module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.GroupTheory.Perm.Cycle.Type | {
"line": 559,
"column": 46
} | {
"line": 559,
"column": 68
} | {
"line": 559,
"column": 69
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nH : Subgroup (Perm α)\nd : DecidablePred fun x ↦ x ∈ H\nτ : Perm α\nh0 : Nat.Prime (Fintype.card α)\nh1 : Fintype.card α ∣ Fintype.card ↥H\nh2 : τ ∈ H\nh3 : τ.IsSwap\nthis : Fact (Nat.Prime (Fintype.card α))\nσ : ↥H\nhσ : orderOf σ = Fintype.card... | [
"α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nH : Subgroup (Perm α)\nd : DecidablePred fun x ↦ x ∈ H\nτ : Perm α\nh0 : Nat.Prime (Fintype.card α)\nh1 : Fintype.card α ∣ Fintype.card ↥H\nh2 : τ ∈ H\nh3 : τ.IsSwap\nthis : Fact (Nat.Prime (Fintype.card α))\nσ : ↥H\nhσ : orderOf σ = Fintype.card α\nhσ1 : or... | Set.insert_subset_iff, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.LinearAlgebra.Matrix.SemiringInverse | {
"line": 112,
"column": 39
} | {
"line": 112,
"column": 44
} | {
"line": 112,
"column": 44
} | [
{
"pp": "n : Type u_1\nR : Type u_3\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommSemiring R\ns : ℤˣ\nA : Matrix n n R\nx✝¹ x✝ : n\n⊢ ∀ (i : Perm n), i ∈ {x ∈ ofSign s | x x✝ = x✝¹} ↔ (Equiv.inv (Perm n)) i ∈ {x ∈ ofSign s | x x✝¹ = x✝}",
"ppTerm": "?m.36",
"assigned": true,
"usedConstant... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.LinearAlgebra.Matrix.SemiringInverse | {
"line": 112,
"column": 39
} | {
"line": 112,
"column": 44
} | {
"line": 112,
"column": 44
} | [
{
"pp": "n : Type u_1\nR : Type u_3\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommSemiring R\ns : ℤˣ\nA : Matrix n n R\nx✝¹ x✝ : n\n⊢ ∀ (i : Perm n), i ∈ {x ∈ ofSign s | x x✝ = x✝¹} ↔ (Equiv.inv (Perm n)) i ∈ {x ∈ ofSign s | x x✝¹ = x✝}",
"ppTerm": "?m.36",
"assigned": true,
"usedConstant... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.Matrix.SemiringInverse | {
"line": 112,
"column": 39
} | {
"line": 112,
"column": 44
} | {
"line": 112,
"column": 44
} | [
{
"pp": "n : Type u_1\nR : Type u_3\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommSemiring R\ns : ℤˣ\nA : Matrix n n R\nx✝¹ x✝ : n\n⊢ ∀ (i : Perm n), i ∈ {x ∈ ofSign s | x x✝ = x✝¹} ↔ (Equiv.inv (Perm n)) i ∈ {x ∈ ofSign s | x x✝¹ = x✝}",
"ppTerm": "?m.36",
"assigned": true,
"usedConstant... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.Matrix.SemiringInverse | {
"line": 112,
"column": 74
} | {
"line": 112,
"column": 79
} | {
"line": 112,
"column": 79
} | [
{
"pp": "n : Type u_1\nR : Type u_3\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommSemiring R\ns : ℤˣ\nA : Matrix n n R\nx✝¹ x✝ : n\nσ : Perm n\nhσ : σ ∈ {x ∈ ofSign s | x x✝ = x✝¹}\n⊢ ∀ (i : n), i ∈ {x✝}ᶜ ↔ σ i ∈ {x✝¹}ᶜ",
"ppTerm": "?m.47",
"assigned": true,
"usedConstants": [
"Eq.m... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.LinearAlgebra.Matrix.SemiringInverse | {
"line": 112,
"column": 74
} | {
"line": 112,
"column": 79
} | {
"line": 112,
"column": 79
} | [
{
"pp": "n : Type u_1\nR : Type u_3\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommSemiring R\ns : ℤˣ\nA : Matrix n n R\nx✝¹ x✝ : n\nσ : Perm n\nhσ : σ ∈ {x ∈ ofSign s | x x✝ = x✝¹}\n⊢ ∀ (i : n), i ∈ {x✝}ᶜ ↔ σ i ∈ {x✝¹}ᶜ",
"ppTerm": "?m.47",
"assigned": true,
"usedConstants": [
"Eq.m... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.Matrix.SemiringInverse | {
"line": 112,
"column": 74
} | {
"line": 112,
"column": 79
} | {
"line": 112,
"column": 79
} | [
{
"pp": "n : Type u_1\nR : Type u_3\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommSemiring R\ns : ℤˣ\nA : Matrix n n R\nx✝¹ x✝ : n\nσ : Perm n\nhσ : σ ∈ {x ∈ ofSign s | x x✝ = x✝¹}\n⊢ ∀ (i : n), i ∈ {x✝}ᶜ ↔ σ i ∈ {x✝¹}ᶜ",
"ppTerm": "?m.47",
"assigned": true,
"usedConstants": [
"Eq.m... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.Matrix.SemiringInverse | {
"line": 120,
"column": 62
} | {
"line": 120,
"column": 67
} | {
"line": 120,
"column": 67
} | [
{
"pp": "n : Type u_1\nR : Type u_3\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommSemiring R\ns : ℤˣ\nA : Matrix (Option n) (Option n) R\ni : Option n\nσ : Perm (Option n)\nx✝ : sign σ = s ∧ σ none = i\n⊢ sign (removeNone σ).optionCongr = sign (swap none i) * s ∧ decomposeOption.symm (i, removeNone σ... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.LinearAlgebra.Matrix.SemiringInverse | {
"line": 120,
"column": 73
} | {
"line": 120,
"column": 78
} | {
"line": 120,
"column": 78
} | [
{
"pp": "n : Type u_1\nR : Type u_3\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommSemiring R\ns : ℤˣ\nA : Matrix (Option n) (Option n) R\ni : Option n\nσ : Perm (Option n)\n⊢ (∃ a, sign a = sign (swap none i) * s ∧ decomposeOption.symm (i, a) = σ) → sign σ = s ∧ σ none = i",
"ppTerm": "?m.239",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.LinearAlgebra.Matrix.SemiringInverse | {
"line": 120,
"column": 73
} | {
"line": 120,
"column": 78
} | {
"line": 120,
"column": 78
} | [
{
"pp": "n : Type u_1\nR : Type u_3\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommSemiring R\ns : ℤˣ\nA : Matrix (Option n) (Option n) R\ni : Option n\nσ : Perm (Option n)\n⊢ (∃ a, sign a = sign (swap none i) * s ∧ decomposeOption.symm (i, a) = σ) → sign σ = s ∧ σ none = i",
"ppTerm": "?m.239",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.Matrix.SemiringInverse | {
"line": 120,
"column": 73
} | {
"line": 120,
"column": 78
} | {
"line": 120,
"column": 78
} | [
{
"pp": "n : Type u_1\nR : Type u_3\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommSemiring R\ns : ℤˣ\nA : Matrix (Option n) (Option n) R\ni : Option n\nσ : Perm (Option n)\n⊢ (∃ a, sign a = sign (swap none i) * s ∧ decomposeOption.symm (i, a) = σ) → sign σ = s ∧ σ none = i",
"ppTerm": "?m.239",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.Matrix.SemiringInverse | {
"line": 133,
"column": 10
} | {
"line": 133,
"column": 15
} | {
"line": 135,
"column": 0
} | [
{
"pp": "case e_A.e_c\nn : Type u_1\nR : Type u_3\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommSemiring R\ns : ℤˣ\ni : n\nA : Matrix (Option n) (Option n) R\nx✝ : n\n⊢ (⇑(swap none (some i)) ∘ some) x✝ = Function.update some i none x✝",
"ppTerm": "?e_A.e_c",
"assigned": true,
"usedConsta... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.LinearAlgebra.Matrix.SemiringInverse | {
"line": 189,
"column": 94
} | {
"line": 189,
"column": 99
} | {
"line": 190,
"column": 2
} | [
{
"pp": "n : Type u_1\nR : Type u_3\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommSemiring R\nA : Matrix n n R\ni j : n\nh : i ≠ j\nA' : Matrix n n R := of (Function.update A j (A i))\ns : ℤˣ\nx✝³ : n\nx✝² : x✝³ ∈ univ\nσ : Perm n\nhσ : σ ∈ {x ∈ ofSign s | x j = x✝³}\nx✝¹ : n\nx✝ : x✝¹ ∈ {j}ᶜ\n⊢ A x✝... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.LinearAlgebra.Matrix.SemiringInverse | {
"line": 189,
"column": 94
} | {
"line": 189,
"column": 99
} | {
"line": 190,
"column": 2
} | [
{
"pp": "n : Type u_1\nR : Type u_3\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommSemiring R\nA : Matrix n n R\ni j : n\nh : i ≠ j\nA' : Matrix n n R := of (Function.update A j (A i))\ns : ℤˣ\nx✝³ : n\nx✝² : x✝³ ∈ univ\nσ : Perm n\nhσ : σ ∈ {x ∈ ofSign s | x j = x✝³}\nx✝¹ : n\nx✝ : x✝¹ ∈ {j}ᶜ\n⊢ A x✝... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.Matrix.SemiringInverse | {
"line": 189,
"column": 94
} | {
"line": 189,
"column": 99
} | {
"line": 190,
"column": 2
} | [
{
"pp": "n : Type u_1\nR : Type u_3\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommSemiring R\nA : Matrix n n R\ni j : n\nh : i ≠ j\nA' : Matrix n n R := of (Function.update A j (A i))\ns : ℤˣ\nx✝³ : n\nx✝² : x✝³ ∈ univ\nσ : Perm n\nhσ : σ ∈ {x ∈ ofSign s | x j = x✝³}\nx✝¹ : n\nx✝ : x✝¹ ∈ {j}ᶜ\n⊢ A x✝... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.Matrix.Determinant.Basic | {
"line": 220,
"column": 2
} | {
"line": 220,
"column": 71
} | {
"line": 222,
"column": 0
} | [
{
"pp": "n : Type u_2\ninst✝² : DecidableEq n\ninst✝¹ : Fintype n\nR : Type v\ninst✝ : CommRing R\nσ : Perm n\nM : Matrix n n R\n⊢ (M.submatrix id ⇑σ).det = ↑↑(sign σ) * M.det",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"Int.cast",
"Units.val",
"Eq.mpr",
"Matrix... | [] | rw [← det_transpose, transpose_submatrix, det_permute, det_transpose] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.LinearAlgebra.Matrix.Determinant.Basic | {
"line": 220,
"column": 2
} | {
"line": 220,
"column": 71
} | {
"line": 222,
"column": 0
} | [
{
"pp": "n : Type u_2\ninst✝² : DecidableEq n\ninst✝¹ : Fintype n\nR : Type v\ninst✝ : CommRing R\nσ : Perm n\nM : Matrix n n R\n⊢ (M.submatrix id ⇑σ).det = ↑↑(sign σ) * M.det",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"Int.cast",
"Units.val",
"Eq.mpr",
"Matrix... | [] | rw [← det_transpose, transpose_submatrix, det_permute, det_transpose] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.Matrix.Determinant.Basic | {
"line": 220,
"column": 2
} | {
"line": 220,
"column": 71
} | {
"line": 222,
"column": 0
} | [
{
"pp": "n : Type u_2\ninst✝² : DecidableEq n\ninst✝¹ : Fintype n\nR : Type v\ninst✝ : CommRing R\nσ : Perm n\nM : Matrix n n R\n⊢ (M.submatrix id ⇑σ).det = ↑↑(sign σ) * M.det",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"Int.cast",
"Units.val",
"Eq.mpr",
"Matrix... | [] | rw [← det_transpose, transpose_submatrix, det_permute, det_transpose] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Filtered.Basic | {
"line": 103,
"column": 34
} | {
"line": 103,
"column": 49
} | {
"line": 103,
"column": 49
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nα : Type u\ninst✝ : SemilatticeSup α\nX Y : α\nf g : X ⟶ Y\n⊢ f ≫ 𝟙 Y = g ≫ 𝟙 Y",
"ppTerm": "?m.41",
"assigned": true,
"usedConstants": [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"PartialOrder.toPreorder",
"Cat... | [] | by subsingleton | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Filtered.Basic | {
"line": 113,
"column": 34
} | {
"line": 113,
"column": 49
} | {
"line": 113,
"column": 49
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\nα : Type u\ninst✝¹ : Preorder α\ninst✝ : IsDirectedOrder α\nX Y : α\nf g : X ⟶ Y\n⊢ f ≫ 𝟙 Y = g ≫ 𝟙 Y",
"ppTerm": "?m.59",
"assigned": true,
"usedConstants": [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory... | [] | by subsingleton | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Filtered.Basic | {
"line": 124,
"column": 54
} | {
"line": 124,
"column": 69
} | {
"line": 124,
"column": 69
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nX Y : Discrete PUnit.{u_1 + 1}\n⊢ Y.as = { as := PUnit.unit }.as",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"instSubsingletonPUnit",
"CategoryTheory.Discrete.mk",
"CategoryTheory.Discrete.as",
"PUnit",
"PUni... | [] | by subsingleton | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Filtered.Basic | {
"line": 125,
"column": 56
} | {
"line": 125,
"column": 71
} | {
"line": 125,
"column": 71
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nX Y : Discrete PUnit.{u_1 + 1}\nf g : X ⟶ Y\n⊢ f ≫ { down := { down := ⋯ } } = g ≫ { down := { down := ⋯ } }",
"ppTerm": "?m.33",
"assigned": true,
"usedConstants": [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTh... | [] | by subsingleton | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Limits.Types.ColimitType | {
"line": 147,
"column": 58
} | {
"line": 147,
"column": 63
} | {
"line": 147,
"column": 63
} | [
{
"pp": "J : Type u\ninst✝ : Category.{v, u} J\nF : J ⥤ Type w₀\nc : F.CoconeTypes\na✝ b✝ : (j : J) × F.obj j\nw✝ : a✝.fst ⟶ b✝.fst\nh✝ : b✝.snd = (ConcreteCategory.hom (F.map w✝)) a✝.snd\n⊢ (match a✝ with\n | ⟨j, x⟩ => c.ι j x) =\n match b✝ with\n | ⟨j, x⟩ => c.ι j x",
"ppTerm": "?m.43",
"assi... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.Limits.Types.ColimitType | {
"line": 209,
"column": 49
} | {
"line": 209,
"column": 54
} | {
"line": 209,
"column": 54
} | [
{
"pp": "J : Type u\ninst✝ : Category.{v, u} J\nF : J ⥤ Type w₀\nc : F.CoconeTypes\nhc : c.IsColimit\nc' : F.CoconeTypes\n⊢ ∀ (j : J), (F.descColimitType c' ∘ ⇑hc.equiv.symm) ∘ c.ι j = c'.ι j",
"ppTerm": "?m.41",
"assigned": true,
"usedConstants": [
"Equiv.instEquivLike",
"congrArg",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.Limits.Types.ColimitType | {
"line": 209,
"column": 49
} | {
"line": 209,
"column": 54
} | {
"line": 209,
"column": 54
} | [
{
"pp": "J : Type u\ninst✝ : Category.{v, u} J\nF : J ⥤ Type w₀\nc : F.CoconeTypes\nhc : c.IsColimit\nc' : F.CoconeTypes\n⊢ ∀ (j : J), (F.descColimitType c' ∘ ⇑hc.equiv.symm) ∘ c.ι j = c'.ι j",
"ppTerm": "?m.41",
"assigned": true,
"usedConstants": [
"Equiv.instEquivLike",
"congrArg",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Limits.Types.ColimitType | {
"line": 209,
"column": 49
} | {
"line": 209,
"column": 54
} | {
"line": 209,
"column": 54
} | [
{
"pp": "J : Type u\ninst✝ : Category.{v, u} J\nF : J ⥤ Type w₀\nc : F.CoconeTypes\nhc : c.IsColimit\nc' : F.CoconeTypes\n⊢ ∀ (j : J), (F.descColimitType c' ∘ ⇑hc.equiv.symm) ∘ c.ι j = c'.ι j",
"ppTerm": "?m.41",
"assigned": true,
"usedConstants": [
"Equiv.instEquivLike",
"congrArg",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Limits.Types.ColimitType | {
"line": 330,
"column": 10
} | {
"line": 335,
"column": 30
} | {
"line": 335,
"column": 31
} | [
{
"pp": "J : Type u\ninst✝ : Category.{v, u} J\nF : J ⥤ Type w₀\nc : F.CoconeTypes\nhc : c.IsColimitCore\n⊢ Function.RightInverse (hc.down.desc F.coconeTypes) (F.descColimitType c)",
"ppTerm": "?m.38",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Function.comp",
... | [] | have : (F.descColimitType c).comp
((down.{max u w₁} hc).desc F.coconeTypes) = id :=
(down.{max u w₀} hc).funext (fun j ↦ by
rw [Function.id_comp, Function.comp_assoc, fac,
coconeTypes_ι, descColimitType_comp_ι])
exact congr_fun this | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Limits.Types.ColimitType | {
"line": 330,
"column": 10
} | {
"line": 335,
"column": 30
} | {
"line": 335,
"column": 31
} | [
{
"pp": "J : Type u\ninst✝ : Category.{v, u} J\nF : J ⥤ Type w₀\nc : F.CoconeTypes\nhc : c.IsColimitCore\n⊢ Function.RightInverse (hc.down.desc F.coconeTypes) (F.descColimitType c)",
"ppTerm": "?m.38",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Function.comp",
... | [] | have : (F.descColimitType c).comp
((down.{max u w₁} hc).desc F.coconeTypes) = id :=
(down.{max u w₀} hc).funext (fun j ↦ by
rw [Function.id_comp, Function.comp_assoc, fac,
coconeTypes_ι, descColimitType_comp_ι])
exact congr_fun this | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Filtered.Basic | {
"line": 623,
"column": 52
} | {
"line": 623,
"column": 67
} | {
"line": 623,
"column": 67
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nx✝ Y : Discrete PUnit.{u_1 + 1}\n⊢ { as := PUnit.unit }.as = Y.as",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"instSubsingletonPUnit",
"CategoryTheory.Discrete.mk",
"CategoryTheory.Discrete.as",
"PUnit",
"PUn... | [] | by subsingleton | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Filtered.Basic | {
"line": 686,
"column": 2
} | {
"line": 689,
"column": 44
} | {
"line": 691,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : IsCofilteredOrEmpty C\nF : C ⥤ Type u_1\nj : C\nx✝¹ x✝ : (i : C) ×' (i ⟶ j)\ni : C\nij : i ⟶ j\nk : C\nkj : k ⟶ j\n⊢ ∃ z,\n (fun x1 x2 ↦ x1 ⊇ x2) ((fun f ↦ Set.range ⇑(ConcreteCategory.hom (F.map f.snd))) ⟨i, ij⟩)\n ((fun f ↦ Set.range ⇑(Concret... | [] | let ⟨l, li, lk, e⟩ := cospan ij kj
refine ⟨⟨l, lk ≫ kj⟩, e ▸ ?_, ?_⟩ <;>
simp_rw [F.map_comp] <;>
convert! Set.range_comp_subset_range _ _ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Filtered.Basic | {
"line": 686,
"column": 2
} | {
"line": 689,
"column": 44
} | {
"line": 691,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : IsCofilteredOrEmpty C\nF : C ⥤ Type u_1\nj : C\nx✝¹ x✝ : (i : C) ×' (i ⟶ j)\ni : C\nij : i ⟶ j\nk : C\nkj : k ⟶ j\n⊢ ∃ z,\n (fun x1 x2 ↦ x1 ⊇ x2) ((fun f ↦ Set.range ⇑(ConcreteCategory.hom (F.map f.snd))) ⟨i, ij⟩)\n ((fun f ↦ Set.range ⇑(Concret... | [] | let ⟨l, li, lk, e⟩ := cospan ij kj
refine ⟨⟨l, lk ≫ kj⟩, e ▸ ?_, ?_⟩ <;>
simp_rw [F.map_comp] <;>
convert! Set.range_comp_subset_range _ _ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Limits.Types.Colimits | {
"line": 106,
"column": 74
} | {
"line": 106,
"column": 79
} | {
"line": 106,
"column": 79
} | [
{
"pp": "J : Type v\ninst✝¹ : Category.{w, v} J\nF : J ⥤ Type u\ninst✝ : Small.{u, max u v} F.ColimitType\n⊢ ∀ (j : J) (x : F.obj j),\n (F.coconeTypesEquiv.symm (colimitCocone F)).ι j x = (equivShrink F.ColimitType) (F.coconeTypes.ι j x)",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.Limits.Types.Colimits | {
"line": 106,
"column": 74
} | {
"line": 106,
"column": 79
} | {
"line": 106,
"column": 79
} | [
{
"pp": "J : Type v\ninst✝¹ : Category.{w, v} J\nF : J ⥤ Type u\ninst✝ : Small.{u, max u v} F.ColimitType\n⊢ ∀ (j : J) (x : F.obj j),\n (F.coconeTypesEquiv.symm (colimitCocone F)).ι j x = (equivShrink F.ColimitType) (F.coconeTypes.ι j x)",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Limits.Types.Colimits | {
"line": 106,
"column": 74
} | {
"line": 106,
"column": 79
} | {
"line": 106,
"column": 79
} | [
{
"pp": "J : Type v\ninst✝¹ : Category.{w, v} J\nF : J ⥤ Type u\ninst✝ : Small.{u, max u v} F.ColimitType\n⊢ ∀ (j : J) (x : F.obj j),\n (F.coconeTypesEquiv.symm (colimitCocone F)).ι j x = (equivShrink F.ColimitType) (F.coconeTypes.ι j x)",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Filtered.Basic | {
"line": 903,
"column": 6
} | {
"line": 903,
"column": 62
} | {
"line": 904,
"column": 6
} | [
{
"pp": "case refine_2\nC : Type u\ninst✝ : Category.{v, u} C\nh : ∀ {J : Type w} [inst : SmallCategory J] [FinCategory J] (F : J ⥤ C), Nonempty (Cone F)\nthis : Nonempty C\nX Y : C\nf g : X ⟶ Y\nc : Cone (ULiftHom.down ⋙ ULift.downFunctor ⋙ parallelPair f g)\nh₁ :\n ((Functor.const (ULiftHom (ULift.{w, 0} Wal... | [
"case refine_2\nC : Type u\ninst✝ : Category.{v, u} C\nh : ∀ {J : Type w} [inst : SmallCategory J] [FinCategory J] (F : J ⥤ C), Nonempty (Cone F)\nthis : Nonempty C\nX Y : C\nf g : X ⟶ Y\nc : Cone (ULiftHom.down ⋙ ULift.downFunctor ⋙ parallelPair f g)\nh₁ :\n ((Functor.const (ULiftHom (ULift.{w, 0} WalkingParallel... | have h₂ := c.π.naturality ⟨WalkingParallelPairHom.right⟩ | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.CategoryTheory.Limits.Types.Images | {
"line": 120,
"column": 4
} | {
"line": 120,
"column": 29
} | {
"line": 121,
"column": 4
} | [
{
"pp": "case hf\nF : ℕᵒᵖ ⥤ Type u\nc : Cone F\nhc : IsLimit c\nhF : ∀ (n : ℕ), Function.Surjective ⇑(ConcreteCategory.hom (F.map (homOfLE ⋯).op))\ni : c.pt ≅ (limitCone F).pt := ⋯\nthis : c.π.app (Opposite.op 0) = i.hom ≫ (limitCone F).π.app (Opposite.op 0)\n⊢ Function.Surjective ⇑(ConcreteCategory.hom i.hom)"... | [
"case hf\nF : ℕᵒᵖ ⥤ Type u\nc : Cone F\nhc : IsLimit c\nhF : ∀ (n : ℕ), Function.Surjective ⇑(ConcreteCategory.hom (F.map (homOfLE ⋯).op))\ni : c.pt ≅ (limitCone F).pt := hc.conePointUniqueUpToIso (limitConeIsLimit F)\nthis : c.π.app (Opposite.op 0) = i.hom ≫ (limitCone F).π.app (Opposite.op 0)\n⊢ Epi i.hom"
] | rw [← epi_iff_surjective] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.LinearAlgebra.Multilinear.Basic | {
"line": 1367,
"column": 10
} | {
"line": 1367,
"column": 21
} | {
"line": 1367,
"column": 22
} | [
{
"pp": "case neg.inr\nR : Type uR\nι : Type uι\nM₁ : ι → Type v₁\nM₂ : Type v₂\ninst✝⁵ : Semiring R\ninst✝⁴ : (i : ι) → AddCommGroup (M₁ i)\ninst✝³ : AddCommGroup M₂\ninst✝² : (i : ι) → Module R (M₁ i)\ninst✝¹ : Module R M₂\nf : MultilinearMap R M₁ M₂\ninst✝ : LinearOrder ι\na b v : (i : ι) → M₁ i\ns : Finset ... | [
"case neg.inr\nR : Type uR\nι : Type uι\nM₁ : ι → Type v₁\nM₂ : Type v₂\ninst✝⁵ : Semiring R\ninst✝⁴ : (i : ι) → AddCommGroup (M₁ i)\ninst✝³ : AddCommGroup M₂\ninst✝² : (i : ι) → Module R (M₁ i)\ninst✝¹ : Module R M₂\nf : MultilinearMap R M₁ M₂\ninst✝ : LinearOrder ι\na b v : (i : ι) → M₁ i\ns : Finset ι\ni : ι\nhi... | if_neg hij, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.CategoryTheory.Limits.Creates | {
"line": 265,
"column": 8
} | {
"line": 265,
"column": 73
} | {
"line": 266,
"column": 8
} | [
{
"pp": "C : Type u₁\ninst✝³ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝² : Category.{v₂, u₂} D\nJ : Type w\ninst✝¹ : Category.{w', w} J\nK✝ K : J ⥤ C\nF : C ⥤ D\ninst✝ : F.ReflectsIsomorphisms\nh : (c : Cone (K ⋙ F)) → (t : IsLimit c) → LiftsToLimit K F c t\nd : Cone K\nhd : IsLimit (F.mapCone d)\n⊢ IsLimit d",
... | [
"C : Type u₁\ninst✝³ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝² : Category.{v₂, u₂} D\nJ : Type w\ninst✝¹ : Category.{w', w} J\nK✝ K : J ⥤ C\nF : C ⥤ D\ninst✝ : F.ReflectsIsomorphisms\nh : (c : Cone (K ⋙ F)) → (t : IsLimit c) → LiftsToLimit K F c t\nd : Cone K\nhd : IsLimit (F.mapCone d)\nd' : Cone K := (h (F.mapCo... | let d' : Cone K := (h (F.mapCone d) hd).toLiftableCone.liftedCone | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticLet___1 | Lean.Parser.Tactic.tacticLet__ |
Mathlib.CategoryTheory.Limits.Yoneda | {
"line": 113,
"column": 4
} | {
"line": 117,
"column": 19
} | {
"line": 117,
"column": 19
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nJ : Type w\ninst✝ : Category.{t, w} J\nF : J ⥤ Cᵒᵖ\nc : Cone F\nhc : (X : C) → IsLimit ((yoneda.obj X).mapCone c)\ns : Cone F\nm : s.pt ⟶ c.pt\nhm : ∀ (j : J), m ≫ c.π.app j = s.π.app j\n⊢ m.unop = (Quiver.Hom.op ((hom ((hc (unop s.pt)).lift ((yoneda.obj (unop s.... | [] | apply (Types.isLimitEquivSections (hc s.pt.unop)).injective
ext j
have eq := congr_hom ((hc s.pt.unop).fac ((yoneda.obj s.pt.unop).mapCone s) j) (𝟙 (unop s.pt))
dsimp [Types.isLimitEquivSections, Types.sectionOfCone]
simp_all [← hm] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Limits.Yoneda | {
"line": 113,
"column": 4
} | {
"line": 117,
"column": 19
} | {
"line": 117,
"column": 19
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nJ : Type w\ninst✝ : Category.{t, w} J\nF : J ⥤ Cᵒᵖ\nc : Cone F\nhc : (X : C) → IsLimit ((yoneda.obj X).mapCone c)\ns : Cone F\nm : s.pt ⟶ c.pt\nhm : ∀ (j : J), m ≫ c.π.app j = s.π.app j\n⊢ m.unop = (Quiver.Hom.op ((hom ((hc (unop s.pt)).lift ((yoneda.obj (unop s.... | [] | apply (Types.isLimitEquivSections (hc s.pt.unop)).injective
ext j
have eq := congr_hom ((hc s.pt.unop).fac ((yoneda.obj s.pt.unop).mapCone s) j) (𝟙 (unop s.pt))
dsimp [Types.isLimitEquivSections, Types.sectionOfCone]
simp_all [← hm] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Limits.FunctorCategory.Basic | {
"line": 177,
"column": 2
} | {
"line": 178,
"column": 54
} | {
"line": 179,
"column": 2
} | [
{
"pp": "C : Type u\ninst✝⁴ : Category.{v, u} C\nD : Type u'\ninst✝³ : Category.{v', u'} D\nJ : Type u₁\ninst✝² : Category.{v₁, u₁} J\nK : Type u₂\ninst✝¹ : Category.{v₂, u₂} K\ninst✝ : HasColimitsOfShape J C\nF : J ⥤ K ⥤ C\n⊢ IsColimit (pointwiseCocone F)",
"ppTerm": "?m.19",
"assigned": true,
"use... | [
"C : Type u\ninst✝⁴ : Category.{v, u} C\nD : Type u'\ninst✝³ : Category.{v', u'} D\nJ : Type u₁\ninst✝² : Category.{v₁, u₁} J\nK : Type u₂\ninst✝¹ : Category.{v₂, u₂} K\ninst✝ : HasColimitsOfShape J C\nF : J ⥤ K ⥤ C\n⊢ (combineCocones F fun k ↦\n { cocone := colimit.cocone (F.flip.obj k), isColimit := colimit.... | apply IsColimit.ofIsoColimit (combinedIsColimit _
(fun k ↦ ⟨colimit.cocone _, colimit.isColimit _⟩)) | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.CategoryTheory.Adjunction.FullyFaithful | {
"line": 279,
"column": 36
} | {
"line": 289,
"column": 32
} | {
"line": 291,
"column": 0
} | [
{
"pp": "C : Type u₁\ninst✝⁴ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝³ : Category.{v₂, u₂} D\nL : C ⥤ D\nR : D ⥤ C\nh : L ⊣ R\nE : Type u_1\ninst✝² : Category.{v_1, u_1} E\nT : C ⥤ E\nS : E ⥤ D\nX : C\nadj2 : T ⊣ S ⋙ R\ninst✝¹ : R.Faithful\ninst✝ : R.Full\n⊢ IsIso (T.map (h.unit.app X))",
"ppTerm": "?m.53"... | [] | by
let FF := FullyFaithful.ofFullyFaithful R
apply isIso_of_coyoneda_map_bijective
intro Y
convert!
((adj2.homEquiv (R.obj (L.obj X)) Y).trans <|
FF.homEquiv.symm.trans <|
(h.homEquiv X (S.obj Y)).trans (adj2.homEquiv X Y).symm).bijective using 1
ext x
have := adj2.counit_naturality x
... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Monoidal.Preadditive | {
"line": 230,
"column": 2
} | {
"line": 230,
"column": 67
} | {
"line": 231,
"column": 2
} | [
{
"pp": "C : Type u_1\ninst✝⁵ : Category.{v_1, u_1} C\ninst✝⁴ : Preadditive C\ninst✝³ : MonoidalCategory C\ninst✝² : MonoidalPreadditive C\ninst✝¹ : HasFiniteBiproducts C\nJ : Type\ninst✝ : Fintype J\nf : J → C\nX : C\nj✝ : J\n⊢ (rightDistributor f X).hom ≫ biproduct.π (fun j ↦ f j ⊗ X) j✝ =\n (∑ j, biproduc... | [
"C : Type u_1\ninst✝⁵ : Category.{v_1, u_1} C\ninst✝⁴ : Preadditive C\ninst✝³ : MonoidalCategory C\ninst✝² : MonoidalPreadditive C\ninst✝¹ : HasFiniteBiproducts C\nJ : Type\ninst✝ : Fintype J\nf : J → C\nX : C\nj✝ : J\n⊢ (biproduct.lift fun j ↦ biproduct.π f j ▷ X) ≫ biproduct.π (fun j ↦ f j ⊗ X) j✝ =\n (∑ j, bi... | dsimp [rightDistributor, Functor.mapBiproduct, Functor.mapBicone] | Lean.Elab.Tactic.evalDSimp | Lean.Parser.Tactic.dsimp |
Mathlib.CategoryTheory.Monoidal.Preadditive | {
"line": 241,
"column": 2
} | {
"line": 241,
"column": 67
} | {
"line": 242,
"column": 2
} | [
{
"pp": "C : Type u_1\ninst✝⁵ : Category.{v_1, u_1} C\ninst✝⁴ : Preadditive C\ninst✝³ : MonoidalCategory C\ninst✝² : MonoidalPreadditive C\ninst✝¹ : HasFiniteBiproducts C\nJ : Type\ninst✝ : Fintype J\nf : J → C\nX : C\nj✝ : J\n⊢ biproduct.ι (fun j ↦ f j ⊗ X) j✝ ≫ (rightDistributor f X).inv =\n biproduct.ι (f... | [
"C : Type u_1\ninst✝⁵ : Category.{v_1, u_1} C\ninst✝⁴ : Preadditive C\ninst✝³ : MonoidalCategory C\ninst✝² : MonoidalPreadditive C\ninst✝¹ : HasFiniteBiproducts C\nJ : Type\ninst✝ : Fintype J\nf : J → C\nX : C\nj✝ : J\n⊢ (biproduct.ι (fun j ↦ f j ⊗ X) j✝ ≫ biproduct.desc fun j ↦ biproduct.ι f j ▷ X) =\n biproduc... | dsimp [rightDistributor, Functor.mapBiproduct, Functor.mapBicone] | Lean.Elab.Tactic.evalDSimp | Lean.Parser.Tactic.dsimp |
Mathlib.CategoryTheory.Monoidal.Preadditive | {
"line": 282,
"column": 2
} | {
"line": 286,
"column": 29
} | {
"line": 287,
"column": 2
} | [
{
"pp": "case intro\nC : Type u_1\ninst✝⁵ : Category.{v_1, u_1} C\ninst✝⁴ : Preadditive C\ninst✝³ : MonoidalCategory C\ninst✝² : MonoidalPreadditive C\ninst✝¹ : HasFiniteBiproducts C\nJ : Type\ninst✝ : Finite J\nf : J → C\nX Y : C\nval✝ : Fintype J\nj✝ : J\n⊢ ((rightDistributor f X ⊗ᵢ asIso (𝟙 Y)) ≪≫ rightDist... | [
"case intro\nC : Type u_1\ninst✝⁵ : Category.{v_1, u_1} C\ninst✝⁴ : Preadditive C\ninst✝³ : MonoidalCategory C\ninst✝² : MonoidalPreadditive C\ninst✝¹ : HasFiniteBiproducts C\nJ : Type\ninst✝ : Finite J\nf : J → C\nX Y : C\nval✝ : Fintype J\nj✝ : J\n⊢ ∑ x, (biproduct.π f x ▷ X ⊗ₘ 𝟙 Y) ≫ (biproduct.ι (fun j ↦ f j ⊗... | simp only [Category.comp_id, Category.assoc, eqToHom_refl, Iso.symm_hom, Iso.trans_hom,
asIso_hom, comp_zero, comp_dite, Preadditive.sum_comp, Preadditive.comp_sum, sum_tensor,
comp_tensor_id, tensorIso_hom, rightDistributor_hom, biproduct.mapIso_hom, biproduct.ι_map,
biproduct.ι_π, Finset.sum_dite_irrel, F... | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Tactic.CategoryTheory.Monoidal.PureCoherence | {
"line": 70,
"column": 6
} | {
"line": 70,
"column": 12
} | {
"line": 70,
"column": 12
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : MonoidalCategory C\np f g h pf pfg : C\nη : g ≅ h\nη_f : p ⊗ f ≅ pf\nη_fg : pf ⊗ g ≅ pfg\nη_fh : pf ⊗ h ≅ pfg\nih_η : pf ◁ η ≪≫ η_fh = η_fg\n⊢ p ◁ f ◁ η ≪≫ normalizeIsoComp η_f η_fh = normalizeIsoComp η_f η_fg",
"ppTerm": "?m.62",
"assigned": true... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : MonoidalCategory C\np f g h pf pfg : C\nη : g ≅ h\nη_f : p ⊗ f ≅ pf\nη_fg : pf ⊗ g ≅ pfg\nη_fh : pf ⊗ h ≅ pfg\nih_η : pf ◁ η ≪≫ η_fh = η_fg\n⊢ p ◁ f ◁ η ≪≫ normalizeIsoComp η_f η_fh = normalizeIsoComp η_f (pf ◁ η ≪≫ η_fh)"
] | ← ih_η | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Tactic.CategoryTheory.Monoidal.PureCoherence | {
"line": 78,
"column": 6
} | {
"line": 78,
"column": 12
} | {
"line": 78,
"column": 12
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : MonoidalCategory C\np f g h pf pfh : C\nη : f ≅ g\nη_f : p ⊗ f ≅ pf\nη_g : p ⊗ g ≅ pf\nη_fh : pf ⊗ h ≅ pfh\nih_η : p ◁ η ≪≫ η_g = η_f\n⊢ p ◁ η ▷ h ≪≫ normalizeIsoComp η_g η_fh = normalizeIsoComp η_f η_fh",
"ppTerm": "?m.62",
"assigned": true,
... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : MonoidalCategory C\np f g h pf pfh : C\nη : f ≅ g\nη_f : p ⊗ f ≅ pf\nη_g : p ⊗ g ≅ pf\nη_fh : pf ⊗ h ≅ pfh\nih_η : p ◁ η ≪≫ η_g = η_f\n⊢ p ◁ η ▷ h ≪≫ normalizeIsoComp η_g η_fh = normalizeIsoComp (p ◁ η ≪≫ η_g) η_fh"
] | ← ih_η | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.CategoryTheory.Monoidal.Functor | {
"line": 323,
"column": 2
} | {
"line": 323,
"column": 62
} | {
"line": 325,
"column": 0
} | [
{
"pp": "C : Type u₁\ninst✝⁴ : Category.{v₁, u₁} C\ninst✝³ : MonoidalCategory C\nD : Type u₂\ninst✝² : Category.{v₂, u₂} D\ninst✝¹ : MonoidalCategory D\nF : C ⥤ D\ninst✝ : F.OplaxMonoidal\nX Y Z : C\n⊢ δ F (X ⊗ Y) Z ≫ δ F X Y ▷ F.obj Z =\n F.map (α_ X Y Z).hom ≫ δ F X (Y ⊗ Z) ≫ F.obj X ◁ δ F Y Z ≫ (α_ (F.obj... | [] | rw [← associativity_assoc, Iso.hom_inv_id, Category.comp_id] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.CategoryTheory.Monoidal.Functor | {
"line": 323,
"column": 2
} | {
"line": 323,
"column": 62
} | {
"line": 325,
"column": 0
} | [
{
"pp": "C : Type u₁\ninst✝⁴ : Category.{v₁, u₁} C\ninst✝³ : MonoidalCategory C\nD : Type u₂\ninst✝² : Category.{v₂, u₂} D\ninst✝¹ : MonoidalCategory D\nF : C ⥤ D\ninst✝ : F.OplaxMonoidal\nX Y Z : C\n⊢ δ F (X ⊗ Y) Z ≫ δ F X Y ▷ F.obj Z =\n F.map (α_ X Y Z).hom ≫ δ F X (Y ⊗ Z) ≫ F.obj X ◁ δ F Y Z ≫ (α_ (F.obj... | [] | rw [← associativity_assoc, Iso.hom_inv_id, Category.comp_id] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Monoidal.Functor | {
"line": 323,
"column": 2
} | {
"line": 323,
"column": 62
} | {
"line": 325,
"column": 0
} | [
{
"pp": "C : Type u₁\ninst✝⁴ : Category.{v₁, u₁} C\ninst✝³ : MonoidalCategory C\nD : Type u₂\ninst✝² : Category.{v₂, u₂} D\ninst✝¹ : MonoidalCategory D\nF : C ⥤ D\ninst✝ : F.OplaxMonoidal\nX Y Z : C\n⊢ δ F (X ⊗ Y) Z ≫ δ F X Y ▷ F.obj Z =\n F.map (α_ X Y Z).hom ≫ δ F X (Y ⊗ Z) ≫ F.obj X ◁ δ F Y Z ≫ (α_ (F.obj... | [] | rw [← associativity_assoc, Iso.hom_inv_id, Category.comp_id] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Monoidal.Functor | {
"line": 648,
"column": 49
} | {
"line": 648,
"column": 83
} | {
"line": 649,
"column": 6
} | [
{
"pp": "C : Type u₁\ninst✝⁶ : Category.{v₁, u₁} C\ninst✝⁵ : MonoidalCategory C\nD : Type u₂\ninst✝⁴ : Category.{v₂, u₂} D\ninst✝³ : MonoidalCategory D\nE : Type u₃\ninst✝² : Category.{v₃, u₃} E\ninst✝¹ : MonoidalCategory E\nC' : Type u₁'\ninst✝ : Category.{v₁', u₁'} C'\nF : C ⥤ D\nεIso : 𝟙_ D ≅ F.obj (𝟙_ C)\... | [
"C : Type u₁\ninst✝⁶ : Category.{v₁, u₁} C\ninst✝⁵ : MonoidalCategory C\nD : Type u₂\ninst✝⁴ : Category.{v₂, u₂} D\ninst✝³ : MonoidalCategory D\nE : Type u₃\ninst✝² : Category.{v₃, u₃} E\ninst✝¹ : MonoidalCategory E\nC' : Type u₁'\ninst✝ : Category.{v₁', u₁'} C'\nF : C ⥤ D\nεIso : 𝟙_ D ≅ F.obj (𝟙_ C)\nμIso : (X Y... | ← cancel_epi (μIso (X ⊗ Y) Z).inv, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.CategoryTheory.Monoidal.Braided.Basic | {
"line": 94,
"column": 2
} | {
"line": 94,
"column": 38
} | {
"line": 95,
"column": 2
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : MonoidalCategory C\ninst✝ : BraidedCategory C\nX Y Z : C\n⊢ (α_ X Y Z).inv ≫ (β_ (X ⊗ Y) Z).hom =\n (α_ X Y Z).inv ≫ (α_ X Y Z).hom ≫ X ◁ (β_ Y Z).hom ≫ (α_ X Z Y).inv ≫ (β_ X Z).hom ▷ Y ≫ (α_ Z X Y).hom",
"ppTerm": "?m.101",
"assigned": true,... | [
"C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : MonoidalCategory C\ninst✝ : BraidedCategory C\nX Y Z : C\n⊢ ((α_ X Y Z).inv ≫ (β_ (X ⊗ Y) Z).hom) ≫ (α_ Z X Y).inv =\n ((α_ X Y Z).inv ≫ (α_ X Y Z).hom ≫ X ◁ (β_ Y Z).hom ≫ (α_ X Z Y).inv ≫ (β_ X Z).hom ▷ Y ≫ (α_ Z X Y).hom) ≫\n (α_ Z X Y).inv"
] | apply (cancel_mono (α_ Z X Y).inv).1 | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.CategoryTheory.MorphismProperty.Concrete | {
"line": 56,
"column": 4
} | {
"line": 56,
"column": 9
} | {
"line": 57,
"column": 2
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\nFC : C → C → Type u_1\nCC : C → Type u_2\ninst✝¹ : (X Y : C) → FunLike (FC X Y) (CC X) (CC Y)\ninst✝ : ConcreteCategory C FC\nX : C\n⊢ ⇑(ConcreteCategory.hom (𝟙 X)) = id",
"ppTerm": "?m.82",
"assigned": true,
"usedConstants": [
"congrArg",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.MorphismProperty.Concrete | {
"line": 66,
"column": 4
} | {
"line": 66,
"column": 9
} | {
"line": 67,
"column": 2
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\nFC : C → C → Type u_1\nCC : C → Type u_2\ninst✝¹ : (X Y : C) → FunLike (FC X Y) (CC X) (CC Y)\ninst✝ : ConcreteCategory C FC\nX : C\n⊢ ⇑(ConcreteCategory.hom (𝟙 X)) = id",
"ppTerm": "?m.82",
"assigned": true,
"usedConstants": [
"congrArg",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.MorphismProperty.Concrete | {
"line": 76,
"column": 4
} | {
"line": 76,
"column": 9
} | {
"line": 77,
"column": 2
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\nFC : C → C → Type u_1\nCC : C → Type u_2\ninst✝¹ : (X Y : C) → FunLike (FC X Y) (CC X) (CC Y)\ninst✝ : ConcreteCategory C FC\nX : C\n⊢ ⇑(ConcreteCategory.hom (𝟙 X)) = id",
"ppTerm": "?m.82",
"assigned": true,
"usedConstants": [
"congrArg",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.ConcreteCategory.EpiMono | {
"line": 106,
"column": 4
} | {
"line": 106,
"column": 29
} | {
"line": 107,
"column": 4
} | [
{
"pp": "case mpr\nC : Type u\ninst✝² : Category.{v, u} C\nFC : C → C → Type u_1\nCC : C → Type w\ninst✝¹ : (X Y : C) → FunLike (FC X Y) (CC X) (CC Y)\ninst✝ : ConcreteCategory C FC\na✝ : (forget C).PreservesEpimorphisms\nX✝ Y✝ : C\nf : X✝ ⟶ Y✝\nhf : epimorphisms C f\nthis : Epi f\n⊢ Function.Surjective ⇑(hom (... | [
"case mpr\nC : Type u\ninst✝² : Category.{v, u} C\nFC : C → C → Type u_1\nCC : C → Type w\ninst✝¹ : (X Y : C) → FunLike (FC X Y) (CC X) (CC Y)\ninst✝ : ConcreteCategory C FC\na✝ : (forget C).PreservesEpimorphisms\nX✝ Y✝ : C\nf : X✝ ⟶ Y✝\nhf : epimorphisms C f\nthis : Epi f\n⊢ Epi ((forget C).map f)"
] | rw [← epi_iff_surjective] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.CategoryTheory.Monoidal.Braided.Basic | {
"line": 678,
"column": 4
} | {
"line": 678,
"column": 28
} | {
"line": 678,
"column": 28
} | [
{
"pp": "case a.a.a.a\nC : Type u₁\ninst✝² : Category.{v₁, u₁} C\ninst✝¹ : MonoidalCategory C\ninst✝ : BraidedCategory C\nX₁ X₂ : C\n| X₁ ◁ ((ρ_ X₂).inv ≫ (β_ X₂ (𝟙_ C)).hom) ▷ 𝟙_ C",
"ppTerm": "?a.a.a.a",
"assigned": true,
"usedConstants": [
"CategoryTheory.MonoidalCategoryStruct.whiskerLef... | [
"case a.a.a.a\nC : Type u₁\ninst✝² : Category.{v₁, u₁} C\ninst✝¹ : MonoidalCategory C\ninst✝ : BraidedCategory C\nX₁ X₂ : C\n| X₁ ◁ (λ_ X₂).inv ▷ 𝟙_ C",
"case a.a.a.a\nC : Type u₁\ninst✝² : Category.{v₁, u₁} C\ninst✝¹ : MonoidalCategory C\ninst✝ : BraidedCategory C\nX₁ X₂ : C\n| X₁ ◁ (α_ (𝟙_ C) X₂ (𝟙_ C)).hom"... | rightUnitor_inv_braiding | Lean.Elab.Tactic.Conv.evalRewrite | null |
Mathlib.CategoryTheory.Monoidal.Functor | {
"line": 1309,
"column": 8
} | {
"line": 1309,
"column": 27
} | {
"line": 1309,
"column": 28
} | [
{
"pp": "C : Type u₁\ninst✝⁷ : Category.{v₁, u₁} C\ninst✝⁶ : MonoidalCategory C\nD : Type u₂\ninst✝⁵ : Category.{v₂, u₂} D\ninst✝⁴ : MonoidalCategory D\nE : Type u₃\ninst✝³ : Category.{v₃, u₃} E\ninst✝² : MonoidalCategory E\nC' : Type u₁'\ninst✝¹ : Category.{v₁', u₁'} C'\nF G : C ⥤ D\ninst✝ : F.Monoidal\ni : F ... | [
"C : Type u₁\ninst✝⁷ : Category.{v₁, u₁} C\ninst✝⁶ : MonoidalCategory C\nD : Type u₂\ninst✝⁵ : Category.{v₂, u₂} D\ninst✝⁴ : MonoidalCategory D\nE : Type u₃\ninst✝³ : Category.{v₃, u₃} E\ninst✝² : MonoidalCategory E\nC' : Type u₁'\ninst✝¹ : Category.{v₁', u₁'} C'\nF G : C ⥤ D\ninst✝ : F.Monoidal\ni : F ≅ G\nX Y Z :... | ← i.hom.naturality, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.CategoryTheory.Monoidal.Functor | {
"line": 1326,
"column": 8
} | {
"line": 1326,
"column": 27
} | {
"line": 1326,
"column": 28
} | [
{
"pp": "C : Type u₁\ninst✝⁷ : Category.{v₁, u₁} C\ninst✝⁶ : MonoidalCategory C\nD : Type u₂\ninst✝⁵ : Category.{v₂, u₂} D\ninst✝⁴ : MonoidalCategory D\nE : Type u₃\ninst✝³ : Category.{v₃, u₃} E\ninst✝² : MonoidalCategory E\nC' : Type u₁'\ninst✝¹ : Category.{v₁', u₁'} C'\nF G : C ⥤ D\ninst✝ : F.Monoidal\ni : F ... | [
"C : Type u₁\ninst✝⁷ : Category.{v₁, u₁} C\ninst✝⁶ : MonoidalCategory C\nD : Type u₂\ninst✝⁵ : Category.{v₂, u₂} D\ninst✝⁴ : MonoidalCategory D\nE : Type u₃\ninst✝³ : Category.{v₃, u₃} E\ninst✝² : MonoidalCategory E\nC' : Type u₁'\ninst✝¹ : Category.{v₁', u₁'} C'\nF G : C ⥤ D\ninst✝ : F.Monoidal\ni : F ≅ G\nX : C\n... | ← i.hom.naturality, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.CategoryTheory.Monoidal.Functor | {
"line": 1333,
"column": 8
} | {
"line": 1333,
"column": 27
} | {
"line": 1333,
"column": 28
} | [
{
"pp": "C : Type u₁\ninst✝⁷ : Category.{v₁, u₁} C\ninst✝⁶ : MonoidalCategory C\nD : Type u₂\ninst✝⁵ : Category.{v₂, u₂} D\ninst✝⁴ : MonoidalCategory D\nE : Type u₃\ninst✝³ : Category.{v₃, u₃} E\ninst✝² : MonoidalCategory E\nC' : Type u₁'\ninst✝¹ : Category.{v₁', u₁'} C'\nF G : C ⥤ D\ninst✝ : F.Monoidal\ni : F ... | [
"C : Type u₁\ninst✝⁷ : Category.{v₁, u₁} C\ninst✝⁶ : MonoidalCategory C\nD : Type u₂\ninst✝⁵ : Category.{v₂, u₂} D\ninst✝⁴ : MonoidalCategory D\nE : Type u₃\ninst✝³ : Category.{v₃, u₃} E\ninst✝² : MonoidalCategory E\nC' : Type u₁'\ninst✝¹ : Category.{v₁', u₁'} C'\nF G : C ⥤ D\ninst✝ : F.Monoidal\ni : F ≅ G\nX : C\n... | ← i.hom.naturality, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.RingTheory.Congruence.Hom | {
"line": 198,
"column": 23
} | {
"line": 198,
"column": 28
} | {
"line": 198,
"column": 28
} | [
{
"pp": "M : Type u_1\nP : Type u_3\ninst✝¹ : NonAssocSemiring M\ninst✝ : NonAssocSemiring P\nc : RingCon M\nf : M →+* P\nH : c ≤ ker f\ng : c.Quotient →+* P\nHg : g.comp c.mk' = f\n⊢ g.comp c.mk' = (c.lift f H).comp c.mk'",
"ppTerm": "?m.41",
"assigned": true,
"usedConstants": [
"RingHom",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.RingTheory.Congruence.Hom | {
"line": 198,
"column": 23
} | {
"line": 198,
"column": 28
} | {
"line": 198,
"column": 28
} | [
{
"pp": "M : Type u_1\nP : Type u_3\ninst✝¹ : NonAssocSemiring M\ninst✝ : NonAssocSemiring P\nc : RingCon M\nf : M →+* P\nH : c ≤ ker f\ng : c.Quotient →+* P\nHg : g.comp c.mk' = f\n⊢ g.comp c.mk' = (c.lift f H).comp c.mk'",
"ppTerm": "?m.41",
"assigned": true,
"usedConstants": [
"RingHom",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.RingTheory.Congruence.Hom | {
"line": 198,
"column": 23
} | {
"line": 198,
"column": 28
} | {
"line": 198,
"column": 28
} | [
{
"pp": "M : Type u_1\nP : Type u_3\ninst✝¹ : NonAssocSemiring M\ninst✝ : NonAssocSemiring P\nc : RingCon M\nf : M →+* P\nH : c ≤ ker f\ng : c.Quotient →+* P\nHg : g.comp c.mk' = f\n⊢ g.comp c.mk' = (c.lift f H).comp c.mk'",
"ppTerm": "?m.41",
"assigned": true,
"usedConstants": [
"RingHom",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.Coalgebra.Basic | {
"line": 257,
"column": 2
} | {
"line": 258,
"column": 76
} | {
"line": 259,
"column": 2
} | [
{
"pp": "case hl\nR : Type u\nA : Type v\nB : Type w\ninst✝⁶ : CommSemiring R\ninst✝⁵ : AddCommMonoid A\ninst✝⁴ : AddCommMonoid B\ninst✝³ : Module R A\ninst✝² : Module R B\ninst✝¹ : Coalgebra R A\ninst✝ : Coalgebra R B\n⊢ (comul ∘ₗ LinearMap.fst R A B) ∘ₗ inl R A B =\n (TensorProduct.map (LinearMap.fst R A B... | [
"case hr\nR : Type u\nA : Type v\nB : Type w\ninst✝⁶ : CommSemiring R\ninst✝⁵ : AddCommMonoid A\ninst✝⁴ : AddCommMonoid B\ninst✝³ : Module R A\ninst✝² : Module R B\ninst✝¹ : Coalgebra R A\ninst✝ : Coalgebra R B\n⊢ (comul ∘ₗ LinearMap.fst R A B) ∘ₗ inr R A B =\n (TensorProduct.map (LinearMap.fst R A B) (LinearMap... | · rw [comp_assoc, fst_comp_inl, comp_id, comp_assoc, comul_comp_inl, ← comp_assoc,
← TensorProduct.map_comp, fst_comp_inl, TensorProduct.map_id, id_comp] | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Algebra.TrivSqZeroExt.Basic | {
"line": 716,
"column": 2
} | {
"line": 716,
"column": 15
} | {
"line": 717,
"column": 2
} | [
{
"pp": "R : Type u\nM : Type v\ninst✝³ : AddCommGroup M\ninst✝² : Semiring R\ninst✝¹ : Module Rᵐᵒᵖ M\ninst✝ : Module R M\nr : R\nx : tsze R M\nh : r * x.fst = 1\n⊢ (inl r + inr (-(r •> x.snd <• r))) * x = 1",
"ppTerm": "?m.46",
"assigned": true,
"usedConstants": [
"TrivSqZeroExt.one",
"... | [
"case h1\nR : Type u\nM : Type v\ninst✝³ : AddCommGroup M\ninst✝² : Semiring R\ninst✝¹ : Module Rᵐᵒᵖ M\ninst✝ : Module R M\nr : R\nx : tsze R M\nh : r * x.fst = 1\n⊢ (r + 0) * x.fst = 1",
"case h2\nR : Type u\nM : Type v\ninst✝³ : AddCommGroup M\ninst✝² : Semiring R\ninst✝¹ : Module Rᵐᵒᵖ M\ninst✝ : Module R M\nr ... | ext <;> dsimp | Lean.Parser.Tactic.«_aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tactic_<;>__1» | Lean.Parser.Tactic.«tactic_<;>_» |
Mathlib.Algebra.TrivSqZeroExt.Basic | {
"line": 723,
"column": 2
} | {
"line": 723,
"column": 15
} | {
"line": 724,
"column": 2
} | [
{
"pp": "R : Type u\nM : Type v\ninst✝³ : AddCommGroup M\ninst✝² : Semiring R\ninst✝¹ : Module Rᵐᵒᵖ M\ninst✝ : Module R M\nx : tsze R M\nr : R\nh : x.fst * r = 1\n⊢ x * (inl r + inr (-(r •> (x.snd <• r)))) = 1",
"ppTerm": "?m.46",
"assigned": true,
"usedConstants": [
"TrivSqZeroExt.one",
... | [
"case h1\nR : Type u\nM : Type v\ninst✝³ : AddCommGroup M\ninst✝² : Semiring R\ninst✝¹ : Module Rᵐᵒᵖ M\ninst✝ : Module R M\nx : tsze R M\nr : R\nh : x.fst * r = 1\n⊢ x.fst * (r + 0) = 1",
"case h2\nR : Type u\nM : Type v\ninst✝³ : AddCommGroup M\ninst✝² : Semiring R\ninst✝¹ : Module Rᵐᵒᵖ M\ninst✝ : Module R M\nx ... | ext <;> dsimp | Lean.Parser.Tactic.«_aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tactic_<;>__1» | Lean.Parser.Tactic.«tactic_<;>_» |
Mathlib.CategoryTheory.Adjunction.Unique | {
"line": 67,
"column": 6
} | {
"line": 67,
"column": 31
} | {
"line": 67,
"column": 32
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Category.{v_2, u_2} D\nF F' : C ⥤ D\nG : D ⥤ C\nadj1 : F ⊣ G\nadj2 : F' ⊣ G\nx : D\n⊢ F.map (adj2.unit.app (G.obj x)) ≫ adj1.counit.app (F'.obj (G.obj x)) ≫ adj2.counit.app x = adj1.counit.app x",
"ppTerm": "?m.69",
"assigned":... | [
"C : Type u_1\nD : Type u_2\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Category.{v_2, u_2} D\nF F' : C ⥤ D\nG : D ⥤ C\nadj1 : F ⊣ G\nadj2 : F' ⊣ G\nx : D\n⊢ F.map (adj2.unit.app (G.obj x)) ≫ F.map (G.map (adj2.counit.app x)) ≫ adj1.counit.app x = adj1.counit.app x"
] | ← adj1.counit_naturality, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Order.Category.BddOrd | {
"line": 176,
"column": 19
} | {
"line": 176,
"column": 50
} | {
"line": 177,
"column": 2
} | [
{
"pp": "α β : BddOrd\ne : ↑α.toPartOrd ≃o ↑β.toPartOrd\n⊢ ofHom ↑e ≫ ofHom ↑e.symm = 𝟙 α",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"PartOrd.str",
"BddOrd.Hom.hom",
"PartialOrder.toPreorder",
"Preorder.toLE",
"BddOrd.toPartOrd",
"CategoryTheory.Ca... | [] | ext; exact e.symm_apply_apply _ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Category.BddOrd | {
"line": 176,
"column": 19
} | {
"line": 176,
"column": 50
} | {
"line": 177,
"column": 2
} | [
{
"pp": "α β : BddOrd\ne : ↑α.toPartOrd ≃o ↑β.toPartOrd\n⊢ ofHom ↑e ≫ ofHom ↑e.symm = 𝟙 α",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"PartOrd.str",
"BddOrd.Hom.hom",
"PartialOrder.toPreorder",
"Preorder.toLE",
"BddOrd.toPartOrd",
"CategoryTheory.Ca... | [] | ext; exact e.symm_apply_apply _ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Category.Semilat | {
"line": 128,
"column": 19
} | {
"line": 128,
"column": 50
} | {
"line": 129,
"column": 2
} | [
{
"pp": "α β : SemilatSupCat\ne : α.X ≃o β.X\n⊢ { toFun := ⇑e, map_sup' := ⋯, map_bot' := ⋯ } ≫ { toFun := ⇑e.symm, map_sup' := ⋯, map_bot' := ⋯ } = 𝟙 α",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"SemilatSupCat.X",
"SemilatSupCat.isSemilatticeSup",
"SupBotHom.ext",
... | [] | ext; exact e.symm_apply_apply _ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Category.Semilat | {
"line": 128,
"column": 19
} | {
"line": 128,
"column": 50
} | {
"line": 129,
"column": 2
} | [
{
"pp": "α β : SemilatSupCat\ne : α.X ≃o β.X\n⊢ { toFun := ⇑e, map_sup' := ⋯, map_bot' := ⋯ } ≫ { toFun := ⇑e.symm, map_sup' := ⋯, map_bot' := ⋯ } = 𝟙 α",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"SemilatSupCat.X",
"SemilatSupCat.isSemilatticeSup",
"SupBotHom.ext",
... | [] | ext; exact e.symm_apply_apply _ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Category.Semilat | {
"line": 146,
"column": 19
} | {
"line": 146,
"column": 50
} | {
"line": 147,
"column": 2
} | [
{
"pp": "α β : SemilatInfCat\ne : α.X ≃o β.X\n⊢ { toFun := ⇑e, map_inf' := ⋯, map_top' := ⋯ } ≫ { toFun := ⇑e.symm, map_inf' := ⋯, map_top' := ⋯ } = 𝟙 α",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"InfTopHom.ext",
"SemilatInfCat.isOrderTop",
"CategoryTheory.ConcreteC... | [] | ext; exact e.symm_apply_apply _ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Category.Semilat | {
"line": 146,
"column": 19
} | {
"line": 146,
"column": 50
} | {
"line": 147,
"column": 2
} | [
{
"pp": "α β : SemilatInfCat\ne : α.X ≃o β.X\n⊢ { toFun := ⇑e, map_inf' := ⋯, map_top' := ⋯ } ≫ { toFun := ⇑e.symm, map_inf' := ⋯, map_top' := ⋯ } = 𝟙 α",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"InfTopHom.ext",
"SemilatInfCat.isOrderTop",
"CategoryTheory.ConcreteC... | [] | ext; exact e.symm_apply_apply _ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Category.BddLat | {
"line": 169,
"column": 19
} | {
"line": 169,
"column": 50
} | {
"line": 170,
"column": 2
} | [
{
"pp": "α β : BddLat\ne : ↑α.toLat ≃o ↑β.toLat\n⊢ ofHom\n (let __src := { toFun := ⇑e, map_sup' := ⋯, map_inf' := ⋯ };\n { toFun := ⇑e, map_sup' := ⋯, map_inf' := ⋯, map_top' := ⋯, map_bot' := ⋯ }) ≫\n ofHom\n (let __src := { toFun := ⇑e.symm, map_sup' := ⋯, map_inf' := ⋯ };\n ... | [] | ext; exact e.symm_apply_apply _ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Category.BddLat | {
"line": 169,
"column": 19
} | {
"line": 169,
"column": 50
} | {
"line": 170,
"column": 2
} | [
{
"pp": "α β : BddLat\ne : ↑α.toLat ≃o ↑β.toLat\n⊢ ofHom\n (let __src := { toFun := ⇑e, map_sup' := ⋯, map_inf' := ⋯ };\n { toFun := ⇑e, map_sup' := ⋯, map_inf' := ⋯, map_top' := ⋯, map_bot' := ⋯ }) ≫\n ofHom\n (let __src := { toFun := ⇑e.symm, map_sup' := ⋯, map_inf' := ⋯ };\n ... | [] | ext; exact e.symm_apply_apply _ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Category.HeytAlg | {
"line": 162,
"column": 19
} | {
"line": 162,
"column": 50
} | {
"line": 163,
"column": 2
} | [
{
"pp": "α β : HeytAlg\ne : ↑α ≃o ↑β\n⊢ ofHom { toFun := ⇑e, map_sup' := ⋯, map_inf' := ⋯, map_bot' := ⋯, map_himp' := ⋯ } ≫\n ofHom { toFun := ⇑e.symm, map_sup' := ⋯, map_inf' := ⋯, map_bot' := ⋯, map_himp' := ⋯ } =\n 𝟙 α",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Hey... | [] | ext; exact e.symm_apply_apply _ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Category.HeytAlg | {
"line": 162,
"column": 19
} | {
"line": 162,
"column": 50
} | {
"line": 163,
"column": 2
} | [
{
"pp": "α β : HeytAlg\ne : ↑α ≃o ↑β\n⊢ ofHom { toFun := ⇑e, map_sup' := ⋯, map_inf' := ⋯, map_bot' := ⋯, map_himp' := ⋯ } ≫\n ofHom { toFun := ⇑e.symm, map_sup' := ⋯, map_inf' := ⋯, map_bot' := ⋯, map_himp' := ⋯ } =\n 𝟙 α",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Hey... | [] | ext; exact e.symm_apply_apply _ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Category.BoolRing | {
"line": 100,
"column": 19
} | {
"line": 100,
"column": 50
} | {
"line": 101,
"column": 2
} | [
{
"pp": "α β : BoolRing\ne : ↑α ≃+* ↑β\n⊢ { hom' := ↑e } ≫ { hom' := ↑e.symm } = 𝟙 α",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"BoolRing.carrier",
"CommSemiring.toSemiring",
"RingEquiv.instEquivLike",
"BoolRing.hom_ext",
"RingEquiv.instRingEquivClass",
... | [] | ext; exact e.symm_apply_apply _ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Category.BoolRing | {
"line": 100,
"column": 19
} | {
"line": 100,
"column": 50
} | {
"line": 101,
"column": 2
} | [
{
"pp": "α β : BoolRing\ne : ↑α ≃+* ↑β\n⊢ { hom' := ↑e } ≫ { hom' := ↑e.symm } = 𝟙 α",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"BoolRing.carrier",
"CommSemiring.toSemiring",
"RingEquiv.instEquivLike",
"BoolRing.hom_ext",
"RingEquiv.instRingEquivClass",
... | [] | ext; exact e.symm_apply_apply _ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Monoidal.Comon_ | {
"line": 257,
"column": 8
} | {
"line": 257,
"column": 28
} | {
"line": 257,
"column": 29
} | [
{
"pp": "C : Type u₁\ninst✝⁴ : Category.{v₁, u₁} C\ninst✝³ : MonoidalCategory C\nM N O : C\ninst✝² : ComonObj M\ninst✝¹ : ComonObj N\ninst✝ : ComonObj O\nA : Comon C\n⊢ Δ.op ▷ op A.X ≫ Δ.op = (α_ (op A.X) (op A.X) (op A.X)).hom ≫ op A.X ◁ Δ.op ≫ Δ.op",
"ppTerm": "?m.95",
"assigned": true,
"usedConst... | [
"C : Type u₁\ninst✝⁴ : Category.{v₁, u₁} C\ninst✝³ : MonoidalCategory C\nM N O : C\ninst✝² : ComonObj M\ninst✝¹ : ComonObj N\ninst✝ : ComonObj O\nA : Comon C\n⊢ Δ.op ▷ op A.X ≫ Δ.op = (α_ A.X A.X A.X).inv.op ≫ op A.X ◁ Δ.op ≫ Δ.op"
] | ← op_inv_associator, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.RingTheory.Localization.Away.Basic | {
"line": 220,
"column": 4
} | {
"line": 220,
"column": 46
} | {
"line": 221,
"column": 4
} | [
{
"pp": "R : Type u_1\ninst✝⁷ : CommSemiring R\nP : Type u_3\ninst✝⁶ : CommSemiring P\nQ : Type u_4\ninst✝⁵ : CommSemiring Q\ninst✝⁴ : Algebra P Q\nS : Type u_5\ninst✝³ : CommRing S\ninst✝² : Algebra R S\nf : R →+* P\nr : R\ninst✝¹ : Away r S\ninst✝ : Away (f r) Q\nH : ∀ (a : R), f a = 0 → ∃ n, r ^ n * a = 0\na... | [
"R : Type u_1\ninst✝⁷ : CommSemiring R\nP : Type u_3\ninst✝⁶ : CommSemiring P\nQ : Type u_4\ninst✝⁵ : CommSemiring Q\ninst✝⁴ : Algebra P Q\nS : Type u_5\ninst✝³ : CommRing S\ninst✝² : Algebra R S\nf : R →+* P\nr : R\ninst✝¹ : Away r S\ninst✝ : Away (f r) Q\nH : ∀ (a : R), f a = 0 → ∃ n, r ^ n * a = 0\na : R\nn : ℕ\... | obtain ⟨m, hm⟩ := H (r ^ n * a) (by simpa) | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.RingTheory.TwoSidedIdeal.Operations | {
"line": 71,
"column": 2
} | {
"line": 71,
"column": 38
} | {
"line": 72,
"column": 2
} | [
{
"pp": "R : Type u_1\ninst✝ : NonUnitalNonAssocRing R\ns : Set R\nx : R\nh : x ∈ { ringCon := sInf {s_1 | ∀ (x y : R), x - y ∈ s → s_1 x y} }\nI : TwoSidedIdeal R\nhI : s ⊆ ↑I\n⊢ x ∈ I",
"ppTerm": "?m.32",
"assigned": true,
"usedConstants": [
"RingCon.instFunLikeForallProp",
"NonUnitalN... | [
"R : Type u_1\ninst✝ : NonUnitalNonAssocRing R\ns : Set R\nx : R\nh : x ∈ { ringCon := sInf {s_1 | ∀ (x y : R), x - y ∈ s → s_1 x y} }\nI : TwoSidedIdeal R\nhI : s ⊆ ↑I\n⊢ I.ringCon ∈ {s_1 | ∀ (x y : R), x - y ∈ s → s_1 x y}"
] | refine sInf_le (α := RingCon R) ?_ h | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.RingTheory.Localization.Away.Basic | {
"line": 404,
"column": 43
} | {
"line": 404,
"column": 70
} | {
"line": 404,
"column": 71
} | [
{
"pp": "R : Type u_1\ninst✝² : CommSemiring R\nS : Type u_2\ninst✝¹ : CommSemiring S\ninst✝ : Algebra R S\ne : R\nhe : IsIdempotentElem e\nH : ∀ (x y : R), (algebraMap R S) x = (algebraMap R S) y ↔ e * x = e * y\nH' : Function.Surjective ⇑(algebraMap R S)\nn : ℕ\n⊢ (algebraMap R S) e = 1",
"ppTerm": "?m.92... | [
"R : Type u_1\ninst✝² : CommSemiring R\nS : Type u_2\ninst✝¹ : CommSemiring S\ninst✝ : Algebra R S\ne : R\nhe : IsIdempotentElem e\nH : ∀ (x y : R), (algebraMap R S) x = (algebraMap R S) y ↔ e * x = e * y\nH' : Function.Surjective ⇑(algebraMap R S)\nn : ℕ\n⊢ (algebraMap R S) e = (algebraMap R S) 1"
] | ← (algebraMap R S).map_one, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.RingTheory.TwoSidedIdeal.Operations | {
"line": 83,
"column": 25
} | {
"line": 83,
"column": 30
} | {
"line": 83,
"column": 30
} | [
{
"pp": "R : Type u_1\ninst✝ : NonUnitalNonAssocRing R\ns : Set R\nI : TwoSidedIdeal R\nh : (fun a b ↦ a - b ∈ s) ≤ ⇑I.ringCon\nx : R\nhx : x ∈ s\n⊢ x ∈ ↑I",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"SetLike.mem_coe._simp_1",
"congrArg",
"TwoSidedIdea... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.RingTheory.TwoSidedIdeal.Operations | {
"line": 83,
"column": 25
} | {
"line": 83,
"column": 30
} | {
"line": 83,
"column": 30
} | [
{
"pp": "R : Type u_1\ninst✝ : NonUnitalNonAssocRing R\ns : Set R\nI : TwoSidedIdeal R\nh : (fun a b ↦ a - b ∈ s) ≤ ⇑I.ringCon\nx : R\nhx : x ∈ s\n⊢ x ∈ ↑I",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"SetLike.mem_coe._simp_1",
"congrArg",
"TwoSidedIdea... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.RingTheory.TwoSidedIdeal.Operations | {
"line": 83,
"column": 25
} | {
"line": 83,
"column": 30
} | {
"line": 83,
"column": 30
} | [
{
"pp": "R : Type u_1\ninst✝ : NonUnitalNonAssocRing R\ns : Set R\nI : TwoSidedIdeal R\nh : (fun a b ↦ a - b ∈ s) ≤ ⇑I.ringCon\nx : R\nhx : x ∈ s\n⊢ x ∈ ↑I",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"SetLike.mem_coe._simp_1",
"congrArg",
"TwoSidedIdea... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.TwoSidedIdeal.Operations | {
"line": 378,
"column": 61
} | {
"line": 378,
"column": 66
} | {
"line": 379,
"column": 2
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nx✝¹ : TwoSidedIdeal R\nx✝ : R\n⊢ (∀ (I : TwoSidedIdeal R), ↑(asIdeal x✝¹) ⊆ ↑I → x✝ ∈ I) ↔ x✝ ∈ x✝¹",
"ppTerm": "?m.109",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.RingTheory.TwoSidedIdeal.Operations | {
"line": 378,
"column": 61
} | {
"line": 378,
"column": 66
} | {
"line": 379,
"column": 2
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nx✝¹ : TwoSidedIdeal R\nx✝ : R\n⊢ (∀ (I : TwoSidedIdeal R), ↑(asIdeal x✝¹) ⊆ ↑I → x✝ ∈ I) ↔ x✝ ∈ x✝¹",
"ppTerm": "?m.109",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.RingTheory.TwoSidedIdeal.Operations | {
"line": 378,
"column": 61
} | {
"line": 378,
"column": 66
} | {
"line": 379,
"column": 2
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nx✝¹ : TwoSidedIdeal R\nx✝ : R\n⊢ (∀ (I : TwoSidedIdeal R), ↑(asIdeal x✝¹) ⊆ ↑I → x✝ ∈ I) ↔ x✝ ∈ x✝¹",
"ppTerm": "?m.109",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.TwoSidedIdeal.Operations | {
"line": 382,
"column": 29
} | {
"line": 382,
"column": 34
} | {
"line": 382,
"column": 34
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nJ : Ideal R\nx : R\n⊢ x ∈ J → ∀ (I : TwoSidedIdeal R), ↑J ⊆ ↑I → x ∈ I",
"ppTerm": "?m.111",
"assigned": true,
"usedConstants": [
"SetLike.mem_coe._simp_1",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"CommR... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.RingTheory.TwoSidedIdeal.Operations | {
"line": 382,
"column": 29
} | {
"line": 382,
"column": 34
} | {
"line": 382,
"column": 34
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nJ : Ideal R\nx : R\n⊢ x ∈ J → ∀ (I : TwoSidedIdeal R), ↑J ⊆ ↑I → x ∈ I",
"ppTerm": "?m.111",
"assigned": true,
"usedConstants": [
"SetLike.mem_coe._simp_1",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"CommR... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.RingTheory.TwoSidedIdeal.Operations | {
"line": 382,
"column": 29
} | {
"line": 382,
"column": 34
} | {
"line": 382,
"column": 34
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nJ : Ideal R\nx : R\n⊢ x ∈ J → ∀ (I : TwoSidedIdeal R), ↑J ⊆ ↑I → x ∈ I",
"ppTerm": "?m.111",
"assigned": true,
"usedConstants": [
"SetLike.mem_coe._simp_1",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"CommR... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.Jacobson.Radical | {
"line": 88,
"column": 46
} | {
"line": 88,
"column": 62
} | {
"line": 88,
"column": 62
} | [
{
"pp": "R : Type u_1\nM : Type u_3\ninst✝² : Ring R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nN : Submodule R M\nle : N ≤ jacobson R M\n⊢ N.mkQ.ker ≤ jacobson R M",
"ppTerm": "?m.71",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Submodule",
"Submodule.Quotient.addCommMonoid... | [] | by rwa [ker_mkQ] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.RingTheory.Jacobson.Ideal | {
"line": 259,
"column": 31
} | {
"line": 259,
"column": 50
} | {
"line": 259,
"column": 50
} | [
{
"pp": "R : Type u\nS : Type v\ninst✝² : Ring R\ninst✝¹ : Ring S\nI✝ I : Ideal R\ninst✝ : I.IsTwoSided\nx r : R\nxJ : x ∈ I.jacobson\n𝔪 : Ideal R\n𝔪_mem : 𝔪 ∈ {J | I ≤ J ∧ J.IsMaximal}\nr𝔪 : r ∉ 𝔪\n𝔪₀ : Ideal R := Submodule.comap (DistribSMul.toLinearMap R R (MulOpposite.op r)) 𝔪\nI𝔪₀ : I ≤ 𝔪₀\nJ : Id... | [
"R : Type u\nS : Type v\ninst✝² : Ring R\ninst✝¹ : Ring S\nI✝ I : Ideal R\ninst✝ : I.IsTwoSided\nx r : R\nxJ : x ∈ I.jacobson\n𝔪 : Ideal R\n𝔪_mem : 𝔪 ∈ {J | I ≤ J ∧ J.IsMaximal}\nr𝔪 : r ∉ 𝔪\n𝔪₀ : Ideal R := Submodule.comap (DistribSMul.toLinearMap R R (MulOpposite.op r)) 𝔪\nI𝔪₀ : I ≤ 𝔪₀\nJ : Ideal R\nb : R... | ← eq_sub_iff_add_eq | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.CategoryTheory.Monoidal.Mon | {
"line": 124,
"column": 4
} | {
"line": 124,
"column": 71
} | {
"line": 125,
"column": 2
} | [
{
"pp": "C : Type u₁\ninst✝² : Category.{v₁, u₁} C\ninst✝¹ : MonoidalCategory C\nM X Y : C\ninst✝ : MonObj M\ne : M ≅ X\n⊢ (ρ_ X).inv ≫ X ◁ η ≫ e.inv ▷ M ≫ μ ≫ e.hom = 𝟙 X",
"ppTerm": "?m.98",
"assigned": true,
"usedConstants": [
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"Cat... | [] | simp [← tensorHom_def'_assoc, rightUnitor_inv_comp_tensorHom_assoc] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.RingTheory.Localization.Integer | {
"line": 83,
"column": 29
} | {
"line": 83,
"column": 41
} | {
"line": 83,
"column": 41
} | [
{
"pp": "R : Type u_1\ninst✝³ : CommSemiring R\nM : Submonoid R\nS : Type u_2\ninst✝² : CommSemiring S\ninst✝¹ : Algebra R S\ninst✝ : IsLocalization M S\na : S\n⊢ ∃ b, IsInteger R ((algebraMap R S) ↑b * a)",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"IsLocalization.IsInteger",
... | [
"R : Type u_1\ninst✝³ : CommSemiring R\nM : Submonoid R\nS : Type u_2\ninst✝² : CommSemiring S\ninst✝¹ : Algebra R S\ninst✝ : IsLocalization M S\na : S\n⊢ ∃ b, IsInteger R (a * (algebraMap R S) ↑b)"
] | mul_comm _ a | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.Pasting | {
"line": 128,
"column": 4
} | {
"line": 128,
"column": 55
} | {
"line": 129,
"column": 4
} | [
{
"pp": "case refine_1.h₀\nC : Type u\ninst✝ : Category.{v, u} C\nX₃ Y₁ Y₂ Y₃ : C\ng₁ : Y₁ ⟶ Y₂\ng₂ : Y₂ ⟶ Y₃\ni₃ : X₃ ⟶ Y₃\nt₂ : PullbackCone g₂ i₃\ni₂ : t₂.pt ⟶ Y₂\nt₁ : PullbackCone g₁ i₂\nhi₂ : i₂ = t₂.fst\nH : IsLimit t₂\nH' : IsLimit (t₂.pasteHoriz t₁ hi₂)\ns : PullbackCone g₁ i₂\nl : s.pt ⟶ (t₂.pasteHori... | [
"case refine_1.h₁\nC : Type u\ninst✝ : Category.{v, u} C\nX₃ Y₁ Y₂ Y₃ : C\ng₁ : Y₁ ⟶ Y₂\ng₂ : Y₂ ⟶ Y₃\ni₃ : X₃ ⟶ Y₃\nt₂ : PullbackCone g₂ i₃\ni₂ : t₂.pt ⟶ Y₂\nt₁ : PullbackCone g₁ i₂\nhi₂ : i₂ = t₂.fst\nH : IsLimit t₂\nH' : IsLimit (t₂.pasteHoriz t₁ hi₂)\ns : PullbackCone g₁ i₂\nl : s.pt ⟶ (t₂.pasteHoriz t₁ hi₂).pt... | · simp [← s.condition, ← hl, ← t₁.condition, ← hi₂] | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic | {
"line": 353,
"column": 8
} | {
"line": 353,
"column": 19
} | {
"line": 353,
"column": 19
} | [
{
"pp": "case h₂\nC : Type u₁\ninst✝² : Category.{v₁, u₁} C\nA B : C\nf : A ⟶ B\nX : C\ninst✝¹ : HasBinaryProduct A X\ninst✝ : HasBinaryProduct B X\ns : PullbackCone f prod.fst\nm : s.pt ⟶ A ⨯ X\nh₁ : m ≫ prod.fst = s.fst\nh₂ : m ≫ prod.map f (𝟙 X) = s.snd\n⊢ m ≫ prod.snd = prod.lift s.fst (s.snd ≫ prod.snd) ≫... | [] | simp [← h₂] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic | {
"line": 353,
"column": 8
} | {
"line": 353,
"column": 19
} | {
"line": 353,
"column": 19
} | [
{
"pp": "case h₂\nC : Type u₁\ninst✝² : Category.{v₁, u₁} C\nA B : C\nf : A ⟶ B\nX : C\ninst✝¹ : HasBinaryProduct A X\ninst✝ : HasBinaryProduct B X\ns : PullbackCone f prod.fst\nm : s.pt ⟶ A ⨯ X\nh₁ : m ≫ prod.fst = s.fst\nh₂ : m ≫ prod.map f (𝟙 X) = s.snd\n⊢ m ≫ prod.snd = prod.lift s.fst (s.snd ≫ prod.snd) ≫... | [] | simp [← h₂] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic | {
"line": 353,
"column": 8
} | {
"line": 353,
"column": 19
} | {
"line": 353,
"column": 19
} | [
{
"pp": "case h₂\nC : Type u₁\ninst✝² : Category.{v₁, u₁} C\nA B : C\nf : A ⟶ B\nX : C\ninst✝¹ : HasBinaryProduct A X\ninst✝ : HasBinaryProduct B X\ns : PullbackCone f prod.fst\nm : s.pt ⟶ A ⨯ X\nh₁ : m ≫ prod.fst = s.fst\nh₂ : m ≫ prod.map f (𝟙 X) = s.snd\n⊢ m ≫ prod.snd = prod.lift s.fst (s.snd ≫ prod.snd) ≫... | [] | simp [← h₂] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
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