ[n + 3, i].toSSet _⦋2⦌ :=... | Quiver.Hom.unop_op, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.CategoryTheory.Functor.FunctorHom | {
"line": 56,
"column": 19
} | {
"line": 56,
"column": 24
} | {
"line": 57,
"column": 2
} | [
{
"pp": "C : 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\nx✝ : F.HomObj G A\n⊢ (fun a ↦ { app := fun X y ↦ ↾fun x ↦ (ConcreteCategory.hom (a.app X)) (x, y), naturality := ⋯ })\n ((fun a ↦\n {\n app := fun X ↦\n ... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.Functor.FunctorHom | {
"line": 56,
"column": 19
} | {
"line": 56,
"column": 24
} | {
"line": 57,
"column": 2
} | [
{
"pp": "C : 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\nx✝ : F.HomObj G A\n⊢ (fun a ↦ { app := fun X y ↦ ↾fun x ↦ (ConcreteCategory.hom (a.app X)) (x, y), naturality := ⋯ })\n ((fun a ↦\n {\n app := fun X ↦\n ... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Functor.FunctorHom | {
"line": 56,
"column": 19
} | {
"line": 56,
"column": 24
} | {
"line": 57,
"column": 2
} | [
{
"pp": "C : 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\nx✝ : F.HomObj G A\n⊢ (fun a ↦ { app := fun X y ↦ ↾fun x ↦ (ConcreteCategory.hom (a.app X)) (x, y), naturality := ⋯ })\n ((fun a ↦\n {\n app := fun X ↦\n ... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Functor.FunctorHom | {
"line": 57,
"column": 20
} | {
"line": 57,
"column": 25
} | {
"line": 59,
"column": 0
} | [
{
"pp": "C : 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\nx✝ : F ⊗ A ⟶ G\n⊢ (fun a ↦\n {\n app := fun X ↦\n ↾fun x ↦\n match x with\n | (x, y) => (ConcreteCategory.hom (a.app X y)) x,\n ... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.Functor.FunctorHom | {
"line": 57,
"column": 20
} | {
"line": 57,
"column": 25
} | {
"line": 59,
"column": 0
} | [
{
"pp": "C : 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\nx✝ : F ⊗ A ⟶ G\n⊢ (fun a ↦\n {\n app := fun X ↦\n ↾fun x ↦\n match x with\n | (x, y) => (ConcreteCategory.hom (a.app X y)) x,\n ... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Functor.FunctorHom | {
"line": 57,
"column": 20
} | {
"line": 57,
"column": 25
} | {
"line": 59,
"column": 0
} | [
{
"pp": "C : 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\nx✝ : F ⊗ A ⟶ G\n⊢ (fun a ↦\n {\n app := fun X ↦\n ↾fun x ↦\n match x with\n | (x, y) => (ConcreteCategory.hom (a.app X y)) x,\n ... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Functor.FunctorHom | {
"line": 149,
"column": 4
} | {
"line": 149,
"column": 9
} | {
"line": 149,
"column": 10
} | [
{
"pp": "case e_a\nC : Type u\ninst✝¹ : Category.{v, u} C\nD : Type u'\ninst✝ : Category.{v', u'} D\nF G : C ⥤ D\nf : 𝟙_ (C ⥤ Type (max v' v u)) ⟶ F.functorHom G\nX Y : C\nφ : X ⟶ Y\nthis :\n ((ConcreteCategory.hom (f.app Y)) PUnit.unit).app Y (𝟙 Y) =\n ((ConcreteCategory.hom (f.app X)) PUnit.unit).app Y ... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.Functor.FunctorHom | {
"line": 155,
"column": 4
} | {
"line": 155,
"column": 9
} | {
"line": 157,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nD : Type u'\ninst✝ : Category.{v', u'} D\nF G : C ⥤ D\nf : 𝟙_ (C ⥤ Type (max v' v u)) ⟶ F.functorHom G\nX : C\na : (𝟙_ (C ⥤ Type (max v' v u))).obj X\nY : C\nφ : X ⟶ Y\nthis :\n ((ConcreteCategory.hom (f.app Y)) PUnit.unit).app Y (𝟙 Y) =\n ((ConcreteCatego... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.Monoidal.Closed.FunctorToTypes | {
"line": 51,
"column": 6
} | {
"line": 51,
"column": 11
} | {
"line": 51,
"column": 13
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nD : Type u'\ninst✝ : Category.{v', u'} D\nF X✝ Y✝ : C ⥤ Type (max w v u)\nf : X✝ ⟶ Y✝\nX : C\na : (F.functorHom X✝).obj X\nc✝ d✝ : C\ng : c✝ ⟶ d✝\nh : (Opposite.unop (coyoneda.rightOp.obj X)).obj c✝\nthis :\n F.map g ≫ a.app d✝ ((ConcreteCategory.hom ((Opposite.... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.Category.ReflQuiv | {
"line": 215,
"column": 13
} | {
"line": 215,
"column": 30
} | {
"line": 216,
"column": 4
} | [
{
"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)",
"ppTerm... | [] | simpa using! id x | Lean.Elab.Tactic.Simpa.evalSimpaUsingBang | Lean.Parser.Tactic.simpaUsingBang |
Mathlib.CategoryTheory.Category.ReflQuiv | {
"line": 215,
"column": 13
} | {
"line": 215,
"column": 30
} | {
"line": 216,
"column": 4
} | [
{
"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)",
"ppTerm... | [] | simpa using! id x | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Category.ReflQuiv | {
"line": 215,
"column": 13
} | {
"line": 215,
"column": 30
} | {
"line": 216,
"column": 4
} | [
{
"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)",
"ppTerm... | [] | simpa using! id x | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Category.ReflQuiv | {
"line": 317,
"column": 26
} | {
"line": 317,
"column": 41
} | {
"line": 318,
"column": 4
} | [
{
"pp": "V✝ : Type u_1\ninst✝³ : ReflQuiver V✝\nV : Type u_2\ninst✝² : ReflQuiver V\ninst✝¹ : Unique V\ninst✝ : ∀ (x y : V), Subsingleton (x ⟶ y)\nx✝ y✝ : FreeRefl V\nx y : V\n⊢ x = y",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Unique.instSubsingleton",
"Subsingleton.elim"... | [] | by subsingleton | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.AlgebraicTopology.SimplicialSet.Coskeletal | {
"line": 74,
"column": 6
} | {
"line": 77,
"column": 60
} | {
"line": 78,
"column": 6
} | [
{
"pp": "X✝ : SSet\nsx✝ : X✝.StrictSegal\nX : SSet\nsx : X.StrictSegal\nn : ℕ\ns : Cone (proj (op ⦋n⦌) (inclusion 2).op ⋙ (inclusion 2).op ⋙ X)\nx : s.pt\ni : Fin n\n⊢ (ConcreteCategory.hom\n (((Truncated.trunc (0 + 1) 1 ⋯).obj ((truncation 1).obj X)).map\n (Hom.tr (SimplexCategory.δ 1) Truncate... | [
"X✝ : SSet\nsx✝ : X✝.StrictSegal\nX : SSet\nsx : X.StrictSegal\nn : ℕ\ns : Cone (proj (op ⦋n⦌) (inclusion 2).op ⋙ (inclusion 2).op ⋙ X)\nx : s.pt\ni : Fin n\nφ : strArrowMk₂ (mkOfLe i.castSucc i.succ ⋯) SSet.StrictSegal.isPointwiseRightKanExtensionAt.lift._proof_3 ⟶\n strArrowMk₂ (⦋0⦌.const ⦋n⦌ i.castSucc) SSet.St... | let φ : strArrowMk₂ (mkOfLe _ _ (Fin.castSucc_le_succ i)) ⟶
strArrowMk₂ (⦋0⦌.const _ i.castSucc) :=
StructuredArrow.homMk (Hom.tr (δ 1)).op
(Quiver.Hom.unop_inj (by ext x; fin_cases x; rfl)) | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticLet___1 | Lean.Parser.Tactic.tacticLet__ |
Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat | {
"line": 287,
"column": 28
} | {
"line": 287,
"column": 33
} | {
"line": 288,
"column": 2
} | [
{
"pp": "V : Truncated 2\nx₀ x₁ : V.obj (op { obj := ⦋0⦌, property := OneTruncation₂._proof_1 })\ne e' : Edge x₀ x₁\nh : e.edge = e'.edge\n⊢ e = e'",
"ppTerm": "?m.142",
"assigned": true,
"usedConstants": [
"CategoryTheory.ObjectProperty.FullSubcategory.mk",
"Opposite",
"congrArg",... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat | {
"line": 287,
"column": 28
} | {
"line": 287,
"column": 33
} | {
"line": 288,
"column": 2
} | [
{
"pp": "V : Truncated 2\nx₀ x₁ : V.obj (op { obj := ⦋0⦌, property := OneTruncation₂._proof_1 })\ne e' : Edge x₀ x₁\nh : e.edge = e'.edge\n⊢ e = e'",
"ppTerm": "?m.142",
"assigned": true,
"usedConstants": [
"CategoryTheory.ObjectProperty.FullSubcategory.mk",
"Opposite",
"congrArg",... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat | {
"line": 287,
"column": 28
} | {
"line": 287,
"column": 33
} | {
"line": 288,
"column": 2
} | [
{
"pp": "V : Truncated 2\nx₀ x₁ : V.obj (op { obj := ⦋0⦌, property := OneTruncation₂._proof_1 })\ne e' : Edge x₀ x₁\nh : e.edge = e'.edge\n⊢ e = e'",
"ppTerm": "?m.142",
"assigned": true,
"usedConstants": [
"CategoryTheory.ObjectProperty.FullSubcategory.mk",
"Opposite",
"congrArg",... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.Reedy.Basic | {
"line": 177,
"column": 51
} | {
"line": 177,
"column": 56
} | {
"line": 177,
"column": 56
} | [
{
"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.degHom f... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.Reedy.Basic | {
"line": 177,
"column": 51
} | {
"line": 177,
"column": 56
} | {
"line": 177,
"column": 56
} | [
{
"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.degHom f... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.Reedy.Basic | {
"line": 177,
"column": 51
} | {
"line": 177,
"column": 56
} | {
"line": 177,
"column": 56
} | [
{
"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.degHom f... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.Reedy.Basic | {
"line": 184,
"column": 51
} | {
"line": 184,
"column": 56
} | {
"line": 184,
"column": 56
} | [
{
"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.degHom f... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.Reedy.Basic | {
"line": 184,
"column": 51
} | {
"line": 184,
"column": 56
} | {
"line": 184,
"column": 56
} | [
{
"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.degHom f... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.Reedy.Basic | {
"line": 184,
"column": 51
} | {
"line": 184,
"column": 56
} | {
"line": 184,
"column": 56
} | [
{
"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.degHom f... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat | {
"line": 459,
"column": 59
} | {
"line": 459,
"column": 74
} | {
"line": 459,
"column": 75
} | [
{
"pp": "V W X : Truncated 2\ninst✝¹ : Unique (X.obj (op { obj := ⦋0⦌, property := OneTruncation₂._proof_1 }))\ninst✝ : Subsingleton (X.obj (op { obj := ⦋1⦌, property := ι0₂._proof_5 }))\n⊢ ∀ {X_1 Y : X.HomotopyCategory} (f : X_1 ⟶ Y), X_1 = Y",
"ppTerm": "?m.54",
"assigned": true,
"usedConstants": ... | [] | by subsingleton | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat | {
"line": 542,
"column": 17
} | {
"line": 542,
"column": 32
} | {
"line": 544,
"column": 0
} | [
{
"pp": "X✝ Y✝ : ((truncation 2).obj Δ[0]).HomotopyCategory\nx✝ : X✝ ⟶ Y✝\n⊢ X✝ = Y✝",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"SSet.instUniqueHomotopyCategoryObjTruncatedOfNatNatTruncationSimplexCategoryStdSimplexMk",
"Opposite",
"CategoryTheory.Functor.category",
... | [] | by subsingleton | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.Basic | {
"line": 179,
"column": 4
} | {
"line": 179,
"column": 36
} | {
"line": 180,
"column": 4
} | [
{
"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... | [
"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✝ : SimplexCatego... | · simpa using! (δ_comp g i hrec) | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.AlgebraicTopology.SimplexCategory.SemiSimplexCategory | {
"line": 106,
"column": 2
} | {
"line": 106,
"column": 7
} | {
"line": 108,
"column": 0
} | [
{
"pp": "n m : SemiSimplexCategory\nf : toSimplexCategory.obj n ⟶ toSimplexCategory.obj m\ninst✝ : Mono f\n⊢ toSimplexCategory.map (homOfMono f) = f",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"PartialOrder.toPreorder",
"SemiSimplexCategory.homOfMono",
"SimplexCategor... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplexCategory.SemiSimplexCategory | {
"line": 106,
"column": 2
} | {
"line": 106,
"column": 7
} | {
"line": 108,
"column": 0
} | [
{
"pp": "n m : SemiSimplexCategory\nf : toSimplexCategory.obj n ⟶ toSimplexCategory.obj m\ninst✝ : Mono f\n⊢ toSimplexCategory.map (homOfMono f) = f",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"PartialOrder.toPreorder",
"SemiSimplexCategory.homOfMono",
"SimplexCategor... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplexCategory.SemiSimplexCategory | {
"line": 106,
"column": 2
} | {
"line": 106,
"column": 7
} | {
"line": 108,
"column": 0
} | [
{
"pp": "n m : SemiSimplexCategory\nf : toSimplexCategory.obj n ⟶ toSimplexCategory.obj m\ninst✝ : Mono f\n⊢ toSimplexCategory.map (homOfMono f) = f",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"PartialOrder.toPreorder",
"SemiSimplexCategory.homOfMono",
"SimplexCategor... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplexCategory.ToMkOne | {
"line": 68,
"column": 6
} | {
"line": 68,
"column": 27
} | {
"line": 68,
"column": 27
} | [
{
"pp": "n : ℕ\nj i : Fin (n + 2)\nh✝ : i.castSucc ≤ j.castSucc\nh : i ≤ j\n⊢ δ j ≫ toMk₁ i.castSucc = toMk₁ (i.castSucc.castPred ⋯)",
"ppTerm": "?m.66",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Eq.mpr",
"lt_of_le_of_lt",
"Fin.ext_iff",
"CategoryTheory.CategoryS... | [
"n : ℕ\nj i : Fin (n + 2)\nh✝ : i.castSucc ≤ j.castSucc\nh : i ≤ j\n⊢ δ j ≫ toMk₁ i.castSucc = toMk₁ i"
] | Fin.castPred_castSucc | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.AlgebraicTopology.SimplicialObject.II | {
"line": 150,
"column": 4
} | {
"line": 150,
"column": 24
} | {
"line": 151,
"column": 4
} | [
{
"pp": "case inl\nn : ℕ\ni x : Fin (n + 2)\n⊢ map' i.succAboveOrderEmb.toOrderHom x.castSucc = i.predAbove x.castSucc",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"Preorder.toLT",
"SimplexCategory.II.map'",
"PartialOrder.toPreorder",
"Eq.mp",
"instOfNatNat"... | [
"case pos\nn : ℕ\ni x : Fin (n + 2)\nhx : x ≤ i\n⊢ map' i.succAboveOrderEmb.toOrderHom x.castSucc = i.predAbove x.castSucc",
"case neg\nn : ℕ\ni x : Fin (n + 2)\nhx : i < x\n⊢ map' i.succAboveOrderEmb.toOrderHom x.castSucc = i.predAbove x.castSucc"
] | by_cases! hx : x ≤ i | Mathlib.Tactic.ByCases._aux_Mathlib_Tactic_ByCases___macroRules_Mathlib_Tactic_ByCases_byCases!_1 | Mathlib.Tactic.ByCases.byCases! |
Mathlib.AlgebraicTopology.SimplicialObject.II | {
"line": 151,
"column": 55
} | {
"line": 151,
"column": 76
} | {
"line": 151,
"column": 76
} | [
{
"pp": "case pos\nn : ℕ\ni x : Fin (n + 2)\nhx : x ≤ i\n⊢ map' i.succAboveOrderEmb.toOrderHom x.castSucc = x.castSucc.castPred ⋯",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Eq.mpr",
"Fin.ext_iff",
"Fin.castPred_castSucc",
"SimplexCategory.II.m... | [
"case pos\nn : ℕ\ni x : Fin (n + 2)\nhx : x ≤ i\n⊢ map' i.succAboveOrderEmb.toOrderHom x.castSucc = x"
] | Fin.castPred_castSucc | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.AlgebraicTopology.SimplicialSet.NonDegenerateSimplicesSubcomplex | {
"line": 128,
"column": 44
} | {
"line": 128,
"column": 49
} | {
"line": 129,
"column": 4
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nY : SSet\nB : Y.Subcomplex\ne : X ≅ Y\nhA : B.preimage e.hom = A\ny : B.N\n⊢ A.preimage e.inv = B",
"ppTerm": "?m.79",
"assigned": true,
"usedConstants": [
"Set.ext",
"Opposite",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"Ca... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialSet.NonDegenerateSimplicesSubcomplex | {
"line": 128,
"column": 44
} | {
"line": 128,
"column": 49
} | {
"line": 129,
"column": 4
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nY : SSet\nB : Y.Subcomplex\ne : X ≅ Y\nhA : B.preimage e.hom = A\ny : B.N\n⊢ A.preimage e.inv = B",
"ppTerm": "?m.79",
"assigned": true,
"usedConstants": [
"Set.ext",
"Opposite",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"Ca... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.NonDegenerateSimplicesSubcomplex | {
"line": 128,
"column": 44
} | {
"line": 128,
"column": 49
} | {
"line": 129,
"column": 4
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nY : SSet\nB : Y.Subcomplex\ne : X ≅ Y\nhA : B.preimage e.hom = A\ny : B.N\n⊢ A.preimage e.inv = B",
"ppTerm": "?m.79",
"assigned": true,
"usedConstants": [
"Set.ext",
"Opposite",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"Ca... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.NonDegenerateSimplicesSubcomplex | {
"line": 130,
"column": 19
} | {
"line": 130,
"column": 24
} | {
"line": 131,
"column": 2
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nY : SSet\nB : Y.Subcomplex\ne : X ≅ Y\nhA : B.preimage e.hom = A\nx✝ : A.N\n⊢ (fun y ↦ { toN := (SSet.N.orderIsoOfIso e).symm y.toN, notMem := ⋯ })\n ((fun x ↦ { toN := (SSet.N.orderIsoOfIso e) x.toN, notMem := ⋯ }) x✝) =\n x✝",
"ppTerm": "?m.93",
"assigned":... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialSet.NonDegenerateSimplicesSubcomplex | {
"line": 130,
"column": 19
} | {
"line": 130,
"column": 24
} | {
"line": 131,
"column": 2
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nY : SSet\nB : Y.Subcomplex\ne : X ≅ Y\nhA : B.preimage e.hom = A\nx✝ : A.N\n⊢ (fun y ↦ { toN := (SSet.N.orderIsoOfIso e).symm y.toN, notMem := ⋯ })\n ((fun x ↦ { toN := (SSet.N.orderIsoOfIso e) x.toN, notMem := ⋯ }) x✝) =\n x✝",
"ppTerm": "?m.93",
"assigned":... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.NonDegenerateSimplicesSubcomplex | {
"line": 130,
"column": 19
} | {
"line": 130,
"column": 24
} | {
"line": 131,
"column": 2
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nY : SSet\nB : Y.Subcomplex\ne : X ≅ Y\nhA : B.preimage e.hom = A\nx✝ : A.N\n⊢ (fun y ↦ { toN := (SSet.N.orderIsoOfIso e).symm y.toN, notMem := ⋯ })\n ((fun x ↦ { toN := (SSet.N.orderIsoOfIso e) x.toN, notMem := ⋯ }) x✝) =\n x✝",
"ppTerm": "?m.93",
"assigned":... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.NonDegenerateSimplicesSubcomplex | {
"line": 131,
"column": 20
} | {
"line": 131,
"column": 25
} | {
"line": 132,
"column": 2
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nY : SSet\nB : Y.Subcomplex\ne : X ≅ Y\nhA : B.preimage e.hom = A\nx✝ : B.N\n⊢ (fun x ↦ { toN := (SSet.N.orderIsoOfIso e) x.toN, notMem := ⋯ })\n ((fun y ↦ { toN := (SSet.N.orderIsoOfIso e).symm y.toN, notMem := ⋯ }) x✝) =\n x✝",
"ppTerm": "?m.94",
"assigned":... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialSet.NonDegenerateSimplicesSubcomplex | {
"line": 131,
"column": 20
} | {
"line": 131,
"column": 25
} | {
"line": 132,
"column": 2
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nY : SSet\nB : Y.Subcomplex\ne : X ≅ Y\nhA : B.preimage e.hom = A\nx✝ : B.N\n⊢ (fun x ↦ { toN := (SSet.N.orderIsoOfIso e) x.toN, notMem := ⋯ })\n ((fun y ↦ { toN := (SSet.N.orderIsoOfIso e).symm y.toN, notMem := ⋯ }) x✝) =\n x✝",
"ppTerm": "?m.94",
"assigned":... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.NonDegenerateSimplicesSubcomplex | {
"line": 131,
"column": 20
} | {
"line": 131,
"column": 25
} | {
"line": 132,
"column": 2
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nY : SSet\nB : Y.Subcomplex\ne : X ≅ Y\nhA : B.preimage e.hom = A\nx✝ : B.N\n⊢ (fun x ↦ { toN := (SSet.N.orderIsoOfIso e) x.toN, notMem := ⋯ })\n ((fun y ↦ { toN := (SSet.N.orderIsoOfIso e).symm y.toN, notMem := ⋯ }) x✝) =\n x✝",
"ppTerm": "?m.94",
"assigned":... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.Pairing | {
"line": 172,
"column": 65
} | {
"line": 176,
"column": 6
} | {
"line": 178,
"column": 0
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nP : A.Pairing\nY : SSet\nB : Y.Subcomplex\ne : Y ≅ X\nhA : A.preimage e.hom = B\nx : ↑P.II\n⊢ (P.ofIso e hA).p ⟨(N.orderIsoOfIso e hA).symm ↑x, ⋯⟩ = ⟨(N.orderIsoOfIso e hA).symm ↑(P.p x), ⋯⟩",
"ppTerm": "?m.55",
"assigned": true,
"usedConstants": [
"Subtype... | [] | by
let e' := Subcomplex.N.orderIsoOfIso e hA
ext
change e'.symm (P.p ⟨e' (e'.symm x), _⟩) = e'.symm (P.p x)
simp | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.Pairing | {
"line": 184,
"column": 27
} | {
"line": 184,
"column": 32
} | {
"line": 184,
"column": 32
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nP : A.Pairing\nY : SSet\nB : Y.Subcomplex\ne : Y ≅ X\nhA : A.preimage e.hom = B\nx y : ↑P.II\n⊢ ⟨(N.orderIsoOfIso e hA).symm ↑x, ⋯⟩ = ⟨(N.orderIsoOfIso e hA).symm ↑y, ⋯⟩ ↔ x = y",
"ppTerm": "?m.57",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Oppo... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.Pairing | {
"line": 184,
"column": 27
} | {
"line": 184,
"column": 32
} | {
"line": 184,
"column": 32
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nP : A.Pairing\nY : SSet\nB : Y.Subcomplex\ne : Y ≅ X\nhA : A.preimage e.hom = B\nx y : ↑P.II\n⊢ ⟨(N.orderIsoOfIso e hA).symm ↑x, ⋯⟩ = ⟨(N.orderIsoOfIso e hA).symm ↑y, ⋯⟩ ↔ x = y",
"ppTerm": "?m.57",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Oppo... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.Pairing | {
"line": 184,
"column": 27
} | {
"line": 184,
"column": 32
} | {
"line": 184,
"column": 32
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nP : A.Pairing\nY : SSet\nB : Y.Subcomplex\ne : Y ≅ X\nhA : A.preimage e.hom = B\nx y : ↑P.II\n⊢ ⟨(N.orderIsoOfIso e hA).symm ↑x, ⋯⟩ = ⟨(N.orderIsoOfIso e hA).symm ↑y, ⋯⟩ ↔ x = y",
"ppTerm": "?m.57",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Oppo... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.ProdStdSimplex | {
"line": 153,
"column": 4
} | {
"line": 153,
"column": 19
} | {
"line": 154,
"column": 4
} | [
{
"pp": "case refine_2\np q n : ℕ\nz : (Δ[p] ⊗ Δ[q]) _⦋n⦌\nhn : p + q = n\n⊢ orderHomOfSimplex z hn = OrderHom.id → Function.Injective ⇑(objEquiv z)",
"ppTerm": "?refine_2",
"assigned": true,
"usedConstants": [
"OrderHom.id",
"Opposite",
"Equiv.instEquivLike",
"CategoryTheory... | [
"case refine_2\np q n : ℕ\nz : (Δ[p] ⊗ Δ[q]) _⦋n⦌\nhn : p + q = n\nh : orderHomOfSimplex z hn = OrderHom.id\na b : Fin (n + 1)\nhab : (objEquiv z) a = (objEquiv z) b\n⊢ a = b"
] | intro h a b hab | Lean.Elab.Tactic.evalIntro | Lean.Parser.Tactic.intro |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RankNat | {
"line": 63,
"column": 2
} | {
"line": 63,
"column": 42
} | {
"line": 64,
"column": 2
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nP : A.Pairing\ny : ↑P.II\nhy : Acc P.AncestralRel y\nx : ↑P.II\nr : P.AncestralRel x y\n⊢ P.rank' ⋯ < P.rank' hy",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"iSup",
"SSet.Subcomplex.N",
"Set.Elem",... | [
"X : SSet\nA : X.Subcomplex\nP : A.Pairing\ny : ↑P.II\nhy : Acc P.AncestralRel y\nx : ↑P.II\nr : P.AncestralRel x y\n⊢ P.rank' ⋯ + 1 ≤ ⨆ x, P.rank' ⋯ + 1"
] | rw [P.rank'_eq hy, ← Nat.add_one_le_iff] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.PairingCore | {
"line": 149,
"column": 4
} | {
"line": 150,
"column": 58
} | {
"line": 151,
"column": 4
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nh : A.PairingCore\ns : A.N\n⊢ s ∈ h.I ∩ h.II ↔ s ∈ ∅",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.PairingCore.ι",
"SSet.Subcomplex.PairingCore.II",
"Eq.mpr",
"_private.Mathlib.AlgebraicTopology.SimplicialSet.A... | [
"X : SSet\nA : X.Subcomplex\nh : A.PairingCore\ns : A.N\n⊢ ∀ (x : h.ι), h.type₁ x = s → ∀ (x : h.ι), ¬h.type₂ x = s"
] | simp only [I, II, Set.mem_inter_iff, Set.mem_range, Set.mem_empty_iff_false,
iff_false, not_and, not_exists, forall_exists_index] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.PairingCore | {
"line": 157,
"column": 4
} | {
"line": 157,
"column": 9
} | {
"line": 158,
"column": 2
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nh : A.PairingCore\ns : A.N\nthis : ∃ s_1, s = h.type₁ s_1 ∨ s = h.type₂ s_1\n⊢ (∃ y, h.type₁ y = s) ∨ ∃ y, h.type₂ y = s",
"ppTerm": "?m.57",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.PairingCore.ι",
"SSet.Subcomplex.PairingCore.type₂",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.PairingCore | {
"line": 216,
"column": 2
} | {
"line": 217,
"column": 6
} | {
"line": 219,
"column": 0
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nh : A.PairingCore\ninst✝ : h.IsProper\ns : h.ι\nd : ℕ\nhd : h.dim s = d\n⊢ ↑(⋯.index hd) = ↑(h.index s)",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.PairingCore.isUniquelyCodimOneFace",
"SSet.Subcomplex.PairingCore.isUniq... | [] | subst hd
simp | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.PairingCore | {
"line": 216,
"column": 2
} | {
"line": 217,
"column": 6
} | {
"line": 219,
"column": 0
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nh : A.PairingCore\ninst✝ : h.IsProper\ns : h.ι\nd : ℕ\nhd : h.dim s = d\n⊢ ↑(⋯.index hd) = ↑(h.index s)",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.PairingCore.isUniquelyCodimOneFace",
"SSet.Subcomplex.PairingCore.isUniq... | [] | subst hd
simp | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialObject.ChainHomotopy | {
"line": 86,
"column": 51
} | {
"line": 86,
"column": 56
} | {
"line": 87,
"column": 2
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Preadditive C\nX Y : SimplicialObject C\nf g : X ⟶ Y\nH : Homotopy f g\nn : ℕ\nα : Fin (n + 1) × Fin (n + 2) → (X _⦋n + 1⦌ ⟶ Y _⦋n + 1⦌) := fun x ↦ (-1) ^ (↑x.1 + ↑x.2) • X.δ x.2 ≫ H.h x.1\nβ : Fin (n + 3) × Fin (n + 2) → (X _⦋n + 1⦌ ⟶ Y _⦋n + 1⦌) := fun ... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialObject.ChainHomotopy | {
"line": 86,
"column": 51
} | {
"line": 86,
"column": 56
} | {
"line": 87,
"column": 2
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Preadditive C\nX Y : SimplicialObject C\nf g : X ⟶ Y\nH : Homotopy f g\nn : ℕ\nα : Fin (n + 1) × Fin (n + 2) → (X _⦋n + 1⦌ ⟶ Y _⦋n + 1⦌) := fun x ↦ (-1) ^ (↑x.1 + ↑x.2) • X.δ x.2 ≫ H.h x.1\nβ : Fin (n + 3) × Fin (n + 2) → (X _⦋n + 1⦌ ⟶ Y _⦋n + 1⦌) := fun ... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialObject.ChainHomotopy | {
"line": 86,
"column": 51
} | {
"line": 86,
"column": 56
} | {
"line": 87,
"column": 2
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Preadditive C\nX Y : SimplicialObject C\nf g : X ⟶ Y\nH : Homotopy f g\nn : ℕ\nα : Fin (n + 1) × Fin (n + 2) → (X _⦋n + 1⦌ ⟶ Y _⦋n + 1⦌) := fun x ↦ (-1) ^ (↑x.1 + ↑x.2) • X.δ x.2 ≫ H.h x.1\nβ : Fin (n + 3) × Fin (n + 2) → (X _⦋n + 1⦌ ⟶ Y _⦋n + 1⦌) := fun ... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialObject.ChainHomotopy | {
"line": 87,
"column": 51
} | {
"line": 87,
"column": 56
} | {
"line": 88,
"column": 2
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Preadditive C\nX Y : SimplicialObject C\nf g : X ⟶ Y\nH : Homotopy f g\nn : ℕ\nα : Fin (n + 1) × Fin (n + 2) → (X _⦋n + 1⦌ ⟶ Y _⦋n + 1⦌) := fun x ↦ (-1) ^ (↑x.1 + ↑x.2) • X.δ x.2 ≫ H.h x.1\nβ : Fin (n + 3) × Fin (n + 2) → (X _⦋n + 1⦌ ⟶ Y _⦋n + 1⦌) := fun ... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialObject.ChainHomotopy | {
"line": 87,
"column": 51
} | {
"line": 87,
"column": 56
} | {
"line": 88,
"column": 2
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Preadditive C\nX Y : SimplicialObject C\nf g : X ⟶ Y\nH : Homotopy f g\nn : ℕ\nα : Fin (n + 1) × Fin (n + 2) → (X _⦋n + 1⦌ ⟶ Y _⦋n + 1⦌) := fun x ↦ (-1) ^ (↑x.1 + ↑x.2) • X.δ x.2 ≫ H.h x.1\nβ : Fin (n + 3) × Fin (n + 2) → (X _⦋n + 1⦌ ⟶ Y _⦋n + 1⦌) := fun ... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialObject.ChainHomotopy | {
"line": 87,
"column": 51
} | {
"line": 87,
"column": 56
} | {
"line": 88,
"column": 2
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Preadditive C\nX Y : SimplicialObject C\nf g : X ⟶ Y\nH : Homotopy f g\nn : ℕ\nα : Fin (n + 1) × Fin (n + 2) → (X _⦋n + 1⦌ ⟶ Y _⦋n + 1⦌) := fun x ↦ (-1) ^ (↑x.1 + ↑x.2) • X.δ x.2 ≫ H.h x.1\nβ : Fin (n + 3) × Fin (n + 2) → (X _⦋n + 1⦌ ⟶ Y _⦋n + 1⦌) := fun ... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialObject.ChainHomotopy | {
"line": 88,
"column": 51
} | {
"line": 88,
"column": 56
} | {
"line": 89,
"column": 2
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Preadditive C\nX Y : SimplicialObject C\nf g : X ⟶ Y\nH : Homotopy f g\nn : ℕ\nα : Fin (n + 1) × Fin (n + 2) → (X _⦋n + 1⦌ ⟶ Y _⦋n + 1⦌) := fun x ↦ (-1) ^ (↑x.1 + ↑x.2) • X.δ x.2 ≫ H.h x.1\nβ : Fin (n + 3) × Fin (n + 2) → (X _⦋n + 1⦌ ⟶ Y _⦋n + 1⦌) := fun ... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialObject.ChainHomotopy | {
"line": 88,
"column": 51
} | {
"line": 88,
"column": 56
} | {
"line": 89,
"column": 2
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Preadditive C\nX Y : SimplicialObject C\nf g : X ⟶ Y\nH : Homotopy f g\nn : ℕ\nα : Fin (n + 1) × Fin (n + 2) → (X _⦋n + 1⦌ ⟶ Y _⦋n + 1⦌) := fun x ↦ (-1) ^ (↑x.1 + ↑x.2) • X.δ x.2 ≫ H.h x.1\nβ : Fin (n + 3) × Fin (n + 2) → (X _⦋n + 1⦌ ⟶ Y _⦋n + 1⦌) := fun ... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialObject.ChainHomotopy | {
"line": 88,
"column": 51
} | {
"line": 88,
"column": 56
} | {
"line": 89,
"column": 2
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Preadditive C\nX Y : SimplicialObject C\nf g : X ⟶ Y\nH : Homotopy f g\nn : ℕ\nα : Fin (n + 1) × Fin (n + 2) → (X _⦋n + 1⦌ ⟶ Y _⦋n + 1⦌) := fun x ↦ (-1) ^ (↑x.1 + ↑x.2) • X.δ x.2 ≫ H.h x.1\nβ : Fin (n + 3) × Fin (n + 2) → (X _⦋n + 1⦌ ⟶ Y _⦋n + 1⦌) := fun ... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialObject.ChainHomotopy | {
"line": 89,
"column": 51
} | {
"line": 89,
"column": 56
} | {
"line": 90,
"column": 2
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Preadditive C\nX Y : SimplicialObject C\nf g : X ⟶ Y\nH : Homotopy f g\nn : ℕ\nα : Fin (n + 1) × Fin (n + 2) → (X _⦋n + 1⦌ ⟶ Y _⦋n + 1⦌) := fun x ↦ (-1) ^ (↑x.1 + ↑x.2) • X.δ x.2 ≫ H.h x.1\nβ : Fin (n + 3) × Fin (n + 2) → (X _⦋n + 1⦌ ⟶ Y _⦋n + 1⦌) := fun ... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialObject.ChainHomotopy | {
"line": 89,
"column": 51
} | {
"line": 89,
"column": 56
} | {
"line": 90,
"column": 2
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Preadditive C\nX Y : SimplicialObject C\nf g : X ⟶ Y\nH : Homotopy f g\nn : ℕ\nα : Fin (n + 1) × Fin (n + 2) → (X _⦋n + 1⦌ ⟶ Y _⦋n + 1⦌) := fun x ↦ (-1) ^ (↑x.1 + ↑x.2) • X.δ x.2 ≫ H.h x.1\nβ : Fin (n + 3) × Fin (n + 2) → (X _⦋n + 1⦌ ⟶ Y _⦋n + 1⦌) := fun ... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialObject.ChainHomotopy | {
"line": 89,
"column": 51
} | {
"line": 89,
"column": 56
} | {
"line": 90,
"column": 2
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Preadditive C\nX Y : SimplicialObject C\nf g : X ⟶ Y\nH : Homotopy f g\nn : ℕ\nα : Fin (n + 1) × Fin (n + 2) → (X _⦋n + 1⦌ ⟶ Y _⦋n + 1⦌) := fun x ↦ (-1) ^ (↑x.1 + ↑x.2) • X.δ x.2 ≫ H.h x.1\nβ : Fin (n + 3) × Fin (n + 2) → (X _⦋n + 1⦌ ⟶ Y _⦋n + 1⦌) := fun ... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex | {
"line": 165,
"column": 6
} | {
"line": 165,
"column": 67
} | {
"line": 166,
"column": 2
} | [
{
"pp": "case a.inr\nX : SSet\nA : X.Subcomplex\nP : A.Pairing\nι : Type v\ninst✝¹ : LinearOrder ι\nf : P.RankFunction ι\ninst✝ : SuccOrder ι\nj : ι\nc : f.Cell j\nhi : ¬IsMax j\nhj : j ≤ j\n⊢ (↑(P.p c.s)).subcomplex ≤ f.filtration j ⊔ ⨆ c, (↑(P.p c.s)).subcomplex",
"ppTerm": "?a.inr✝",
"assigned": true... | [] | exact le_trans (le_trans (by rfl) (le_iSup _ c)) le_sup_right | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex | {
"line": 165,
"column": 6
} | {
"line": 165,
"column": 67
} | {
"line": 166,
"column": 2
} | [
{
"pp": "case a.inr\nX : SSet\nA : X.Subcomplex\nP : A.Pairing\nι : Type v\ninst✝¹ : LinearOrder ι\nf : P.RankFunction ι\ninst✝ : SuccOrder ι\nj : ι\nc : f.Cell j\nhi : ¬IsMax j\nhj : j ≤ j\n⊢ (↑(P.p c.s)).subcomplex ≤ f.filtration j ⊔ ⨆ c, (↑(P.p c.s)).subcomplex",
"ppTerm": "?a.inr✝",
"assigned": true... | [] | exact le_trans (le_trans (by rfl) (le_iSup _ c)) le_sup_right | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
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