module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Algebra.GroupWithZero.Range | {
"line": 141,
"column": 17
} | {
"line": 141,
"column": 22
} | {
"line": 142,
"column": 2
} | [
{
"pp": "A : Type u_1\nB : Type u_2\ninst✝¹ : MonoidWithZero A\ninst✝ : GroupWithZero B\nf : A →*₀ B\n⊢ ∀ (x y : A),\n (if h : f (x * y) = 0 then 0 else ↑⟨Units.mk0 (f (x * y)) h, ⋯⟩) =\n (if h : f x = 0 then 0 else ↑⟨Units.mk0 (f x) h, ⋯⟩) * if h : f y = 0 then 0 else ↑⟨Units.mk0 (f y) h, ⋯⟩",
"ppT... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.GroupWithZero.Range | {
"line": 169,
"column": 2
} | {
"line": 169,
"column": 7
} | {
"line": 171,
"column": 0
} | [
{
"pp": "A : Type u_1\nB : Type u_2\ninst✝¹ : MonoidWithZero A\ninst✝ : GroupWithZero B\nf : A →*₀ B\na : A\n⊢ WithZero.recZeroCoe 0 Units.val\n ((WithZero.map' f.valueGroup.subtype) (if h : f a = 0 then 0 else ↑⟨Units.mk0 (f a) h, ⋯⟩)) =\n f a",
"ppTerm": "?m.17",
"assigned": true,
"usedCon... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Algebra.GroupWithZero.Range | {
"line": 263,
"column": 45
} | {
"line": 263,
"column": 50
} | {
"line": 263,
"column": 50
} | [
{
"pp": "A : Type u_1\nB : Type u_2\ninst✝¹ : MonoidWithZero A\ninst✝ : CommGroupWithZero B\nf : A →*₀ B\ny : Bˣ\nx✝ : ∃ a, f a ≠ 0 ∧ ∃ x, f a * ↑y = f x\na : A\nha : f a ≠ 0\nx : A\nhax : f a * ↑y = f x\n⊢ f x ≠ 0",
"ppTerm": "?m.59",
"assigned": true,
"usedConstants": [
"Units.val",
"G... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Algebra.GroupWithZero.Range | {
"line": 263,
"column": 45
} | {
"line": 263,
"column": 50
} | {
"line": 263,
"column": 50
} | [
{
"pp": "A : Type u_1\nB : Type u_2\ninst✝¹ : MonoidWithZero A\ninst✝ : CommGroupWithZero B\nf : A →*₀ B\ny : Bˣ\nx✝ : ∃ a, f a ≠ 0 ∧ ∃ x, f a * ↑y = f x\na : A\nha : f a ≠ 0\nx : A\nhax : f a * ↑y = f x\n⊢ f x ≠ 0",
"ppTerm": "?m.59",
"assigned": true,
"usedConstants": [
"Units.val",
"G... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.GroupWithZero.Range | {
"line": 263,
"column": 45
} | {
"line": 263,
"column": 50
} | {
"line": 263,
"column": 50
} | [
{
"pp": "A : Type u_1\nB : Type u_2\ninst✝¹ : MonoidWithZero A\ninst✝ : CommGroupWithZero B\nf : A →*₀ B\ny : Bˣ\nx✝ : ∃ a, f a ≠ 0 ∧ ∃ x, f a * ↑y = f x\na : A\nha : f a ≠ 0\nx : A\nhax : f a * ↑y = f x\n⊢ f x ≠ 0",
"ppTerm": "?m.59",
"assigned": true,
"usedConstants": [
"Units.val",
"G... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.FintypeCat | {
"line": 275,
"column": 2
} | {
"line": 275,
"column": 7
} | {
"line": 277,
"column": 0
} | [
{
"pp": "X Y : FintypeCat\nf : X ⟶ Y\nx : (uSwitch.obj X).obj\n⊢ (ConcreteCategory.hom f) ((Fintype.equivFin X.obj).symm x.down) =\n (Fintype.equivFin Y.obj).symm\n ((ULift.up ∘\n ⇑(Fintype.equivFin Y.obj) ∘ ⇑(ConcreteCategory.hom f.hom) ∘ ⇑(Fintype.equivFin X.obj).symm ∘ ULift.down)\n ... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 35,
"column": 20
} | {
"line": 35,
"column": 25
} | {
"line": 35,
"column": 25
} | [
{
"pp": "a b : SimplexCategory\nx✝² x✝¹ : a ⟶ b\nx✝ : (fun f ↦ (Hom.toOrderHom f).toFun) x✝² = (fun f ↦ (Hom.toOrderHom f).toFun) x✝¹\n⊢ x✝² = x✝¹",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"PartialOrder.toPreor... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 35,
"column": 20
} | {
"line": 35,
"column": 25
} | {
"line": 35,
"column": 25
} | [
{
"pp": "a b : SimplexCategory\nx✝² x✝¹ : a ⟶ b\nx✝ : (fun f ↦ (Hom.toOrderHom f).toFun) x✝² = (fun f ↦ (Hom.toOrderHom f).toFun) x✝¹\n⊢ x✝² = x✝¹",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"PartialOrder.toPreor... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 35,
"column": 20
} | {
"line": 35,
"column": 25
} | {
"line": 35,
"column": 25
} | [
{
"pp": "a b : SimplexCategory\nx✝² x✝¹ : a ⟶ b\nx✝ : (fun f ↦ (Hom.toOrderHom f).toFun) x✝² = (fun f ↦ (Hom.toOrderHom f).toFun) x✝¹\n⊢ x✝² = x✝¹",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"PartialOrder.toPreor... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 50,
"column": 48
} | {
"line": 50,
"column": 53
} | {
"line": 52,
"column": 0
} | [
{
"pp": "⊢ ⦋0⦌.const ⦋0⦌ 0 = 𝟙 ⦋0⦌",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"OrderHom.id",
"instNeZeroNatHAdd_1",
"OrderHom.id_coe",
"congrArg",
"PartialOrder.toPreorder",
"CategoryTheory.CategoryStruct.id",
"id",
"Fin.instOfNat",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 50,
"column": 48
} | {
"line": 50,
"column": 53
} | {
"line": 52,
"column": 0
} | [
{
"pp": "⊢ ⦋0⦌.const ⦋0⦌ 0 = 𝟙 ⦋0⦌",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"OrderHom.id",
"instNeZeroNatHAdd_1",
"OrderHom.id_coe",
"congrArg",
"PartialOrder.toPreorder",
"CategoryTheory.CategoryStruct.id",
"id",
"Fin.instOfNat",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 50,
"column": 48
} | {
"line": 50,
"column": 53
} | {
"line": 52,
"column": 0
} | [
{
"pp": "⊢ ⦋0⦌.const ⦋0⦌ 0 = 𝟙 ⦋0⦌",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"OrderHom.id",
"instNeZeroNatHAdd_1",
"OrderHom.id_coe",
"congrArg",
"PartialOrder.toPreorder",
"CategoryTheory.CategoryStruct.id",
"id",
"Fin.instOfNat",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 98,
"column": 11
} | {
"line": 98,
"column": 33
} | {
"line": 99,
"column": 2
} | [
{
"pp": "f : ⦋1⦌ ⟶ ⦋1⦌\ne0 : (Hom.toOrderHom f) 0 = 0\ne1 : (Hom.toOrderHom f) 1 = 0\ni : Fin (⦋1⦌.len + 1)\n⊢ (Hom.toOrderHom f) 1 = (Hom.toOrderHom (⦋1⦌.const ⦋1⦌ ((Hom.toOrderHom f) 0))) 1",
"ppTerm": "?m.639",
"assigned": true,
"usedConstants": [
"instNeZeroNatHAdd_1",
"PartialOrder.... | [] | exact e1.trans e0.symm | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 98,
"column": 11
} | {
"line": 98,
"column": 33
} | {
"line": 99,
"column": 2
} | [
{
"pp": "f : ⦋1⦌ ⟶ ⦋1⦌\ne0 : (Hom.toOrderHom f) 0 = 0\ne1 : (Hom.toOrderHom f) 1 = 0\ni : Fin (⦋1⦌.len + 1)\n⊢ (Hom.toOrderHom f) 1 = (Hom.toOrderHom (⦋1⦌.const ⦋1⦌ ((Hom.toOrderHom f) 0))) 1",
"ppTerm": "?m.639",
"assigned": true,
"usedConstants": [
"instNeZeroNatHAdd_1",
"PartialOrder.... | [] | exact e1.trans e0.symm | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 98,
"column": 11
} | {
"line": 98,
"column": 33
} | {
"line": 99,
"column": 2
} | [
{
"pp": "f : ⦋1⦌ ⟶ ⦋1⦌\ne0 : (Hom.toOrderHom f) 0 = 0\ne1 : (Hom.toOrderHom f) 1 = 0\ni : Fin (⦋1⦌.len + 1)\n⊢ (Hom.toOrderHom f) 1 = (Hom.toOrderHom (⦋1⦌.const ⦋1⦌ ((Hom.toOrderHom f) 0))) 1",
"ppTerm": "?m.639",
"assigned": true,
"usedConstants": [
"instNeZeroNatHAdd_1",
"PartialOrder.... | [] | exact e1.trans e0.symm | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 98,
"column": 11
} | {
"line": 98,
"column": 33
} | {
"line": 99,
"column": 2
} | [
{
"pp": "f : ⦋1⦌ ⟶ ⦋1⦌\ne0 : (Hom.toOrderHom f) 0 = 1\ne1 : (Hom.toOrderHom f) 1 = 1\ni : Fin (⦋1⦌.len + 1)\n⊢ (Hom.toOrderHom f) 1 = (Hom.toOrderHom (⦋1⦌.const ⦋1⦌ ((Hom.toOrderHom f) 0))) 1",
"ppTerm": "?m.863",
"assigned": true,
"usedConstants": [
"instNeZeroNatHAdd_1",
"PartialOrder.... | [] | exact e1.trans e0.symm | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 98,
"column": 11
} | {
"line": 98,
"column": 33
} | {
"line": 99,
"column": 2
} | [
{
"pp": "f : ⦋1⦌ ⟶ ⦋1⦌\ne0 : (Hom.toOrderHom f) 0 = 1\ne1 : (Hom.toOrderHom f) 1 = 1\ni : Fin (⦋1⦌.len + 1)\n⊢ (Hom.toOrderHom f) 1 = (Hom.toOrderHom (⦋1⦌.const ⦋1⦌ ((Hom.toOrderHom f) 0))) 1",
"ppTerm": "?m.863",
"assigned": true,
"usedConstants": [
"instNeZeroNatHAdd_1",
"PartialOrder.... | [] | exact e1.trans e0.symm | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 98,
"column": 11
} | {
"line": 98,
"column": 33
} | {
"line": 99,
"column": 2
} | [
{
"pp": "f : ⦋1⦌ ⟶ ⦋1⦌\ne0 : (Hom.toOrderHom f) 0 = 1\ne1 : (Hom.toOrderHom f) 1 = 1\ni : Fin (⦋1⦌.len + 1)\n⊢ (Hom.toOrderHom f) 1 = (Hom.toOrderHom (⦋1⦌.const ⦋1⦌ ((Hom.toOrderHom f) 0))) 1",
"ppTerm": "?m.863",
"assigned": true,
"usedConstants": [
"instNeZeroNatHAdd_1",
"PartialOrder.... | [] | exact e1.trans e0.symm | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 243,
"column": 2
} | {
"line": 243,
"column": 22
} | {
"line": 244,
"column": 2
} | [
{
"pp": "n : ℕ\nk : Fin (⦋n⦌.len + 1)\ni : ℕ\nisLt✝¹ : i < n + 2\nj : ℕ\nisLt✝ : j < n + 2\nH : ⟨i, isLt✝¹⟩ ≤ ⟨j, isLt✝⟩\n⊢ ↑(if (if k.castSucc < ⟨i, isLt✝¹⟩ then k.castSucc else k.succ).castSucc < ⟨j, isLt✝⟩.succ then\n (if k.castSucc < ⟨i, isLt✝¹⟩ then k.castSucc else k.succ).castSucc\n else (if k... | [
"n i : ℕ\nisLt✝² : i < n + 2\nj : ℕ\nisLt✝¹ : j < n + 2\nH : ⟨i, isLt✝²⟩ ≤ ⟨j, isLt✝¹⟩\nk : ℕ\nisLt✝ : k < ⦋n⦌.len + 1\n⊢ ↑(if\n (if ⟨k, isLt✝⟩.castSucc < ⟨i, isLt✝²⟩ then ⟨k, isLt✝⟩.castSucc else ⟨k, isLt✝⟩.succ).castSucc <\n ⟨j, isLt✝¹⟩.succ then\n (if ⟨k, isLt✝⟩.castSucc < ⟨i, isLt✝²⟩ ... | rcases k with ⟨k, _⟩ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRCases | Lean.Parser.Tactic.rcases |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 278,
"column": 2
} | {
"line": 293,
"column": 31
} | {
"line": 295,
"column": 0
} | [
{
"pp": "n : ℕ\ni : Fin (n + 2)\nj : Fin (n + 1)\nH : i ≤ j.castSucc\n⊢ δ i.castSucc ≫ σ j.succ = σ j ≫ δ i",
"ppTerm": "?m.34",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Fin.succAbove_of_le_castSucc",
"Fin.succAbove",
"Eq.mpr",
"Fin.ext_iff",
"Preorder.toL... | [] | ext k : 3
dsimp [σ, δ]
rcases le_or_gt i k with (hik | hik)
· rw [Fin.succAbove_of_le_castSucc _ _ (Fin.castSucc_le_castSucc_iff.mpr hik),
Fin.succ_predAbove_succ, Fin.succAbove_of_le_castSucc]
rcases le_or_gt k (j.castSucc) with (hjk | hjk)
· rwa [Fin.predAbove_of_le_castSucc _ _ hjk, Fin.castSucc_ca... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 278,
"column": 2
} | {
"line": 293,
"column": 31
} | {
"line": 295,
"column": 0
} | [
{
"pp": "n : ℕ\ni : Fin (n + 2)\nj : Fin (n + 1)\nH : i ≤ j.castSucc\n⊢ δ i.castSucc ≫ σ j.succ = σ j ≫ δ i",
"ppTerm": "?m.34",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Fin.succAbove_of_le_castSucc",
"Fin.succAbove",
"Eq.mpr",
"Fin.ext_iff",
"Preorder.toL... | [] | ext k : 3
dsimp [σ, δ]
rcases le_or_gt i k with (hik | hik)
· rw [Fin.succAbove_of_le_castSucc _ _ (Fin.castSucc_le_castSucc_iff.mpr hik),
Fin.succ_predAbove_succ, Fin.succAbove_of_le_castSucc]
rcases le_or_gt k (j.castSucc) with (hjk | hjk)
· rwa [Fin.predAbove_of_le_castSucc _ _ hjk, Fin.castSucc_ca... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 386,
"column": 10
} | {
"line": 386,
"column": 31
} | {
"line": 386,
"column": 31
} | [
{
"pp": "case inl\nn : ℕ\ni j : Fin (n + 1)\nH : i ≤ j\nk : Fin (n + 1)\nh : i ≤ k\nhkj : k ≤ j\n⊢ i ≤ k.castSucc.castPred ⋯",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Eq.mpr",
"Fin.ext_iff",
"Fin.castPred_castSucc",
"congrArg",
"Fin.ne_o... | [
"case inl\nn : ℕ\ni j : Fin (n + 1)\nH : i ≤ j\nk : Fin (n + 1)\nh : i ≤ k\nhkj : k ≤ j\n⊢ i ≤ k"
] | Fin.castPred_castSucc | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 391,
"column": 8
} | {
"line": 393,
"column": 32
} | {
"line": 394,
"column": 8
} | [
{
"pp": "case cast.succ.inr\nn : ℕ\ni j : Fin (n + 1)\nH : i ≤ j\nk : Fin (n + 1)\nh : k < i\n⊢ j.predAbove (i.castSucc.predAbove k.succ.castSucc) = i.predAbove (j.succ.predAbove k.succ.castSucc)",
"ppTerm": "?cast.succ.inr",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Eq.mpr",
... | [
"case cast.succ.inr\nn : ℕ\ni j : Fin (n + 1)\nH : i ≤ j\nk : Fin (n + 1)\nh : k < i\n⊢ j.predAbove k.succ = i.predAbove (j.predAbove k.castSucc).succ"
] | simp_rw [Fin.predAbove_of_le_castSucc i.castSucc _ (Fin.castSucc_le_castSucc_iff.mpr
(Fin.succ_le_castSucc_iff.mpr h)), Fin.castPred_castSucc, ← Fin.succ_castSucc,
Fin.succ_predAbove_succ] | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | Mathlib.Tactic.tacticSimp_rw___ |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 507,
"column": 11
} | {
"line": 507,
"column": 33
} | {
"line": 508,
"column": 2
} | [
{
"pp": "f : ⦋1⦌ ⟶ ⦋2⦌\nthis : (Hom.toOrderHom f) 0 ≤ (Hom.toOrderHom f) 1\ne0 : (Hom.toOrderHom f) 0 = 0\ne1 : (Hom.toOrderHom f) 1 = 0\ni : Fin (⦋1⦌.len + 1)\n⊢ (Hom.toOrderHom f) 1 = (Hom.toOrderHom (⦋1⦌.const ⦋2⦌ ((Hom.toOrderHom f) 0))) 1",
"ppTerm": "?m.1786",
"assigned": true,
"usedConstants"... | [] | exact e1.trans e0.symm | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 507,
"column": 11
} | {
"line": 507,
"column": 33
} | {
"line": 508,
"column": 2
} | [
{
"pp": "f : ⦋1⦌ ⟶ ⦋2⦌\nthis : (Hom.toOrderHom f) 0 ≤ (Hom.toOrderHom f) 1\ne0 : (Hom.toOrderHom f) 0 = 0\ne1 : (Hom.toOrderHom f) 1 = 0\ni : Fin (⦋1⦌.len + 1)\n⊢ (Hom.toOrderHom f) 1 = (Hom.toOrderHom (⦋1⦌.const ⦋2⦌ ((Hom.toOrderHom f) 0))) 1",
"ppTerm": "?m.1786",
"assigned": true,
"usedConstants"... | [] | exact e1.trans e0.symm | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 507,
"column": 11
} | {
"line": 507,
"column": 33
} | {
"line": 508,
"column": 2
} | [
{
"pp": "f : ⦋1⦌ ⟶ ⦋2⦌\nthis : (Hom.toOrderHom f) 0 ≤ (Hom.toOrderHom f) 1\ne0 : (Hom.toOrderHom f) 0 = 0\ne1 : (Hom.toOrderHom f) 1 = 0\ni : Fin (⦋1⦌.len + 1)\n⊢ (Hom.toOrderHom f) 1 = (Hom.toOrderHom (⦋1⦌.const ⦋2⦌ ((Hom.toOrderHom f) 0))) 1",
"ppTerm": "?m.1786",
"assigned": true,
"usedConstants"... | [] | exact e1.trans e0.symm | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 507,
"column": 11
} | {
"line": 507,
"column": 33
} | {
"line": 508,
"column": 2
} | [
{
"pp": "f : ⦋1⦌ ⟶ ⦋2⦌\nthis : (Hom.toOrderHom f) 0 ≤ (Hom.toOrderHom f) 1\ne0 : (Hom.toOrderHom f) 0 = 1\ne1 : (Hom.toOrderHom f) 1 = 1\ni : Fin (⦋1⦌.len + 1)\n⊢ (Hom.toOrderHom f) 1 = (Hom.toOrderHom (⦋1⦌.const ⦋2⦌ ((Hom.toOrderHom f) 0))) 1",
"ppTerm": "?m.2010",
"assigned": true,
"usedConstants"... | [] | exact e1.trans e0.symm | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 507,
"column": 11
} | {
"line": 507,
"column": 33
} | {
"line": 508,
"column": 2
} | [
{
"pp": "f : ⦋1⦌ ⟶ ⦋2⦌\nthis : (Hom.toOrderHom f) 0 ≤ (Hom.toOrderHom f) 1\ne0 : (Hom.toOrderHom f) 0 = 1\ne1 : (Hom.toOrderHom f) 1 = 1\ni : Fin (⦋1⦌.len + 1)\n⊢ (Hom.toOrderHom f) 1 = (Hom.toOrderHom (⦋1⦌.const ⦋2⦌ ((Hom.toOrderHom f) 0))) 1",
"ppTerm": "?m.2010",
"assigned": true,
"usedConstants"... | [] | exact e1.trans e0.symm | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 507,
"column": 11
} | {
"line": 507,
"column": 33
} | {
"line": 508,
"column": 2
} | [
{
"pp": "f : ⦋1⦌ ⟶ ⦋2⦌\nthis : (Hom.toOrderHom f) 0 ≤ (Hom.toOrderHom f) 1\ne0 : (Hom.toOrderHom f) 0 = 1\ne1 : (Hom.toOrderHom f) 1 = 1\ni : Fin (⦋1⦌.len + 1)\n⊢ (Hom.toOrderHom f) 1 = (Hom.toOrderHom (⦋1⦌.const ⦋2⦌ ((Hom.toOrderHom f) 0))) 1",
"ppTerm": "?m.2010",
"assigned": true,
"usedConstants"... | [] | exact e1.trans e0.symm | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 507,
"column": 11
} | {
"line": 507,
"column": 33
} | {
"line": 508,
"column": 2
} | [
{
"pp": "f : ⦋1⦌ ⟶ ⦋2⦌\nthis : (Hom.toOrderHom f) 0 ≤ (Hom.toOrderHom f) 1\ne0 : (Hom.toOrderHom f) 0 = 2\ne1 : (Hom.toOrderHom f) 1 = 2\ni : Fin (⦋1⦌.len + 1)\n⊢ (Hom.toOrderHom f) 1 = (Hom.toOrderHom (⦋1⦌.const ⦋2⦌ ((Hom.toOrderHom f) 0))) 1",
"ppTerm": "?m.2234",
"assigned": true,
"usedConstants"... | [] | exact e1.trans e0.symm | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 507,
"column": 11
} | {
"line": 507,
"column": 33
} | {
"line": 508,
"column": 2
} | [
{
"pp": "f : ⦋1⦌ ⟶ ⦋2⦌\nthis : (Hom.toOrderHom f) 0 ≤ (Hom.toOrderHom f) 1\ne0 : (Hom.toOrderHom f) 0 = 2\ne1 : (Hom.toOrderHom f) 1 = 2\ni : Fin (⦋1⦌.len + 1)\n⊢ (Hom.toOrderHom f) 1 = (Hom.toOrderHom (⦋1⦌.const ⦋2⦌ ((Hom.toOrderHom f) 0))) 1",
"ppTerm": "?m.2234",
"assigned": true,
"usedConstants"... | [] | exact e1.trans e0.symm | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 507,
"column": 11
} | {
"line": 507,
"column": 33
} | {
"line": 508,
"column": 2
} | [
{
"pp": "f : ⦋1⦌ ⟶ ⦋2⦌\nthis : (Hom.toOrderHom f) 0 ≤ (Hom.toOrderHom f) 1\ne0 : (Hom.toOrderHom f) 0 = 2\ne1 : (Hom.toOrderHom f) 1 = 2\ni : Fin (⦋1⦌.len + 1)\n⊢ (Hom.toOrderHom f) 1 = (Hom.toOrderHom (⦋1⦌.const ⦋2⦌ ((Hom.toOrderHom f) 0))) 1",
"ppTerm": "?m.2234",
"assigned": true,
"usedConstants"... | [] | exact e1.trans e0.symm | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 691,
"column": 27
} | {
"line": 691,
"column": 32
} | {
"line": 692,
"column": 2
} | [
{
"pp": "n m : SimplexCategory\nf : n ⟶ m\nhf : Mono f\nh : n.len = m.len\n⊢ n = m",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"congrArg",
"SimplexCategory.ext",
"Nat",
"True",
"eq_self",
"of_eq_true",
"congrFun'",
"Eq",
"Eq.trans",... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 691,
"column": 27
} | {
"line": 691,
"column": 32
} | {
"line": 692,
"column": 2
} | [
{
"pp": "n m : SimplexCategory\nf : n ⟶ m\nhf : Mono f\nh : n.len = m.len\n⊢ n = m",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"congrArg",
"SimplexCategory.ext",
"Nat",
"True",
"eq_self",
"of_eq_true",
"congrFun'",
"Eq",
"Eq.trans",... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 691,
"column": 27
} | {
"line": 691,
"column": 32
} | {
"line": 692,
"column": 2
} | [
{
"pp": "n m : SimplexCategory\nf : n ⟶ m\nhf : Mono f\nh : n.len = m.len\n⊢ n = m",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"congrArg",
"SimplexCategory.ext",
"Nat",
"True",
"eq_self",
"of_eq_true",
"congrFun'",
"Eq",
"Eq.trans",... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 702,
"column": 27
} | {
"line": 702,
"column": 32
} | {
"line": 703,
"column": 2
} | [
{
"pp": "n m : SimplexCategory\nf : n ⟶ m\nhf : Epi f\nh : n.len = m.len\n⊢ n = m",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"congrArg",
"SimplexCategory.ext",
"Nat",
"True",
"eq_self",
"of_eq_true",
"congrFun'",
"Eq",
"Eq.trans",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 702,
"column": 27
} | {
"line": 702,
"column": 32
} | {
"line": 703,
"column": 2
} | [
{
"pp": "n m : SimplexCategory\nf : n ⟶ m\nhf : Epi f\nh : n.len = m.len\n⊢ n = m",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"congrArg",
"SimplexCategory.ext",
"Nat",
"True",
"eq_self",
"of_eq_true",
"congrFun'",
"Eq",
"Eq.trans",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 702,
"column": 27
} | {
"line": 702,
"column": 32
} | {
"line": 703,
"column": 2
} | [
{
"pp": "n m : SimplexCategory\nf : n ⟶ m\nhf : Epi f\nh : n.len = m.len\n⊢ n = m",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"congrArg",
"SimplexCategory.ext",
"Nat",
"True",
"eq_self",
"of_eq_true",
"congrFun'",
"Eq",
"Eq.trans",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialObject.DeltaZeroIter | {
"line": 126,
"column": 2
} | {
"line": 127,
"column": 65
} | {
"line": 129,
"column": 0
} | [
{
"pp": "C : Type u_1\ninst✝ : Category.{v_1, u_1} C\nX : SimplicialObject C\ni n m : ℕ\nj : Fin (m + 1)\nhi : n + i = m\nhj : ↑j ≤ i\n⊢ X.σ₀Iter i hi ≫ X.σ j = X.σ₀Iter (i + 1) ⋯",
"ppTerm": "?m.42",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"CategoryTheory.op_comp",
"Opposit... | [] | dsimp [σ, σ₀Iter]
rw [← Functor.map_comp, ← op_comp, SimplexCategory.σ_σ₀Iter ..] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialObject.DeltaZeroIter | {
"line": 126,
"column": 2
} | {
"line": 127,
"column": 65
} | {
"line": 129,
"column": 0
} | [
{
"pp": "C : Type u_1\ninst✝ : Category.{v_1, u_1} C\nX : SimplicialObject C\ni n m : ℕ\nj : Fin (m + 1)\nhi : n + i = m\nhj : ↑j ≤ i\n⊢ X.σ₀Iter i hi ≫ X.σ j = X.σ₀Iter (i + 1) ⋯",
"ppTerm": "?m.42",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"CategoryTheory.op_comp",
"Opposit... | [] | dsimp [σ, σ₀Iter]
rw [← Functor.map_comp, ← op_comp, SimplexCategory.σ_σ₀Iter ..] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 758,
"column": 6
} | {
"line": 758,
"column": 46
} | {
"line": 759,
"column": 6
} | [
{
"pp": "case pos.e_6\nn : ℕ\nΔ' : SimplexCategory\nθ : ⦋n + 1⦌ ⟶ Δ'\ni : Fin (n + 1)\nhi : (Hom.toOrderHom θ) i.castSucc = (Hom.toOrderHom θ) i.succ\nx : Fin (⦋n + 1⦌.len + 1)\nh'✝ : i.castSucc < x\ny : Fin ⦋n + 1⦌.len := x.pred ⋯\nh' : i.castSucc < y.succ\nhy : x = y.succ\nh'' : y = i\n⊢ i.castSucc = i.succ.s... | [
"case pos.e_6.h\nn : ℕ\nΔ' : SimplexCategory\nθ : ⦋n + 1⦌ ⟶ Δ'\ni : Fin (n + 1)\nhi : (Hom.toOrderHom θ) i.castSucc = (Hom.toOrderHom θ) i.succ\nx : Fin (⦋n + 1⦌.len + 1)\nh'✝ : i.castSucc < x\ny : Fin ⦋n + 1⦌.len := x.pred ⋯\nh' : i.castSucc < y.succ\nhy : x = y.succ\nh'' : y = i\n⊢ i.castSucc < i.succ"
] | rw [Fin.succAbove_of_castSucc_lt i.succ] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.AlgebraicTopology.SimplexCategory.Rev | {
"line": 75,
"column": 2
} | {
"line": 75,
"column": 7
} | {
"line": 77,
"column": 0
} | [
{
"pp": "n m : SimplexCategory\nf : n ⟶ m\n⊢ rev.map (rev.map f) = f",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"congrArg",
"PartialOrder.toPreorder",
"SimplexCategory.Hom.ext",
"instOfNatNat",
"Fin.ext",
"Fin.val",
"CategoryTheory.Functor.map... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplexCategory.Rev | {
"line": 75,
"column": 2
} | {
"line": 75,
"column": 7
} | {
"line": 77,
"column": 0
} | [
{
"pp": "n m : SimplexCategory\nf : n ⟶ m\n⊢ rev.map (rev.map f) = f",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"congrArg",
"PartialOrder.toPreorder",
"SimplexCategory.Hom.ext",
"instOfNatNat",
"Fin.ext",
"Fin.val",
"CategoryTheory.Functor.map... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplexCategory.Rev | {
"line": 75,
"column": 2
} | {
"line": 75,
"column": 7
} | {
"line": 77,
"column": 0
} | [
{
"pp": "n m : SimplexCategory\nf : n ⟶ m\n⊢ rev.map (rev.map f) = f",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"congrArg",
"PartialOrder.toPreorder",
"SimplexCategory.Hom.ext",
"instOfNatNat",
"Fin.ext",
"Fin.val",
"CategoryTheory.Functor.map... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 824,
"column": 4
} | {
"line": 824,
"column": 29
} | {
"line": 825,
"column": 4
} | [
{
"pp": "n : ℕ\nθ : ⦋n⦌ ⟶ ⦋n + 1⦌\ninst✝ : Mono θ\n⊢ ¬Function.Surjective ⇑(Hom.toOrderHom θ)",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"CategoryTheory.Epi",
"congrArg",
"PartialOrder.toPreorder",
"id",
"instOfNatNat",
"instHAdd",
... | [
"n : ℕ\nθ : ⦋n⦌ ⟶ ⦋n + 1⦌\ninst✝ : Mono θ\n⊢ ¬Epi θ"
] | rw [← epi_iff_surjective] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.AlgebraicTopology.SimplexCategory.Basic | {
"line": 827,
"column": 2
} | {
"line": 829,
"column": 18
} | {
"line": 830,
"column": 2
} | [
{
"pp": "case h\nn : ℕ\nθ : ⦋n⦌ ⟶ ⦋n + 1⦌\ninst✝ : Mono θ\ni : Fin (n + 2)\nθ' : ⦋n⦌ ⟶ ⦋n⦌\nh : θ = θ' ≫ δ i\n⊢ θ = δ i",
"ppTerm": "?h",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"CategoryTheory.Mono",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congr... | [
"case h\nn : ℕ\nθ : ⦋n⦌ ⟶ ⦋n + 1⦌\ninst✝ : Mono θ\ni : Fin (n + 2)\nθ' : ⦋n⦌ ⟶ ⦋n⦌\nh : θ = θ' ≫ δ i\nthis : Mono (θ' ≫ δ i)\n⊢ θ = δ i"
] | haveI : Mono (θ' ≫ δ i) := by
rw [← h]
infer_instance | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHaveI___1 | Lean.Parser.Tactic.tacticHaveI__ |
Mathlib.CategoryTheory.Subfunctor.OfSection | {
"line": 56,
"column": 53
} | {
"line": 61,
"column": 39
} | {
"line": 63,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF : Cᵒᵖ ⥤ Type w\nX : Cᵒᵖ\nx : F.obj X\nF' : Cᵒᵖ ⥤ Type w\nf : F ⟶ F'\n⊢ (ofSection x).image f = ofSection ((ConcreteCategory.hom (f.app X)) x)",
"ppTerm": "?m.32",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"CategoryTheory.Subfunctor.i... | [] | by
apply le_antisymm
· rw [image_le_iff, ofSection_le_iff, preimage_obj, Set.mem_preimage]
exact ⟨𝟙 X, by simp⟩
· simp only [ofSection_le_iff, image_obj, Set.mem_image]
exact ⟨x, mem_ofSection_obj x, rfl⟩ | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.AlgebraicTopology.CechNerve | {
"line": 373,
"column": 42
} | {
"line": 373,
"column": 57
} | {
"line": 373,
"column": 57
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : HasTerminal C\nι : Type w\ninst✝¹ : HasFiniteProducts C\ninst✝ : Finite ι\nX : C\ns : Cone (wideCospan ι X)\nj : WidePullbackShape ι\n⊢ (Pi.lift fun j ↦ s.π.app (some j)) ≫\n { pt := ∏ᶜ fun x ↦ X,\n π :=\n {\n ... | [] | by subsingleton | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.AlgebraicTopology.SimplicialSet.Degenerate | {
"line": 75,
"column": 71
} | {
"line": 75,
"column": 76
} | {
"line": 75,
"column": 76
} | [
{
"pp": "X : SSet\nn : ℕ\nx : X _⦋n⦌\nm : ℕ\nhm : m < n\nf : ⦋n⦌ ⟶ ⦋m⦌\ny : X _⦋m⦌\nhy : (ConcreteCategory.hom (X.map ((image.ι f).op ≫ (factorThruImage f).op))) y = x\nthis : (image f).len ≤ m\n⊢ x ∈ Set.range ⇑(ConcreteCategory.hom (X.map (factorThruImage f).op))",
"ppTerm": "?m.129",
"assigned": true... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialSet.Degenerate | {
"line": 75,
"column": 71
} | {
"line": 75,
"column": 76
} | {
"line": 75,
"column": 76
} | [
{
"pp": "X : SSet\nn : ℕ\nx : X _⦋n⦌\nm : ℕ\nhm : m < n\nf : ⦋n⦌ ⟶ ⦋m⦌\ny : X _⦋m⦌\nhy : (ConcreteCategory.hom (X.map ((image.ι f).op ≫ (factorThruImage f).op))) y = x\nthis : (image f).len ≤ m\n⊢ x ∈ Set.range ⇑(ConcreteCategory.hom (X.map (factorThruImage f).op))",
"ppTerm": "?m.129",
"assigned": true... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.Degenerate | {
"line": 75,
"column": 71
} | {
"line": 75,
"column": 76
} | {
"line": 75,
"column": 76
} | [
{
"pp": "X : SSet\nn : ℕ\nx : X _⦋n⦌\nm : ℕ\nhm : m < n\nf : ⦋n⦌ ⟶ ⦋m⦌\ny : X _⦋m⦌\nhy : (ConcreteCategory.hom (X.map ((image.ι f).op ≫ (factorThruImage f).op))) y = x\nthis : (image f).len ≤ m\n⊢ x ∈ Set.range ⇑(ConcreteCategory.hom (X.map (factorThruImage f).op))",
"ppTerm": "?m.129",
"assigned": true... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.Degenerate | {
"line": 108,
"column": 4
} | {
"line": 108,
"column": 9
} | {
"line": 109,
"column": 2
} | [
{
"pp": "case mp\nX : SSet\nn m : ℕ\nhm : m < n + 1\ny : X _⦋m⦌\ni : Fin (n + 1)\nθ : ⦋n⦌ ⟶ ⦋m⦌\nhf : Epi (SimplexCategory.σ i ≫ θ)\n⊢ (ConcreteCategory.hom (X.map (SimplexCategory.σ i ≫ θ).op)) y ∈\n ⋃ i, Set.range ⇑(ConcreteCategory.hom (SimplicialObject.σ X i))",
"ppTerm": "?mp",
"assigned": true,... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialSet.Simplices | {
"line": 97,
"column": 4
} | {
"line": 97,
"column": 9
} | {
"line": 97,
"column": 9
} | [
{
"pp": "X : SSet\nw✝³ : ℕ\nw✝² : X _⦋w✝³⦌\nw✝¹ : ℕ\nw✝ : X _⦋w✝¹⦌\nx✝ :\n ∃ (h : { dim := w✝³, simplex := w✝² }.dim = { dim := w✝¹, simplex := w✝ }.dim),\n ({ dim := w✝³, simplex := w✝² }.cast h).simplex = { dim := w✝¹, simplex := w✝ }.simplex\nh₁ : { dim := w✝³, simplex := w✝² }.dim = { dim := w✝¹, simple... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialSet.Dimension | {
"line": 127,
"column": 2
} | {
"line": 127,
"column": 7
} | {
"line": 129,
"column": 0
} | [
{
"pp": "X : SSet\nι : Type u_1\nA : ι → X.Subcomplex\nd : ℕ\n⊢ (∀ (n : ℕ), d ≤ n → X.degenerate n ⊓ (⨆ i, A i).obj (op ⦋n⦌) = (⨆ i, A i).obj (op ⦋n⦌)) ↔\n ∀ (i : ι) (n : ℕ), d ≤ n → X.degenerate n ⊓ (A i).obj (op ⦋n⦌) = (A i).obj (op ⦋n⦌)",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialSet.Simplices | {
"line": 165,
"column": 4
} | {
"line": 166,
"column": 22
} | {
"line": 168,
"column": 0
} | [
{
"pp": "case mpr\nX : SSet\nx y : X.S\n⊢ Nonempty (equivElements y ⟶ equivElements x) → ∃ f, (ConcreteCategory.hom (X.map f.op)) y.simplex = x.simplex",
"ppTerm": "?mpr",
"assigned": true,
"usedConstants": [
"SSet.S.simplex",
"CategoryTheory.categoryOfElements",
"SSet.S",
"C... | [] | rintro ⟨f, hf⟩
exact ⟨f.unop, hf⟩ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.Simplices | {
"line": 165,
"column": 4
} | {
"line": 166,
"column": 22
} | {
"line": 168,
"column": 0
} | [
{
"pp": "case mpr\nX : SSet\nx y : X.S\n⊢ Nonempty (equivElements y ⟶ equivElements x) → ∃ f, (ConcreteCategory.hom (X.map f.op)) y.simplex = x.simplex",
"ppTerm": "?mpr",
"assigned": true,
"usedConstants": [
"SSet.S.simplex",
"CategoryTheory.categoryOfElements",
"SSet.S",
"C... | [] | rintro ⟨f, hf⟩
exact ⟨f.unop, hf⟩ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex | {
"line": 39,
"column": 6
} | {
"line": 39,
"column": 31
} | {
"line": 40,
"column": 6
} | [
{
"pp": "case right\nX✝¹ Y✝ : SSet\nf : X✝¹ ⟶ Y✝\nx✝¹ : Mono f\nx✝ : Epi f\nX✝ : SimplexCategoryᵒᵖ\n⊢ Function.Surjective ⇑(ConcreteCategory.hom (f.app X✝))",
"ppTerm": "?right",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Opposite",
"CategoryTheory.epi_iff_surjective",
"... | [
"case right\nX✝¹ Y✝ : SSet\nf : X✝¹ ⟶ Y✝\nx✝¹ : Mono f\nx✝ : Epi f\nX✝ : SimplexCategoryᵒᵖ\n⊢ Epi (f.app X✝)"
] | rw [← epi_iff_surjective] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex | {
"line": 132,
"column": 29
} | {
"line": 132,
"column": 46
} | {
"line": 132,
"column": 47
} | [
{
"pp": "X Y : SSet\nx✝² x✝¹ : SimplexCategoryᵒᵖ\nx✝ : x✝² ⟶ x✝¹\n⊢ (⊥.toSSet.map x✝ ≫\n ↾fun x ↦\n match x with\n | ⟨val, h⟩ => ⋯.elim) =\n (↾fun x ↦\n match x with\n | ⟨val, h⟩ => ⋯.elim) ≫\n Y.map x✝",
"ppTerm": "?m.45",
"assigned": true,
"usedConstants": ... | [] | ext ⟨_, h⟩; tauto | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex | {
"line": 132,
"column": 29
} | {
"line": 132,
"column": 46
} | {
"line": 132,
"column": 47
} | [
{
"pp": "X Y : SSet\nx✝² x✝¹ : SimplexCategoryᵒᵖ\nx✝ : x✝² ⟶ x✝¹\n⊢ (⊥.toSSet.map x✝ ≫\n ↾fun x ↦\n match x with\n | ⟨val, h⟩ => ⋯.elim) =\n (↾fun x ↦\n match x with\n | ⟨val, h⟩ => ⋯.elim) ≫\n Y.map x✝",
"ppTerm": "?m.45",
"assigned": true,
"usedConstants": ... | [] | ext ⟨_, h⟩; tauto | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex | {
"line": 133,
"column": 10
} | {
"line": 133,
"column": 25
} | {
"line": 135,
"column": 0
} | [
{
"pp": "X Y : SSet\n⊢ ∀ (a : ⊥.toSSet ⟶ Y),\n a =\n {\n app := fun x ↦\n ↾fun x_1 ↦\n match x_1 with\n | ⟨val, h⟩ => ⋯.elim,\n naturality := ⋯ }",
"ppTerm": "?m.81",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.toSSet",
"Fals... | [] | by subsingleton | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex | {
"line": 160,
"column": 2
} | {
"line": 160,
"column": 7
} | {
"line": 162,
"column": 0
} | [
{
"pp": "X : SSet\nn : ℕ\nx : X _⦋n⦌\nm : SimplexCategoryᵒᵖ\ny : X.obj m\n⊢ (∃ f, (ConcreteCategory.hom (X.map f)) x = y) ↔ ∃ f, (ConcreteCategory.hom (X.map f.op)) x = y",
"ppTerm": "?m.37",
"assigned": true,
"usedConstants": [
"Opposite",
"Quiver.opposite",
"CategoryTheory.Catego... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialSet.Finite | {
"line": 39,
"column": 4
} | {
"line": 39,
"column": 9
} | {
"line": 39,
"column": 9
} | [
{
"pp": "X : SSet\ninst✝ : X.Finite\nn : ℕ\nx y : ↑(X.nonDegenerate n)\nh :\n ∃ (h : ((fun x ↦ N.mk ↑x ⋯) x).dim = ((fun x ↦ N.mk ↑x ⋯) y).dim),\n (((fun x ↦ N.mk ↑x ⋯) x).cast h).simplex = ((fun x ↦ N.mk ↑x ⋯) y).simplex\n⊢ x = y",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex | {
"line": 249,
"column": 56
} | {
"line": 249,
"column": 61
} | {
"line": 251,
"column": 0
} | [
{
"pp": "X Y : SSet\nι : Type u_1\nA : ι → X.Subcomplex\np : Y ⟶ X\n⊢ (⨆ i, A i).preimage p = ⨆ i, (A i).preimage p",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Set.ext",
"Opposite",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"iSup",
"Set.mem... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex | {
"line": 249,
"column": 56
} | {
"line": 249,
"column": 61
} | {
"line": 251,
"column": 0
} | [
{
"pp": "X Y : SSet\nι : Type u_1\nA : ι → X.Subcomplex\np : Y ⟶ X\n⊢ (⨆ i, A i).preimage p = ⨆ i, (A i).preimage p",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Set.ext",
"Opposite",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"iSup",
"Set.mem... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex | {
"line": 249,
"column": 56
} | {
"line": 249,
"column": 61
} | {
"line": 251,
"column": 0
} | [
{
"pp": "X Y : SSet\nι : Type u_1\nA : ι → X.Subcomplex\np : Y ⟶ X\n⊢ (⨆ i, A i).preimage p = ⨆ i, (A i).preimage p",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Set.ext",
"Opposite",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"iSup",
"Set.mem... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex | {
"line": 253,
"column": 56
} | {
"line": 253,
"column": 61
} | {
"line": 255,
"column": 0
} | [
{
"pp": "X Y : SSet\nι : Type u_1\nA : ι → X.Subcomplex\np : Y ⟶ X\n⊢ (⨅ i, A i).preimage p = ⨅ i, (A i).preimage p",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Set.ext",
"iInf",
"Opposite",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"Set.iIn... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex | {
"line": 253,
"column": 56
} | {
"line": 253,
"column": 61
} | {
"line": 255,
"column": 0
} | [
{
"pp": "X Y : SSet\nι : Type u_1\nA : ι → X.Subcomplex\np : Y ⟶ X\n⊢ (⨅ i, A i).preimage p = ⨅ i, (A i).preimage p",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Set.ext",
"iInf",
"Opposite",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"Set.iIn... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex | {
"line": 253,
"column": 56
} | {
"line": 253,
"column": 61
} | {
"line": 255,
"column": 0
} | [
{
"pp": "X Y : SSet\nι : Type u_1\nA : ι → X.Subcomplex\np : Y ⟶ X\n⊢ (⨅ i, A i).preimage p = ⨅ i, (A i).preimage p",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Set.ext",
"iInf",
"Opposite",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"Set.iIn... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex | {
"line": 262,
"column": 63
} | {
"line": 262,
"column": 68
} | {
"line": 264,
"column": 0
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\n⊢ A.preimage A.ι = ⊤",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.toSSet",
"Set.ext",
"Lattice.toSemilatticeSup",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CompleteL... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex | {
"line": 262,
"column": 63
} | {
"line": 262,
"column": 68
} | {
"line": 264,
"column": 0
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\n⊢ A.preimage A.ι = ⊤",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.toSSet",
"Set.ext",
"Lattice.toSemilatticeSup",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CompleteL... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex | {
"line": 262,
"column": 63
} | {
"line": 262,
"column": 68
} | {
"line": 264,
"column": 0
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\n⊢ A.preimage A.ι = ⊤",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.toSSet",
"Set.ext",
"Lattice.toSemilatticeSup",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CompleteL... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex | {
"line": 278,
"column": 61
} | {
"line": 278,
"column": 66
} | {
"line": 280,
"column": 0
} | [
{
"pp": "X Y : SSet\nf : X ⟶ Y\n⊢ ⊤.image f = range f",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Set.ext",
"SSet.Subcomplex.range",
"Set.image_univ",
"Lattice.toSemilatticeSup",
"Opposite",
"SSet.Subcomplex.image_obj",
"CompleteLattice.toLatt... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex | {
"line": 278,
"column": 61
} | {
"line": 278,
"column": 66
} | {
"line": 280,
"column": 0
} | [
{
"pp": "X Y : SSet\nf : X ⟶ Y\n⊢ ⊤.image f = range f",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Set.ext",
"SSet.Subcomplex.range",
"Set.image_univ",
"Lattice.toSemilatticeSup",
"Opposite",
"SSet.Subcomplex.image_obj",
"CompleteLattice.toLatt... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex | {
"line": 278,
"column": 61
} | {
"line": 278,
"column": 66
} | {
"line": 280,
"column": 0
} | [
{
"pp": "X Y : SSet\nf : X ⟶ Y\n⊢ ⊤.image f = range f",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Set.ext",
"SSet.Subcomplex.range",
"Set.image_univ",
"Lattice.toSemilatticeSup",
"Opposite",
"SSet.Subcomplex.image_obj",
"CompleteLattice.toLatt... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex | {
"line": 281,
"column": 41
} | {
"line": 281,
"column": 46
} | {
"line": 283,
"column": 0
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\n⊢ A.image (𝟙 X) = A",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Set.ext",
"Opposite",
"SSet.Subcomplex.image_obj",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"Set.image_id'",
"CategoryTheory.Functor... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex | {
"line": 281,
"column": 41
} | {
"line": 281,
"column": 46
} | {
"line": 283,
"column": 0
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\n⊢ A.image (𝟙 X) = A",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Set.ext",
"Opposite",
"SSet.Subcomplex.image_obj",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"Set.image_id'",
"CategoryTheory.Functor... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex | {
"line": 281,
"column": 41
} | {
"line": 281,
"column": 46
} | {
"line": 283,
"column": 0
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\n⊢ A.image (𝟙 X) = A",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Set.ext",
"Opposite",
"SSet.Subcomplex.image_obj",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"Set.image_id'",
"CategoryTheory.Functor... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex | {
"line": 284,
"column": 48
} | {
"line": 284,
"column": 53
} | {
"line": 286,
"column": 0
} | [
{
"pp": "X Y : SSet\nA : X.Subcomplex\nf : X ⟶ Y\nZ : SSet\ng : Y ⟶ Z\n⊢ A.image (f ≫ g) = (A.image f).image g",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Set.ext",
"Opposite",
"SSet.Subcomplex.image_obj",
"congrArg",
"CategoryTheory.ConcreteCategory.hom"... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex | {
"line": 284,
"column": 48
} | {
"line": 284,
"column": 53
} | {
"line": 286,
"column": 0
} | [
{
"pp": "X Y : SSet\nA : X.Subcomplex\nf : X ⟶ Y\nZ : SSet\ng : Y ⟶ Z\n⊢ A.image (f ≫ g) = (A.image f).image g",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Set.ext",
"Opposite",
"SSet.Subcomplex.image_obj",
"congrArg",
"CategoryTheory.ConcreteCategory.hom"... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex | {
"line": 284,
"column": 48
} | {
"line": 284,
"column": 53
} | {
"line": 286,
"column": 0
} | [
{
"pp": "X Y : SSet\nA : X.Subcomplex\nf : X ⟶ Y\nZ : SSet\ng : Y ⟶ Z\n⊢ A.image (f ≫ g) = (A.image f).image g",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Set.ext",
"Opposite",
"SSet.Subcomplex.image_obj",
"congrArg",
"CategoryTheory.ConcreteCategory.hom"... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex | {
"line": 287,
"column": 66
} | {
"line": 287,
"column": 71
} | {
"line": 289,
"column": 0
} | [
{
"pp": "X Y : SSet\nf : X ⟶ Y\nZ : SSet\ng : Y ⟶ Z\n⊢ range (f ≫ g) = (range f).image g",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Set.ext",
"SSet.Subcomplex.range",
"Opposite",
"SSet.Subcomplex.image_obj",
"congrArg",
"CategoryTheory.ConcreteCate... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex | {
"line": 287,
"column": 66
} | {
"line": 287,
"column": 71
} | {
"line": 289,
"column": 0
} | [
{
"pp": "X Y : SSet\nf : X ⟶ Y\nZ : SSet\ng : Y ⟶ Z\n⊢ range (f ≫ g) = (range f).image g",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Set.ext",
"SSet.Subcomplex.range",
"Opposite",
"SSet.Subcomplex.image_obj",
"congrArg",
"CategoryTheory.ConcreteCate... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex | {
"line": 287,
"column": 66
} | {
"line": 287,
"column": 71
} | {
"line": 289,
"column": 0
} | [
{
"pp": "X Y : SSet\nf : X ⟶ Y\nZ : SSet\ng : Y ⟶ Z\n⊢ range (f ≫ g) = (range f).image g",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Set.ext",
"SSet.Subcomplex.range",
"Opposite",
"SSet.Subcomplex.image_obj",
"congrArg",
"CategoryTheory.ConcreteCate... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex | {
"line": 290,
"column": 57
} | {
"line": 290,
"column": 62
} | {
"line": 292,
"column": 0
} | [
{
"pp": "X Y : SSet\nA : X.Subcomplex\nf : X ⟶ Y\n⊢ A.image f = range (A.ι ≫ f)",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.toSSet",
"Set.ext",
"Eq.mpr",
"SSet.Subcomplex.range",
"Opposite",
"congrArg",
"CategoryTheory.Concrete... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex | {
"line": 290,
"column": 57
} | {
"line": 290,
"column": 62
} | {
"line": 292,
"column": 0
} | [
{
"pp": "X Y : SSet\nA : X.Subcomplex\nf : X ⟶ Y\n⊢ A.image f = range (A.ι ≫ f)",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.toSSet",
"Set.ext",
"Eq.mpr",
"SSet.Subcomplex.range",
"Opposite",
"congrArg",
"CategoryTheory.Concrete... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex | {
"line": 290,
"column": 57
} | {
"line": 290,
"column": 62
} | {
"line": 292,
"column": 0
} | [
{
"pp": "X Y : SSet\nA : X.Subcomplex\nf : X ⟶ Y\n⊢ A.image f = range (A.ι ≫ f)",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.toSSet",
"Set.ext",
"Eq.mpr",
"SSet.Subcomplex.range",
"Opposite",
"congrArg",
"CategoryTheory.Concrete... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex | {
"line": 294,
"column": 2
} | {
"line": 294,
"column": 7
} | {
"line": 296,
"column": 0
} | [
{
"pp": "X Y : SSet\nι : Type u_1\nS : ι → X.Subcomplex\nf : X ⟶ Y\n⊢ (⨆ i, S i).image f = ⨆ i, (S i).image f",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"Opposite",
"SSet.Subcomplex.image_obj",
"congrArg",
"CategoryTheory.Concre... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex | {
"line": 294,
"column": 2
} | {
"line": 294,
"column": 7
} | {
"line": 296,
"column": 0
} | [
{
"pp": "X Y : SSet\nι : Type u_1\nS : ι → X.Subcomplex\nf : X ⟶ Y\n⊢ (⨆ i, S i).image f = ⨆ i, (S i).image f",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"Opposite",
"SSet.Subcomplex.image_obj",
"congrArg",
"CategoryTheory.Concre... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex | {
"line": 294,
"column": 2
} | {
"line": 294,
"column": 7
} | {
"line": 296,
"column": 0
} | [
{
"pp": "X Y : SSet\nι : Type u_1\nS : ι → X.Subcomplex\nf : X ⟶ Y\n⊢ (⨆ i, S i).image f = ⨆ i, (S i).image f",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"Opposite",
"SSet.Subcomplex.image_obj",
"congrArg",
"CategoryTheory.Concre... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.Degenerate | {
"line": 292,
"column": 4
} | {
"line": 292,
"column": 9
} | {
"line": 293,
"column": 2
} | [
{
"pp": "case mp\nX : SSet\nA B : X.Subcomplex\n⊢ A ≤ B → ∀ (n : ℕ) (x : ↑(X.nonDegenerate n)), ↑x ∈ A.obj (op ⦋n⦌) → ↑x ∈ B.obj (op ⦋n⦌)",
"ppTerm": "?mp",
"assigned": true,
"usedConstants": [
"Opposite",
"PartialOrder.toPreorder",
"SSet.nonDegenerate",
"Subtype.casesOn",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialSet.Degenerate | {
"line": 292,
"column": 4
} | {
"line": 292,
"column": 9
} | {
"line": 293,
"column": 2
} | [
{
"pp": "case mp\nX : SSet\nA B : X.Subcomplex\n⊢ A ≤ B → ∀ (n : ℕ) (x : ↑(X.nonDegenerate n)), ↑x ∈ A.obj (op ⦋n⦌) → ↑x ∈ B.obj (op ⦋n⦌)",
"ppTerm": "?mp",
"assigned": true,
"usedConstants": [
"Opposite",
"PartialOrder.toPreorder",
"SSet.nonDegenerate",
"Subtype.casesOn",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.Degenerate | {
"line": 292,
"column": 4
} | {
"line": 292,
"column": 9
} | {
"line": 293,
"column": 2
} | [
{
"pp": "case mp\nX : SSet\nA B : X.Subcomplex\n⊢ A ≤ B → ∀ (n : ℕ) (x : ↑(X.nonDegenerate n)), ↑x ∈ A.obj (op ⦋n⦌) → ↑x ∈ B.obj (op ⦋n⦌)",
"ppTerm": "?mp",
"assigned": true,
"usedConstants": [
"Opposite",
"PartialOrder.toPreorder",
"SSet.nonDegenerate",
"Subtype.casesOn",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.NonDegenerateSimplices | {
"line": 116,
"column": 4
} | {
"line": 116,
"column": 9
} | {
"line": 118,
"column": 0
} | [
{
"pp": "X : SSet\nn₁ : ℕ\nx₁ : X _⦋n₁⦌\nhx₁ : x₁ ∈ X.nonDegenerate n₁\nx₂ : X _⦋n₁⦌\nhx₂ : x₂ ∈ X.nonDegenerate n₁\nh' : mk ↑⟨x₂, hx₂⟩ ⋯ ≤ mk ↑⟨x₁, hx₁⟩ ⋯\nhf : Mono (𝟙 ⦋(mk ↑⟨x₁, hx₁⟩ ⋯).dim⦌)\nh : (ConcreteCategory.hom (X.map (𝟙 ⦋(mk ↑⟨x₁, hx₁⟩ ⋯).dim⦌).op)) (mk ↑⟨x₂, hx₂⟩ ⋯).simplex = (mk ↑⟨x₁, hx₁⟩ ⋯).si... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialSet.Degenerate | {
"line": 366,
"column": 44
} | {
"line": 366,
"column": 49
} | {
"line": 366,
"column": 49
} | [
{
"pp": "X : SSet\nn✝ : ℕ\nY : SSet\ne : X ≅ Y\nn : ℕ\nx✝ : ↑(X.nonDegenerate n)\nx : X _⦋n⦌\nhx : x ∈ X.nonDegenerate n\n⊢ (ConcreteCategory.hom (e.hom.app (op ⦋n⦌))) x ∈ Y.nonDegenerate n",
"ppTerm": "?m.73",
"assigned": true,
"usedConstants": [
"Opposite",
"CategoryTheory.ConcreteCate... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialSet.Degenerate | {
"line": 366,
"column": 44
} | {
"line": 366,
"column": 49
} | {
"line": 366,
"column": 49
} | [
{
"pp": "X : SSet\nn✝ : ℕ\nY : SSet\ne : X ≅ Y\nn : ℕ\nx✝ : ↑(X.nonDegenerate n)\nx : X _⦋n⦌\nhx : x ∈ X.nonDegenerate n\n⊢ (ConcreteCategory.hom (e.hom.app (op ⦋n⦌))) x ∈ Y.nonDegenerate n",
"ppTerm": "?m.73",
"assigned": true,
"usedConstants": [
"Opposite",
"CategoryTheory.ConcreteCate... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.Degenerate | {
"line": 366,
"column": 44
} | {
"line": 366,
"column": 49
} | {
"line": 366,
"column": 49
} | [
{
"pp": "X : SSet\nn✝ : ℕ\nY : SSet\ne : X ≅ Y\nn : ℕ\nx✝ : ↑(X.nonDegenerate n)\nx : X _⦋n⦌\nhx : x ∈ X.nonDegenerate n\n⊢ (ConcreteCategory.hom (e.hom.app (op ⦋n⦌))) x ∈ Y.nonDegenerate n",
"ppTerm": "?m.73",
"assigned": true,
"usedConstants": [
"Opposite",
"CategoryTheory.ConcreteCate... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.Degenerate | {
"line": 367,
"column": 45
} | {
"line": 367,
"column": 50
} | {
"line": 367,
"column": 50
} | [
{
"pp": "X : SSet\nn✝ : ℕ\nY : SSet\ne : X ≅ Y\nn : ℕ\nx✝ : ↑(Y.nonDegenerate n)\ny : Y _⦋n⦌\nhy : y ∈ Y.nonDegenerate n\n⊢ (ConcreteCategory.hom (e.inv.app (op ⦋n⦌))) y ∈ X.nonDegenerate n",
"ppTerm": "?m.74",
"assigned": true,
"usedConstants": [
"Opposite",
"CategoryTheory.ConcreteCate... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialSet.Degenerate | {
"line": 367,
"column": 45
} | {
"line": 367,
"column": 50
} | {
"line": 367,
"column": 50
} | [
{
"pp": "X : SSet\nn✝ : ℕ\nY : SSet\ne : X ≅ Y\nn : ℕ\nx✝ : ↑(Y.nonDegenerate n)\ny : Y _⦋n⦌\nhy : y ∈ Y.nonDegenerate n\n⊢ (ConcreteCategory.hom (e.inv.app (op ⦋n⦌))) y ∈ X.nonDegenerate n",
"ppTerm": "?m.74",
"assigned": true,
"usedConstants": [
"Opposite",
"CategoryTheory.ConcreteCate... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.Degenerate | {
"line": 367,
"column": 45
} | {
"line": 367,
"column": 50
} | {
"line": 367,
"column": 50
} | [
{
"pp": "X : SSet\nn✝ : ℕ\nY : SSet\ne : X ≅ Y\nn : ℕ\nx✝ : ↑(Y.nonDegenerate n)\ny : Y _⦋n⦌\nhy : y ∈ Y.nonDegenerate n\n⊢ (ConcreteCategory.hom (e.inv.app (op ⦋n⦌))) y ∈ X.nonDegenerate n",
"ppTerm": "?m.74",
"assigned": true,
"usedConstants": [
"Opposite",
"CategoryTheory.ConcreteCate... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.Degenerate | {
"line": 368,
"column": 19
} | {
"line": 368,
"column": 24
} | {
"line": 369,
"column": 2
} | [
{
"pp": "X : SSet\nn✝ : ℕ\nY : SSet\ne : X ≅ Y\nn : ℕ\nx✝ : ↑(X.nonDegenerate n)\n⊢ (fun x ↦\n match x with\n | ⟨y, hy⟩ => ⟨(ConcreteCategory.hom (e.inv.app (op ⦋n⦌))) y, ⋯⟩)\n ((fun x ↦\n match x with\n | ⟨x, hx⟩ => ⟨(ConcreteCategory.hom (e.hom.app (op ⦋n⦌))) x, ⋯⟩)\n ... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.