module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.CategoryTheory.Limits.Types.Pushouts | {
"line": 174,
"column": 6
} | {
"line": 174,
"column": 10
} | {
"line": 175,
"column": 6
} | [
{
"pp": "case inl_inl\nS X₁ X₂ : Type u\nf : S ⟶ X₁\ng : S ⟶ X₂\nx₀ y₀ : S\nh : (ConcreteCategory.hom g) x₀ = (ConcreteCategory.hom g) y₀\nh₀ : Rel f g (Sum.inl ((ConcreteCategory.hom f) x₀)) (Sum.inr ((ConcreteCategory.hom g) x₀))\n⊢ Quot.mk (Rel f g) (Sum.inr ((ConcreteCategory.hom g) y₀)) = Quot.mk (Rel f g)... | [
"case inl_inl\nS X₁ X₂ : Type u\nf : S ⟶ X₁\ng : S ⟶ X₂\nx₀ y₀ : S\nh : (ConcreteCategory.hom g) x₀ = (ConcreteCategory.hom g) y₀\nh₀ : Rel f g (Sum.inl ((ConcreteCategory.hom f) x₀)) (Sum.inr ((ConcreteCategory.hom g) x₀))\n⊢ Quot.mk (Rel f g) (Sum.inl ((ConcreteCategory.hom f) y₀)) = Quot.mk (Rel f g) (Sum.inr ((... | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.CategoryTheory.Limits.Types.Pushouts | {
"line": 179,
"column": 6
} | {
"line": 179,
"column": 10
} | {
"line": 180,
"column": 6
} | [
{
"pp": "case inr_inl\nS X₁ X₂ : Type u\nf : S ⟶ X₁\ng : S ⟶ X₂\ns✝ : S\n⊢ Quot.mk (Rel f g) (Sum.inr ((ConcreteCategory.hom g) s✝)) = Quot.mk (Rel f g) (Sum.inl ((ConcreteCategory.hom f) s✝))",
"ppTerm": "?inr_inl",
"assigned": true,
"usedConstants": [
"CategoryTheory.ConcreteCategory.hom",
... | [
"case inr_inl\nS X₁ X₂ : Type u\nf : S ⟶ X₁\ng : S ⟶ X₂\ns✝ : S\n⊢ Quot.mk (Rel f g) (Sum.inl ((ConcreteCategory.hom f) s✝)) = Quot.mk (Rel f g) (Sum.inr ((ConcreteCategory.hom g) s✝))"
] | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.AlgebraicTopology.SimplicialSet.Skeleton | {
"line": 99,
"column": 76
} | {
"line": 112,
"column": 47
} | {
"line": 114,
"column": 0
} | [
{
"pp": "X : SSet\nn : ℕ\n⊢ X.skeleton (n + 1) = X.skeleton n ⊔ ⨆ x, Subcomplex.ofSimplex ↑x",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"le_refl",
"SSet.Subcomplex.ofSimplex",
"SSet.ofSimplex_le_skeleton",
"Preorder.toLT",
"Lattice.toSemil... | [] | by
apply le_antisymm
· conv_lhs => dsimp [skeleton]
simp only [iSup_le_iff]
rintro ⟨d, hd⟩ x
rw [Nat.lt_succ_iff] at hd
obtain hd | rfl := hd.lt_or_eq
· exact (X.ofSimplex_le_skeleton _ hd).trans le_sup_left
· exact le_trans (le_trans (by rfl) (le_iSup _ x)) le_sup_right
· simp only [sup_l... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.AlgebraicTopology.Quasicategory.InnerFibration | {
"line": 87,
"column": 2
} | {
"line": 87,
"column": 6
} | {
"line": 88,
"column": 2
} | [
{
"pp": "X Y : SSet\np : X ⟶ Y\nhY : IsTerminal Y\n⊢ innerFibrations (terminal.from X) ↔ innerFibrations p",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Opposite",
"CategoryTheory.typesCartesianMonoidalCategory",
"CategoryTheory.Functor.category",
"CategoryTheory.... | [
"X Y : SSet\np : X ⟶ Y\nhY : IsTerminal Y\n⊢ innerFibrations p ↔ innerFibrations (terminal.from X)"
] | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | {
"line": 60,
"column": 12
} | {
"line": 60,
"column": 18
} | {
"line": 62,
"column": 0
} | [
{
"pp": "case commf\n⊢ (stdSimplex.faceSingletonIso 0).hom ≫ Subcomplex.homOfLE ⋯ = stdSimplex.δ 1 ≫ (stdSimplex.facePairIso 0 1 ⋯).hom",
"ppTerm": "?commf",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.toSSet",
"Opposite",
"Lattice.BicartSq.le₁₂",
"of_decide_eq_true... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | {
"line": 60,
"column": 12
} | {
"line": 60,
"column": 18
} | {
"line": 62,
"column": 0
} | [
{
"pp": "case commf\n⊢ (stdSimplex.faceSingletonIso 0).hom ≫ Subcomplex.homOfLE ⋯ = stdSimplex.δ 1 ≫ (stdSimplex.facePairIso 0 1 ⋯).hom",
"ppTerm": "?commf",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.toSSet",
"Opposite",
"Lattice.BicartSq.le₁₂",
"of_decide_eq_true... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | {
"line": 60,
"column": 12
} | {
"line": 60,
"column": 18
} | {
"line": 62,
"column": 0
} | [
{
"pp": "case commf\n⊢ (stdSimplex.faceSingletonIso 0).hom ≫ Subcomplex.homOfLE ⋯ = stdSimplex.δ 1 ≫ (stdSimplex.facePairIso 0 1 ⋯).hom",
"ppTerm": "?commf",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.toSSet",
"Opposite",
"Lattice.BicartSq.le₁₂",
"of_decide_eq_true... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | {
"line": 60,
"column": 12
} | {
"line": 60,
"column": 18
} | {
"line": 62,
"column": 0
} | [
{
"pp": "case commg\n⊢ (stdSimplex.faceSingletonIso 0).hom ≫ Subcomplex.homOfLE ⋯ = stdSimplex.δ 1 ≫ (stdSimplex.facePairIso 0 2 ⋯).hom",
"ppTerm": "?commg",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.toSSet",
"Opposite",
"of_decide_eq_true",
"CategoryTheory.Catego... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | {
"line": 60,
"column": 12
} | {
"line": 60,
"column": 18
} | {
"line": 62,
"column": 0
} | [
{
"pp": "case commg\n⊢ (stdSimplex.faceSingletonIso 0).hom ≫ Subcomplex.homOfLE ⋯ = stdSimplex.δ 1 ≫ (stdSimplex.facePairIso 0 2 ⋯).hom",
"ppTerm": "?commg",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.toSSet",
"Opposite",
"of_decide_eq_true",
"CategoryTheory.Catego... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | {
"line": 60,
"column": 12
} | {
"line": 60,
"column": 18
} | {
"line": 62,
"column": 0
} | [
{
"pp": "case commg\n⊢ (stdSimplex.faceSingletonIso 0).hom ≫ Subcomplex.homOfLE ⋯ = stdSimplex.δ 1 ≫ (stdSimplex.facePairIso 0 2 ⋯).hom",
"ppTerm": "?commg",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.toSSet",
"Opposite",
"of_decide_eq_true",
"CategoryTheory.Catego... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | {
"line": 60,
"column": 12
} | {
"line": 60,
"column": 18
} | {
"line": 62,
"column": 0
} | [
{
"pp": "case comminl\n⊢ (stdSimplex.facePairIso 0 1 ⋯).hom ≫ Subcomplex.homOfLE ⋯ = ι₀₁ ≫ (Iso.refl Λ[2, 0].toSSet).hom",
"ppTerm": "?comminl",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.toSSet",
"Opposite",
"of_decide_eq_true",
"CategoryTheory.CategoryStruct.toQu... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | {
"line": 60,
"column": 12
} | {
"line": 60,
"column": 18
} | {
"line": 62,
"column": 0
} | [
{
"pp": "case comminl\n⊢ (stdSimplex.facePairIso 0 1 ⋯).hom ≫ Subcomplex.homOfLE ⋯ = ι₀₁ ≫ (Iso.refl Λ[2, 0].toSSet).hom",
"ppTerm": "?comminl",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.toSSet",
"Opposite",
"of_decide_eq_true",
"CategoryTheory.CategoryStruct.toQu... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | {
"line": 60,
"column": 12
} | {
"line": 60,
"column": 18
} | {
"line": 62,
"column": 0
} | [
{
"pp": "case comminl\n⊢ (stdSimplex.facePairIso 0 1 ⋯).hom ≫ Subcomplex.homOfLE ⋯ = ι₀₁ ≫ (Iso.refl Λ[2, 0].toSSet).hom",
"ppTerm": "?comminl",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.toSSet",
"Opposite",
"of_decide_eq_true",
"CategoryTheory.CategoryStruct.toQu... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | {
"line": 60,
"column": 12
} | {
"line": 60,
"column": 18
} | {
"line": 62,
"column": 0
} | [
{
"pp": "case comminr\n⊢ (stdSimplex.facePairIso 0 2 ⋯).hom ≫ Subcomplex.homOfLE ⋯ = ι₀₂ ≫ (Iso.refl Λ[2, 0].toSSet).hom",
"ppTerm": "?comminr",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.toSSet",
"Opposite",
"of_decide_eq_true",
"CategoryTheory.CategoryStruct.toQu... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | {
"line": 60,
"column": 12
} | {
"line": 60,
"column": 18
} | {
"line": 62,
"column": 0
} | [
{
"pp": "case comminr\n⊢ (stdSimplex.facePairIso 0 2 ⋯).hom ≫ Subcomplex.homOfLE ⋯ = ι₀₂ ≫ (Iso.refl Λ[2, 0].toSSet).hom",
"ppTerm": "?comminr",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.toSSet",
"Opposite",
"of_decide_eq_true",
"CategoryTheory.CategoryStruct.toQu... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | {
"line": 60,
"column": 12
} | {
"line": 60,
"column": 18
} | {
"line": 62,
"column": 0
} | [
{
"pp": "case comminr\n⊢ (stdSimplex.facePairIso 0 2 ⋯).hom ≫ Subcomplex.homOfLE ⋯ = ι₀₂ ≫ (Iso.refl Λ[2, 0].toSSet).hom",
"ppTerm": "?comminr",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.toSSet",
"Opposite",
"of_decide_eq_true",
"CategoryTheory.CategoryStruct.toQu... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | {
"line": 93,
"column": 12
} | {
"line": 93,
"column": 18
} | {
"line": 95,
"column": 0
} | [
{
"pp": "case commf\n⊢ (stdSimplex.faceSingletonIso 1).hom ≫ Subcomplex.homOfLE ⋯ = stdSimplex.δ 0 ≫ (stdSimplex.facePairIso 0 1 ⋯).hom",
"ppTerm": "?commf",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.toSSet",
"Opposite",
"Lattice.BicartSq.le₁₂",
"of_decide_eq_true... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | {
"line": 93,
"column": 12
} | {
"line": 93,
"column": 18
} | {
"line": 95,
"column": 0
} | [
{
"pp": "case commf\n⊢ (stdSimplex.faceSingletonIso 1).hom ≫ Subcomplex.homOfLE ⋯ = stdSimplex.δ 0 ≫ (stdSimplex.facePairIso 0 1 ⋯).hom",
"ppTerm": "?commf",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.toSSet",
"Opposite",
"Lattice.BicartSq.le₁₂",
"of_decide_eq_true... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | {
"line": 93,
"column": 12
} | {
"line": 93,
"column": 18
} | {
"line": 95,
"column": 0
} | [
{
"pp": "case commf\n⊢ (stdSimplex.faceSingletonIso 1).hom ≫ Subcomplex.homOfLE ⋯ = stdSimplex.δ 0 ≫ (stdSimplex.facePairIso 0 1 ⋯).hom",
"ppTerm": "?commf",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.toSSet",
"Opposite",
"Lattice.BicartSq.le₁₂",
"of_decide_eq_true... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | {
"line": 93,
"column": 12
} | {
"line": 93,
"column": 18
} | {
"line": 95,
"column": 0
} | [
{
"pp": "case commg\n⊢ (stdSimplex.faceSingletonIso 1).hom ≫ Subcomplex.homOfLE ⋯ = stdSimplex.δ 1 ≫ (stdSimplex.facePairIso 1 2 ⋯).hom",
"ppTerm": "?commg",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.toSSet",
"Opposite",
"of_decide_eq_true",
"CategoryTheory.Catego... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | {
"line": 93,
"column": 12
} | {
"line": 93,
"column": 18
} | {
"line": 95,
"column": 0
} | [
{
"pp": "case commg\n⊢ (stdSimplex.faceSingletonIso 1).hom ≫ Subcomplex.homOfLE ⋯ = stdSimplex.δ 1 ≫ (stdSimplex.facePairIso 1 2 ⋯).hom",
"ppTerm": "?commg",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.toSSet",
"Opposite",
"of_decide_eq_true",
"CategoryTheory.Catego... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | {
"line": 93,
"column": 12
} | {
"line": 93,
"column": 18
} | {
"line": 95,
"column": 0
} | [
{
"pp": "case commg\n⊢ (stdSimplex.faceSingletonIso 1).hom ≫ Subcomplex.homOfLE ⋯ = stdSimplex.δ 1 ≫ (stdSimplex.facePairIso 1 2 ⋯).hom",
"ppTerm": "?commg",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.toSSet",
"Opposite",
"of_decide_eq_true",
"CategoryTheory.Catego... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | {
"line": 93,
"column": 12
} | {
"line": 93,
"column": 18
} | {
"line": 95,
"column": 0
} | [
{
"pp": "case comminl\n⊢ (stdSimplex.facePairIso 0 1 ⋯).hom ≫ Subcomplex.homOfLE ⋯ = ι₀₁ ≫ (Iso.refl Λ[2, 1].toSSet).hom",
"ppTerm": "?comminl",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.toSSet",
"Opposite",
"of_decide_eq_true",
"CategoryTheory.CategoryStruct.toQu... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | {
"line": 93,
"column": 12
} | {
"line": 93,
"column": 18
} | {
"line": 95,
"column": 0
} | [
{
"pp": "case comminl\n⊢ (stdSimplex.facePairIso 0 1 ⋯).hom ≫ Subcomplex.homOfLE ⋯ = ι₀₁ ≫ (Iso.refl Λ[2, 1].toSSet).hom",
"ppTerm": "?comminl",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.toSSet",
"Opposite",
"of_decide_eq_true",
"CategoryTheory.CategoryStruct.toQu... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | {
"line": 93,
"column": 12
} | {
"line": 93,
"column": 18
} | {
"line": 95,
"column": 0
} | [
{
"pp": "case comminl\n⊢ (stdSimplex.facePairIso 0 1 ⋯).hom ≫ Subcomplex.homOfLE ⋯ = ι₀₁ ≫ (Iso.refl Λ[2, 1].toSSet).hom",
"ppTerm": "?comminl",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.toSSet",
"Opposite",
"of_decide_eq_true",
"CategoryTheory.CategoryStruct.toQu... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | {
"line": 93,
"column": 12
} | {
"line": 93,
"column": 18
} | {
"line": 95,
"column": 0
} | [
{
"pp": "case comminr\n⊢ (stdSimplex.facePairIso 1 2 ⋯).hom ≫ Subcomplex.homOfLE ⋯ = ι₁₂ ≫ (Iso.refl Λ[2, 1].toSSet).hom",
"ppTerm": "?comminr",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.toSSet",
"Opposite",
"of_decide_eq_true",
"CategoryTheory.CategoryStruct.toQu... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | {
"line": 93,
"column": 12
} | {
"line": 93,
"column": 18
} | {
"line": 95,
"column": 0
} | [
{
"pp": "case comminr\n⊢ (stdSimplex.facePairIso 1 2 ⋯).hom ≫ Subcomplex.homOfLE ⋯ = ι₁₂ ≫ (Iso.refl Λ[2, 1].toSSet).hom",
"ppTerm": "?comminr",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.toSSet",
"Opposite",
"of_decide_eq_true",
"CategoryTheory.CategoryStruct.toQu... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | {
"line": 93,
"column": 12
} | {
"line": 93,
"column": 18
} | {
"line": 95,
"column": 0
} | [
{
"pp": "case comminr\n⊢ (stdSimplex.facePairIso 1 2 ⋯).hom ≫ Subcomplex.homOfLE ⋯ = ι₁₂ ≫ (Iso.refl Λ[2, 1].toSSet).hom",
"ppTerm": "?comminr",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.toSSet",
"Opposite",
"of_decide_eq_true",
"CategoryTheory.CategoryStruct.toQu... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | {
"line": 126,
"column": 12
} | {
"line": 126,
"column": 18
} | {
"line": 128,
"column": 0
} | [
{
"pp": "case commf\n⊢ (stdSimplex.faceSingletonIso 2).hom ≫ Subcomplex.homOfLE ⋯ = stdSimplex.δ 0 ≫ (stdSimplex.facePairIso 0 2 ⋯).hom",
"ppTerm": "?commf",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.toSSet",
"Opposite",
"Lattice.BicartSq.le₁₂",
"of_decide_eq_true... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | {
"line": 126,
"column": 12
} | {
"line": 126,
"column": 18
} | {
"line": 128,
"column": 0
} | [
{
"pp": "case commf\n⊢ (stdSimplex.faceSingletonIso 2).hom ≫ Subcomplex.homOfLE ⋯ = stdSimplex.δ 0 ≫ (stdSimplex.facePairIso 0 2 ⋯).hom",
"ppTerm": "?commf",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.toSSet",
"Opposite",
"Lattice.BicartSq.le₁₂",
"of_decide_eq_true... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | {
"line": 126,
"column": 12
} | {
"line": 126,
"column": 18
} | {
"line": 128,
"column": 0
} | [
{
"pp": "case commf\n⊢ (stdSimplex.faceSingletonIso 2).hom ≫ Subcomplex.homOfLE ⋯ = stdSimplex.δ 0 ≫ (stdSimplex.facePairIso 0 2 ⋯).hom",
"ppTerm": "?commf",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.toSSet",
"Opposite",
"Lattice.BicartSq.le₁₂",
"of_decide_eq_true... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | {
"line": 126,
"column": 12
} | {
"line": 126,
"column": 18
} | {
"line": 128,
"column": 0
} | [
{
"pp": "case commg\n⊢ (stdSimplex.faceSingletonIso 2).hom ≫ Subcomplex.homOfLE ⋯ = stdSimplex.δ 0 ≫ (stdSimplex.facePairIso 1 2 ⋯).hom",
"ppTerm": "?commg",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.toSSet",
"Opposite",
"of_decide_eq_true",
"CategoryTheory.Catego... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | {
"line": 126,
"column": 12
} | {
"line": 126,
"column": 18
} | {
"line": 128,
"column": 0
} | [
{
"pp": "case commg\n⊢ (stdSimplex.faceSingletonIso 2).hom ≫ Subcomplex.homOfLE ⋯ = stdSimplex.δ 0 ≫ (stdSimplex.facePairIso 1 2 ⋯).hom",
"ppTerm": "?commg",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.toSSet",
"Opposite",
"of_decide_eq_true",
"CategoryTheory.Catego... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | {
"line": 126,
"column": 12
} | {
"line": 126,
"column": 18
} | {
"line": 128,
"column": 0
} | [
{
"pp": "case commg\n⊢ (stdSimplex.faceSingletonIso 2).hom ≫ Subcomplex.homOfLE ⋯ = stdSimplex.δ 0 ≫ (stdSimplex.facePairIso 1 2 ⋯).hom",
"ppTerm": "?commg",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.toSSet",
"Opposite",
"of_decide_eq_true",
"CategoryTheory.Catego... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | {
"line": 126,
"column": 12
} | {
"line": 126,
"column": 18
} | {
"line": 128,
"column": 0
} | [
{
"pp": "case comminl\n⊢ (stdSimplex.facePairIso 0 2 ⋯).hom ≫ Subcomplex.homOfLE ⋯ = ι₀₂ ≫ (Iso.refl Λ[2, 2].toSSet).hom",
"ppTerm": "?comminl",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.toSSet",
"Opposite",
"of_decide_eq_true",
"CategoryTheory.CategoryStruct.toQu... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | {
"line": 126,
"column": 12
} | {
"line": 126,
"column": 18
} | {
"line": 128,
"column": 0
} | [
{
"pp": "case comminl\n⊢ (stdSimplex.facePairIso 0 2 ⋯).hom ≫ Subcomplex.homOfLE ⋯ = ι₀₂ ≫ (Iso.refl Λ[2, 2].toSSet).hom",
"ppTerm": "?comminl",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.toSSet",
"Opposite",
"of_decide_eq_true",
"CategoryTheory.CategoryStruct.toQu... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | {
"line": 126,
"column": 12
} | {
"line": 126,
"column": 18
} | {
"line": 128,
"column": 0
} | [
{
"pp": "case comminl\n⊢ (stdSimplex.facePairIso 0 2 ⋯).hom ≫ Subcomplex.homOfLE ⋯ = ι₀₂ ≫ (Iso.refl Λ[2, 2].toSSet).hom",
"ppTerm": "?comminl",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.toSSet",
"Opposite",
"of_decide_eq_true",
"CategoryTheory.CategoryStruct.toQu... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | {
"line": 126,
"column": 12
} | {
"line": 126,
"column": 18
} | {
"line": 128,
"column": 0
} | [
{
"pp": "case comminr\n⊢ (stdSimplex.facePairIso 1 2 ⋯).hom ≫ Subcomplex.homOfLE ⋯ = ι₁₂ ≫ (Iso.refl Λ[2, 2].toSSet).hom",
"ppTerm": "?comminr",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.toSSet",
"Opposite",
"of_decide_eq_true",
"CategoryTheory.CategoryStruct.toQu... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | {
"line": 126,
"column": 12
} | {
"line": 126,
"column": 18
} | {
"line": 128,
"column": 0
} | [
{
"pp": "case comminr\n⊢ (stdSimplex.facePairIso 1 2 ⋯).hom ≫ Subcomplex.homOfLE ⋯ = ι₁₂ ≫ (Iso.refl Λ[2, 2].toSSet).hom",
"ppTerm": "?comminr",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.toSSet",
"Opposite",
"of_decide_eq_true",
"CategoryTheory.CategoryStruct.toQu... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | {
"line": 126,
"column": 12
} | {
"line": 126,
"column": 18
} | {
"line": 128,
"column": 0
} | [
{
"pp": "case comminr\n⊢ (stdSimplex.facePairIso 1 2 ⋯).hom ≫ Subcomplex.homOfLE ⋯ = ι₁₂ ≫ (Iso.refl Λ[2, 2].toSSet).hom",
"ppTerm": "?comminr",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.toSSet",
"Opposite",
"of_decide_eq_true",
"CategoryTheory.CategoryStruct.toQu... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.Skeleton | {
"line": 391,
"column": 6
} | {
"line": 392,
"column": 90
} | {
"line": 393,
"column": 6
} | [
{
"pp": "case refine_3\nX Y : SSet\ni : X ⟶ Y\nd : ℕ\nx✝ : SimplexCategoryᵒᵖ\nn : ℕ\nc₁ : Cell i d\nf₁ : ⦋n⦌ ⟶ ⦋d⦌\nw✝¹ : Epi f₁\nhx₁ :\n (ConcreteCategory.hom (c₁.ιSigmaStdSimplex.app (op ⦋n⦌))) (stdSimplex.objEquiv.symm f₁) ∉\n Set.range ⇑(ConcreteCategory.hom ((l i d).app (op ⦋n⦌)))\nc₂ : Cell i d\nf₂ : ... | [
"case refine_3\nX Y : SSet\ni : X ⟶ Y\nd : ℕ\nx✝ : SimplexCategoryᵒᵖ\nn : ℕ\nc₁ : Cell i d\nf₁ : ⦋n⦌ ⟶ ⦋d⦌\nw✝¹ : Epi f₁\nhx₁ :\n (ConcreteCategory.hom (c₁.ιSigmaStdSimplex.app (op ⦋n⦌))) (stdSimplex.objEquiv.symm f₁) ∉\n Set.range ⇑(ConcreteCategory.hom ((l i d).app (op ⦋n⦌)))\nc₂ : Cell i d\nf₂ : ⦋n⦌ ⟶ ⦋d⦌\nw... | replace h : Y.map f₁.op c₁.simplex = Y.map f₂.op c₂.simplex := by
rwa [← c₁.b_app_ι_app_objEquiv_symm_val f₁, ← c₂.b_app_ι_app_objEquiv_symm_val f₂] | Lean.Elab.Tactic.evalReplace | Lean.Parser.Tactic.replace |
Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | {
"line": 280,
"column": 25
} | {
"line": 280,
"column": 31
} | {
"line": 281,
"column": 6
} | [
{
"pp": "case e'_2\nX : SSet\nf₀ f₂ f₃ : Δ[2] ⟶ X\nh₁₂ : stdSimplex.δ 2 ≫ f₀ = stdSimplex.δ 0 ≫ f₃\nh₁₃ : stdSimplex.δ 1 ≫ f₀ = stdSimplex.δ 0 ≫ f₂\nh₂₃ : stdSimplex.δ 2 ≫ f₂ = stdSimplex.δ 2 ≫ f₃\n⊢ ((stdSimplex.facePairIso 1 3 ⋯).hom ≫ Subcomplex.homOfLE ⋯) ≫ (stdSimplex.faceSingletonComplIso 0).inv =\n st... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | {
"line": 280,
"column": 25
} | {
"line": 280,
"column": 31
} | {
"line": 281,
"column": 6
} | [
{
"pp": "case e'_3\nX : SSet\nf₀ f₂ f₃ : Δ[2] ⟶ X\nh₁₂ : stdSimplex.δ 2 ≫ f₀ = stdSimplex.δ 0 ≫ f₃\nh₁₃ : stdSimplex.δ 1 ≫ f₀ = stdSimplex.δ 0 ≫ f₂\nh₂₃ : stdSimplex.δ 2 ≫ f₂ = stdSimplex.δ 2 ≫ f₃\n⊢ ((stdSimplex.facePairIso 1 3 ⋯).hom ≫ Subcomplex.homOfLE ⋯) ≫ (stdSimplex.faceSingletonComplIso 2).inv =\n st... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicTopology.SimplicialSet.Path | {
"line": 313,
"column": 4
} | {
"line": 313,
"column": 8
} | {
"line": 314,
"column": 4
} | [
{
"pp": "case succ\nX : SSet\nm : ℕ\nx : X _⦋m + 1 + 1⦌\ni : Fin (m + 1)\n⊢ (ConcreteCategory.hom (X.map (mkOfSucc i.succ).op)) x = ((X.spine (m + 1 + 1) x).interval 1 (m + 1) ⋯).arrow i",
"ppTerm": "?succ",
"assigned": true,
"usedConstants": [
"SSet.spine_δ₀._proof_2",
"Opposite",
... | [
"case succ\nX : SSet\nm : ℕ\nx : X _⦋m + 1 + 1⦌\ni : Fin (m + 1)\n⊢ ((X.spine (m + 1 + 1) x).interval 1 (m + 1) ⋯).arrow i = (ConcreteCategory.hom (X.map (mkOfSucc i.succ).op)) x"
] | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | {
"line": 284,
"column": 25
} | {
"line": 284,
"column": 31
} | {
"line": 285,
"column": 6
} | [
{
"pp": "case e'_2\nX : SSet\nf₀ f₂ f₃ : Δ[2] ⟶ X\nh₁₂ : stdSimplex.δ 2 ≫ f₀ = stdSimplex.δ 0 ≫ f₃\nh₁₃ : stdSimplex.δ 1 ≫ f₀ = stdSimplex.δ 0 ≫ f₂\nh₂₃ : stdSimplex.δ 2 ≫ f₂ = stdSimplex.δ 2 ≫ f₃\n⊢ ((stdSimplex.facePairIso 1 2 ⋯).hom ≫ Subcomplex.homOfLE ⋯) ≫ (stdSimplex.faceSingletonComplIso 0).inv =\n st... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | {
"line": 284,
"column": 25
} | {
"line": 284,
"column": 31
} | {
"line": 285,
"column": 6
} | [
{
"pp": "case e'_3\nX : SSet\nf₀ f₂ f₃ : Δ[2] ⟶ X\nh₁₂ : stdSimplex.δ 2 ≫ f₀ = stdSimplex.δ 0 ≫ f₃\nh₁₃ : stdSimplex.δ 1 ≫ f₀ = stdSimplex.δ 0 ≫ f₂\nh₂₃ : stdSimplex.δ 2 ≫ f₂ = stdSimplex.δ 2 ≫ f₃\n⊢ ((stdSimplex.facePairIso 1 2 ⋯).hom ≫ Subcomplex.homOfLE ⋯) ≫ (stdSimplex.faceSingletonComplIso 3).inv =\n st... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | {
"line": 288,
"column": 25
} | {
"line": 288,
"column": 31
} | {
"line": 288,
"column": 31
} | [
{
"pp": "case e'_2\nX : SSet\nf₀ f₂ f₃ : Δ[2] ⟶ X\nh₁₂ : stdSimplex.δ 2 ≫ f₀ = stdSimplex.δ 0 ≫ f₃\nh₁₃ : stdSimplex.δ 1 ≫ f₀ = stdSimplex.δ 0 ≫ f₂\nh₂₃ : stdSimplex.δ 2 ≫ f₂ = stdSimplex.δ 2 ≫ f₃\n⊢ ((stdSimplex.facePairIso 0 1 ⋯).hom ≫ Subcomplex.homOfLE ⋯) ≫ (stdSimplex.faceSingletonComplIso 2).inv =\n st... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | {
"line": 288,
"column": 25
} | {
"line": 288,
"column": 31
} | {
"line": 288,
"column": 31
} | [
{
"pp": "case e'_3\nX : SSet\nf₀ f₂ f₃ : Δ[2] ⟶ X\nh₁₂ : stdSimplex.δ 2 ≫ f₀ = stdSimplex.δ 0 ≫ f₃\nh₁₃ : stdSimplex.δ 1 ≫ f₀ = stdSimplex.δ 0 ≫ f₂\nh₂₃ : stdSimplex.δ 2 ≫ f₂ = stdSimplex.δ 2 ≫ f₃\n⊢ ((stdSimplex.facePairIso 0 1 ⋯).hom ≫ Subcomplex.homOfLE ⋯) ≫ (stdSimplex.faceSingletonComplIso 3).inv =\n st... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | {
"line": 368,
"column": 25
} | {
"line": 368,
"column": 31
} | {
"line": 369,
"column": 6
} | [
{
"pp": "case e'_2\nX : SSet\nf₀ f₁ f₃ : Δ[2] ⟶ X\nh₀₂ : stdSimplex.δ 2 ≫ f₁ = stdSimplex.δ 1 ≫ f₃\nh₁₂ : stdSimplex.δ 2 ≫ f₀ = stdSimplex.δ 0 ≫ f₃\nh₂₃ : stdSimplex.δ 0 ≫ f₀ = stdSimplex.δ 0 ≫ f₁\n⊢ ((stdSimplex.facePairIso 2 3 ⋯).hom ≫ Subcomplex.homOfLE ⋯) ≫ (stdSimplex.faceSingletonComplIso 0).inv =\n st... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | {
"line": 368,
"column": 25
} | {
"line": 368,
"column": 31
} | {
"line": 369,
"column": 6
} | [
{
"pp": "case e'_3\nX : SSet\nf₀ f₁ f₃ : Δ[2] ⟶ X\nh₀₂ : stdSimplex.δ 2 ≫ f₁ = stdSimplex.δ 1 ≫ f₃\nh₁₂ : stdSimplex.δ 2 ≫ f₀ = stdSimplex.δ 0 ≫ f₃\nh₂₃ : stdSimplex.δ 0 ≫ f₀ = stdSimplex.δ 0 ≫ f₁\n⊢ ((stdSimplex.facePairIso 2 3 ⋯).hom ≫ Subcomplex.homOfLE ⋯) ≫ (stdSimplex.faceSingletonComplIso 1).inv =\n st... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | {
"line": 372,
"column": 25
} | {
"line": 372,
"column": 31
} | {
"line": 373,
"column": 6
} | [
{
"pp": "case e'_2\nX : SSet\nf₀ f₁ f₃ : Δ[2] ⟶ X\nh₀₂ : stdSimplex.δ 2 ≫ f₁ = stdSimplex.δ 1 ≫ f₃\nh₁₂ : stdSimplex.δ 2 ≫ f₀ = stdSimplex.δ 0 ≫ f₃\nh₂₃ : stdSimplex.δ 0 ≫ f₀ = stdSimplex.δ 0 ≫ f₁\n⊢ ((stdSimplex.facePairIso 1 2 ⋯).hom ≫ Subcomplex.homOfLE ⋯) ≫ (stdSimplex.faceSingletonComplIso 0).inv =\n st... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | {
"line": 372,
"column": 25
} | {
"line": 372,
"column": 31
} | {
"line": 373,
"column": 6
} | [
{
"pp": "case e'_3\nX : SSet\nf₀ f₁ f₃ : Δ[2] ⟶ X\nh₀₂ : stdSimplex.δ 2 ≫ f₁ = stdSimplex.δ 1 ≫ f₃\nh₁₂ : stdSimplex.δ 2 ≫ f₀ = stdSimplex.δ 0 ≫ f₃\nh₂₃ : stdSimplex.δ 0 ≫ f₀ = stdSimplex.δ 0 ≫ f₁\n⊢ ((stdSimplex.facePairIso 1 2 ⋯).hom ≫ Subcomplex.homOfLE ⋯) ≫ (stdSimplex.faceSingletonComplIso 3).inv =\n st... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | {
"line": 376,
"column": 25
} | {
"line": 376,
"column": 31
} | {
"line": 376,
"column": 31
} | [
{
"pp": "case e'_2\nX : SSet\nf₀ f₁ f₃ : Δ[2] ⟶ X\nh₀₂ : stdSimplex.δ 2 ≫ f₁ = stdSimplex.δ 1 ≫ f₃\nh₁₂ : stdSimplex.δ 2 ≫ f₀ = stdSimplex.δ 0 ≫ f₃\nh₂₃ : stdSimplex.δ 0 ≫ f₀ = stdSimplex.δ 0 ≫ f₁\n⊢ ((stdSimplex.facePairIso 0 2 ⋯).hom ≫ Subcomplex.homOfLE ⋯) ≫ (stdSimplex.faceSingletonComplIso 1).inv =\n st... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | {
"line": 376,
"column": 25
} | {
"line": 376,
"column": 31
} | {
"line": 376,
"column": 31
} | [
{
"pp": "case e'_3\nX : SSet\nf₀ f₁ f₃ : Δ[2] ⟶ X\nh₀₂ : stdSimplex.δ 2 ≫ f₁ = stdSimplex.δ 1 ≫ f₃\nh₁₂ : stdSimplex.δ 2 ≫ f₀ = stdSimplex.δ 0 ≫ f₃\nh₂₃ : stdSimplex.δ 0 ≫ f₀ = stdSimplex.δ 0 ≫ f₁\n⊢ ((stdSimplex.facePairIso 0 2 ⋯).hom ≫ Subcomplex.homOfLE ⋯) ≫ (stdSimplex.faceSingletonComplIso 3).inv =\n st... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal | {
"line": 456,
"column": 12
} | {
"line": 456,
"column": 40
} | {
"line": 457,
"column": 2
} | [
{
"pp": "case zero\nX : SSet\nh : (n : ℕ) → X.StrictSegalCore n\np : X.Path 0\n⊢ { s // X.spine 0 s = p }",
"ppTerm": "?zero",
"assigned": true,
"usedConstants": [
"SSet.Path",
"Opposite",
"SSet.StrictSegalCore.spineToSimplexAux._proof_2",
"instOfNatNat",
"Subtype.mk",
... | [] | exact ⟨p.vertex 0, by aesop⟩ | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal | {
"line": 456,
"column": 12
} | {
"line": 456,
"column": 40
} | {
"line": 457,
"column": 2
} | [
{
"pp": "case zero\nX : SSet\nh : (n : ℕ) → X.StrictSegalCore n\np : X.Path 0\n⊢ { s // X.spine 0 s = p }",
"ppTerm": "?zero",
"assigned": true,
"usedConstants": [
"SSet.Path",
"Opposite",
"SSet.StrictSegalCore.spineToSimplexAux._proof_2",
"instOfNatNat",
"Subtype.mk",
... | [] | exact ⟨p.vertex 0, by aesop⟩ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal | {
"line": 456,
"column": 12
} | {
"line": 456,
"column": 40
} | {
"line": 457,
"column": 2
} | [
{
"pp": "case zero\nX : SSet\nh : (n : ℕ) → X.StrictSegalCore n\np : X.Path 0\n⊢ { s // X.spine 0 s = p }",
"ppTerm": "?zero",
"assigned": true,
"usedConstants": [
"SSet.Path",
"Opposite",
"SSet.StrictSegalCore.spineToSimplexAux._proof_2",
"instOfNatNat",
"Subtype.mk",
... | [] | exact ⟨p.vertex 0, by aesop⟩ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Bicategory.CatEnriched | {
"line": 277,
"column": 57
} | {
"line": 278,
"column": 53
} | {
"line": 280,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : EnrichedOrdinaryCategory Cat C\na b c : CatEnrichedOrdinary C\nf₁ f₂ f₃ : a ⟶ b\ng₁ g₂ g₃ : b ⟶ c\nη : f₁ ⟶ f₂\nη' : f₂ ⟶ f₃\nθ : g₁ ⟶ g₂\nθ' : g₂ ⟶ g₃\n⊢ hComp η θ ≫ hComp η' θ' = hComp (η ≫ η') (θ ≫ θ')",
"ppTerm": "?m.70",
"assigned": true,
... | [] | by
simp [hComp, ← CatEnriched.hComp_comp, Hom.comp_eq] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat | {
"line": 195,
"column": 54
} | {
"line": 195,
"column": 60
} | {
"line": 195,
"column": 60
} | [
{
"pp": "V : Truncated 2\nφ : V.obj (op { obj := ⦋2⦌, property := ι0₂._proof_3 })\n⊢ 0 ≤ 1",
"ppTerm": "?m.74",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"LE.le",
"instLEFin",
"Bool.true",
"instHAdd",
"HAdd.hAdd",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat | {
"line": 195,
"column": 54
} | {
"line": 195,
"column": 60
} | {
"line": 195,
"column": 60
} | [
{
"pp": "V : Truncated 2\nφ : V.obj (op { obj := ⦋2⦌, property := ι0₂._proof_3 })\n⊢ 0 ≤ 1",
"ppTerm": "?m.74",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"LE.le",
"instLEFin",
"Bool.true",
"instHAdd",
"HAdd.hAdd",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat | {
"line": 195,
"column": 54
} | {
"line": 195,
"column": 60
} | {
"line": 195,
"column": 60
} | [
{
"pp": "V : Truncated 2\nφ : V.obj (op { obj := ⦋2⦌, property := ι0₂._proof_3 })\n⊢ 0 ≤ 1",
"ppTerm": "?m.74",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"LE.le",
"instLEFin",
"Bool.true",
"instHAdd",
"HAdd.hAdd",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat | {
"line": 335,
"column": 4
} | {
"line": 335,
"column": 65
} | {
"line": 336,
"column": 4
} | [
{
"pp": "V : Truncated 2\nx y : V.HomotopyCategory\nf : x.as ⟶ y.as\nx✝ : ⊤ ((quotientFunctor V).map f)\n⊢ (Cat.FreeRefl.morphismPropertyHomMk (OneTruncation₂ V)).multiplicativeClosure.strictMap (quotientFunctor V)\n ((quotientFunctor V).map f)",
"ppTerm": "?m.64",
"assigned": true,
"usedConstant... | [
"V : Truncated 2\nx y : V.HomotopyCategory\nf : x.as ⟶ y.as\nx✝ : ⊤ ((quotientFunctor V).map f)\n⊢ ⊤.strictMap (quotientFunctor V) ((quotientFunctor V).map f)"
] | rw [Cat.FreeRefl.multiplicativeClosure_morphismPropertyHomMk] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.AlgebraicTopology.SimplicialSet.Coskeletal | {
"line": 134,
"column": 6
} | {
"line": 135,
"column": 40
} | {
"line": 136,
"column": 6
} | [
{
"pp": "case succ\nX : SSet\nsx : X.StrictSegal\nn : ℕ\ns : Cone (proj (op ⦋n⦌) (inclusion 2).op ⋙ (inclusion 2).op ⋙ X)\nx : s.pt\nk : ℕ\nhk :\n ∀ (i j : ℕ) (hij : i ≤ j) (hj : j ≤ n),\n i + k = j →\n (ConcreteCategory.hom (X.map (mkOfLe ⟨i, ⋯⟩ ⟨j, ⋯⟩ hij).op)) (lift sx s x) =\n (ConcreteCateg... | [
"case succ\nX : SSet\nsx : X.StrictSegal\nn : ℕ\ns : Cone (proj (op ⦋n⦌) (inclusion 2).op ⋙ (inclusion 2).op ⋙ X)\nx : s.pt\nk : ℕ\nhk :\n ∀ (i j : ℕ) (hij : i ≤ j) (hj : j ≤ n),\n i + k = j →\n (ConcreteCategory.hom (X.map (mkOfLe ⟨i, ⋯⟩ ⟨j, ⋯⟩ hij).op)) (lift sx s x) =\n (ConcreteCategory.hom (s.π... | let β₂ : α ⟶ α₂ := StructuredArrow.homMk ((Hom.tr (mkOfSucc 0)).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.Coskeletal | {
"line": 173,
"column": 63
} | {
"line": 173,
"column": 69
} | {
"line": 173,
"column": 69
} | [
{
"pp": "X : SSet\nsx : X.StrictSegal\nn : ℕ\ns : Cone (proj (op ⦋n⦌) (inclusion 2).op ⋙ (inclusion 2).op ⋙ X)\nx : s.pt\nφ : ⦋1⦌ ⟶ ⦋n⦌\n⊢ 0 ≤ 1",
"ppTerm": "?m.109",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"PartialOrder.toPreorder",
"Preorder.toLE",
"id",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicTopology.SimplicialSet.Coskeletal | {
"line": 173,
"column": 63
} | {
"line": 173,
"column": 69
} | {
"line": 173,
"column": 69
} | [
{
"pp": "X : SSet\nsx : X.StrictSegal\nn : ℕ\ns : Cone (proj (op ⦋n⦌) (inclusion 2).op ⋙ (inclusion 2).op ⋙ X)\nx : s.pt\nφ : ⦋1⦌ ⟶ ⦋n⦌\n⊢ 0 ≤ 1",
"ppTerm": "?m.109",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"PartialOrder.toPreorder",
"Preorder.toLE",
"id",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.Coskeletal | {
"line": 173,
"column": 63
} | {
"line": 173,
"column": 69
} | {
"line": 173,
"column": 69
} | [
{
"pp": "X : SSet\nsx : X.StrictSegal\nn : ℕ\ns : Cone (proj (op ⦋n⦌) (inclusion 2).op ⋙ (inclusion 2).op ⋙ X)\nx : s.pt\nφ : ⦋1⦌ ⟶ ⦋n⦌\n⊢ 0 ≤ 1",
"ppTerm": "?m.109",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"PartialOrder.toPreorder",
"Preorder.toLE",
"id",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal | {
"line": 183,
"column": 4
} | {
"line": 183,
"column": 47
} | {
"line": 184,
"column": 4
} | [
{
"pp": "X X' Y Y' Z : Truncated 2\nx₀ : X.obj (Opposite.op { obj := ⦋0⦌, property := OneTruncation₂._proof_1 })\ny₀ : Y.obj (Opposite.op { obj := ⦋0⦌, property := OneTruncation₂._proof_1 })\nx₁ : X.obj (Opposite.op { obj := ⦋0⦌, property := OneTruncation₂._proof_1 })\ny₁ : Y.obj (Opposite.op { obj := ⦋0⦌, prop... | [
"X X' Y Y' Z : Truncated 2\nx₀ : X.obj (Opposite.op { obj := ⦋0⦌, property := OneTruncation₂._proof_1 })\ny₀ : Y.obj (Opposite.op { obj := ⦋0⦌, property := OneTruncation₂._proof_1 })\nx₁ : X.obj (Opposite.op { obj := ⦋0⦌, property := OneTruncation₂._proof_1 })\ny₁ : Y.obj (Opposite.op { obj := ⦋0⦌, property := OneT... | obtain ⟨ex, ey, rfl⟩ := e.tensor_surjective | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.NormalForms | {
"line": 304,
"column": 4
} | {
"line": 304,
"column": 59
} | {
"line": 305,
"column": 4
} | [
{
"pp": "case comp_of.σ\nx y : SimplexCategoryGenRel\nf : x ⟶ y\nm : ℕ\nk : Fin (m + 1)\nL₁ : List ℕ\nm₁ b₁ : ℕ\nh₁' : mk m₁ = mk (m + 1)\ng : mk (m₁ + b₁) ⟶ mk (m + 1)\nhg : degeneracies.multiplicativeClosure g\nh' : L₁.length = b₁\nhL₁ : IsAdmissible m₁ L₁\ne₁ : g = standardσ L₁ ⋯\n⊢ ∃ L m_1 b,\n ∃ (h₁ : m... | [
"case comp_of.σ\nx y : SimplexCategoryGenRel\nf : x ⟶ y\nm : ℕ\nk : Fin (m + 1)\nL₁ : List ℕ\nb₁ : ℕ\nh' : L₁.length = b₁\nh₁' : mk (m + 1) = mk (m + 1)\ng : mk (m + 1 + b₁) ⟶ mk (m + 1)\nhg : degeneracies.multiplicativeClosure g\nhL₁ : IsAdmissible (m + 1) L₁\ne₁ : g = standardσ L₁ ⋯\n⊢ ∃ L m_1 b,\n ∃ (h₁ : mk ... | obtain rfl : m₁ = m + 1 := congrArg (fun x ↦ x.len) h₁' | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.AlgebraicTopology.SimplicialObject.II | {
"line": 125,
"column": 6
} | {
"line": 139,
"column": 46
} | {
"line": 140,
"column": 4
} | [
{
"pp": "case inl.inl\nn 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 : map' g x.castSucc = y.castSucc\n⊢ map' f (map' g x.castSucc) = map' (g.comp f) x.castSucc",
"ppTerm": "?inl.inl",
"assigned": true,
"usedConstants": [
"Eq.mp... | [] | rw [hy]
rw [map'_eq_castSucc_iff] at hy
obtain ⟨z, hz⟩ | hz := Fin.eq_castSucc_or_eq_last (map' f y.castSucc)
· rw [hz, Eq.comm]
rw [map'_eq_castSucc_iff] at hz ⊢
constructor
· refine hy.1.trans ?_
simp only [OrderHom.comp_coe, Function.comp_apply, Fin.castSucc_le_cas... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialObject.II | {
"line": 125,
"column": 6
} | {
"line": 139,
"column": 46
} | {
"line": 140,
"column": 4
} | [
{
"pp": "case inl.inl\nn 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 : map' g x.castSucc = y.castSucc\n⊢ map' f (map' g x.castSucc) = map' (g.comp f) x.castSucc",
"ppTerm": "?inl.inl",
"assigned": true,
"usedConstants": [
"Eq.mp... | [] | rw [hy]
rw [map'_eq_castSucc_iff] at hy
obtain ⟨z, hz⟩ | hz := Fin.eq_castSucc_or_eq_last (map' f y.castSucc)
· rw [hz, Eq.comm]
rw [map'_eq_castSucc_iff] at hz ⊢
constructor
· refine hy.1.trans ?_
simp only [OrderHom.comp_coe, Function.comp_apply, Fin.castSucc_le_cas... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialObject.II | {
"line": 211,
"column": 2
} | {
"line": 215,
"column": 11
} | {
"line": 217,
"column": 0
} | [
{
"pp": "n m : ℕ\nf : Fin (n + 1) →o Fin (m + 1)\nx y : Fin (m + 2)\nhxy : x ≤ y\n⊢ map' f x ≤ map' f y",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"SimplexCategory.II.finset",
"SimplexCategory.II.castSucc_mem_finset_iff._simp_1",
"Finset",
"Part... | [] | 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) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.IsUniquelyCodimOneFace | {
"line": 138,
"column": 2
} | {
"line": 138,
"column": 6
} | {
"line": 139,
"column": 2
} | [
{
"pp": "X Y : SSet\ne : X ≅ Y\ndx : ℕ\nx : X _⦋dx⦌\ny : X _⦋dx + 1⦌\nhxy : { dim := dx, simplex := x }.IsUniquelyCodimOneFace { dim := dx + 1, simplex := y }\n⊢ ⋯.index ⋯ = hxy.index ⋯",
"ppTerm": "?m.105",
"assigned": true,
"usedConstants": [
"SSet.S.simplex",
"Opposite",
"SSet.S... | [
"X Y : SSet\ne : X ≅ Y\ndx : ℕ\nx : X _⦋dx⦌\ny : X _⦋dx + 1⦌\nhxy : { dim := dx, simplex := x }.IsUniquelyCodimOneFace { dim := dx + 1, simplex := y }\n⊢ hxy.index ⋯ = ⋯.index ⋯"
] | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.AlgebraicTopology.SimplicialNerve | {
"line": 196,
"column": 4
} | {
"line": 196,
"column": 85
} | {
"line": 197,
"column": 4
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : SimplicialCategory C\ni : SimplexCategoryᵒᵖ\nx✝ : EnrichedFunctor SSet (SimplicialThickening (ULift.{v, 0} (Fin ((Opposite.unop i).len + 1)))) C\n⊢ (ConcreteCategory.hom\n (↾EnrichedFunctor.comp SSet\n (SimplicialThickening.functor (... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : SimplicialCategory C\ni : SimplexCategoryᵒᵖ\nx✝ : EnrichedFunctor SSet (SimplicialThickening (ULift.{v, 0} (Fin ((Opposite.unop i).len + 1)))) C\n⊢ EnrichedFunctor.comp SSet (SimplicialThickening.functor OrderHom.id) x✝ =\n (ConcreteCategory.hom\n (𝟙 (En... | change EnrichedFunctor.comp SSet (SimplicialThickening.functor OrderHom.id) _ = _ | Lean.Elab.Tactic.evalChange | Lean.Parser.Tactic.change |
Mathlib.AlgebraicTopology.SimplicialSet.Nonsingular | {
"line": 177,
"column": 2
} | {
"line": 177,
"column": 6
} | {
"line": 178,
"column": 2
} | [
{
"pp": "X : SSet\ninst✝ : X.Nonsingular\nx y z : X.N\nh : x ≤ y\nh' : y ≤ z\n⊢ monoOfLE h ≫ monoOfLE h' = monoOfLE ⋯",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"SSet.N.instPreorder",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"SSet.N.monoOfLE",
... | [
"X : SSet\ninst✝ : X.Nonsingular\nx y z : X.N\nh : x ≤ y\nh' : y ≤ z\n⊢ monoOfLE ⋯ = monoOfLE h ≫ monoOfLE h'"
] | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.PairingCore | {
"line": 93,
"column": 6
} | {
"line": 93,
"column": 49
} | {
"line": 94,
"column": 4
} | [
{
"pp": "case inl\nX : SSet\nA : X.Subcomplex\nP : A.Pairing\ninst✝ : P.IsProper\ns : ↑P.II\n⊢ (↑s).toS =\n { dim := (↑s).dim,\n simplex := (ConcreteCategory.hom (SimplicialObject.δ X (⋯.index ⋯))) ((↑(P.p s)).cast ⋯).simplex }",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"... | [] | simp [(P.isUniquelyCodimOneFace s).δ_index] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.PairingCore | {
"line": 209,
"column": 2
} | {
"line": 209,
"column": 6
} | {
"line": 210,
"column": 2
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nh : A.PairingCore\ninst✝ : h.IsProper\ns : h.ι\n⊢ ⋯.index ⋯ = h.index s",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.PairingCore.isUniquelyCodimOneFace",
"SSet.Subcomplex.PairingCore.type₂",
"SSet.S.IsUniquelyCodimO... | [
"X : SSet\nA : X.Subcomplex\nh : A.PairingCore\ninst✝ : h.IsProper\ns : h.ι\n⊢ h.index s = ⋯.index ⋯"
] | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.UnionProd | {
"line": 189,
"column": 4
} | {
"line": 189,
"column": 30
} | {
"line": 190,
"column": 4
} | [
{
"pp": "case refine_2\nm : ℕ\nk : Fin (m + 1)\nn : ℕ\nx : (Λ[m + 1, k.castSucc].unionProd ∂Δ[n]).N\nd : ℕ\nhd : x.dim = d\nl : Fin d\nhl : IsIndex x hd l.succ\ni : Fin (d + 1)\nhi : l.succ ≤ i\n⊢ k.succ ≤ (x.cast hd).simplex.1 i",
"ppTerm": "?refine_2",
"assigned": true,
"usedConstants": [
"S... | [
"case refine_2\nm : ℕ\nk : Fin (m + 1)\nn : ℕ\nx : (Λ[m + 1, k.castSucc].unionProd ∂Δ[n]).N\nd : ℕ\nhd : x.dim = d\nl : Fin d\nhl : IsIndex x hd l.succ\ni : Fin (d + 1)\nhi : l.succ ≤ i\n⊢ (x.cast hd).simplex.1 l.succ ≤ (x.cast hd).simplex.1 i"
] | rw [← hl.simplex_fst_succ] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.Inner.PushoutProduct | {
"line": 73,
"column": 2
} | {
"line": 91,
"column": 72
} | {
"line": 93,
"column": 0
} | [
{
"pp": "X₁ Y₁ E B : SSet\ni : X₁ ⟶ Y₁\np : E ⟶ B\ninst✝¹ : Mono i\ninst✝ : InnerFibration p\nsq₁₃ : MonoidalClosed.internalHom.PullbackObjObj i p\n⊢ InnerFibration sq₁₃.π",
"ppTerm": "?m.42",
"assigned": true,
"usedConstants": [
"CategoryTheory.HasLiftingProperty",
"SSet.Subcomplex.toSS... | [] | rw [innerFibration_iff]
intro _ _ _ ⟨k, h0, hn⟩
let sq₁₂ := Functor.PushoutObjObj.ofHasPushout (curriedTensor SSet) i Λ[_, k].ι
rw [← internalHomAdjunction₂.hasLiftingProperty_iff sq₁₂]
suffices innerAnodyneExtensions sq₁₂.ι from
this _ (by rwa [← innerFibration_iff])
intro E B p hp
rw [HasLiftingProper... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.Inner.PushoutProduct | {
"line": 73,
"column": 2
} | {
"line": 91,
"column": 72
} | {
"line": 93,
"column": 0
} | [
{
"pp": "X₁ Y₁ E B : SSet\ni : X₁ ⟶ Y₁\np : E ⟶ B\ninst✝¹ : Mono i\ninst✝ : InnerFibration p\nsq₁₃ : MonoidalClosed.internalHom.PullbackObjObj i p\n⊢ InnerFibration sq₁₃.π",
"ppTerm": "?m.42",
"assigned": true,
"usedConstants": [
"CategoryTheory.HasLiftingProperty",
"SSet.Subcomplex.toSS... | [] | rw [innerFibration_iff]
intro _ _ _ ⟨k, h0, hn⟩
let sq₁₂ := Functor.PushoutObjObj.ofHasPushout (curriedTensor SSet) i Λ[_, k].ι
rw [← internalHomAdjunction₂.hasLiftingProperty_iff sq₁₂]
suffices innerAnodyneExtensions sq₁₂.ι from
this _ (by rwa [← innerFibration_iff])
intro E B p hp
rw [HasLiftingProper... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.ProdStdSimplexOne | {
"line": 43,
"column": 10
} | {
"line": 43,
"column": 41
} | {
"line": 43,
"column": 41
} | [
{
"pp": "p : ℕ\ni : Fin (p + 1)\n⊢ (stdSimplex.objEquiv.symm (SimplexCategory.σ i), objMk₁ i.succ.castSucc) ∈ (Δ[p] ⊗ Δ[1]).nonDegenerate (p + 1)",
"ppTerm": "?m.45",
"assigned": true,
"usedConstants": [
"OrderHom.id",
"Eq.mpr",
"Opposite",
"Equiv.instEquivLike",
"Categ... | [
"p : ℕ\ni : Fin (p + 1)\n⊢ orderHomOfSimplex (stdSimplex.objEquiv.symm (SimplexCategory.σ i), objMk₁ i.succ.castSucc) ⋯ = OrderHom.id"
] | nonDegenerate_max_dim_iff _ rfl | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.AlgebraicTopology.SimplicialSet.ProdStdSimplexOne | {
"line": 58,
"column": 10
} | {
"line": 58,
"column": 41
} | {
"line": 58,
"column": 41
} | [
{
"pp": "case refine_2\np : ℕ\nx✝ : ↑((Δ[p] ⊗ Δ[1]).nonDegenerate (p + 1))\ns₁ : Δ[p] _⦋p + 1⦌\ns₂ : Δ[1] _⦋p + 1⦌\nhs : (s₁, s₂) ∈ (Δ[p] ⊗ Δ[1]).nonDegenerate (p + 1)\n⊢ ∃ a, (fun i ↦ ⟨(stdSimplex.objEquiv.symm (SimplexCategory.σ i), objMk₁ i.succ.castSucc), ⋯⟩) a = ⟨(s₁, s₂), hs⟩",
"ppTerm": "?refine_2",
... | [
"case refine_2\np : ℕ\nx✝ : ↑((Δ[p] ⊗ Δ[1]).nonDegenerate (p + 1))\ns₁ : Δ[p] _⦋p + 1⦌\ns₂ : Δ[1] _⦋p + 1⦌\nhs✝ : (s₁, s₂) ∈ (Δ[p] ⊗ Δ[1]).nonDegenerate (p + 1)\nhs : orderHomOfSimplex (s₁, s₂) ⋯ = OrderHom.id\n⊢ ∃ a, (fun i ↦ ⟨(stdSimplex.objEquiv.symm (SimplexCategory.σ i), objMk₁ i.succ.castSucc), ⋯⟩) a = ⟨(s₁, ... | nonDegenerate_max_dim_iff _ rfl | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.AlgebraicTopology.SimplicialSet.RelativeMorphism | {
"line": 75,
"column": 2
} | {
"line": 77,
"column": 7
} | {
"line": 79,
"column": 0
} | [
{
"pp": "X Y : SSet\nA : X.Subcomplex\nB : Y.Subcomplex\nφ : A.toSSet ⟶ B.toSSet\nf : RelativeMorphism A B φ\n⊢ A.image f.map ≤ B",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.toSSet",
"Opposite",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",... | [] | rintro n _ ⟨a, ha, rfl⟩
have := f.map_coe ⟨a, ha⟩
aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.RelativeMorphism | {
"line": 75,
"column": 2
} | {
"line": 77,
"column": 7
} | {
"line": 79,
"column": 0
} | [
{
"pp": "X Y : SSet\nA : X.Subcomplex\nB : Y.Subcomplex\nφ : A.toSSet ⟶ B.toSSet\nf : RelativeMorphism A B φ\n⊢ A.image f.map ≤ B",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.toSSet",
"Opposite",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",... | [] | rintro n _ ⟨a, ha, rfl⟩
have := f.map_coe ⟨a, ha⟩
aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.RelativeMorphism | {
"line": 146,
"column": 12
} | {
"line": 146,
"column": 37
} | {
"line": 148,
"column": 0
} | [
{
"pp": "X Y Z : SSet\nA : X.Subcomplex\nB : Y.Subcomplex\nφ : A.toSSet ⟶ B.toSSet\nf g : RelativeMorphism A B φ\nC : Z.Subcomplex\nψ : B.toSSet ⟶ C.toSSet\nh : f.Homotopy g\nf' : RelativeMorphism B C ψ\nφψ : A.toSSet ⟶ C.toSSet\nfac : φ ≫ ψ = φψ\n⊢ A.ι ▷ Δ[1] ≫ h.h ≫ f'.map = fst A.toSSet Δ[1] ≫ φψ ≫ C.ι",
... | [] | simp [h.rel_assoc, ← fac] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.AlgebraicTopology.SimplicialSet.RelativeMorphism | {
"line": 146,
"column": 12
} | {
"line": 146,
"column": 37
} | {
"line": 148,
"column": 0
} | [
{
"pp": "X Y Z : SSet\nA : X.Subcomplex\nB : Y.Subcomplex\nφ : A.toSSet ⟶ B.toSSet\nf g : RelativeMorphism A B φ\nC : Z.Subcomplex\nψ : B.toSSet ⟶ C.toSSet\nh : f.Homotopy g\nf' : RelativeMorphism B C ψ\nφψ : A.toSSet ⟶ C.toSSet\nfac : φ ≫ ψ = φψ\n⊢ A.ι ▷ Δ[1] ≫ h.h ≫ f'.map = fst A.toSSet Δ[1] ≫ φψ ≫ C.ι",
... | [] | simp [h.rel_assoc, ← fac] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.RelativeMorphism | {
"line": 146,
"column": 12
} | {
"line": 146,
"column": 37
} | {
"line": 148,
"column": 0
} | [
{
"pp": "X Y Z : SSet\nA : X.Subcomplex\nB : Y.Subcomplex\nφ : A.toSSet ⟶ B.toSSet\nf g : RelativeMorphism A B φ\nC : Z.Subcomplex\nψ : B.toSSet ⟶ C.toSSet\nh : f.Homotopy g\nf' : RelativeMorphism B C ψ\nφψ : A.toSSet ⟶ C.toSSet\nfac : φ ≫ ψ = φψ\n⊢ A.ι ▷ Δ[1] ≫ h.h ≫ f'.map = fst A.toSSet Δ[1] ≫ φψ ≫ C.ι",
... | [] | simp [h.rel_assoc, ← fac] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Calculus.IteratedDeriv.ConvergenceOnBall | {
"line": 41,
"column": 2
} | {
"line": 41,
"column": 6
} | {
"line": 42,
"column": 2
} | [
{
"pp": "𝕜 : Type u_1\ninst✝ : RCLike 𝕜\nf : 𝕜 → 𝕜\nx : 𝕜\nr : ENNReal\nhr_pos : 0 < r\nh : AnalyticOnNhd 𝕜 f (Metric.eball x r)\np : FormalMultilinearSeries 𝕜 𝕜 𝕜 := ⋯\nhr : r ≤ p.radius\ng : 𝕜 → 𝕜 := ⋯\nhg : HasFPowerSeriesOnBall g p x p.radius\nhg' :\n IsPreconnected (Metric.eball x r) →\n ∀ {... | [
"𝕜 : Type u_1\ninst✝ : RCLike 𝕜\nf : 𝕜 → 𝕜\nx : 𝕜\nr : ENNReal\nhr_pos : 0 < r\nh : AnalyticOnNhd 𝕜 f (Metric.eball x r)\np : FormalMultilinearSeries 𝕜 𝕜 𝕜 := ⋯\nhr : r ≤ p.radius\ng : 𝕜 → 𝕜 := ⋯\nhg : HasFPowerSeriesOnBall g p x p.radius\nhg' :\n IsPreconnected (Metric.eball x r) →\n ∀ {z₀ : 𝕜}, z₀... | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.Analysis.AbsoluteValue.Equivalence | {
"line": 325,
"column": 2
} | {
"line": 325,
"column": 45
} | {
"line": 327,
"column": 0
} | [
{
"pp": "F : Type u_1\ninst✝ : Field F\nv w : AbsoluteValue F ℝ\nh : v.IsEquiv w\na : F\nha₀ : a ≠ 0\nha₁ : v a ≠ 1\nb : F\nhb₀ : b ≠ 0\nhb₁ : v b ≠ 1\nh_ne : log (v b) / log (w b) ≠ log (v a) / log (w a)\nha : 1 < v a\nhb : 1 < v b\nh_lt : log (v b) / log (v a) < log (w b) / log (w a)\nhwa : 1 < w a\nhwb : 1 <... | [] | exact not_lt_of_gt (h.lt_one_iff.1 hq₁) hq₂ | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Analysis.AbsoluteValue.Equivalence | {
"line": 341,
"column": 57
} | {
"line": 341,
"column": 70
} | {
"line": 341,
"column": 71
} | [
{
"pp": "case pos.inr.inr\nF : Type u_1\ninst✝ : Field F\nv w : AbsoluteValue F ℝ\nh : v.IsEquiv w\nhw : w.IsNontrivial\na : F\nha₀ : a ≠ 0\nha₁ : w a ≠ 1\nb : F\nhb₀ : b ≠ 0\nhb₁ : w b ≠ 1\n⊢ rexp 1 ^ log (w b) = w b",
"ppTerm": "?pos.inr.inr✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
... | [
"case pos.inr.inr\nF : Type u_1\ninst✝ : Field F\nv w : AbsoluteValue F ℝ\nh : v.IsEquiv w\nhw : w.IsNontrivial\na : F\nha₀ : a ≠ 0\nha₁ : w a ≠ 1\nb : F\nhb₀ : b ≠ 0\nhb₁ : w b ≠ 1\n⊢ rexp (log (w b)) = w b"
] | exp_one_rpow, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.Analytic.Order | {
"line": 183,
"column": 6
} | {
"line": 183,
"column": 72
} | {
"line": 183,
"column": 72
} | [
{
"pp": "case neg\n𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf g : 𝕜 → E\nz₀ : 𝕜\nhfg : f =ᶠ[𝓝 z₀] g\nhf : ¬AnalyticAt 𝕜 f z₀\n⊢ 0 = analyticOrderAt g z₀",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
... | [
"case neg\n𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf g : 𝕜 → E\nz₀ : 𝕜\nhfg : f =ᶠ[𝓝 z₀] g\nhf : ¬AnalyticAt 𝕜 f z₀\n⊢ 0 = 0"
] | analyticOrderAt_of_not_analyticAt fun hg ↦ hf <| hg.congr hfg.symm | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.SpecialFunctions.OrdinaryHypergeometric | {
"line": 170,
"column": 6
} | {
"line": 170,
"column": 31
} | {
"line": 171,
"column": 2
} | [
{
"pp": "case refine_1.inl.inl.inr\n𝕂 : Type u_1\n𝔸 : Type u_2\ninst✝² : RCLike 𝕂\ninst✝¹ : NormedDivisionRing 𝔸\ninst✝ : NormedAlgebra 𝕂 𝔸\na b c : 𝕂\nn : ℕ\nh : Polynomial.eval a (ascPochhammer 𝕂 n) = 0\nkn : ℕ\nhkn : kn < n\nhn : ↑kn = -a\n⊢ ∃ k < n, ↑k = -a ∨ ↑k = -b ∨ ↑k = -c",
"ppTerm": "?refi... | [] | exact ⟨kn, hkn, by tauto⟩ | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Analysis.SpecialFunctions.OrdinaryHypergeometric | {
"line": 170,
"column": 6
} | {
"line": 170,
"column": 31
} | {
"line": 171,
"column": 2
} | [
{
"pp": "case refine_1.inl.inr\n𝕂 : Type u_1\n𝔸 : Type u_2\ninst✝² : RCLike 𝕂\ninst✝¹ : NormedDivisionRing 𝔸\ninst✝ : NormedAlgebra 𝕂 𝔸\na b c : 𝕂\nn : ℕ\nh : Polynomial.eval b (ascPochhammer 𝕂 n) = 0\nkn : ℕ\nhkn : kn < n\nhn : ↑kn = -b\n⊢ ∃ k < n, ↑k = -a ∨ ↑k = -b ∨ ↑k = -c",
"ppTerm": "?refine_1... | [] | exact ⟨kn, hkn, by tauto⟩ | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Analysis.SpecialFunctions.OrdinaryHypergeometric | {
"line": 170,
"column": 6
} | {
"line": 170,
"column": 31
} | {
"line": 171,
"column": 2
} | [
{
"pp": "case refine_1.inr\n𝕂 : Type u_1\n𝔸 : Type u_2\ninst✝² : RCLike 𝕂\ninst✝¹ : NormedDivisionRing 𝔸\ninst✝ : NormedAlgebra 𝕂 𝔸\na b c : 𝕂\nn : ℕ\nh : Polynomial.eval c (ascPochhammer 𝕂 n) = 0\nkn : ℕ\nhkn : kn < n\nhn : ↑kn = -c\n⊢ ∃ k < n, ↑k = -a ∨ ↑k = -b ∨ ↑k = -c",
"ppTerm": "?refine_1.inr... | [] | exact ⟨kn, hkn, by tauto⟩ | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Analysis.SpecialFunctions.Pow.Deriv | {
"line": 244,
"column": 36
} | {
"line": 244,
"column": 66
} | {
"line": 244,
"column": 66
} | [
{
"pp": "case pos\nf : ℂ → ℂ\ns : Set ℂ\nx : ℂ\nhf : DifferentiableWithinAt ℂ f s x\nc : ℂ\nh : AccPt x (𝓟 s)\nhc : c = 0\n⊢ derivWithin (fun x ↦ c ^ f x) s x = log c * derivWithin f s x * c ^ f x",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstants": [
"congrArg",
"Filter.NeBot",
... | [
"case pos\nf : ℂ → ℂ\ns : Set ℂ\nx : ℂ\nhf : DifferentiableWithinAt ℂ f s x\nc : ℂ\nh : (𝓝[s \\ {x}] x).NeBot\nhc : c = 0\n⊢ derivWithin (fun x ↦ c ^ f x) s x = log c * derivWithin f s x * c ^ f x"
] | accPt_principal_iff_nhdsWithin | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.Analytic.Binomial | {
"line": 124,
"column": 4
} | {
"line": 124,
"column": 8
} | {
"line": 125,
"column": 4
} | [
{
"pp": "a : ℂ\nn : ℕ\nB : Set ℂ := Metric.ball 0 1\nthis : iteratedDeriv n (fun x ↦ (1 + x) ^ a) 0 = (fun x ↦ (descPochhammer ℤ n).smeval a * (1 + x) ^ (a - ↑n)) 0\n⊢ (descPochhammer ℤ n).smeval a = iteratedDeriv n (fun x ↦ (1 + x) ^ a) 0",
"ppTerm": "?m.752",
"assigned": true,
"usedConstants": [
... | [
"a : ℂ\nn : ℕ\nB : Set ℂ := ⋯\nthis : iteratedDeriv n (fun x ↦ (1 + x) ^ a) 0 = (fun x ↦ (descPochhammer ℤ n).smeval a * (1 + x) ^ (a - ↑n)) 0\n⊢ iteratedDeriv n (fun x ↦ (1 + x) ^ a) 0 = (descPochhammer ℤ n).smeval a"
] | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.Analysis.Analytic.IteratedFDeriv | {
"line": 155,
"column": 6
} | {
"line": 155,
"column": 16
} | {
"line": 156,
"column": 6
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type u_3\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx : E\nr : ℝ≥0∞\nh : HasFPowerSeriesWithinOnBall f... | [
"𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type u_3\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx : E\nr : ℝ≥0∞\nh : HasFPowerSeriesWithinOnBall f p s x r\nh'... | intro m hm | Lean.Elab.Tactic.evalIntro | Lean.Parser.Tactic.intro |
Mathlib.Analysis.Analytic.Binomial | {
"line": 182,
"column": 2
} | {
"line": 193,
"column": 68
} | {
"line": 195,
"column": 0
} | [
{
"pp": "a : ℕ\nz : ℂ\nhz : z ≠ 0\n⊢ HasFPowerSeriesOnBall (fun x ↦ 1 / (z - x) ^ (a + 1))\n (FormalMultilinearSeries.ofScalars ℂ fun n ↦ (z ^ (n + a + 1))⁻¹ * ↑((a + n).choose a)) 0 ‖z‖ₑ",
"ppTerm": "?m.72",
"assigned": true,
"usedConstants": [
"HasFPowerSeriesOnBall.congr",
"enorm_s... | [] | have := one_div_one_sub_pow_hasFPowerSeriesOnBall_zero a
rw [← map_zero (z⁻¹ • 1 : ℂ →L[ℂ] ℂ)] at this
have := this.compContinuousLinearMap
have H : 1 / ‖(z⁻¹ • 1 : ℂ →L[ℂ] ℂ)‖ₑ = ‖z‖ₑ := by simp [enorm_smul, enorm_inv, hz]
simp only [one_div, FunLike.coe_smul, H, Function.comp_def] at this
convert (this.cons... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Analytic.Binomial | {
"line": 182,
"column": 2
} | {
"line": 193,
"column": 68
} | {
"line": 195,
"column": 0
} | [
{
"pp": "a : ℕ\nz : ℂ\nhz : z ≠ 0\n⊢ HasFPowerSeriesOnBall (fun x ↦ 1 / (z - x) ^ (a + 1))\n (FormalMultilinearSeries.ofScalars ℂ fun n ↦ (z ^ (n + a + 1))⁻¹ * ↑((a + n).choose a)) 0 ‖z‖ₑ",
"ppTerm": "?m.72",
"assigned": true,
"usedConstants": [
"HasFPowerSeriesOnBall.congr",
"enorm_s... | [] | have := one_div_one_sub_pow_hasFPowerSeriesOnBall_zero a
rw [← map_zero (z⁻¹ • 1 : ℂ →L[ℂ] ℂ)] at this
have := this.compContinuousLinearMap
have H : 1 / ‖(z⁻¹ • 1 : ℂ →L[ℂ] ℂ)‖ₑ = ‖z‖ₑ := by simp [enorm_smul, enorm_inv, hz]
simp only [one_div, FunLike.coe_smul, H, Function.comp_def] at this
convert (this.cons... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Analytic.Binomial | {
"line": 276,
"column": 4
} | {
"line": 276,
"column": 98
} | {
"line": 278,
"column": 0
} | [
{
"pp": "case convert_2\na : ℝ\nthis✝¹ :\n HasFPowerSeriesOnBall (fun x ↦ 1 / (1 - x) ^ ↑a)\n (FormalMultilinearSeries.restrictScalars ℝ\n (FormalMultilinearSeries.ofScalars ℂ fun n ↦ Ring.choose (↑a + ↑n - 1) n))\n (Complex.ofRealCLM 0) 1\nx : ℝ\nhx : x ∈ Metric.eball 0 (1 / ‖Complex.ofRealCLM‖ₑ)\n... | [] | simp [-Complex.inv_re, ← Complex.ofReal_one, ← Complex.ofReal_sub, ← Complex.ofReal_cpow this] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Analysis.Analytic.IteratedFDeriv | {
"line": 237,
"column": 81
} | {
"line": 241,
"column": 60
} | {
"line": 243,
"column": 0
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type u_3\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\ns : Set E\nx : E\nh : AnalyticOn 𝕜 f s\nhs : UniqueDiffOn 𝕜 s\nhx : x ∈ s\nn : ℕ\nv : Fin n → E... | [] | by
rcases h x hx with ⟨p, r, hp⟩
rw [hp.iteratedFDerivWithin_eq_sum h hs hx, hp.iteratedFDerivWithin_eq_sum h hs hx]
conv_rhs => rw [← Equiv.sum_comp (Equiv.mulLeft σ)]
simp only [coe_mulLeft, Perm.coe_mul, Function.comp_apply] | [anonymous] | Lean.Parser.Term.byTactic |
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