module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Algebra.BigOperators.ModEq | {
"line": 163,
"column": 2
} | {
"line": 163,
"column": 13
} | {
"line": 163,
"column": 14
} | [
{
"pp": "n : ℤ\ns : Multiset ℤ\nh : ∀ x ∈ s, x ≡ 0 [ZMOD n]\n⊢ s.sum ≡ 0 [ZMOD n]",
"ppTerm": "?m.11",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"n : ℤ\ns : Multiset ℤ\nh : ∀ x ∈ s, x ≡ 0 [ZMOD n]\n⊢ s.sum ≡ 0 [ZMOD n]"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.BigOperators.ModEq | {
"line": 171,
"column": 2
} | {
"line": 171,
"column": 13
} | {
"line": 171,
"column": 14
} | [
{
"pp": "α : Type u_1\nn : ℤ\nf : α → ℤ\ns : Finset α\nh : ∀ x ∈ s, f x ≡ 1 [ZMOD n]\n⊢ ∏ x ∈ s, f x ≡ 1 [ZMOD n]",
"ppTerm": "?m.14",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nn : ℤ\nf : α → ℤ\ns : Finset α\nh : ∀ x ∈ s, f x ≡ 1 [ZMOD n]\n⊢ ∏ x ∈ s, f x ≡ 1 [ZMOD n]"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Multiset.Sym | {
"line": 85,
"column": 2
} | {
"line": 85,
"column": 53
} | {
"line": 85,
"column": 54
} | [
{
"pp": "case h\nα : Type u_1\nxs ys : List α\nh : ⟦xs⟧ ≤ ⟦ys⟧\n⊢ xs <+~ ys",
"ppTerm": "?h",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case h\nα : Type u_1\nxs ys : List α\nh : ⟦xs⟧ ≤ ⟦ys⟧\n⊢ xs <+~ ys"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.IsTensorProduct | {
"line": 128,
"column": 2
} | {
"line": 128,
"column": 37
} | {
"line": 128,
"column": 38
} | [
{
"pp": "R : Type u_1\ninst✝⁶ : CommSemiring R\nM₁ : Type u_2\nM₂ : Type u_3\nM : Type u_4\ninst✝⁵ : AddCommMonoid M₁\ninst✝⁴ : AddCommMonoid M₂\ninst✝³ : AddCommMonoid M\ninst✝² : Module R M₁\ninst✝¹ : Module R M₂\ninst✝ : Module R M\nf : M₁ →ₗ[R] M₂ →ₗ[R] M\ne : M₁ ⊗[R] M₂ ≃ₗ[R] M\nhe : ∀ (x : M₁) (y : M₂), e... | [
"R : Type u_1\ninst✝⁶ : CommSemiring R\nM₁ : Type u_2\nM₂ : Type u_3\nM : Type u_4\ninst✝⁵ : AddCommMonoid M₁\ninst✝⁴ : AddCommMonoid M₂\ninst✝³ : AddCommMonoid M\ninst✝² : Module R M₁\ninst✝¹ : Module R M₂\ninst✝ : Module R M\nf : M₁ →ₗ[R] M₂ →ₗ[R] M\ne : M₁ ⊗[R] M₂ ≃ₗ[R] M\nhe : ∀ (x : M₁) (y : M₂), e (x ⊗ₜ[R] y)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finset.Sym | {
"line": 98,
"column": 2
} | {
"line": 98,
"column": 13
} | {
"line": 98,
"column": 14
} | [
{
"pp": "α : Type u_1\ns t : Finset α\nh : s.sym2 = t.sym2\nx : α\n⊢ x ∈ s ↔ x ∈ t",
"ppTerm": "?m.16",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ns t : Finset α\nh : s.sym2 = t.sym2\nx : α\n⊢ x ∈ s ↔ x ∈ t"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.IsTensorProduct | {
"line": 185,
"column": 75
} | {
"line": 189,
"column": 29
} | {
"line": 190,
"column": 2
} | [
{
"pp": "R✝ : Type u_1\ninst✝³⁵ : CommSemiring R✝\nM₁✝ : Type u_2\nM₂✝ : Type u_3\nM : Type u_4\nM' : Type u_5\ninst✝³⁴ : AddCommMonoid M₁✝\ninst✝³³ : AddCommMonoid M₂✝\ninst✝³² : AddCommMonoid M\ninst✝³¹ : AddCommMonoid M'\ninst✝³⁰ : Module R✝ M₁✝\ninst✝²⁹ : Module R✝ M₂✝\ninst✝²⁸ : Module R✝ M\ninst✝²⁷ : Modu... | [] | by
change hf.equiv.symm (s • _) = _
dsimp
rw [← map_smul]
apply hf.equiv_symm_apply | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.List.Sym | {
"line": 172,
"column": 4
} | {
"line": 172,
"column": 46
} | {
"line": 174,
"column": 4
} | [
{
"pp": "case swap\nα : Type u_1\nxs✝ ys : List α\nx y : α\nxs : List α\n⊢ s(y, y) :: s(y, x) :: (List.map (fun y_1 ↦ s(y, y_1)) xs ++ s(x, x) :: (List.map (fun y ↦ s(x, y)) xs ++ xs.sym2)) ~\n s(x, x) :: s(x, y) :: (List.map (fun y ↦ s(x, y)) xs ++ s(y, y) :: (List.map (fun y_1 ↦ s(y, y_1)) xs ++ xs.sym2))"... | [
"case swap\nα : Type u_1\nxs✝ ys : List α\nx y : α\nxs : List α\n⊢ s(y, y) :: s(x, y) :: (List.map (fun y_1 ↦ s(y, y_1)) xs ++ s(x, x) :: (List.map (fun y ↦ s(x, y)) xs ++ xs.sym2)) ~\n s(x, x) :: s(x, y) :: (List.map (fun y ↦ s(x, y)) xs ++ s(y, y) :: (List.map (fun y_1 ↦ s(y, y_1)) xs ++ xs.sym2))"
] | conv => enter [1, 2, 1]; rw [Sym2.eq_swap] | Lean.Elab.Tactic.Conv.evalConv | Lean.Parser.Tactic.Conv.conv |
Mathlib.Data.List.Sym | {
"line": 191,
"column": 2
} | {
"line": 191,
"column": 26
} | {
"line": 192,
"column": 2
} | [
{
"pp": "α : Type u_1\nxs ys : List α\nh : xs <+~ ys\n⊢ xs.sym2 <+~ ys.sym2",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"List.Perm",
"And.casesOn",
"List",
"And",
"List.sym2",
"Exists.casesOn",
"List.Subperm",
"List.Sublist",
"Sym2"
... | [
"α : Type u_1\nxs ys xs' : List α\nhx : xs' ~ xs\nh : xs' <+ ys\n⊢ xs.sym2 <+~ ys.sym2"
] | obtain ⟨xs', hx, h⟩ := h | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.Algebra.BigOperators.Sym | {
"line": 28,
"column": 2
} | {
"line": 28,
"column": 17
} | {
"line": 30,
"column": 0
} | [
{
"pp": "case refine_1\nι : Type u_1\nM : Type u_2\ninst✝¹ : LinearOrder ι\ninst✝ : AddCommMonoid M\ns : Finset ι\np : Sym2 ι → M\n⊢ ∀ (i : { p // p.1 ≤ p.2 }),\n i ∈ Finset.subtype (fun i ↦ i.1 ≤ i.2) s.offDiag ↔ Sym2.sortEquiv.symm i ∈ {i ∈ s.sym2 | ¬i.IsDiag}",
"ppTerm": "?refine_1",
"assigned": t... | [] | all_goals aesop | Lean.Elab.Tactic.evalAllGoals | Lean.Parser.Tactic.allGoals |
Mathlib.RingTheory.IsTensorProduct | {
"line": 239,
"column": 4
} | {
"line": 239,
"column": 17
} | {
"line": 240,
"column": 6
} | [
{
"pp": "case tmul.tmul\nR✝ : Type u_1\ninst✝⁴² : CommSemiring R✝\nM₁✝ : Type u_2\nM₂✝ : Type u_3\nM : Type u_4\nM' : Type u_5\ninst✝⁴¹ : AddCommMonoid M₁✝\ninst✝⁴⁰ : AddCommMonoid M₂✝\ninst✝³⁹ : AddCommMonoid M\ninst✝³⁸ : AddCommMonoid M'\ninst✝³⁷ : Module R✝ M₁✝\ninst✝³⁶ : Module R✝ M₂✝\ninst✝³⁵ : Module R✝ M... | [] | | tmul x z => | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | null |
Mathlib.RingTheory.IsTensorProduct | {
"line": 428,
"column": 4
} | {
"line": 428,
"column": 15
} | {
"line": 428,
"column": 16
} | [
{
"pp": "R : Type u_1\nS : Type v₃\ninst✝² : CommSemiring R\ninst✝¹ : CommSemiring S\ninst✝ : Algebra R S\nx : R\n⊢ (AlgebraTensorModule.rid R S S) (1 ⊗ₜ[R] x) = (Algebra.linearMap R S) x",
"ppTerm": "?m.74",
"assigned": true,
"usedConstants": [
"NonAssocSemiring.toAddCommMonoidWithOne",
... | [
"R : Type u_1\nS : Type v₃\ninst✝² : CommSemiring R\ninst✝¹ : CommSemiring S\ninst✝ : Algebra R S\nx : R\n⊢ x • 1 = (algebraMap R S) x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Quiver.Prefunctor | {
"line": 50,
"column": 2
} | {
"line": 50,
"column": 13
} | {
"line": 50,
"column": 14
} | [
{
"pp": "V : Type u\ninst✝¹ : Quiver V\nW : Type u₂\ninst✝ : Quiver W\nF_obj : V → W\nmap✝¹ map✝ : {X Y : V} → (X ⟶ Y) → (F_obj X ⟶ F_obj Y)\nh_obj : ∀ (X : V), { obj := F_obj, map := map✝¹ }.obj X = { obj := F_obj, map := map✝ }.obj X\nh_map :\n ∀ (X Y : V) (f : X ⟶ Y),\n { obj := F_obj, map := map✝¹ }.map... | [
"V : Type u\ninst✝¹ : Quiver V\nW : Type u₂\ninst✝ : Quiver W\nF_obj : V → W\nmap✝¹ map✝ : {X Y : V} → (X ⟶ Y) → (F_obj X ⟶ F_obj Y)\nh_obj : ∀ (X : V), { obj := F_obj, map := map✝¹ }.obj X = { obj := F_obj, map := map✝ }.obj X\nh_map :\n ∀ (X Y : V) (f : X ⟶ Y),\n { obj := F_obj, map := map✝¹ }.map f = Eq.recO... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Quiver.Prefunctor | {
"line": 62,
"column": 2
} | {
"line": 62,
"column": 39
} | {
"line": 62,
"column": 40
} | [
{
"pp": "V W : Type u\ninst✝¹ : Quiver V\ninst✝ : Quiver W\nFobj : V → W\nFmap Gmap : {X Y : V} → (X ⟶ Y) → (Fobj X ⟶ Fobj Y)\nh_obj : ∀ (X : V), { obj := Fobj, map := Fmap }.obj X = { obj := Fobj, map := Gmap }.obj X\nh_map :\n ∀ (X Y : V) (f : X ⟶ Y), { obj := Fobj, map := Fmap }.map f = Quiver.homOfEq ({ ob... | [
"V W : Type u\ninst✝¹ : Quiver V\ninst✝ : Quiver W\nFobj : V → W\nFmap Gmap : {X Y : V} → (X ⟶ Y) → (Fobj X ⟶ Fobj Y)\nh_obj : ∀ (X : V), { obj := Fobj, map := Fmap }.obj X = { obj := Fobj, map := Gmap }.obj X\nh_map :\n ∀ (X Y : V) (f : X ⟶ Y), { obj := Fobj, map := Fmap }.map f = Quiver.homOfEq ({ obj := Fobj, m... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Sym.Sym2 | {
"line": 621,
"column": 2
} | {
"line": 621,
"column": 17
} | {
"line": 621,
"column": 18
} | [
{
"pp": "α : Type u_1\nr : α → α → Prop\nsym : Std.Symm r\nh : fromRel sym = ∅\nx y : α\n⊢ r x y ↔ ⊥ x y",
"ppTerm": "?m.47",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"iff_false",
"id",
"Pi.instBotForall",
"Bot.bot",
"Iff",
"Prop.instBooleanAlgebra",
... | [
"α : Type u_1\nr : α → α → Prop\nsym : Std.Symm r\nh : fromRel sym = ∅\nx y : α\n⊢ ¬r x y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Sym.Sym2 | {
"line": 630,
"column": 2
} | {
"line": 630,
"column": 17
} | {
"line": 630,
"column": 18
} | [
{
"pp": "α : Type u_1\nr : α → α → Prop\nsym : Std.Symm r\nh : fromRel sym = Set.univ\nx y : α\n⊢ r x y ↔ ⊤ x y",
"ppTerm": "?m.48",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"iff_true",
"id",
"Iff",
"BooleanAlgebra.toTop",
"Prop.instBooleanAlgebra",
"P... | [
"α : Type u_1\nr : α → α → Prop\nsym : Std.Symm r\nh : fromRel sym = Set.univ\nx y : α\n⊢ r x y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Functor.Basic | {
"line": 151,
"column": 34
} | {
"line": 151,
"column": 68
} | {
"line": 151,
"column": 69
} | [
{
"pp": "C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝ : Category.{v₂, u₂} D\nobj : C → D\nmap : {X Y : C} → (X ⟶ Y) → (obj X ⟶ obj Y)\nmap_id✝¹ : ∀ (X : C), map (𝟙 X) = 𝟙 (obj X)\nmap_comp✝¹ : ∀ {X Y Z : C} (f : X ⟶ Y) (g : Y ⟶ Z), map (f ≫ g) = map f ≫ map g\nmap' : {X Y : C} → (X ⟶ Y) → (ob... | [
"C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝ : Category.{v₂, u₂} D\nobj : C → D\nmap : {X Y : C} → (X ⟶ Y) → (obj X ⟶ obj Y)\nmap_id✝¹ : ∀ (X : C), map (𝟙 X) = 𝟙 (obj X)\nmap_comp✝¹ : ∀ {X Y Z : C} (f : X ⟶ Y) (g : Y ⟶ Z), map (f ≫ g) = map f ≫ map g\nmap' : {X Y : C} → (X ⟶ Y) → (obj X ⟶ obj Y)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Sym.Sym2 | {
"line": 865,
"column": 10
} | {
"line": 865,
"column": 36
} | {
"line": 865,
"column": 37
} | [] | [] | first | done | constructor | Lean.Elab.Tactic.evalFirst | Lean.Parser.Tactic.first |
Mathlib.CategoryTheory.Category.Basic | {
"line": 343,
"column": 35
} | {
"line": 343,
"column": 46
} | {
"line": 343,
"column": 47
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nX Y Z : C\nf : X ⟶ Y\ninst✝ : Epi f\ng h : Y ⟶ Z\nW : C\nk l : Z ⟶ W\np : (f ≫ g) ≫ k = (f ≫ h) ≫ l\n⊢ f ≫ g ≫ k = f ≫ h ≫ l",
"ppTerm": "?m.60",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"C : Type u\ninst✝¹ : Category.{v, u} C\nX Y Z : C\nf : X ⟶ Y\ninst✝ : Epi f\ng h : Y ⟶ Z\nW : C\nk l : Z ⟶ W\np : (f ≫ g) ≫ k = (f ≫ h) ≫ l\n⊢ f ≫ g ≫ k = f ≫ h ≫ l"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Sym.Sym2 | {
"line": 865,
"column": 10
} | {
"line": 865,
"column": 36
} | {
"line": 865,
"column": 37
} | [
{
"pp": "α : Type u_1\na₁ b₁ a₂ b₂ : α\nh₁ : a₁ = b₂\nh₂ : b₁ = a₂\n⊢ [b₂, a₂].Perm [a₂, b₂]",
"ppTerm": "?m.211",
"assigned": true,
"usedConstants": [
"List.Perm.swap",
"List.nil"
],
"usedFVars": [
"α",
"a₂",
"b₂"
],
"usedGoals": []
}
] | [] | first | done | constructor | Lean.Elab.Tactic.evalFirst | Lean.Parser.Tactic.first |
Mathlib.CategoryTheory.Functor.FullyFaithful | {
"line": 210,
"column": 2
} | {
"line": 210,
"column": 13
} | {
"line": 210,
"column": 14
} | [
{
"pp": "C : Type u₁\ninst✝² : Category.{v₁, u₁} C\nD : Type u₂\ninst✝¹ : Category.{v₂, u₂} D\nF : C ⥤ D\nhF : F.FullyFaithful\nX Y : C\nf : X ⟶ Y\ninst✝ : IsIso (F.map f)\n⊢ IsIso f",
"ppTerm": "?m.23",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"C : Type u₁\ninst✝² : Category.{v₁, u₁} C\nD : Type u₂\ninst✝¹ : Category.{v₂, u₂} D\nF : C ⥤ D\nhF : F.FullyFaithful\nX Y : C\nf : X ⟶ Y\ninst✝ : IsIso (F.map f)\n⊢ IsIso f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.IsTensorProduct | {
"line": 601,
"column": 2
} | {
"line": 601,
"column": 13
} | {
"line": 601,
"column": 14
} | [
{
"pp": "R : Type u_1\nM : Type v₁\nN : Type v₂\nS : Type v₃\ninst✝⁸ : AddCommMonoid M\ninst✝⁷ : AddCommMonoid N\ninst✝⁶ : CommSemiring R\ninst✝⁵ : CommSemiring S\ninst✝⁴ : Algebra R S\ninst✝³ : Module R M\ninst✝² : Module R N\ninst✝¹ : Module S N\ninst✝ : IsScalarTower R S N\nf : M →ₗ[R] N\nhf : IsBaseChange S... | [
"R : Type u_1\nM : Type v₁\nN : Type v₂\nS : Type v₃\ninst✝⁸ : AddCommMonoid M\ninst✝⁷ : AddCommMonoid N\ninst✝⁶ : CommSemiring R\ninst✝⁵ : CommSemiring S\ninst✝⁴ : Algebra R S\ninst✝³ : Module R M\ninst✝² : Module R N\ninst✝¹ : Module S N\ninst✝ : IsScalarTower R S N\nf : M →ₗ[R] N\nhf : IsBaseChange S f\nx : R\ny... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.ObjectProperty.Basic | {
"line": 183,
"column": 6
} | {
"line": 183,
"column": 40
} | {
"line": 183,
"column": 40
} | [
{
"pp": "C : Type u\nD : Type u'\ninst✝¹ : Category.{v, u} C\ninst✝ : Category.{v', u'} D\nP : ObjectProperty C\nF : C ⥤ D\nY : D\n⊢ P.strictMap F Y → ∃ X, P X ∧ F.obj X = Y",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"CategoryTheory.ObjectProperty.strictMap",
"HEq.refl",
... | [] | rintro ⟨X, hX⟩; exact ⟨X, hX, rfl⟩ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.ObjectProperty.Basic | {
"line": 183,
"column": 6
} | {
"line": 183,
"column": 40
} | {
"line": 183,
"column": 40
} | [
{
"pp": "C : Type u\nD : Type u'\ninst✝¹ : Category.{v, u} C\ninst✝ : Category.{v', u'} D\nP : ObjectProperty C\nF : C ⥤ D\nY : D\n⊢ P.strictMap F Y → ∃ X, P X ∧ F.obj X = Y",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"CategoryTheory.ObjectProperty.strictMap",
"HEq.refl",
... | [] | rintro ⟨X, hX⟩; exact ⟨X, hX, rfl⟩ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.IsTensorProduct | {
"line": 693,
"column": 2
} | {
"line": 693,
"column": 13
} | {
"line": 693,
"column": 14
} | [
{
"pp": "case e'_14\nR : Type u_8\nS : Type u_9\nA : Type u_10\nB : Type u_11\ninst✝⁸ : CommSemiring R\ninst✝⁷ : CommSemiring S\ninst✝⁶ : CommSemiring A\ninst✝⁵ : CommSemiring B\ninst✝⁴ : Algebra R A\ninst✝³ : Algebra R B\ninst✝² : Algebra A B\ninst✝¹ : IsScalarTower R A B\ninst✝ : Algebra R S\nx✝¹ : Algebra (A... | [
"case e'_14\nR : Type u_8\nS : Type u_9\nA : Type u_10\nB : Type u_11\ninst✝⁸ : CommSemiring R\ninst✝⁷ : CommSemiring S\ninst✝⁶ : CommSemiring A\ninst✝⁵ : CommSemiring B\ninst✝⁴ : Algebra R A\ninst✝³ : Algebra R B\ninst✝² : Algebra A B\ninst✝¹ : IsScalarTower R A B\ninst✝ : Algebra R S\nx✝¹ : Algebra (A ⊗[R] S) (B ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.IsTensorProduct | {
"line": 780,
"column": 2
} | {
"line": 780,
"column": 28
} | {
"line": 780,
"column": 29
} | [
{
"pp": "R : Type u_1\nS : Type v₃\ninst✝¹⁶ : CommSemiring R\ninst✝¹⁵ : CommSemiring S\ninst✝¹⁴ : Algebra R S\nR' : Type u_6\nS' : Type u_7\ninst✝¹³ : CommSemiring R'\ninst✝¹² : CommSemiring S'\ninst✝¹¹ : Algebra R R'\ninst✝¹⁰ : Algebra S S'\ninst✝⁹ : Algebra R' S'\ninst✝⁸ : Algebra R S'\ninst✝⁷ : IsScalarTower... | [
"R : Type u_1\nS : Type v₃\ninst✝¹⁶ : CommSemiring R\ninst✝¹⁵ : CommSemiring S\ninst✝¹⁴ : Algebra R S\nR' : Type u_6\nS' : Type u_7\ninst✝¹³ : CommSemiring R'\ninst✝¹² : CommSemiring S'\ninst✝¹¹ : Algebra R R'\ninst✝¹⁰ : Algebra S S'\ninst✝⁹ : Algebra R' S'\ninst✝⁸ : Algebra R S'\ninst✝⁷ : IsScalarTower R R' S'\nin... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Quiver.Symmetric | {
"line": 66,
"column": 4
} | {
"line": 66,
"column": 15
} | {
"line": 66,
"column": 16
} | [
{
"pp": "case mp\nV : Type u_2\ninst✝ : Quiver V\nh✝ : HasInvolutiveReverse V\na b : V\nf g : a ⟶ b\nh : reverse f = reverse g\n⊢ f = g",
"ppTerm": "?mp",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case mp\nV : Type u_2\ninst✝ : Quiver V\nh✝ : HasInvolutiveReverse V\na b : V\nf g : a ⟶ b\nh : reverse f = reverse g\n⊢ f = g"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Quiver.Path | {
"line": 137,
"column": 7
} | {
"line": 137,
"column": 22
} | {
"line": 137,
"column": 23
} | [
{
"pp": "V : Type u\ninst✝ : Quiver V\na b c : V\np₁ p₂ : Path a b\nq₁ q₂ : Path b c\nh : p₁.length = p₂.length\nh_eq : p₁.comp q₁ = p₂.comp q₂\n⊢ p₂.length + q₁.length = p₂.length + q₂.length",
"ppTerm": "?m.49",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"id",
"instHAdd",
... | [
"V : Type u\ninst✝ : Quiver V\na b c : V\np₁ p₂ : Path a b\nq₁ q₂ : Path b c\nh : p₁.length = p₂.length\nh_eq : p₁.comp q₁ = p₂.comp q₂\n⊢ q₁.length = q₂.length"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.EqToHom | {
"line": 270,
"column": 4
} | {
"line": 270,
"column": 15
} | {
"line": 270,
"column": 16
} | [
{
"pp": "C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝ : Category.{v₂, u₂} D\nF G : C ⥤ D\nF_obj : C → D\nmap✝¹ : {X Y : C} → (X ⟶ Y) → (F_obj X ⟶ F_obj Y)\nmap_id✝¹ : ∀ (X : C), map✝¹ (𝟙 X) = 𝟙 (F_obj X)\nmap_comp✝¹ : ∀ {X Y Z : C} (f : X ⟶ Y) (g : Y ⟶ Z), map✝¹ (f ≫ g) = map✝¹ f ≫ map✝¹ g\nm... | [
"C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝ : Category.{v₂, u₂} D\nF G : C ⥤ D\nF_obj : C → D\nmap✝¹ : {X Y : C} → (X ⟶ Y) → (F_obj X ⟶ F_obj Y)\nmap_id✝¹ : ∀ (X : C), map✝¹ (𝟙 X) = 𝟙 (F_obj X)\nmap_comp✝¹ : ∀ {X Y Z : C} (f : X ⟶ Y) (g : Y ⟶ Z), map✝¹ (f ≫ g) = map✝¹ f ≫ map✝¹ g\nmap✝ : {X Y :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Opposites | {
"line": 306,
"column": 47
} | {
"line": 306,
"column": 58
} | {
"line": 306,
"column": 59
} | [
{
"pp": "C : Type u₁\ninst✝² : Category.{v₁, u₁} C\nD : Type u₂\ninst✝¹ : Category.{v₂, u₂} D\nF : C ⥤ D\ninst✝ : F.Faithful\nX✝ Y✝ : Cᵒᵖ\na₁✝ a₂✝ : X✝ ⟶ Y✝\nh : F.op.map a₁✝ = F.op.map a₂✝\n⊢ a₁✝.unop = a₂✝.unop",
"ppTerm": "?m.27",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"... | [
"C : Type u₁\ninst✝² : Category.{v₁, u₁} C\nD : Type u₂\ninst✝¹ : Category.{v₂, u₂} D\nF : C ⥤ D\ninst✝ : F.Faithful\nX✝ Y✝ : Cᵒᵖ\na₁✝ a₂✝ : X✝ ⟶ Y✝\nh : F.op.map a₁✝ = F.op.map a₂✝\n⊢ a₁✝.unop = a₂✝.unop"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Equivalence | {
"line": 116,
"column": 2
} | {
"line": 116,
"column": 36
} | {
"line": 116,
"column": 37
} | [
{
"pp": "C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝ : Category.{v₂, u₂} D\ne : C ≌ D\nX : C\n⊢ e.counitIso.inv.app (e.functor.obj X) ≫ e.functor.map (e.unitIso.inv.app X) = 𝟙 (e.functor.obj X)",
"ppTerm": "?m.67",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"... | [
"C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝ : Category.{v₂, u₂} D\ne : C ≌ D\nX : C\n⊢ e.counitIso.inv.app (e.functor.obj X) ≫ e.functor.map (e.unitIso.inv.app X) = 𝟙 (e.functor.obj X)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Equivalence | {
"line": 131,
"column": 4
} | {
"line": 131,
"column": 38
} | {
"line": 131,
"column": 39
} | [
{
"pp": "C✝ : Type u₁\ninst✝³ : Category.{v₁, u₁} C✝\nD✝ : Type u₂\ninst✝² : Category.{v₂, u₂} D✝\nC : Type u₁\nD : Type u₂\ninst✝¹ : Category.{v₁, u₁} C\ninst✝ : Category.{v₂, u₂} D\nfunctor : C ⥤ D\ninverse : D ⥤ C\nunitIso : 𝟭 C ≅ functor ⋙ inverse\ncounitIso : inverse ⋙ functor ≅ 𝟭 D\nfunctor_unitIso_comp... | [
"C✝ : Type u₁\ninst✝³ : Category.{v₁, u₁} C✝\nD✝ : Type u₂\ninst✝² : Category.{v₂, u₂} D✝\nC : Type u₁\nD : Type u₂\ninst✝¹ : Category.{v₁, u₁} C\ninst✝ : Category.{v₂, u₂} D\nfunctor : C ⥤ D\ninverse : D ⥤ C\nunitIso : 𝟭 C ≅ functor ⋙ inverse\ncounitIso : inverse ⋙ functor ≅ 𝟭 D\nfunctor_unitIso_comp :\n ∀ (X :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Equivalence | {
"line": 269,
"column": 2
} | {
"line": 269,
"column": 13
} | {
"line": 269,
"column": 14
} | [
{
"pp": "C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝ : Category.{v₂, u₂} D\ne : C ≌ D\nX : C\n⊢ e.counit.app (e.functor.obj X) = e.functor.map (e.unitInv.app X)",
"ppTerm": "?m.42",
"assigned": true,
"usedConstants": [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.H... | [
"C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝ : Category.{v₂, u₂} D\ne : C ≌ D\nX : C\n⊢ e.counit.app (e.functor.obj X) = e.functor.map (e.unitInv.app X)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Equivalence | {
"line": 310,
"column": 2
} | {
"line": 310,
"column": 13
} | {
"line": 310,
"column": 14
} | [
{
"pp": "C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝ : Category.{v₂, u₂} D\ne : C ≌ D\nY : D\n⊢ e.unit.app (e.inverse.obj Y) = e.inverse.map (e.counitInv.app Y)",
"ppTerm": "?m.42",
"assigned": true,
"usedConstants": [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.H... | [
"C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝ : Category.{v₂, u₂} D\ne : C ≌ D\nY : D\n⊢ e.unit.app (e.inverse.obj Y) = e.inverse.map (e.counitInv.app Y)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Discrete.Basic | {
"line": 271,
"column": 19
} | {
"line": 271,
"column": 30
} | {
"line": 271,
"column": 31
} | [
{
"pp": "α✝ : Type u₁\nC : Type u₂\ninst✝ : Category.{v₂, u₂} C\nα : Type u₁\nβ : Type u₂\nh : Discrete α ≌ Discrete β\na : α\n⊢ (as ∘ h.inverse.obj ∘ mk) ((as ∘ h.functor.obj ∘ mk) a) = a",
"ppTerm": "?m.43",
"assigned": true,
"usedConstants": [
"Function.comp",
"id",
"CategoryThe... | [
"α✝ : Type u₁\nC : Type u₂\ninst✝ : Category.{v₂, u₂} C\nα : Type u₁\nβ : Type u₂\nh : Discrete α ≌ Discrete β\na : α\n⊢ (h.inverse.obj (h.functor.obj { as := a })).as = a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Discrete.Basic | {
"line": 272,
"column": 20
} | {
"line": 272,
"column": 31
} | {
"line": 272,
"column": 32
} | [
{
"pp": "α✝ : Type u₁\nC : Type u₂\ninst✝ : Category.{v₂, u₂} C\nα : Type u₁\nβ : Type u₂\nh : Discrete α ≌ Discrete β\na : β\n⊢ (as ∘ h.functor.obj ∘ mk) ((as ∘ h.inverse.obj ∘ mk) a) = a",
"ppTerm": "?m.72",
"assigned": true,
"usedConstants": [
"Function.comp",
"id",
"CategoryThe... | [
"α✝ : Type u₁\nC : Type u₂\ninst✝ : Category.{v₂, u₂} C\nα : Type u₁\nβ : Type u₂\nh : Discrete α ≌ Discrete β\na : β\n⊢ (h.functor.obj (h.inverse.obj { as := a })).as = a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Equivalence | {
"line": 713,
"column": 34
} | {
"line": 713,
"column": 45
} | {
"line": 713,
"column": 46
} | [
{
"pp": "C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝ : Category.{v₂, u₂} D\nC' : Type u_1\ne : C' ≃ D\nY : D\n⊢ Nonempty ((inducedFunctor ⇑e).obj (e.symm Y) ≅ Y)",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Equiv.apply_symm_apply",
"Equiv.i... | [
"C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝ : Category.{v₂, u₂} D\nC' : Type u_1\ne : C' ≃ D\nY : D\n⊢ Nonempty (Y ≅ Y)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Groupoid | {
"line": 210,
"column": 4
} | {
"line": 210,
"column": 43
} | {
"line": 211,
"column": 4
} | [
{
"pp": "case mp\nC : Type u_1\ninst✝ : Category.{v_1, u_1} C\na✝ : IsGroupoid C\nX✝ : C\n⊢ ∀ ⦃Y : C⦄ (f : X✝ ⟶ Y), ⊤ f → isomorphisms C f",
"ppTerm": "?mp",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"CategoryTheory.MorphismProperty",
"CategoryTheory.IsIso",
"CategoryThe... | [
"case mp\nC : Type u_1\ninst✝ : Category.{v_1, u_1} C\na✝ : IsGroupoid C\nX✝ : C\n⊢ ∀ ⦃Y : C⦄ (f : X✝ ⟶ Y), True → IsIso f"
] | simp only [isomorphisms.iff, top_apply] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.CategoryTheory.CommSq | {
"line": 161,
"column": 6
} | {
"line": 161,
"column": 17
} | {
"line": 161,
"column": 18
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\nD : Type u_2\ninst✝ : Category.{v_2, u_2} D\nF : C ⥤ D\nW X Y Z : C\nf : W ⟶ X\ng : W ⟶ Y\nh : X ⟶ Z\ni : Y ⟶ Z\ns : CommSq f g h i\n⊢ F.map f ≫ F.map h = F.map g ≫ F.map i",
"ppTerm": "?m.57",
"assigned": false,
"usedConstants": [],
"usedFV... | [
"C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\nD : Type u_2\ninst✝ : Category.{v_2, u_2} D\nF : C ⥤ D\nW X Y Z : C\nf : W ⟶ X\ng : W ⟶ Y\nh : X ⟶ Z\ni : Y ⟶ Z\ns : CommSq f g h i\n⊢ F.map f ≫ F.map h = F.map g ≫ F.map i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.EpiMono | {
"line": 128,
"column": 72
} | {
"line": 128,
"column": 83
} | {
"line": 128,
"column": 84
} | [
{
"pp": "C : Type u₁\ninst✝ : Category.{v₁, u₁} C\nX Y : C\nf : X ⟶ Y\nse : SplitEpi f\nZ✝ : C\ng h : Y ⟶ Z✝\nw : se.section_ ≫ f ≫ g = se.section_ ≫ f ≫ h\n⊢ g = h",
"ppTerm": "?m.37",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"C : Type u₁\ninst✝ : Category.{v₁, u₁} C\nX Y : C\nf : X ⟶ Y\nse : SplitEpi f\nZ✝ : C\ng h : Y ⟶ Z✝\nw : se.section_ ≫ f ≫ g = se.section_ ≫ f ≫ h\n⊢ g = h"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.EpiMono | {
"line": 218,
"column": 2
} | {
"line": 218,
"column": 13
} | {
"line": 218,
"column": 14
} | [
{
"pp": "C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nX Y Z : C\nf : X ⟶ Y\ng : Y ⟶ Z\ninst✝ : IsIso g\nh : Epi (f ≫ g)\n⊢ Epi f",
"ppTerm": "?m.26",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nX Y Z : C\nf : X ⟶ Y\ng : Y ⟶ Z\ninst✝ : IsIso g\nh : Epi (f ≫ g)\n⊢ Epi f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.MorphismProperty.Basic | {
"line": 517,
"column": 15
} | {
"line": 517,
"column": 26
} | {
"line": 517,
"column": 27
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nP : MorphismProperty C\nhP : P.RespectsIso\nX Y Z : C\nf : X ⟶ Y\ng : Y ⟶ Z\ninst✝ : IsIso f\nh : P (f ≫ g)\n⊢ P g",
"ppTerm": "?m.24",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"C : Type u\ninst✝¹ : Category.{v, u} C\nP : MorphismProperty C\nhP : P.RespectsIso\nX Y Z : C\nf : X ⟶ Y\ng : Y ⟶ Z\ninst✝ : IsIso f\nh : P (f ≫ g)\n⊢ P g"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.MorphismProperty.Basic | {
"line": 521,
"column": 15
} | {
"line": 521,
"column": 26
} | {
"line": 521,
"column": 27
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nP : MorphismProperty C\nhP : P.RespectsIso\nX Y Z : C\nf : X ⟶ Y\ng : Y ⟶ Z\ninst✝ : IsIso g\nh : P (f ≫ g)\n⊢ P f",
"ppTerm": "?m.24",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"C : Type u\ninst✝¹ : Category.{v, u} C\nP : MorphismProperty C\nhP : P.RespectsIso\nX Y Z : C\nf : X ⟶ Y\ng : Y ⟶ Z\ninst✝ : IsIso g\nh : P (f ≫ g)\n⊢ P f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.MorphismProperty.Basic | {
"line": 621,
"column": 4
} | {
"line": 621,
"column": 75
} | {
"line": 621,
"column": 76
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\nD : Type u_1\ninst✝¹ : Category.{v_1, u_1} D\nP : MorphismProperty D\ninst✝ : P.RespectsIso\nF : C ⥤ D\nX Y Z : C\ne : X ⟶ Y\nhe : IsIso e\nf : Y ⟶ Z\nhf : P.inverseImage F f\n⊢ P.inverseImage F (e ≫ f)",
"ppTerm": "?m.26",
"assigned": true,
"usedCons... | [
"C : Type u\ninst✝² : Category.{v, u} C\nD : Type u_1\ninst✝¹ : Category.{v_1, u_1} D\nP : MorphismProperty D\ninst✝ : P.RespectsIso\nF : C ⥤ D\nX Y Z : C\ne : X ⟶ Y\nhe : IsIso e\nf : Y ⟶ Z\nhf : P.inverseImage F f\n⊢ P (F.map f)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.MorphismProperty.Basic | {
"line": 623,
"column": 4
} | {
"line": 623,
"column": 76
} | {
"line": 623,
"column": 77
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\nD : Type u_1\ninst✝¹ : Category.{v_1, u_1} D\nP : MorphismProperty D\ninst✝ : P.RespectsIso\nF : C ⥤ D\nX Y Z : C\ne : Y ⟶ Z\nhe : IsIso e\nf : X ⟶ Y\nhf : P.inverseImage F f\n⊢ P.inverseImage F (f ≫ e)",
"ppTerm": "?m.38",
"assigned": true,
"usedCons... | [
"C : Type u\ninst✝² : Category.{v, u} C\nD : Type u_1\ninst✝¹ : Category.{v_1, u_1} D\nP : MorphismProperty D\ninst✝ : P.RespectsIso\nF : C ⥤ D\nX Y Z : C\ne : Y ⟶ Z\nhe : IsIso e\nf : X ⟶ Y\nhf : P.inverseImage F f\n⊢ P (F.map f)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.MorphismProperty.Basic | {
"line": 657,
"column": 2
} | {
"line": 658,
"column": 54
} | {
"line": 660,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\nD : Type u_1\ninst✝² : Category.{v_1, u_1} D\nP : MorphismProperty D\ninst✝¹ : P.RespectsIso\nF : C ⥤ D\ninst✝ : F.IsEquivalence\n⊢ (P.inverseImage F).map F = P",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"CategoryTheory.MorphismPr... | [] | erw [P.inverseImage_equivalence_inverse_eq_map_functor F.asEquivalence, map_map,
P.map_eq_of_iso F.asEquivalence.counitIso, map_id] | Lean.Parser.Tactic._aux_Init_Meta___macroRules_Lean_Parser_Tactic_tacticErw____1 | Lean.Parser.Tactic.tacticErw___ |
Mathlib.CategoryTheory.MorphismProperty.Basic | {
"line": 657,
"column": 2
} | {
"line": 658,
"column": 54
} | {
"line": 660,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\nD : Type u_1\ninst✝² : Category.{v_1, u_1} D\nP : MorphismProperty D\ninst✝¹ : P.RespectsIso\nF : C ⥤ D\ninst✝ : F.IsEquivalence\n⊢ (P.inverseImage F).map F = P",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"CategoryTheory.MorphismPr... | [] | erw [P.inverseImage_equivalence_inverse_eq_map_functor F.asEquivalence, map_map,
P.map_eq_of_iso F.asEquivalence.counitIso, map_id] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.MorphismProperty.Basic | {
"line": 657,
"column": 2
} | {
"line": 658,
"column": 54
} | {
"line": 660,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\nD : Type u_1\ninst✝² : Category.{v_1, u_1} D\nP : MorphismProperty D\ninst✝¹ : P.RespectsIso\nF : C ⥤ D\ninst✝ : F.IsEquivalence\n⊢ (P.inverseImage F).map F = P",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"CategoryTheory.MorphismPr... | [] | erw [P.inverseImage_equivalence_inverse_eq_map_functor F.asEquivalence, map_map,
P.map_eq_of_iso F.asEquivalence.counitIso, map_id] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Comma.Basic | {
"line": 257,
"column": 11
} | {
"line": 262,
"column": 56
} | {
"line": 262,
"column": 57
} | [
{
"pp": "A : Type u₁\ninst✝⁵ : Category.{v₁, u₁} A\nB : Type u₂\ninst✝⁴ : Category.{v₂, u₂} B\nT : Type u₃\ninst✝³ : Category.{v₃, u₃} T\nA' : Type u₄\ninst✝² : Category.{v₄, u₄} A'\nB' : Type u₅\ninst✝¹ : Category.{v₅, u₅} B'\nT' : Type u₆\ninst✝ : Category.{v₆, u₆} T'\nL : A ⥤ T\nR : B ⥤ T\nL₁ L₂ L₃ : A ⥤ T\n... | [] | by
dsimp
rw [assoc, assoc, ← Functor.comp_map, α.naturality_assoc, ← Functor.comp_map,
← β.naturality]
dsimp
rw [← F.map_comp_assoc, ← F.map_comp_assoc, φ.w] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Comma.Basic | {
"line": 294,
"column": 20
} | {
"line": 294,
"column": 57
} | {
"line": 294,
"column": 58
} | [
{
"pp": "A : Type u₁\ninst✝¹⁰ : Category.{v₁, u₁} A\nB : Type u₂\ninst✝⁹ : Category.{v₂, u₂} B\nT : Type u₃\ninst✝⁸ : Category.{v₃, u₃} T\nA' : Type u₄\ninst✝⁷ : Category.{v₄, u₄} A'\nB' : Type u₅\ninst✝⁶ : Category.{v₅, u₅} B'\nT' : Type u₆\ninst✝⁵ : Category.{v₆, u₆} T'\nL : A ⥤ T\nR : B ⥤ T\nL₁ L₂ L₃ : A ⥤ T... | [] | rw [← Functor.comp_map, β.naturality] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.CategoryTheory.Comma.Basic | {
"line": 294,
"column": 20
} | {
"line": 294,
"column": 57
} | {
"line": 294,
"column": 58
} | [
{
"pp": "A : Type u₁\ninst✝¹⁰ : Category.{v₁, u₁} A\nB : Type u₂\ninst✝⁹ : Category.{v₂, u₂} B\nT : Type u₃\ninst✝⁸ : Category.{v₃, u₃} T\nA' : Type u₄\ninst✝⁷ : Category.{v₄, u₄} A'\nB' : Type u₅\ninst✝⁶ : Category.{v₅, u₅} B'\nT' : Type u₆\ninst✝⁵ : Category.{v₆, u₆} T'\nL : A ⥤ T\nR : B ⥤ T\nL₁ L₂ L₃ : A ⥤ T... | [] | rw [← Functor.comp_map, β.naturality] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Comma.Basic | {
"line": 294,
"column": 20
} | {
"line": 294,
"column": 57
} | {
"line": 294,
"column": 58
} | [
{
"pp": "A : Type u₁\ninst✝¹⁰ : Category.{v₁, u₁} A\nB : Type u₂\ninst✝⁹ : Category.{v₂, u₂} B\nT : Type u₃\ninst✝⁸ : Category.{v₃, u₃} T\nA' : Type u₄\ninst✝⁷ : Category.{v₄, u₄} A'\nB' : Type u₅\ninst✝⁶ : Category.{v₅, u₅} B'\nT' : Type u₆\ninst✝⁵ : Category.{v₆, u₆} T'\nL : A ⥤ T\nR : B ⥤ T\nL₁ L₂ L₃ : A ⥤ T... | [] | rw [← Functor.comp_map, β.naturality] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Category.Grp.Basic | {
"line": 486,
"column": 2
} | {
"line": 486,
"column": 13
} | {
"line": 486,
"column": 14
} | [
{
"pp": "G : AddCommGrpCat\nh k : ↑G\nw : asHom h = asHom k\n⊢ h = k",
"ppTerm": "?m.6",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"G : AddCommGrpCat\nh k : ↑G\nw : asHom h = asHom k\n⊢ h = k"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Adjunction.Basic | {
"line": 263,
"column": 14
} | {
"line": 264,
"column": 11
} | {
"line": 264,
"column": 12
} | [
{
"pp": "C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝ : Category.{v₂, u₂} D\nF : C ⥤ D\nG : D ⥤ C\nadj : F ⊣ G\nX' X : C\nY Y' : D\nf : X' ⟶ X\ng : F.obj X ⟶ Y'\nh : F.obj X' ⟶ Y\nk : Y ⟶ Y'\nw : f ≫ (adj.homEquiv X Y') g = (adj.homEquiv X' Y) h ≫ G.map k\n⊢ F.map f ≫ g = h ≫ k",
"ppTerm": ... | [
"C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝ : Category.{v₂, u₂} D\nF : C ⥤ D\nG : D ⥤ C\nadj : F ⊣ G\nX' X : C\nY Y' : D\nf : X' ⟶ X\ng : F.obj X ⟶ Y'\nh : F.obj X' ⟶ Y\nk : Y ⟶ Y'\nw : f ≫ (adj.homEquiv X Y') g = (adj.homEquiv X' Y) h ≫ G.map k\n⊢ F.map f ≫ g = h ≫ k"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Adjunction.Basic | {
"line": 272,
"column": 14
} | {
"line": 273,
"column": 11
} | {
"line": 273,
"column": 12
} | [
{
"pp": "C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝ : Category.{v₂, u₂} D\nF : C ⥤ D\nG : D ⥤ C\nadj : F ⊣ G\nX' X : C\nY Y' : D\nf : X' ⟶ X\ng : X ⟶ G.obj Y'\nh : X' ⟶ G.obj Y\nk : Y ⟶ Y'\nw : F.map f ≫ (adj.homEquiv X Y').symm g = (adj.homEquiv X' Y).symm h ≫ k\n⊢ f ≫ g = h ≫ G.map k",
... | [
"C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝ : Category.{v₂, u₂} D\nF : C ⥤ D\nG : D ⥤ C\nadj : F ⊣ G\nX' X : C\nY Y' : D\nf : X' ⟶ X\ng : X ⟶ G.obj Y'\nh : X' ⟶ G.obj Y\nk : Y ⟶ Y'\nw : F.map f ≫ (adj.homEquiv X Y').symm g = (adj.homEquiv X' Y).symm h ≫ k\n⊢ f ≫ g = h ≫ G.map k"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Adjunction.Basic | {
"line": 469,
"column": 4
} | {
"line": 469,
"column": 47
} | {
"line": 469,
"column": 48
} | [
{
"pp": "C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝ : Category.{v₂, u₂} D\nF : C ⥤ D\nG : D ⥤ C\nadj : CoreUnitCounit F G\nX : C\nthis :\n ∀ (x : C),\n (whiskerRight adj.unit F ≫ (F.associator G F).hom ≫ F.whiskerLeft adj.counit).app x = (NatTrans.id (𝟭 C ⋙ F)).app x\n⊢ F.map (adj.unit.a... | [
"C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝ : Category.{v₂, u₂} D\nF : C ⥤ D\nG : D ⥤ C\nadj : CoreUnitCounit F G\nX : C\nthis :\n ∀ (x : C),\n (whiskerRight adj.unit F ≫ (F.associator G F).hom ≫ F.whiskerLeft adj.counit).app x = (NatTrans.id (𝟭 C ⋙ F)).app x\n⊢ F.map (adj.unit.app X) ≫ adj.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Adjunction.Basic | {
"line": 473,
"column": 4
} | {
"line": 473,
"column": 48
} | {
"line": 473,
"column": 49
} | [
{
"pp": "C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝ : Category.{v₂, u₂} D\nF : C ⥤ D\nG : D ⥤ C\nadj : CoreUnitCounit F G\nY : D\nthis :\n ∀ (x : D),\n (G.whiskerLeft adj.unit ≫ (G.associator F G).inv ≫ whiskerRight adj.counit G).app x = (NatTrans.id (G ⋙ 𝟭 C)).app x\n⊢ adj.unit.app (G.o... | [
"C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝ : Category.{v₂, u₂} D\nF : C ⥤ D\nG : D ⥤ C\nadj : CoreUnitCounit F G\nY : D\nthis :\n ∀ (x : D),\n (G.whiskerLeft adj.unit ≫ (G.associator F G).inv ≫ whiskerRight adj.counit G).app x = (NatTrans.id (G ⋙ 𝟭 C)).app x\n⊢ adj.unit.app (G.obj Y) ≫ G.ma... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Category.Preorder | {
"line": 273,
"column": 2
} | {
"line": 275,
"column": 18
} | {
"line": 276,
"column": 0
} | [
{
"pp": "case mpr\nX : Type u\ninst✝ : PartialOrder X\na b : X\nf : a ⟶ b\n⊢ a = b → IsIso f",
"ppTerm": "?mpr",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"CategoryTheory.IsIso",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"PartialOrde... | [] | · rintro rfl
rw [Subsingleton.elim f (𝟙 _)]
infer_instance | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.CategoryTheory.Bicategory.Basic | {
"line": 416,
"column": 74
} | {
"line": 417,
"column": 38
} | {
"line": 417,
"column": 39
} | [
{
"pp": "B : Type u\ninst✝ : Bicategory B\na b c : B\nf : a ⟶ b\ng : b ⟶ c\n⊢ (α_ f (g ≫ 𝟙 c) (𝟙 c)).inv ≫ (f ◁ (ρ_ g).hom) ▷ 𝟙 c =\n (α_ f (g ≫ 𝟙 c) (𝟙 c)).inv ≫ (α_ f g (𝟙 c)).inv ▷ 𝟙 c ≫ (ρ_ (f ≫ g)).hom ▷ 𝟙 c",
"ppTerm": "?m.94",
"assigned": true,
"usedConstants": [
"Eq.mpr",
... | [
"B : Type u\ninst✝ : Bicategory B\na b c : B\nf : a ⟶ b\ng : b ⟶ c\n⊢ f ◁ (α_ g (𝟙 c) (𝟙 c)).inv ≫ (α_ f (g ≫ 𝟙 c) (𝟙 c)).inv ≫ (f ◁ (ρ_ g).hom) ▷ 𝟙 c =\n f ◁ (α_ g (𝟙 c) (𝟙 c)).inv ≫ (α_ f (g ≫ 𝟙 c) (𝟙 c)).inv ≫ (α_ f g (𝟙 c)).inv ▷ 𝟙 c ≫ (ρ_ (f ≫ g)).hom ▷ 𝟙 c"
] | ←
cancel_epi (f ◁ (α_ _ _ _).inv), | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.CategoryTheory.Yoneda | {
"line": 789,
"column": 2
} | {
"line": 790,
"column": 78
} | {
"line": 792,
"column": 0
} | [
{
"pp": "C : Type u₁\ninst✝ : Category.{v₁, u₁} C\nX Y : Cᵒᵖ\nf : X ⟶ Y\nF : Cᵒᵖ ⥤ Type v₁\nt : F.obj X\n⊢ yonedaEquiv.symm ((ConcreteCategory.hom (F.map f)) t) = yoneda.map f.unop ≫ yonedaEquiv.symm t",
"ppTerm": "?m.48",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"CategoryTheory.Fu... | [] | obtain ⟨u, rfl⟩ := yonedaEquiv.surjective t
rw [yonedaEquiv_naturality', Equiv.symm_apply_apply, Equiv.symm_apply_apply] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Yoneda | {
"line": 789,
"column": 2
} | {
"line": 790,
"column": 78
} | {
"line": 792,
"column": 0
} | [
{
"pp": "C : Type u₁\ninst✝ : Category.{v₁, u₁} C\nX Y : Cᵒᵖ\nf : X ⟶ Y\nF : Cᵒᵖ ⥤ Type v₁\nt : F.obj X\n⊢ yonedaEquiv.symm ((ConcreteCategory.hom (F.map f)) t) = yoneda.map f.unop ≫ yonedaEquiv.symm t",
"ppTerm": "?m.48",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"CategoryTheory.Fu... | [] | obtain ⟨u, rfl⟩ := yonedaEquiv.surjective t
rw [yonedaEquiv_naturality', Equiv.symm_apply_apply, Equiv.symm_apply_apply] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.EssentiallySmall | {
"line": 294,
"column": 28
} | {
"line": 294,
"column": 39
} | {
"line": 294,
"column": 40
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : Small.{w, u} C\ninst✝ : LocallySmall.{w, v, u} C\nφ : Arrow C → (s : C) × (t : C) × (s ⟶ t) := fun f ↦ ⟨f.left, ⟨f.right, f.hom⟩⟩\ns t : C\nf f' : (𝟭 C).obj s ⟶ (𝟭 C).obj t\nh :\n Arrow.right { left := s, right := t, hom := f } = Arrow.right { left :=... | [
"C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : Small.{w, u} C\ninst✝ : LocallySmall.{w, v, u} C\nφ : Arrow C → (s : C) × (t : C) × (s ⟶ t) := fun f ↦ ⟨f.left, ⟨f.right, f.hom⟩⟩\ns t : C\nf f' : (𝟭 C).obj s ⟶ (𝟭 C).obj t\nh :\n Arrow.right { left := s, right := t, hom := f } = Arrow.right { left := s, right :=... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Yoneda | {
"line": 942,
"column": 58
} | {
"line": 945,
"column": 6
} | {
"line": 947,
"column": 0
} | [
{
"pp": "C : Type u₁\ninst✝ : Category.{v₁, u₁} C\nX Y : Cᵒᵖ\nf : X ⟶ Y\nF : Cᵒᵖ ⥤ Type (max w v₁)\nt : F.obj X\n⊢ uliftYonedaEquiv.symm ((ConcreteCategory.hom (F.map f)) t) =\n uliftYoneda.{w, v₁, u₁}.map f.unop ≫ uliftYonedaEquiv.symm t",
"ppTerm": "?m.48",
"assigned": true,
"usedConstants": [
... | [] | by
obtain ⟨u, rfl⟩ := uliftYonedaEquiv.surjective t
rw [uliftYonedaEquiv_naturality]
simp | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Yoneda | {
"line": 967,
"column": 2
} | {
"line": 967,
"column": 47
} | {
"line": 968,
"column": 4
} | [
{
"pp": "C : Type u₁\ninst✝ : Category.{v₁, u₁} C\nP Q : Cᵒᵖ ⥤ Type (max w v₁)\nf g : P ⟶ Q\nh : ∀ (X : C) (p : uliftYoneda.{w, v₁, u₁}.obj X ⟶ P), p ≫ f = p ≫ g\nX : Cᵒᵖ\nx : P.obj X\n⊢ (ConcreteCategory.hom (f.app X)).toFun x = (ConcreteCategory.hom (g.app X)).toFun x",
"ppTerm": "?m.67",
"assigned": ... | [
"C : Type u₁\ninst✝ : Category.{v₁, u₁} C\nP Q : Cᵒᵖ ⥤ Type (max w v₁)\nf g : P ⟶ Q\nh : ∀ (X : C) (p : uliftYoneda.{w, v₁, u₁}.obj X ⟶ P), p ≫ f = p ≫ g\nX : Cᵒᵖ\nx : P.obj X\n⊢ (ConcreteCategory.hom (f.app X)) x = (ConcreteCategory.hom (g.app X)) x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Yoneda | {
"line": 983,
"column": 8
} | {
"line": 983,
"column": 19
} | {
"line": 983,
"column": 20
} | [
{
"pp": "C✝ : Type u₁\ninst✝¹ : Category.{v₁, u₁} C✝\nC : Type u₁\ninst✝ : Category.{v₁, u₁} C\nX : Cᵒᵖ\nY Z : Cᵒᵖ ⥤ Type (max w v₁)\nf : Y ⟶ Z\ng : ((uliftYoneda.{w, v₁, u₁}.op ⋙ coyoneda).obj X).obj Y\n⊢ ((ConcreteCategory.hom\n (((uliftYoneda.{w, v₁, u₁}.op ⋙ coyoneda).obj X).map f ≫\n ... | [
"C✝ : Type u₁\ninst✝¹ : Category.{v₁, u₁} C✝\nC : Type u₁\ninst✝ : Category.{v₁, u₁} C\nX : Cᵒᵖ\nY Z : Cᵒᵖ ⥤ Type (max w v₁)\nf : Y ⟶ Z\ng : ((uliftYoneda.{w, v₁, u₁}.op ⋙ coyoneda).obj X).obj Y\n⊢ uliftYonedaEquiv (g ≫ f) = (ConcreteCategory.hom (f.app X)) (uliftYonedaEquiv g)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Yoneda | {
"line": 988,
"column": 6
} | {
"line": 988,
"column": 17
} | {
"line": 988,
"column": 18
} | [
{
"pp": "C✝ : Type u₁\ninst✝¹ : Category.{v₁, u₁} C✝\nC : Type u₁\ninst✝ : Category.{v₁, u₁} C\nY Z : Cᵒᵖ\nf : Y ⟶ Z\nF : Cᵒᵖ ⥤ Type (max w v₁)\ng : ((uliftYoneda.{w, v₁, u₁}.op ⋙ coyoneda).obj Y).obj F\n⊢ ((ConcreteCategory.hom\n (((uliftYoneda.{w, v₁, u₁}.op ⋙ coyoneda).map f ≫\n (... | [
"C✝ : Type u₁\ninst✝¹ : Category.{v₁, u₁} C✝\nC : Type u₁\ninst✝ : Category.{v₁, u₁} C\nY Z : Cᵒᵖ\nf : Y ⟶ Z\nF : Cᵒᵖ ⥤ Type (max w v₁)\ng : ((uliftYoneda.{w, v₁, u₁}.op ⋙ coyoneda).obj Y).obj F\n⊢ uliftYonedaEquiv (uliftYoneda.{w, v₁, u₁}.map f.unop ≫ g) = (ConcreteCategory.hom (F.map f)) (uliftYonedaEquiv g)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Yoneda | {
"line": 1110,
"column": 8
} | {
"line": 1110,
"column": 19
} | {
"line": 1110,
"column": 20
} | [
{
"pp": "C✝ : Type u₁\ninst✝¹ : Category.{v₁, u₁} C✝\nC : Type u₁\ninst✝ : Category.{v₁, u₁} C\nX : C\nY Z : C ⥤ Type v₁\nf : Y ⟶ Z\ng : ((coyoneda.rightOp ⋙ coyoneda).obj X).obj Y\n⊢ ((ConcreteCategory.hom\n (((coyoneda.rightOp ⋙ coyoneda).obj X).map f ≫ (coyonedaEquiv.trans Equiv.ulift.symm).toIso.... | [
"C✝ : Type u₁\ninst✝¹ : Category.{v₁, u₁} C✝\nC : Type u₁\ninst✝ : Category.{v₁, u₁} C\nX : C\nY Z : C ⥤ Type v₁\nf : Y ⟶ Z\ng : ((coyoneda.rightOp ⋙ coyoneda).obj X).obj Y\n⊢ coyonedaEquiv (g ≫ f) = (ConcreteCategory.hom (f.app X)) (coyonedaEquiv g)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Yoneda | {
"line": 1115,
"column": 6
} | {
"line": 1115,
"column": 17
} | {
"line": 1115,
"column": 18
} | [
{
"pp": "C✝ : Type u₁\ninst✝¹ : Category.{v₁, u₁} C✝\nC : Type u₁\ninst✝ : Category.{v₁, u₁} C\nY Z : C\nf : Y ⟶ Z\nF : C ⥤ Type v₁\ng : ((coyoneda.rightOp ⋙ coyoneda).obj Y).obj F\n⊢ ((ConcreteCategory.hom\n (((coyoneda.rightOp ⋙ coyoneda).map f ≫\n (NatIso.ofComponents (fun x ↦ (co... | [
"C✝ : Type u₁\ninst✝¹ : Category.{v₁, u₁} C✝\nC : Type u₁\ninst✝ : Category.{v₁, u₁} C\nY Z : C\nf : Y ⟶ Z\nF : C ⥤ Type v₁\ng : ((coyoneda.rightOp ⋙ coyoneda).obj Y).obj F\n⊢ coyonedaEquiv (coyoneda.map f.op ≫ g) = (ConcreteCategory.hom (F.map f)) (coyonedaEquiv g)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Cones | {
"line": 157,
"column": 2
} | {
"line": 157,
"column": 13
} | {
"line": 157,
"column": 14
} | [
{
"pp": "J : Type u₁\ninst✝¹ : Category.{v₁, u₁} J\nC : Type u₃\ninst✝ : Category.{v₃, u₃} C\nF : J ⥤ C\nc : Cone F\nj j' : J\nf : j ⟶ j'\n⊢ c.π.app j ≫ F.map f = c.π.app j'",
"ppTerm": "?m.45",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"J : Type u₁\ninst✝¹ : Category.{v₁, u₁} J\nC : Type u₃\ninst✝ : Category.{v₃, u₃} C\nF : J ⥤ C\nc : Cone F\nj j' : J\nf : j ⟶ j'\n⊢ c.π.app j ≫ F.map f = c.π.app j'"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Yoneda | {
"line": 1199,
"column": 2
} | {
"line": 1200,
"column": 9
} | {
"line": 1200,
"column": 10
} | [
{
"pp": "C : Type u₁\ninst✝ : Category.{v₁, u₁} C\nP Q : C ⥤ Type (max w v₁)\nf g : P ⟶ Q\nh : ∀ (X : Cᵒᵖ) (p : uliftCoyoneda.{w, v₁, u₁}.obj X ⟶ P), p ≫ f = p ≫ g\nX : C\nx : P.obj X\n⊢ (ConcreteCategory.hom (f.app X)).toFun x = (ConcreteCategory.hom (g.app X)).toFun x",
"ppTerm": "?m.67",
"assigned": ... | [
"C : Type u₁\ninst✝ : Category.{v₁, u₁} C\nP Q : C ⥤ Type (max w v₁)\nf g : P ⟶ Q\nh : ∀ (X : Cᵒᵖ) (p : uliftCoyoneda.{w, v₁, u₁}.obj X ⟶ P), p ≫ f = p ≫ g\nX : C\nx : P.obj X\n⊢ (ConcreteCategory.hom (f.app X)) x = (ConcreteCategory.hom (g.app X)) x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Yoneda | {
"line": 1214,
"column": 8
} | {
"line": 1214,
"column": 19
} | {
"line": 1214,
"column": 20
} | [
{
"pp": "C✝ : Type u₁\ninst✝¹ : Category.{v₁, u₁} C✝\nC : Type u₁\ninst✝ : Category.{v₁, u₁} C\nX : C\nY Z : C ⥤ Type (max w v₁)\nf : Y ⟶ Z\ng : ((uliftCoyoneda.{w, v₁, u₁}.rightOp ⋙ coyoneda).obj X).obj Y\n⊢ ((ConcreteCategory.hom\n (((uliftCoyoneda.{w, v₁, u₁}.rightOp ⋙ coyoneda).obj X).map f ≫\n ... | [
"C✝ : Type u₁\ninst✝¹ : Category.{v₁, u₁} C✝\nC : Type u₁\ninst✝ : Category.{v₁, u₁} C\nX : C\nY Z : C ⥤ Type (max w v₁)\nf : Y ⟶ Z\ng : ((uliftCoyoneda.{w, v₁, u₁}.rightOp ⋙ coyoneda).obj X).obj Y\n⊢ uliftCoyonedaEquiv (g ≫ f) = (ConcreteCategory.hom (f.app X)) (uliftCoyonedaEquiv g)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Yoneda | {
"line": 1219,
"column": 6
} | {
"line": 1219,
"column": 17
} | {
"line": 1219,
"column": 18
} | [
{
"pp": "C✝ : Type u₁\ninst✝¹ : Category.{v₁, u₁} C✝\nC : Type u₁\ninst✝ : Category.{v₁, u₁} C\nY Z : C\nf : Y ⟶ Z\nF : C ⥤ Type (max w v₁)\ng : ((uliftCoyoneda.{w, v₁, u₁}.rightOp ⋙ coyoneda).obj Y).obj F\n⊢ ((ConcreteCategory.hom\n (((uliftCoyoneda.{w, v₁, u₁}.rightOp ⋙ coyoneda).map f ≫\n ... | [
"C✝ : Type u₁\ninst✝¹ : Category.{v₁, u₁} C✝\nC : Type u₁\ninst✝ : Category.{v₁, u₁} C\nY Z : C\nf : Y ⟶ Z\nF : C ⥤ Type (max w v₁)\ng : ((uliftCoyoneda.{w, v₁, u₁}.rightOp ⋙ coyoneda).obj Y).obj F\n⊢ uliftCoyonedaEquiv (uliftCoyoneda.{w, v₁, u₁}.map f.op ≫ g) = (ConcreteCategory.hom (F.map f)) (uliftCoyonedaEquiv ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Cones | {
"line": 455,
"column": 12
} | {
"line": 455,
"column": 46
} | {
"line": 455,
"column": 47
} | [
{
"pp": "J : Type u₁\ninst✝⁴ : Category.{v₁, u₁} J\nK : Type u₂\ninst✝³ : Category.{v₂, u₂} K\nC : Type u₃\ninst✝² : Category.{v₃, u₃} C\nD : Type u₄\ninst✝¹ : Category.{v₄, u₄} D\nE : Type u₅\ninst✝ : Category.{v₅, u₅} E\nF : J ⥤ C\ne : K ≌ J\ns : Cone (e.functor ⋙ F)\nk : K\n⊢ (((whiskering e.inverse ⋙ postco... | [
"J : Type u₁\ninst✝⁴ : Category.{v₁, u₁} J\nK : Type u₂\ninst✝³ : Category.{v₂, u₂} K\nC : Type u₃\ninst✝² : Category.{v₃, u₃} C\nD : Type u₄\ninst✝¹ : Category.{v₄, u₄} D\nE : Type u₅\ninst✝ : Category.{v₅, u₅} E\nF : J ⥤ C\ne : K ≌ J\ns : Cone (e.functor ⋙ F)\nk : K\n⊢ s.π.app (e.inverse.obj (e.functor.obj k)) ≫ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Cones | {
"line": 502,
"column": 41
} | {
"line": 502,
"column": 52
} | {
"line": 502,
"column": 53
} | [
{
"pp": "J : Type u₁\ninst✝⁶ : Category.{v₁, u₁} J\nK : Type u₂\ninst✝⁵ : Category.{v₂, u₂} K\nC : Type u₃\ninst✝⁴ : Category.{v₃, u₃} C\nD : Type u₄\ninst✝³ : Category.{v₄, u₄} D\nE : Type u₅\ninst✝² : Category.{v₅, u₅} E\nF : J ⥤ C\nG : C ⥤ D\ninst✝¹ : G.Full\ninst✝ : G.Faithful\nX✝ Y✝ : Cone F\nt : (functori... | [
"J : Type u₁\ninst✝⁶ : Category.{v₁, u₁} J\nK : Type u₂\ninst✝⁵ : Category.{v₂, u₂} K\nC : Type u₃\ninst✝⁴ : Category.{v₃, u₃} C\nD : Type u₄\ninst✝³ : Category.{v₄, u₄} D\nE : Type u₅\ninst✝² : Category.{v₅, u₅} E\nF : J ⥤ C\nG : C ⥤ D\ninst✝¹ : G.Full\ninst✝ : G.Faithful\nX✝ Y✝ : Cone F\nt : (functoriality F G).o... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Functor.EpiMono | {
"line": 319,
"column": 2
} | {
"line": 320,
"column": 18
} | {
"line": 322,
"column": 0
} | [
{
"pp": "case mpr\nC : Type u_1\nD : Type u_2\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Category.{v_2, u_2} D\nF : C ⥤ D\nA B : C\nf : A ⟶ B\ninst✝ : F.IsEquivalence\n⊢ StrongEpi f → StrongEpi (F.map f)",
"ppTerm": "?mpr",
"assigned": true,
"usedConstants": [
"inferInstance",
"CategoryTh... | [] | · intro
infer_instance | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.CategoryTheory.Limits.HasLimits | {
"line": 559,
"column": 59
} | {
"line": 559,
"column": 70
} | {
"line": 559,
"column": 71
} | [
{
"pp": "J : Type u₁\ninst✝⁵ : Category.{v₁, u₁} J\nK : Type u₂\ninst✝⁴ : Category.{v₂, u₂} K\nC : Type u\ninst✝³ : Category.{v, u} C\nF✝ F G : J ⥤ C\ninst✝² : HasLimit F\ninst✝¹ : HasLimit G\nα : F ⟶ G\ninst✝ : ∀ (j : J), Mono (α.app j)\nZ : C\nu v : Z ⟶ limit F\nh : u ≫ limMap α = v ≫ limMap α\nj : J\n⊢ (u ≫ ... | [
"J : Type u₁\ninst✝⁵ : Category.{v₁, u₁} J\nK : Type u₂\ninst✝⁴ : Category.{v₂, u₂} K\nC : Type u\ninst✝³ : Category.{v, u} C\nF✝ F G : J ⥤ C\ninst✝² : HasLimit F\ninst✝¹ : HasLimit G\nα : F ⟶ G\ninst✝ : ∀ (j : J), Mono (α.app j)\nZ : C\nu v : Z ⟶ limit F\nh : u ≫ limMap α = v ≫ limMap α\nj : J\n⊢ u ≫ limit.π F j ≫... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.IsTerminal | {
"line": 395,
"column": 8
} | {
"line": 396,
"column": 84
} | {
"line": 396,
"column": 85
} | [
{
"pp": "C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nJ : Type u\ninst✝ : Category.{v, u} J\nX : J\ntX : IsTerminal X\nF : J ⥤ C\nj j' : J\nk : j ⟶ j'\n⊢ F.map k ≫ F.map (tX.from j') = F.map (tX.from j) ≫ ((Functor.const J).obj (F.obj X)).map k",
"ppTerm": "?m.39",
"assigned": true,
"usedConstants": [... | [] | dsimp
rw [← F.map_comp, Category.comp_id, tX.hom_ext (k ≫ tX.from j') (tX.from j)] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Limits.Shapes.IsTerminal | {
"line": 395,
"column": 8
} | {
"line": 396,
"column": 84
} | {
"line": 396,
"column": 85
} | [
{
"pp": "C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nJ : Type u\ninst✝ : Category.{v, u} J\nX : J\ntX : IsTerminal X\nF : J ⥤ C\nj j' : J\nk : j ⟶ j'\n⊢ F.map k ≫ F.map (tX.from j') = F.map (tX.from j) ≫ ((Functor.const J).obj (F.obj X)).map k",
"ppTerm": "?m.39",
"assigned": true,
"usedConstants": [... | [] | dsimp
rw [← F.map_comp, Category.comp_id, tX.hom_ext (k ≫ tX.from j') (tX.from j)] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Limits.HasLimits | {
"line": 1171,
"column": 60
} | {
"line": 1171,
"column": 71
} | {
"line": 1171,
"column": 72
} | [
{
"pp": "J : Type u₁\ninst✝⁵ : Category.{v₁, u₁} J\nK : Type u₂\ninst✝⁴ : Category.{v₂, u₂} K\nC : Type u\ninst✝³ : Category.{v, u} C\nF✝ F G : J ⥤ C\ninst✝² : HasColimit F\ninst✝¹ : HasColimit G\nα : F ⟶ G\ninst✝ : ∀ (j : J), Epi (α.app j)\nZ : C\nu v : colimit G ⟶ Z\nh : colimMap α ≫ u = colimMap α ≫ v\nj : J... | [
"J : Type u₁\ninst✝⁵ : Category.{v₁, u₁} J\nK : Type u₂\ninst✝⁴ : Category.{v₂, u₂} K\nC : Type u\ninst✝³ : Category.{v, u} C\nF✝ F G : J ⥤ C\ninst✝² : HasColimit F\ninst✝¹ : HasColimit G\nα : F ⟶ G\ninst✝ : ∀ (j : J), Epi (α.app j)\nZ : C\nu v : colimit G ⟶ Z\nh : colimMap α ≫ u = colimMap α ≫ v\nj : J\n⊢ α.app j ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts | {
"line": 437,
"column": 42
} | {
"line": 437,
"column": 77
} | {
"line": 437,
"column": 78
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nX Y : C\nh : IsTerminal Y\nc : BinaryFan X Y\nH : IsLimit c\nl : X ⟶ c.pt\nhl : l ≫ c.fst = 𝟙 X\n⊢ (c.fst ≫ l) ≫ c.fst = 𝟙 (((Functor.const (Discrete WalkingPair)).obj c.pt).obj { as := left }) ≫ c.fst",
"ppTerm": "?m.78",
"assigned": true,
"usedCons... | [
"C : Type u\ninst✝ : Category.{v, u} C\nX Y : C\nh : IsTerminal Y\nc : BinaryFan X Y\nH : IsLimit c\nl : X ⟶ c.pt\nhl : l ≫ c.fst = 𝟙 X\n⊢ c.fst ≫ 𝟙 X = c.fst"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Products | {
"line": 822,
"column": 8
} | {
"line": 822,
"column": 19
} | {
"line": 822,
"column": 20
} | [
{
"pp": "β : Type w\nα : Type w₂\nγ : Type w₃\nC : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Unique β\nf : β → C\ns : Cone (Discrete.functor f)\nm :\n s.pt ⟶\n { pt := f default,\n π :=\n Discrete.natTrans fun x ↦\n match x with\n | { as := j } => eqToHom ⋯ }.pt\nw :\... | [
"β : Type w\nα : Type w₂\nγ : Type w₃\nC : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Unique β\nf : β → C\ns : Cone (Discrete.functor f)\nm :\n s.pt ⟶\n { pt := f default,\n π :=\n Discrete.natTrans fun x ↦\n match x with\n | { as := j } => eqToHom ⋯ }.pt\nw :\n m ≫\n ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Products | {
"line": 851,
"column": 4
} | {
"line": 851,
"column": 37
} | {
"line": 851,
"column": 38
} | [
{
"pp": "case refine_2\nβ : Type w\nα : Type w₂\nγ : Type w₃\nC : Type u\ninst✝¹ : Category.{v, u} C\nX Y : C\ne : X ≅ Y\nJ : Type u_1\ninst✝ : Unique J\ns : Fan fun x ↦ Y\nm : s.pt ⟶ (mk X fun x ↦ e.hom).pt\nhm : ∀ (j : J), m ≫ (mk X fun x ↦ e.hom).proj j = s.proj j\n⊢ m = s.proj default ≫ e.inv",
"ppTerm"... | [
"case refine_2\nβ : Type w\nα : Type w₂\nγ : Type w₃\nC : Type u\ninst✝¹ : Category.{v, u} C\nX Y : C\ne : X ≅ Y\nJ : Type u_1\ninst✝ : Unique J\ns : Fan fun x ↦ Y\nm : s.pt ⟶ (mk X fun x ↦ e.hom).pt\nhm : ∀ (j : J), m ≫ (mk X fun x ↦ e.hom).proj j = s.proj j\n⊢ m ≫ e.hom = s.proj default"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Products | {
"line": 901,
"column": 4
} | {
"line": 901,
"column": 36
} | {
"line": 901,
"column": 37
} | [
{
"pp": "case refine_2\nβ : Type w\nα : Type w₂\nγ : Type w₃\nC : Type u\ninst✝¹ : Category.{v, u} C\nX Y : C\ne : X ≅ Y\nJ : Type u_1\ninst✝ : Unique J\ns : Cofan fun x ↦ X\nm : (mk Y fun x ↦ e.hom).pt ⟶ s.pt\nhm : ∀ (j : J), (mk Y fun x ↦ e.hom).inj j ≫ m = s.inj j\n⊢ m = e.inv ≫ s.inj default",
"ppTerm":... | [
"case refine_2\nβ : Type w\nα : Type w₂\nγ : Type w₃\nC : Type u\ninst✝¹ : Category.{v, u} C\nX Y : C\ne : X ≅ Y\nJ : Type u_1\ninst✝ : Unique J\ns : Cofan fun x ↦ X\nm : (mk Y fun x ↦ e.hom).pt ⟶ s.pt\nhm : ∀ (j : J), (mk Y fun x ↦ e.hom).inj j ≫ m = s.inj j\n⊢ e.hom ≫ m = s.inj default"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Products | {
"line": 984,
"column": 4
} | {
"line": 984,
"column": 15
} | {
"line": 984,
"column": 16
} | [
{
"pp": "β : Type w\nα : Type w₂\nγ : Type w₃\nC : Type u\ninst✝³ : Category.{v, u} C\nJ : Type u₂\ninst✝² : Category.{v₂, u₂} J\nF : J ⥤ C\ninst✝¹ : HasLimit F\ninst✝ : HasProduct F.obj\nZ✝ : C\nx✝¹ x✝ : Z✝ ⟶ limit F\nh : x✝¹ ≫ Pi.lift (limit.π F) = x✝ ≫ Pi.lift (limit.π F)\nj : J\n⊢ x✝¹ ≫ limit.π F j = x✝ ≫ l... | [
"β : Type w\nα : Type w₂\nγ : Type w₃\nC : Type u\ninst✝³ : Category.{v, u} C\nJ : Type u₂\ninst✝² : Category.{v₂, u₂} J\nF : J ⥤ C\ninst✝¹ : HasLimit F\ninst✝ : HasProduct F.obj\nZ✝ : C\nx✝¹ x✝ : Z✝ ⟶ limit F\nh : x✝¹ ≫ Pi.lift (limit.π F) = x✝ ≫ Pi.lift (limit.π F)\nj : J\n⊢ x✝¹ ≫ limit.π F j = x✝ ≫ limit.π F j"
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Products | {
"line": 990,
"column": 4
} | {
"line": 990,
"column": 15
} | {
"line": 990,
"column": 16
} | [
{
"pp": "β : Type w\nα : Type w₂\nγ : Type w₃\nC : Type u\ninst✝³ : Category.{v, u} C\nJ : Type u₂\ninst✝² : Category.{v₂, u₂} J\nF : J ⥤ C\ninst✝¹ : HasColimit F\ninst✝ : HasCoproduct F.obj\nZ✝ : C\nx✝¹ x✝ : colimit F ⟶ Z✝\nh : Sigma.desc (colimit.ι F) ≫ x✝¹ = Sigma.desc (colimit.ι F) ≫ x✝\nj : J\n⊢ colimit.ι ... | [
"β : Type w\nα : Type w₂\nγ : Type w₃\nC : Type u\ninst✝³ : Category.{v, u} C\nJ : Type u₂\ninst✝² : Category.{v₂, u₂} J\nF : J ⥤ C\ninst✝¹ : HasColimit F\ninst✝ : HasCoproduct F.obj\nZ✝ : C\nx✝¹ x✝ : colimit F ⟶ Z✝\nh : Sigma.desc (colimit.ι F) ≫ x✝¹ = Sigma.desc (colimit.ι F) ≫ x✝\nj : J\n⊢ colimit.ι F j ≫ x✝¹ = ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Products | {
"line": 1028,
"column": 53
} | {
"line": 1028,
"column": 64
} | {
"line": 1028,
"column": 65
} | [
{
"pp": "β : Type w\nα : Type w₂\nγ : Type w₃\nC : Type u\ninst✝ : Category.{v, u} C\nι : Type u_1\nι' : Type u_2\nX : ι → ι' → C\nc : (i : ι) → Fan fun j ↦ X i j\nhc : (i : ι) → IsLimit (c i)\nc' : Fan fun i ↦ (c i).pt\nhc' : IsLimit c'\nt : Fan fun p ↦ X p.1 p.2\nm : t.pt ⟶ (Fan.mk c'.pt fun p ↦ c'.proj p.1 ≫... | [
"β : Type w\nα : Type w₂\nγ : Type w₃\nC : Type u\ninst✝ : Category.{v, u} C\nι : Type u_1\nι' : Type u_2\nX : ι → ι' → C\nc : (i : ι) → Fan fun j ↦ X i j\nhc : (i : ι) → IsLimit (c i)\nc' : Fan fun i ↦ (c i).pt\nhc' : IsLimit c'\nt : Fan fun p ↦ X p.1 p.2\nm : t.pt ⟶ (Fan.mk c'.pt fun p ↦ c'.proj p.1 ≫ (c p.1).pro... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts | {
"line": 513,
"column": 6
} | {
"line": 513,
"column": 17
} | {
"line": 513,
"column": 18
} | [
{
"pp": "case uniq.h₁\nC : Type u\ninst✝¹ : Category.{v, u} C\nX✝ Y✝ X Y X' : C\nc : BinaryCofan X Y\nf : X' ⟶ X\ninst✝ : IsIso f\nh : IsColimit c\ns : BinaryCofan X' ((pair X Y).obj { as := right })\nm : ((Functor.const (Discrete WalkingPair)).obj c.pt).obj { as := left } ⟶ s.pt\ne₁ : (f ≫ c.inl) ≫ m = s.inl\n... | [
"case uniq.h₁\nC : Type u\ninst✝¹ : Category.{v, u} C\nX✝ Y✝ X Y X' : C\nc : BinaryCofan X Y\nf : X' ⟶ X\ninst✝ : IsIso f\nh : IsColimit c\ns : BinaryCofan X' ((pair X Y).obj { as := right })\nm : ((Functor.const (Discrete WalkingPair)).obj c.pt).obj { as := left } ⟶ s.pt\ne₁ : (f ≫ c.inl) ≫ m = s.inl\ne₂ : c.inr ≫... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Products | {
"line": 1039,
"column": 57
} | {
"line": 1039,
"column": 68
} | {
"line": 1039,
"column": 69
} | [
{
"pp": "β : Type w\nα : Type w₂\nγ : Type w₃\nC : Type u\ninst✝ : Category.{v, u} C\nι : Type u_1\nι' : Type u_2\nX : ι → ι' → C\nc : (i : ι) → Cofan fun j ↦ X i j\nhc : (i : ι) → IsColimit (c i)\nc' : Cofan fun i ↦ (c i).pt\nhc' : IsColimit c'\nt : Cofan fun p ↦ X p.1 p.2\nm : (Cofan.mk c'.pt fun p ↦ (c p.1).... | [
"β : Type w\nα : Type w₂\nγ : Type w₃\nC : Type u\ninst✝ : Category.{v, u} C\nι : Type u_1\nι' : Type u_2\nX : ι → ι' → C\nc : (i : ι) → Cofan fun j ↦ X i j\nhc : (i : ι) → IsColimit (c i)\nc' : Cofan fun i ↦ (c i).pt\nhc' : IsColimit c'\nt : Cofan fun p ↦ X p.1 p.2\nm : (Cofan.mk c'.pt fun p ↦ (c p.1).inj p.2 ≫ c'... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts | {
"line": 753,
"column": 6
} | {
"line": 753,
"column": 17
} | {
"line": 753,
"column": 18
} | [
{
"pp": "case h₁\nC✝ : Type u\ninst✝⁵ : Category.{v, u} C✝\nX✝ Y✝ : C✝\nC : Type u_1\ninst✝⁴ : Category.{v_1, u_1} C\nW X Y Z : C\nf : W ⟶ Y\ng : X ⟶ Z\ninst✝³ : Mono f\ninst✝² : Mono g\ninst✝¹ : HasBinaryProduct W X\ninst✝ : HasBinaryProduct Y Z\nZ✝ : C\ni₁ i₂ : Z✝ ⟶ W ⨯ X\nh : i₁ ≫ map f g = i₂ ≫ map f g\n⊢ (... | [
"case h₁\nC✝ : Type u\ninst✝⁵ : Category.{v, u} C✝\nX✝ Y✝ : C✝\nC : Type u_1\ninst✝⁴ : Category.{v_1, u_1} C\nW X Y Z : C\nf : W ⟶ Y\ng : X ⟶ Z\ninst✝³ : Mono f\ninst✝² : Mono g\ninst✝¹ : HasBinaryProduct W X\ninst✝ : HasBinaryProduct Y Z\nZ✝ : C\ni₁ i₂ : Z✝ ⟶ W ⨯ X\nh : i₁ ≫ map f g = i₂ ≫ map f g\n⊢ i₁ ≫ fst ≫ f ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts | {
"line": 755,
"column": 6
} | {
"line": 755,
"column": 17
} | {
"line": 755,
"column": 18
} | [
{
"pp": "case h₂\nC✝ : Type u\ninst✝⁵ : Category.{v, u} C✝\nX✝ Y✝ : C✝\nC : Type u_1\ninst✝⁴ : Category.{v_1, u_1} C\nW X Y Z : C\nf : W ⟶ Y\ng : X ⟶ Z\ninst✝³ : Mono f\ninst✝² : Mono g\ninst✝¹ : HasBinaryProduct W X\ninst✝ : HasBinaryProduct Y Z\nZ✝ : C\ni₁ i₂ : Z✝ ⟶ W ⨯ X\nh : i₁ ≫ map f g = i₂ ≫ map f g\n⊢ (... | [
"case h₂\nC✝ : Type u\ninst✝⁵ : Category.{v, u} C✝\nX✝ Y✝ : C✝\nC : Type u_1\ninst✝⁴ : Category.{v_1, u_1} C\nW X Y Z : C\nf : W ⟶ Y\ng : X ⟶ Z\ninst✝³ : Mono f\ninst✝² : Mono g\ninst✝¹ : HasBinaryProduct W X\ninst✝ : HasBinaryProduct Y Z\nZ✝ : C\ni₁ i₂ : Z✝ ⟶ W ⨯ X\nh : i₁ ≫ map f g = i₂ ≫ map f g\n⊢ i₁ ≫ snd ≫ g ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Comma.StructuredArrow.Basic | {
"line": 72,
"column": 2
} | {
"line": 72,
"column": 13
} | {
"line": 72,
"column": 14
} | [
{
"pp": "C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝ : Category.{v₂, u₂} D\nS : D\nT : C ⥤ D\nX Y : StructuredArrow S T\nf : X ⟶ Y\n⊢ X.hom ≫ T.map (Hom.right f) = Y.hom",
"ppTerm": "?m.45",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝ : Category.{v₂, u₂} D\nS : D\nT : C ⥤ D\nX Y : StructuredArrow S T\nf : X ⟶ Y\n⊢ X.hom ≫ T.map (Hom.right f) = Y.hom"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts | {
"line": 862,
"column": 6
} | {
"line": 862,
"column": 17
} | {
"line": 862,
"column": 18
} | [
{
"pp": "case h₁\nC✝ : Type u\ninst✝⁵ : Category.{v, u} C✝\nX✝ Y✝ : C✝\nC : Type u_1\ninst✝⁴ : Category.{v_1, u_1} C\nW X Y Z : C\nf : W ⟶ Y\ng : X ⟶ Z\ninst✝³ : Epi f\ninst✝² : Epi g\ninst✝¹ : HasBinaryCoproduct W X\ninst✝ : HasBinaryCoproduct Y Z\nZ✝ : C\ni₁ i₂ : Y ⨿ Z ⟶ Z✝\nh : map f g ≫ i₁ = map f g ≫ i₂\n⊢... | [
"case h₁\nC✝ : Type u\ninst✝⁵ : Category.{v, u} C✝\nX✝ Y✝ : C✝\nC : Type u_1\ninst✝⁴ : Category.{v_1, u_1} C\nW X Y Z : C\nf : W ⟶ Y\ng : X ⟶ Z\ninst✝³ : Epi f\ninst✝² : Epi g\ninst✝¹ : HasBinaryCoproduct W X\ninst✝ : HasBinaryCoproduct Y Z\nZ✝ : C\ni₁ i₂ : Y ⨿ Z ⟶ Z✝\nh : map f g ≫ i₁ = map f g ≫ i₂\n⊢ f ≫ inl ≫ i... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts | {
"line": 864,
"column": 6
} | {
"line": 864,
"column": 17
} | {
"line": 864,
"column": 18
} | [
{
"pp": "case h₂\nC✝ : Type u\ninst✝⁵ : Category.{v, u} C✝\nX✝ Y✝ : C✝\nC : Type u_1\ninst✝⁴ : Category.{v_1, u_1} C\nW X Y Z : C\nf : W ⟶ Y\ng : X ⟶ Z\ninst✝³ : Epi f\ninst✝² : Epi g\ninst✝¹ : HasBinaryCoproduct W X\ninst✝ : HasBinaryCoproduct Y Z\nZ✝ : C\ni₁ i₂ : Y ⨿ Z ⟶ Z✝\nh : map f g ≫ i₁ = map f g ≫ i₂\n⊢... | [
"case h₂\nC✝ : Type u\ninst✝⁵ : Category.{v, u} C✝\nX✝ Y✝ : C✝\nC : Type u_1\ninst✝⁴ : Category.{v_1, u_1} C\nW X Y Z : C\nf : W ⟶ Y\ng : X ⟶ Z\ninst✝³ : Epi f\ninst✝² : Epi g\ninst✝¹ : HasBinaryCoproduct W X\ninst✝ : HasBinaryCoproduct Y Z\nZ✝ : C\ni₁ i₂ : Y ⨿ Z ⟶ Z✝\nh : map f g ≫ i₁ = map f g ≫ i₂\n⊢ g ≫ inr ≫ i... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Comma.StructuredArrow.Basic | {
"line": 183,
"column": 39
} | {
"line": 183,
"column": 50
} | {
"line": 183,
"column": 51
} | [
{
"pp": "C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝ : Category.{v₂, u₂} D\nS S' S'' : D\nY Y' Y'' : C\nT T' : C ⥤ D\nf f' : StructuredArrow S T\ng : f.right ≅ f'.right\nw : f.hom ≫ T.map g.hom = f'.hom\n⊢ (Functor.fromPUnit S).map (eqToIso ⋯).hom ≫ f'.hom = f.hom ≫ T.map g.hom",
"ppTerm":... | [
"C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝ : Category.{v₂, u₂} D\nS S' S'' : D\nY Y' Y'' : C\nT T' : C ⥤ D\nf f' : StructuredArrow S T\ng : f.right ≅ f'.right\nw : f.hom ≫ T.map g.hom = f'.hom\n⊢ f'.hom = f.hom ≫ T.map g.hom"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Comma.StructuredArrow.Basic | {
"line": 315,
"column": 34
} | {
"line": 315,
"column": 55
} | {
"line": 315,
"column": 56
} | [
{
"pp": "C : Type u₁\ninst✝³ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝² : Category.{v₂, u₂} D\nS✝ S' S'' : D\nY Y' Y'' : C\nT T' : C ⥤ D\nA : Type u₃\ninst✝¹ : Category.{v₃, u₃} A\nB : Type u₄\ninst✝ : Category.{v₄, u₄} B\nS : C\nF : B ⥤ C\nG : C ⥤ D\nx✝³ x✝² : StructuredArrow S F\nx✝¹ x✝ : x✝³ ⟶ x✝²\nh : (post... | [
"C : Type u₁\ninst✝³ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝² : Category.{v₂, u₂} D\nS✝ S' S'' : D\nY Y' Y'' : C\nT T' : C ⥤ D\nA : Type u₃\ninst✝¹ : Category.{v₃, u₃} A\nB : Type u₄\ninst✝ : Category.{v₄, u₄} B\nS : C\nF : B ⥤ C\nG : C ⥤ D\nx✝³ x✝² : StructuredArrow S F\nx✝¹ x✝ : x✝³ ⟶ x✝²\nh : (post S F G).map ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Comma.StructuredArrow.Basic | {
"line": 319,
"column": 58
} | {
"line": 319,
"column": 69
} | {
"line": 319,
"column": 70
} | [
{
"pp": "C : Type u₁\ninst✝⁴ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝³ : Category.{v₂, u₂} D\nS✝ S' S'' : D\nY Y' Y'' : C\nT T' : C ⥤ D\nA : Type u₃\ninst✝² : Category.{v₃, u₃} A\nB : Type u₄\ninst✝¹ : Category.{v₄, u₄} B\nS : C\nF : B ⥤ C\nG : C ⥤ D\ninst✝ : G.Faithful\nX✝ Y✝ : StructuredArrow S F\nf : (post ... | [
"C : Type u₁\ninst✝⁴ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝³ : Category.{v₂, u₂} D\nS✝ S' S'' : D\nY Y' Y'' : C\nT T' : C ⥤ D\nA : Type u₃\ninst✝² : Category.{v₃, u₃} A\nB : Type u₄\ninst✝¹ : Category.{v₄, u₄} B\nS : C\nF : B ⥤ C\nG : C ⥤ D\ninst✝ : G.Faithful\nX✝ Y✝ : StructuredArrow S F\nf : (post S F G).obj X... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Comma.StructuredArrow.Basic | {
"line": 429,
"column": 4
} | {
"line": 429,
"column": 15
} | {
"line": 429,
"column": 16
} | [
{
"pp": "C : Type u₁\ninst✝³ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝² : Category.{v₂, u₂} D\nS S' S'' : D\nY Y' Y'' : C\nT T' : C ⥤ D\nA : Type u₃\ninst✝¹ : Category.{v₃, u₃} A\nB : Type u₄\ninst✝ : Category.{v₄, u₄} B\nL : D\nR : C ⥤ D\nL' : B\nR' : A ⥤ B\nF✝ : C ⥤ A\nG✝ : D ⥤ B\nα✝ : L' ⟶ G✝.obj L\nβ✝ : R ⋙... | [
"C : Type u₁\ninst✝³ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝² : Category.{v₂, u₂} D\nS S' S'' : D\nY Y' Y'' : C\nT T' : C ⥤ D\nA : Type u₃\ninst✝¹ : Category.{v₃, u₃} A\nB : Type u₄\ninst✝ : Category.{v₄, u₄} B\nL : D\nR : C ⥤ D\nL' : B\nR' : A ⥤ B\nF✝ : C ⥤ A\nG✝ : D ⥤ B\nα✝ : L' ⟶ G✝.obj L\nβ✝ : R ⋙ G✝ ⟶ F✝ ⋙ R... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Comma.StructuredArrow.Basic | {
"line": 432,
"column": 4
} | {
"line": 432,
"column": 15
} | {
"line": 432,
"column": 16
} | [
{
"pp": "C : Type u₁\ninst✝³ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝² : Category.{v₂, u₂} D\nS S' S'' : D\nY Y' Y'' : C\nT T' : C ⥤ D\nA : Type u₃\ninst✝¹ : Category.{v₃, u₃} A\nB : Type u₄\ninst✝ : Category.{v₄, u₄} B\nL : D\nR : C ⥤ D\nL' : B\nR' : A ⥤ B\nF✝ : C ⥤ A\nG✝ : D ⥤ B\nα✝ : L' ⟶ G✝.obj L\nβ✝ : R ⋙... | [
"C : Type u₁\ninst✝³ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝² : Category.{v₂, u₂} D\nS S' S'' : D\nY Y' Y'' : C\nT T' : C ⥤ D\nA : Type u₃\ninst✝¹ : Category.{v₃, u₃} A\nB : Type u₄\ninst✝ : Category.{v₄, u₄} B\nL : D\nR : C ⥤ D\nL' : B\nR' : A ⥤ B\nF✝ : C ⥤ A\nG✝ : D ⥤ B\nα✝ : L' ⟶ G✝.obj L\nβ✝ : R ⋙ G✝ ⟶ F✝ ⋙ R... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts | {
"line": 1548,
"column": 8
} | {
"line": 1548,
"column": 19
} | {
"line": 1548,
"column": 20
} | [
{
"pp": "case left.left\nC : Type u\ninst✝ : Category.{v, u} C\nX Y Z P✝ : C\nsXY : BinaryFan X Y\nsYZ : BinaryFan Y Z\nP : IsLimit sXY\nQ : IsLimit sYZ\ns : BinaryFan sXY.pt Z\nR : IsLimit s\nt : Cone (pair X sYZ.pt)\nm : t.pt ⟶ (BinaryFan.assoc Q s).pt\nw : ∀ (j : Discrete WalkingPair), m ≫ (BinaryFan.assoc Q... | [
"case left.left\nC : Type u\ninst✝ : Category.{v, u} C\nX Y Z P✝ : C\nsXY : BinaryFan X Y\nsYZ : BinaryFan Y Z\nP : IsLimit sXY\nQ : IsLimit sYZ\ns : BinaryFan sXY.pt Z\nR : IsLimit s\nt : Cone (pair X sYZ.pt)\nm : t.pt ⟶ (BinaryFan.assoc Q s).pt\nw : ∀ (j : Discrete WalkingPair), m ≫ (BinaryFan.assoc Q s).π.app j ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone | {
"line": 111,
"column": 14
} | {
"line": 111,
"column": 25
} | {
"line": 111,
"column": 26
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nX Y Z : C\nf : X ⟶ Z\ng : Y ⟶ Z\nt : PullbackCone f g\nw : 𝟙 t.pt ≫ t.π.app WalkingCospan.one = t.π.app WalkingCospan.left ≫ f\n⊢ t.π.app WalkingCospan.one = t.fst ≫ f",
"ppTerm": "?m.51",
"assigned": true,
"usedConstants": [
"CategoryTheory.Lim... | [
"C : Type u\ninst✝ : Category.{v, u} C\nX Y Z : C\nf : X ⟶ Z\ng : Y ⟶ Z\nt : PullbackCone f g\nw : 𝟙 t.pt ≫ t.π.app WalkingCospan.one = t.π.app WalkingCospan.left ≫ f\n⊢ t.π.app WalkingCospan.one = t.fst ≫ f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Comma.StructuredArrow.Basic | {
"line": 532,
"column": 2
} | {
"line": 532,
"column": 13
} | {
"line": 532,
"column": 14
} | [
{
"pp": "C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝ : Category.{v₂, u₂} D\nS : C ⥤ D\nT : D\nX Y : CostructuredArrow S T\nf : X ⟶ Y\n⊢ S.map f.left ≫ Y.hom = X.hom",
"ppTerm": "?m.49",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝ : Category.{v₂, u₂} D\nS : C ⥤ D\nT : D\nX Y : CostructuredArrow S T\nf : X ⟶ Y\n⊢ S.map f.left ≫ Y.hom = X.hom"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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