module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Control.Bifunctor | {
"line": 124,
"column": 17
} | {
"line": 124,
"column": 22
} | {
"line": 125,
"column": 2
} | [
{
"pp": "F : Type u₀ → Type u₁ → Type u₂\ninst✝ : Bifunctor F\n⊢ ∀ {α : Type u_1} {β : Type u_2} (x : α ⊕ β), bimap id id x = x",
"ppTerm": "?m.4",
"assigned": true,
"usedConstants": [
"Sum.casesOn",
"Sum",
"id",
"Sum.bifunctor",
"Bifunctor.bimap",
"Sum.inl",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Control.Bifunctor | {
"line": 124,
"column": 17
} | {
"line": 124,
"column": 22
} | {
"line": 125,
"column": 2
} | [
{
"pp": "F : Type u₀ → Type u₁ → Type u₂\ninst✝ : Bifunctor F\n⊢ ∀ {α : Type u_1} {β : Type u_2} (x : α ⊕ β), bimap id id x = x",
"ppTerm": "?m.4",
"assigned": true,
"usedConstants": [
"Sum.casesOn",
"Sum",
"id",
"Sum.bifunctor",
"Bifunctor.bimap",
"Sum.inl",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Control.Bifunctor | {
"line": 124,
"column": 17
} | {
"line": 124,
"column": 22
} | {
"line": 125,
"column": 2
} | [
{
"pp": "F : Type u₀ → Type u₁ → Type u₂\ninst✝ : Bifunctor F\n⊢ ∀ {α : Type u_1} {β : Type u_2} (x : α ⊕ β), bimap id id x = x",
"ppTerm": "?m.4",
"assigned": true,
"usedConstants": [
"Sum.casesOn",
"Sum",
"id",
"Sum.bifunctor",
"Bifunctor.bimap",
"Sum.inl",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Control.Bifunctor | {
"line": 125,
"column": 20
} | {
"line": 125,
"column": 25
} | {
"line": 127,
"column": 0
} | [
{
"pp": "F : Type u₀ → Type u₁ → Type u₂\ninst✝ : Bifunctor F\n⊢ ∀ {α₀ α₁ α₂ : Type u_1} {β₀ β₁ β₂ : Type u_2} (f : α₀ → α₁) (f' : α₁ → α₂) (g : β₀ → β₁) (g' : β₁ → β₂) (x : α₀ ⊕ β₀),\n bimap f' g' (bimap f g x) = bimap (f' ∘ f) (g' ∘ g) x",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Control.Bifunctor | {
"line": 125,
"column": 20
} | {
"line": 125,
"column": 25
} | {
"line": 127,
"column": 0
} | [
{
"pp": "F : Type u₀ → Type u₁ → Type u₂\ninst✝ : Bifunctor F\n⊢ ∀ {α₀ α₁ α₂ : Type u_1} {β₀ β₁ β₂ : Type u_2} (f : α₀ → α₁) (f' : α₁ → α₂) (g : β₀ → β₁) (g' : β₁ → β₂) (x : α₀ ⊕ β₀),\n bimap f' g' (bimap f g x) = bimap (f' ∘ f) (g' ∘ g) x",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Control.Bifunctor | {
"line": 125,
"column": 20
} | {
"line": 125,
"column": 25
} | {
"line": 127,
"column": 0
} | [
{
"pp": "F : Type u₀ → Type u₁ → Type u₂\ninst✝ : Bifunctor F\n⊢ ∀ {α₀ α₁ α₂ : Type u_1} {β₀ β₁ β₂ : Type u_2} (f : α₀ → α₁) (f' : α₁ → α₂) (g : β₀ → β₁) (g' : β₁ → β₂) (x : α₀ ⊕ β₀),\n bimap f' g' (bimap f g x) = bimap (f' ∘ f) (g' ∘ g) x",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic | {
"line": 954,
"column": 57
} | {
"line": 954,
"column": 72
} | {
"line": 954,
"column": 72
} | [
{
"pp": "C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\ninst✝ : Quiver.IsThin C\nP X Y Z : C\nfst : P ⟶ X\nsnd : P ⟶ Y\nf : X ⟶ Z\ng : Y ⟶ Z\nh : IsPullback fst snd f g\nT✝ : C\nu : T✝ ⟶ X\nv : T✝ ⟶ Y\n⊢ u ≫ f = v ≫ g",
"ppTerm": "?m.54",
"assigned": true,
"usedConstants": [
"CategoryTheory.Catego... | [] | by subsingleton | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic | {
"line": 955,
"column": 7
} | {
"line": 955,
"column": 22
} | {
"line": 955,
"column": 22
} | [
{
"pp": "C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\ninst✝ : Quiver.IsThin C\nP X Y Z : C\nfst : P ⟶ X\nsnd : P ⟶ Y\nf : X ⟶ Z\ng : Y ⟶ Z\nh : IsPullback fst snd f g\n⊢ ∀ {T : C} (f_1 : T ⟶ X) (g_1 : T ⟶ Y), h.lift f_1 g_1 ⋯ ≫ (BinaryFan.mk fst snd).fst = f_1",
"ppTerm": "?m.57",
"assigned": true,
"u... | [] | by subsingleton | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic | {
"line": 955,
"column": 25
} | {
"line": 955,
"column": 40
} | {
"line": 955,
"column": 40
} | [
{
"pp": "C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\ninst✝ : Quiver.IsThin C\nP X Y Z : C\nfst : P ⟶ X\nsnd : P ⟶ Y\nf : X ⟶ Z\ng : Y ⟶ Z\nh : IsPullback fst snd f g\n⊢ ∀ {T : C} (f_1 : T ⟶ X) (g_1 : T ⟶ Y), h.lift f_1 g_1 ⋯ ≫ (BinaryFan.mk fst snd).snd = g_1",
"ppTerm": "?m.58",
"assigned": true,
"u... | [] | by subsingleton | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic | {
"line": 955,
"column": 43
} | {
"line": 955,
"column": 58
} | {
"line": 955,
"column": 58
} | [
{
"pp": "C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\ninst✝ : Quiver.IsThin C\nP X Y Z : C\nfst : P ⟶ X\nsnd : P ⟶ Y\nf : X ⟶ Z\ng : Y ⟶ Z\nh : IsPullback fst snd f g\n⊢ ∀ {T : C} (f_1 : T ⟶ X) (g_1 : T ⟶ Y) (m : T ⟶ (BinaryFan.mk fst snd).pt),\n m ≫ (BinaryFan.mk fst snd).fst = f_1 → m ≫ (BinaryFan.mk fst snd... | [] | by subsingleton | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic | {
"line": 956,
"column": 12
} | {
"line": 956,
"column": 27
} | {
"line": 956,
"column": 27
} | [
{
"pp": "C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\ninst✝ : Quiver.IsThin C\nP X Y Z : C\nfst : P ⟶ X\nsnd : P ⟶ Y\nf : X ⟶ Z\ng : Y ⟶ Z\nh : Nonempty (IsLimit (BinaryFan.mk fst snd))\n⊢ fst ≫ f = snd ≫ g",
"ppTerm": "?m.86",
"assigned": true,
"usedConstants": [
"CategoryTheory.CategoryStruct.... | [] | by subsingleton | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic | {
"line": 958,
"column": 7
} | {
"line": 958,
"column": 22
} | {
"line": 958,
"column": 22
} | [
{
"pp": "C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\ninst✝ : Quiver.IsThin C\nP X Y Z : C\nfst : P ⟶ X\nsnd : P ⟶ Y\nf : X ⟶ Z\ng : Y ⟶ Z\nh : Nonempty (IsLimit (BinaryFan.mk fst snd))\n⊢ ∀ (s : PullbackCone f g), BinaryFan.IsLimit.lift h.some s.fst s.snd ≫ fst = s.fst",
"ppTerm": "?m.121",
"assigned": t... | [] | by subsingleton | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic | {
"line": 958,
"column": 25
} | {
"line": 958,
"column": 40
} | {
"line": 958,
"column": 40
} | [
{
"pp": "C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\ninst✝ : Quiver.IsThin C\nP X Y Z : C\nfst : P ⟶ X\nsnd : P ⟶ Y\nf : X ⟶ Z\ng : Y ⟶ Z\nh : Nonempty (IsLimit (BinaryFan.mk fst snd))\n⊢ ∀ (s : PullbackCone f g), BinaryFan.IsLimit.lift h.some s.fst s.snd ≫ snd = s.snd",
"ppTerm": "?m.122",
"assigned": t... | [] | by subsingleton | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic | {
"line": 958,
"column": 43
} | {
"line": 958,
"column": 58
} | {
"line": 958,
"column": 58
} | [
{
"pp": "C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\ninst✝ : Quiver.IsThin C\nP X Y Z : C\nfst : P ⟶ X\nsnd : P ⟶ Y\nf : X ⟶ Z\ng : Y ⟶ Z\nh : Nonempty (IsLimit (BinaryFan.mk fst snd))\n⊢ ∀ (s : PullbackCone f g) (m : s.pt ⟶ P),\n m ≫ fst = s.fst → m ≫ snd = s.snd → m = BinaryFan.IsLimit.lift h.some s.fst s.s... | [] | by subsingleton | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic | {
"line": 964,
"column": 61
} | {
"line": 964,
"column": 76
} | {
"line": 964,
"column": 76
} | [
{
"pp": "C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\ninst✝ : Quiver.IsThin C\nP X Y Z : C\nf : Z ⟶ X\ng : Z ⟶ Y\ninl : X ⟶ P\ninr : Y ⟶ P\nh : IsPushout f g inl inr\nT✝ : C\nu : X ⟶ T✝\nv : Y ⟶ T✝\n⊢ f ≫ u = g ≫ v",
"ppTerm": "?m.54",
"assigned": true,
"usedConstants": [
"CategoryTheory.Categor... | [] | by subsingleton | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic | {
"line": 965,
"column": 7
} | {
"line": 965,
"column": 22
} | {
"line": 965,
"column": 22
} | [
{
"pp": "C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\ninst✝ : Quiver.IsThin C\nP X Y Z : C\nf : Z ⟶ X\ng : Z ⟶ Y\ninl : X ⟶ P\ninr : Y ⟶ P\nh : IsPushout f g inl inr\n⊢ ∀ {T : C} (f_1 : X ⟶ T) (g_1 : Y ⟶ T), (BinaryCofan.mk inl inr).inl ≫ h.desc f_1 g_1 ⋯ = f_1",
"ppTerm": "?m.57",
"assigned": true,
"... | [] | by subsingleton | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic | {
"line": 965,
"column": 25
} | {
"line": 965,
"column": 40
} | {
"line": 965,
"column": 40
} | [
{
"pp": "C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\ninst✝ : Quiver.IsThin C\nP X Y Z : C\nf : Z ⟶ X\ng : Z ⟶ Y\ninl : X ⟶ P\ninr : Y ⟶ P\nh : IsPushout f g inl inr\n⊢ ∀ {T : C} (f_1 : X ⟶ T) (g_1 : Y ⟶ T), (BinaryCofan.mk inl inr).inr ≫ h.desc f_1 g_1 ⋯ = g_1",
"ppTerm": "?m.58",
"assigned": true,
"... | [] | by subsingleton | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic | {
"line": 965,
"column": 43
} | {
"line": 965,
"column": 58
} | {
"line": 965,
"column": 58
} | [
{
"pp": "C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\ninst✝ : Quiver.IsThin C\nP X Y Z : C\nf : Z ⟶ X\ng : Z ⟶ Y\ninl : X ⟶ P\ninr : Y ⟶ P\nh : IsPushout f g inl inr\n⊢ ∀ {T : C} (f_1 : X ⟶ T) (g_1 : Y ⟶ T) (m : (BinaryCofan.mk inl inr).pt ⟶ T),\n (BinaryCofan.mk inl inr).inl ≫ m = f_1 → (BinaryCofan.mk inl in... | [] | by subsingleton | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic | {
"line": 966,
"column": 12
} | {
"line": 966,
"column": 27
} | {
"line": 966,
"column": 27
} | [
{
"pp": "C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\ninst✝ : Quiver.IsThin C\nP X Y Z : C\nf : Z ⟶ X\ng : Z ⟶ Y\ninl : X ⟶ P\ninr : Y ⟶ P\nh : Nonempty (IsColimit (BinaryCofan.mk inl inr))\n⊢ f ≫ inl = g ≫ inr",
"ppTerm": "?m.86",
"assigned": true,
"usedConstants": [
"CategoryTheory.CategoryStr... | [] | by subsingleton | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic | {
"line": 968,
"column": 7
} | {
"line": 968,
"column": 22
} | {
"line": 968,
"column": 22
} | [
{
"pp": "C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\ninst✝ : Quiver.IsThin C\nP X Y Z : C\nf : Z ⟶ X\ng : Z ⟶ Y\ninl : X ⟶ P\ninr : Y ⟶ P\nh : Nonempty (IsColimit (BinaryCofan.mk inl inr))\n⊢ ∀ (s : PushoutCocone f g), inl ≫ BinaryCofan.IsColimit.desc h.some s.inl s.inr = s.inl",
"ppTerm": "?m.121",
"ass... | [] | by subsingleton | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic | {
"line": 968,
"column": 25
} | {
"line": 968,
"column": 40
} | {
"line": 968,
"column": 40
} | [
{
"pp": "C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\ninst✝ : Quiver.IsThin C\nP X Y Z : C\nf : Z ⟶ X\ng : Z ⟶ Y\ninl : X ⟶ P\ninr : Y ⟶ P\nh : Nonempty (IsColimit (BinaryCofan.mk inl inr))\n⊢ ∀ (s : PushoutCocone f g), inr ≫ BinaryCofan.IsColimit.desc h.some s.inl s.inr = s.inr",
"ppTerm": "?m.122",
"ass... | [] | by subsingleton | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic | {
"line": 968,
"column": 43
} | {
"line": 968,
"column": 58
} | {
"line": 968,
"column": 58
} | [
{
"pp": "C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\ninst✝ : Quiver.IsThin C\nP X Y Z : C\nf : Z ⟶ X\ng : Z ⟶ Y\ninl : X ⟶ P\ninr : Y ⟶ P\nh : Nonempty (IsColimit (BinaryCofan.mk inl inr))\n⊢ ∀ (s : PushoutCocone f g) (m : P ⟶ s.pt),\n inl ≫ m = s.inl → inr ≫ m = s.inr → m = BinaryCofan.IsColimit.desc h.some ... | [] | by subsingleton | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.RingTheory.Localization.BaseChange | {
"line": 248,
"column": 2
} | {
"line": 248,
"column": 84
} | {
"line": 249,
"column": 2
} | [
{
"pp": "R : Type u_1\ninst✝²¹ : CommSemiring R\nS✝ : Submonoid R\nA : Type u_2\ninst✝²⁰ : CommSemiring A\ninst✝¹⁹ : Algebra R A\ninst✝¹⁸ : IsLocalization S✝ A\nM : Type u_3\ninst✝¹⁷ : AddCommMonoid M\ninst✝¹⁶ : Module R M\nM' : Type u_4\ninst✝¹⁵ : AddCommMonoid M'\ninst✝¹⁴ : Module R M'\ninst✝¹³ : Module A M'\... | [
"R : Type u_1\ninst✝²¹ : CommSemiring R\nS✝ : Submonoid R\nA : Type u_2\ninst✝²⁰ : CommSemiring A\ninst✝¹⁹ : Algebra R A\ninst✝¹⁸ : IsLocalization S✝ A\nM : Type u_3\ninst✝¹⁷ : AddCommMonoid M\ninst✝¹⁶ : Module R M\nM' : Type u_4\ninst✝¹⁵ : AddCommMonoid M'\ninst✝¹⁴ : Module R M'\ninst✝¹³ : Module A M'\ninst✝¹² : I... | haveI : IsScalarTower A Aₚ M' := (IsLocalizedModule.iso S g).symm.isScalarTower Aₚ | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHaveI___1 | Lean.Parser.Tactic.tacticHaveI__ |
Mathlib.CategoryTheory.Monad.Basic | {
"line": 352,
"column": 4
} | {
"line": 352,
"column": 38
} | {
"line": 353,
"column": 4
} | [
{
"pp": "C : Type u₁\ninst✝ : Category.{v₁, u₁} C\nT✝ : Monad C\nG : Comonad C\nF : C ⥤ C\nT : Comonad C\ni : T.toFunctor ≅ F\nX : C\n⊢ i.inv.app X ≫ T.δ.app X ≫ i.hom.app (T.obj X) ≫ F.map (i.hom.app X) ≫ F.map (i.inv.app X) ≫ F.map (T.ε.app X) =\n 𝟙 (F.obj X)",
"ppTerm": "?m.206",
"assigned": true... | [
"C : Type u₁\ninst✝ : Category.{v₁, u₁} C\nT✝ : Monad C\nG : Comonad C\nF : C ⥤ C\nT : Comonad C\ni : T.toFunctor ≅ F\nX : C\n⊢ i.inv.app X ≫ T.δ.app X ≫ i.hom.app (T.obj X) ≫ F.map (i.hom.app X ≫ i.inv.app X) ≫ F.map (T.ε.app X) = 𝟙 (F.obj X)"
] | slice_lhs 4 5 => rw [← F.map_comp] | Mathlib.Tactic.Slice._aux_Mathlib_Tactic_CategoryTheory_Slice___macroRules_Mathlib_Tactic_Slice_sliceLHS_1 | Mathlib.Tactic.Slice.sliceLHS |
Mathlib.Algebra.Module.LocalizedModule.Basic | {
"line": 576,
"column": 56
} | {
"line": 576,
"column": 84
} | {
"line": 576,
"column": 84
} | [
{
"pp": "R : Type u_1\ninst✝¹¹ : CommSemiring R\nS : Submonoid R\nM : Type u_2\nM' : Type u_3\nM'' : Type u_4\ninst✝¹⁰ : AddCommMonoid M\ninst✝⁹ : AddCommMonoid M'\ninst✝⁸ : AddCommMonoid M''\nA : Type u_5\ninst✝⁷ : CommSemiring A\ninst✝⁶ : Algebra R A\ninst✝⁵ : Module A M'\ninst✝⁴ : IsLocalization S A\ninst✝³ ... | [
"R : Type u_1\ninst✝¹¹ : CommSemiring R\nS : Submonoid R\nM : Type u_2\nM' : Type u_3\nM'' : Type u_4\ninst✝¹⁰ : AddCommMonoid M\ninst✝⁹ : AddCommMonoid M'\ninst✝⁸ : AddCommMonoid M''\nA : Type u_5\ninst✝⁷ : CommSemiring A\ninst✝⁶ : Algebra R A\ninst✝⁵ : Module A M'\ninst✝⁴ : IsLocalization S A\ninst✝³ : Module R M... | LinearEquiv.apply_symm_apply | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Category.Ring.Constructions | {
"line": 112,
"column": 4
} | {
"line": 112,
"column": 38
} | {
"line": 113,
"column": 4
} | [
{
"pp": "case property.right.right\nR A B : Type u\ninst✝⁴ : CommRing R\ninst✝³ : CommRing A\ninst✝² : CommRing B\ninst✝¹ : Algebra R A\ninst✝ : Algebra R B\ns : PushoutCocone (ofHom (algebraMap R A)) (ofHom (algebraMap R B))\nthis✝ : Algebra R ↑s.pt := ((Hom.hom s.inl).comp (algebraMap R A)).toAlgebra\nf' : A ... | [
"case property.right.right\nR A B : Type u\ninst✝⁴ : CommRing R\ninst✝³ : CommRing A\ninst✝² : CommRing B\ninst✝¹ : Algebra R A\ninst✝ : Algebra R B\ns : PushoutCocone (ofHom (algebraMap R A)) (ofHom (algebraMap R B))\nthis✝ : Algebra R ↑s.pt := ((Hom.hom s.inl).comp (algebraMap R A)).toAlgebra\nf' : A →ₐ[R] ↑s.pt ... | change _ = h (a ⊗ₜ 1) * h (1 ⊗ₜ b) | Lean.Elab.Tactic.evalChange | Lean.Parser.Tactic.change |
Mathlib.CategoryTheory.Adjunction.Comma | {
"line": 145,
"column": 4
} | {
"line": 145,
"column": 32
} | {
"line": 147,
"column": 0
} | [
{
"pp": "C : Type u₁\nD : Type u₂\ninst✝¹ : Category.{v₁, u₁} C\ninst✝ : Category.{v₂, u₂} D\nG : D ⥤ C\nF : C ⥤ D\nh : F ⊣ G\nA : C\ns : Cocone (Functor.empty (StructuredArrow A G))\nm : (asEmptyCocone (StructuredArrow.mk (h.unit.app A))).pt ⟶ s.pt\nx✝ : ∀ (j : Discrete PEmpty.{1}), (asEmptyCocone (StructuredA... | [] | simp [← StructuredArrow.w m] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.Module.LocalizedModule.Basic | {
"line": 901,
"column": 6
} | {
"line": 901,
"column": 34
} | {
"line": 901,
"column": 34
} | [
{
"pp": "R : Type u_1\ninst✝⁵ : CommSemiring R\nS : Submonoid R\nM : Type u_2\nM' : Type u_3\ninst✝⁴ : AddCommMonoid M\ninst✝³ : AddCommMonoid M'\ninst✝² : Module R M\ninst✝¹ : Module R M'\nf : M →ₗ[R] M'\ninst✝ : IsLocalizedModule S f\nm : M'\n⊢ (iso S f) ((iso S f).symm m) = (iso S f) (LocalizedModule.mk ⋯.ch... | [
"R : Type u_1\ninst✝⁵ : CommSemiring R\nS : Submonoid R\nM : Type u_2\nM' : Type u_3\ninst✝⁴ : AddCommMonoid M\ninst✝³ : AddCommMonoid M'\ninst✝² : Module R M\ninst✝¹ : Module R M'\nf : M →ₗ[R] M'\ninst✝ : IsLocalizedModule S f\nm : M'\n⊢ m = (iso S f) (LocalizedModule.mk ⋯.choose.1 ⋯.choose.2)"
] | LinearEquiv.apply_symm_apply | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Module.LocalizedModule.Basic | {
"line": 1184,
"column": 4
} | {
"line": 1184,
"column": 32
} | {
"line": 1185,
"column": 2
} | [
{
"pp": "R : Type u_1\ninst✝¹⁸ : CommSemiring R\nS : Submonoid R\nM : Type u_2\nM' : Type u_3\nM'' : Type u_4\ninst✝¹⁷ : AddCommMonoid M\ninst✝¹⁶ : AddCommMonoid M'\ninst✝¹⁵ : AddCommMonoid M''\nA : Type u_5\ninst✝¹⁴ : CommSemiring A\ninst✝¹³ : Algebra R A\ninst✝¹² : Module A M'\ninst✝¹¹ : IsLocalization S A\ni... | [] | exact ⟨⟨f₁ y', s⟩, by simpa⟩ | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Algebra.Module.LocalizedModule.Basic | {
"line": 1226,
"column": 4
} | {
"line": 1226,
"column": 67
} | {
"line": 1227,
"column": 4
} | [
{
"pp": "R : Type u_1\ninst✝¹⁷ : CommSemiring R\nS : Submonoid R\nM : Type u_2\nM' : Type u_3\nM'' : Type u_4\ninst✝¹⁶ : AddCommMonoid M\ninst✝¹⁵ : AddCommMonoid M'\ninst✝¹⁴ : AddCommMonoid M''\nA : Type u_5\ninst✝¹³ : CommSemiring A\ninst✝¹² : Algebra R A\ninst✝¹¹ : Module A M'\ninst✝¹⁰ : IsLocalization S A\ni... | [
"R : Type u_1\ninst✝¹⁷ : CommSemiring R\nS : Submonoid R\nM : Type u_2\nM' : Type u_3\nM'' : Type u_4\ninst✝¹⁶ : AddCommMonoid M\ninst✝¹⁵ : AddCommMonoid M'\ninst✝¹⁴ : AddCommMonoid M''\nA : Type u_5\ninst✝¹³ : CommSemiring A\ninst✝¹² : Algebra R A\ninst✝¹¹ : Module A M'\ninst✝¹⁰ : IsLocalization S A\ninst✝⁹ : Modu... | apply IsLocalizedModule.ext S f (IsLocalizedModule.map_units g) | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.Algebra.Module.LocalizedModule.Basic | {
"line": 1229,
"column": 4
} | {
"line": 1229,
"column": 67
} | {
"line": 1230,
"column": 4
} | [
{
"pp": "R : Type u_1\ninst✝¹⁷ : CommSemiring R\nS : Submonoid R\nM : Type u_2\nM' : Type u_3\nM'' : Type u_4\ninst✝¹⁶ : AddCommMonoid M\ninst✝¹⁵ : AddCommMonoid M'\ninst✝¹⁴ : AddCommMonoid M''\nA : Type u_5\ninst✝¹³ : CommSemiring A\ninst✝¹² : Algebra R A\ninst✝¹¹ : Module A M'\ninst✝¹⁰ : IsLocalization S A\ni... | [
"R : Type u_1\ninst✝¹⁷ : CommSemiring R\nS : Submonoid R\nM : Type u_2\nM' : Type u_3\nM'' : Type u_4\ninst✝¹⁶ : AddCommMonoid M\ninst✝¹⁵ : AddCommMonoid M'\ninst✝¹⁴ : AddCommMonoid M''\nA : Type u_5\ninst✝¹³ : CommSemiring A\ninst✝¹² : Algebra R A\ninst✝¹¹ : Module A M'\ninst✝¹⁰ : IsLocalization S A\ninst✝⁹ : Modu... | apply IsLocalizedModule.ext S f (IsLocalizedModule.map_units g) | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.CategoryTheory.WithTerminal.Cone | {
"line": 78,
"column": 26
} | {
"line": 78,
"column": 31
} | {
"line": 79,
"column": 4
} | [
{
"pp": "C : Type u₁\ninst✝² : Category.{v₁, u₁} C\nD : Type u₂\ninst✝¹ : Category.{v₂, u₂} D\nJ : Type w\ninst✝ : Category.{w', w} J\nX : C\nK : J ⥤ Over X\nF : C ⥤ D\nt✝ t : Cone K\nx✝ : star ⟶ star\n⊢ (((Functor.const (WithTerminal J)).obj t.pt.left).map x✝ ≫\n match star with\n | of a => Over.Hom.... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.WithTerminal.Cone | {
"line": 78,
"column": 26
} | {
"line": 78,
"column": 31
} | {
"line": 79,
"column": 4
} | [
{
"pp": "C : Type u₁\ninst✝² : Category.{v₁, u₁} C\nD : Type u₂\ninst✝¹ : Category.{v₂, u₂} D\nJ : Type w\ninst✝ : Category.{w', w} J\nX : C\nK : J ⥤ Over X\nF : C ⥤ D\nt✝ t : Cone K\nx✝ : star ⟶ star\n⊢ (((Functor.const (WithTerminal J)).obj t.pt.left).map x✝ ≫\n match star with\n | of a => Over.Hom.... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.WithTerminal.Cone | {
"line": 78,
"column": 26
} | {
"line": 78,
"column": 31
} | {
"line": 79,
"column": 4
} | [
{
"pp": "C : Type u₁\ninst✝² : Category.{v₁, u₁} C\nD : Type u₂\ninst✝¹ : Category.{v₂, u₂} D\nJ : Type w\ninst✝ : Category.{w', w} J\nX : C\nK : J ⥤ Over X\nF : C ⥤ D\nt✝ t : Cone K\nx✝ : star ⟶ star\n⊢ (((Functor.const (WithTerminal J)).obj t.pt.left).map x✝ ≫\n match star with\n | of a => Over.Hom.... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.WithTerminal.Cone | {
"line": 78,
"column": 26
} | {
"line": 78,
"column": 31
} | {
"line": 79,
"column": 4
} | [
{
"pp": "C : Type u₁\ninst✝² : Category.{v₁, u₁} C\nD : Type u₂\ninst✝¹ : Category.{v₂, u₂} D\nJ : Type w\ninst✝ : Category.{w', w} J\nX : C\nK : J ⥤ Over X\nF : C ⥤ D\nt✝ t : Cone K\na : J\nx✝ : of a ⟶ star\n⊢ (((Functor.const (WithTerminal J)).obj t.pt.left).map x✝ ≫\n match star with\n | of a => Ov... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.WithTerminal.Cone | {
"line": 78,
"column": 26
} | {
"line": 78,
"column": 31
} | {
"line": 79,
"column": 4
} | [
{
"pp": "C : Type u₁\ninst✝² : Category.{v₁, u₁} C\nD : Type u₂\ninst✝¹ : Category.{v₂, u₂} D\nJ : Type w\ninst✝ : Category.{w', w} J\nX : C\nK : J ⥤ Over X\nF : C ⥤ D\nt✝ t : Cone K\na : J\nx✝ : of a ⟶ star\n⊢ (((Functor.const (WithTerminal J)).obj t.pt.left).map x✝ ≫\n match star with\n | of a => Ov... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.WithTerminal.Cone | {
"line": 78,
"column": 26
} | {
"line": 78,
"column": 31
} | {
"line": 79,
"column": 4
} | [
{
"pp": "C : Type u₁\ninst✝² : Category.{v₁, u₁} C\nD : Type u₂\ninst✝¹ : Category.{v₂, u₂} D\nJ : Type w\ninst✝ : Category.{w', w} J\nX : C\nK : J ⥤ Over X\nF : C ⥤ D\nt✝ t : Cone K\na : J\nx✝ : of a ⟶ star\n⊢ (((Functor.const (WithTerminal J)).obj t.pt.left).map x✝ ≫\n match star with\n | of a => Ov... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.WithTerminal.Cone | {
"line": 190,
"column": 26
} | {
"line": 190,
"column": 31
} | {
"line": 191,
"column": 4
} | [
{
"pp": "C : Type u₁\ninst✝² : Category.{v₁, u₁} C\nD : Type u₂\ninst✝¹ : Category.{v₂, u₂} D\nJ : Type w\ninst✝ : Category.{w', w} J\nX : C\nK : J ⥤ Under X\nF : C ⥤ D\nt✝ t : Cocone K\nx✝ : star ⟶ star\n⊢ ((liftFromUnder.obj K).map x✝ ≫\n match star with\n | of a => Under.Hom.right (t.ι.app a)\n ... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.WithTerminal.Cone | {
"line": 190,
"column": 26
} | {
"line": 190,
"column": 31
} | {
"line": 191,
"column": 4
} | [
{
"pp": "C : Type u₁\ninst✝² : Category.{v₁, u₁} C\nD : Type u₂\ninst✝¹ : Category.{v₂, u₂} D\nJ : Type w\ninst✝ : Category.{w', w} J\nX : C\nK : J ⥤ Under X\nF : C ⥤ D\nt✝ t : Cocone K\nx✝ : star ⟶ star\n⊢ ((liftFromUnder.obj K).map x✝ ≫\n match star with\n | of a => Under.Hom.right (t.ι.app a)\n ... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.WithTerminal.Cone | {
"line": 190,
"column": 26
} | {
"line": 190,
"column": 31
} | {
"line": 191,
"column": 4
} | [
{
"pp": "C : Type u₁\ninst✝² : Category.{v₁, u₁} C\nD : Type u₂\ninst✝¹ : Category.{v₂, u₂} D\nJ : Type w\ninst✝ : Category.{w', w} J\nX : C\nK : J ⥤ Under X\nF : C ⥤ D\nt✝ t : Cocone K\nx✝ : star ⟶ star\n⊢ ((liftFromUnder.obj K).map x✝ ≫\n match star with\n | of a => Under.Hom.right (t.ι.app a)\n ... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.WithTerminal.Cone | {
"line": 190,
"column": 26
} | {
"line": 190,
"column": 31
} | {
"line": 191,
"column": 4
} | [
{
"pp": "C : Type u₁\ninst✝² : Category.{v₁, u₁} C\nD : Type u₂\ninst✝¹ : Category.{v₂, u₂} D\nJ : Type w\ninst✝ : Category.{w', w} J\nX : C\nK : J ⥤ Under X\nF : C ⥤ D\nt✝ t : Cocone K\nb : J\nx✝ : star ⟶ of b\n⊢ ((liftFromUnder.obj K).map x✝ ≫\n match of b with\n | of a => Under.Hom.right (t.ι.app a... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.WithTerminal.Cone | {
"line": 190,
"column": 26
} | {
"line": 190,
"column": 31
} | {
"line": 191,
"column": 4
} | [
{
"pp": "C : Type u₁\ninst✝² : Category.{v₁, u₁} C\nD : Type u₂\ninst✝¹ : Category.{v₂, u₂} D\nJ : Type w\ninst✝ : Category.{w', w} J\nX : C\nK : J ⥤ Under X\nF : C ⥤ D\nt✝ t : Cocone K\nb : J\nx✝ : star ⟶ of b\n⊢ ((liftFromUnder.obj K).map x✝ ≫\n match of b with\n | of a => Under.Hom.right (t.ι.app a... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.WithTerminal.Cone | {
"line": 190,
"column": 26
} | {
"line": 190,
"column": 31
} | {
"line": 191,
"column": 4
} | [
{
"pp": "C : Type u₁\ninst✝² : Category.{v₁, u₁} C\nD : Type u₂\ninst✝¹ : Category.{v₂, u₂} D\nJ : Type w\ninst✝ : Category.{w', w} J\nX : C\nK : J ⥤ Under X\nF : C ⥤ D\nt✝ t : Cocone K\nb : J\nx✝ : star ⟶ of b\n⊢ ((liftFromUnder.obj K).map x✝ ≫\n match of b with\n | of a => Under.Hom.right (t.ι.app a... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.ObjectProperty.Small | {
"line": 73,
"column": 32
} | {
"line": 73,
"column": 37
} | {
"line": 73,
"column": 37
} | [
{
"pp": "case inl\nC : Type u\ninst✝³ : Category.{v, u} C\nD : Type u'\ninst✝² : Category.{v', u'} D\nP Q : ObjectProperty C\ninst✝¹ : ObjectProperty.Small.{w, v, u} P\ninst✝ : ObjectProperty.Small.{w, v, u} Q\nx : C\nhx : P x\n⊢ ∃ a,\n (fun x ↦\n match x with\n | Sum.inl x => ⟨↑x, ⋯⟩\n ... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.ObjectProperty.Small | {
"line": 73,
"column": 32
} | {
"line": 73,
"column": 37
} | {
"line": 73,
"column": 37
} | [
{
"pp": "case inr\nC : Type u\ninst✝³ : Category.{v, u} C\nD : Type u'\ninst✝² : Category.{v', u'} D\nP Q : ObjectProperty C\ninst✝¹ : ObjectProperty.Small.{w, v, u} P\ninst✝ : ObjectProperty.Small.{w, v, u} Q\nx : C\nhx : Q x\n⊢ ∃ a,\n (fun x ↦\n match x with\n | Sum.inl x => ⟨↑x, ⋯⟩\n ... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.ObjectProperty.Small | {
"line": 78,
"column": 70
} | {
"line": 78,
"column": 75
} | {
"line": 78,
"column": 75
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\nD : Type u'\ninst✝² : Category.{v', u'} D\nα : Type u_1\nP : α → ObjectProperty C\ninst✝¹ : ∀ (a : α), ObjectProperty.Small.{w, v, u} (P a)\ninst✝ : Small.{w, u_1} α\nx : (a : α) × Subtype (P a)\n⊢ (⨆ a, P a) ↑x.snd",
"ppTerm": "?m.23",
"assigned": true,
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.ObjectProperty.Small | {
"line": 78,
"column": 70
} | {
"line": 78,
"column": 75
} | {
"line": 78,
"column": 75
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\nD : Type u'\ninst✝² : Category.{v', u'} D\nα : Type u_1\nP : α → ObjectProperty C\ninst✝¹ : ∀ (a : α), ObjectProperty.Small.{w, v, u} (P a)\ninst✝ : Small.{w, u_1} α\nx : (a : α) × Subtype (P a)\n⊢ (⨆ a, P a) ↑x.snd",
"ppTerm": "?m.23",
"assigned": true,
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.ObjectProperty.Small | {
"line": 78,
"column": 70
} | {
"line": 78,
"column": 75
} | {
"line": 78,
"column": 75
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\nD : Type u'\ninst✝² : Category.{v', u'} D\nα : Type u_1\nP : α → ObjectProperty C\ninst✝¹ : ∀ (a : α), ObjectProperty.Small.{w, v, u} (P a)\ninst✝ : Small.{w, u_1} α\nx : (a : α) × Subtype (P a)\n⊢ (⨆ a, P a) ↑x.snd",
"ppTerm": "?m.23",
"assigned": true,
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.ObjectProperty.Small | {
"line": 79,
"column": 22
} | {
"line": 79,
"column": 27
} | {
"line": 79,
"column": 27
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\nD : Type u'\ninst✝² : Category.{v', u'} D\nα : Type u_1\nP : α → ObjectProperty C\ninst✝¹ : ∀ (a : α), ObjectProperty.Small.{w, v, u} (P a)\ninst✝ : Small.{w, u_1} α\nx✝ : Subtype (⨆ a, P a)\nx : C\nhx : (⨆ a, P a) x\n⊢ ∃ a, (fun x ↦ ⟨↑x.snd, ⋯⟩) a = ⟨x, hx⟩",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.ObjectProperty.Small | {
"line": 79,
"column": 22
} | {
"line": 79,
"column": 27
} | {
"line": 79,
"column": 27
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\nD : Type u'\ninst✝² : Category.{v', u'} D\nα : Type u_1\nP : α → ObjectProperty C\ninst✝¹ : ∀ (a : α), ObjectProperty.Small.{w, v, u} (P a)\ninst✝ : Small.{w, u_1} α\nx✝ : Subtype (⨆ a, P a)\nx : C\nhx : (⨆ a, P a) x\n⊢ ∃ a, (fun x ↦ ⟨↑x.snd, ⋯⟩) a = ⟨x, hx⟩",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.ObjectProperty.Small | {
"line": 79,
"column": 22
} | {
"line": 79,
"column": 27
} | {
"line": 79,
"column": 27
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\nD : Type u'\ninst✝² : Category.{v', u'} D\nα : Type u_1\nP : α → ObjectProperty C\ninst✝¹ : ∀ (a : α), ObjectProperty.Small.{w, v, u} (P a)\ninst✝ : Small.{w, u_1} α\nx✝ : Subtype (⨆ a, P a)\nx : C\nhx : (⨆ a, P a) x\n⊢ ∃ a, (fun x ↦ ⟨↑x.snd, ⋯⟩) a = ⟨x, hx⟩",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.ObjectProperty.Small | {
"line": 178,
"column": 4
} | {
"line": 178,
"column": 66
} | {
"line": 179,
"column": 4
} | [
{
"pp": "case refine_1\nC : Type u\ninst✝ : Category.{v, u} C\nP : ObjectProperty C\nx✝ : ObjectProperty.EssentiallySmall.{w, v, u} P.op\n⊢ ObjectProperty.EssentiallySmall.{w, v, u} P",
"ppTerm": "?refine_1",
"assigned": true,
"usedConstants": [
"CategoryTheory.ObjectProperty.EssentiallySmall"... | [
"case refine_1\nC : Type u\ninst✝ : Category.{v, u} C\nP : ObjectProperty C\nx✝ : ObjectProperty.EssentiallySmall.{w, v, u} P.op\nQ : ObjectProperty Cᵒᵖ\nh₁ : ObjectProperty.Small.{w, v, u} Q\nleft✝ : Q ≤ P.op\nh₂ : P.op ≤ Q.isoClosure\n⊢ ObjectProperty.EssentiallySmall.{w, v, u} P"
] | obtain ⟨Q, h₁, _, h₂⟩ := EssentiallySmall.exists_small_le P.op | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.CategoryTheory.Elements | {
"line": 302,
"column": 37
} | {
"line": 302,
"column": 42
} | {
"line": 302,
"column": 42
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF✝ : C ⥤ Type w\nF : Cᵒᵖ ⥤ Type (max w v)\nX✝ Y✝ : F.Elementsᵒᵖ\nf : X✝ ⟶ Y✝\n⊢ ((𝟭 F.Elementsᵒᵖ).map f ≫\n (isoMk\n (F.elementsMk\n (op\n ({ obj := fun x ↦ CostructuredArrow.mk (uliftYonedaEquiv.symm (unop x).s... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.Elements | {
"line": 302,
"column": 37
} | {
"line": 302,
"column": 42
} | {
"line": 302,
"column": 42
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF✝ : C ⥤ Type w\nF : Cᵒᵖ ⥤ Type (max w v)\nX✝ Y✝ : F.Elementsᵒᵖ\nf : X✝ ⟶ Y✝\n⊢ ((𝟭 F.Elementsᵒᵖ).map f ≫\n (isoMk\n (F.elementsMk\n (op\n ({ obj := fun x ↦ CostructuredArrow.mk (uliftYonedaEquiv.symm (unop x).s... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Elements | {
"line": 302,
"column": 37
} | {
"line": 302,
"column": 42
} | {
"line": 302,
"column": 42
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF✝ : C ⥤ Type w\nF : Cᵒᵖ ⥤ Type (max w v)\nX✝ Y✝ : F.Elementsᵒᵖ\nf : X✝ ⟶ Y✝\n⊢ ((𝟭 F.Elementsᵒᵖ).map f ≫\n (isoMk\n (F.elementsMk\n (op\n ({ obj := fun x ↦ CostructuredArrow.mk (uliftYonedaEquiv.symm (unop x).s... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Grothendieck | {
"line": 159,
"column": 53
} | {
"line": 161,
"column": 6
} | {
"line": 163,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF : C ⥤ Cat\nX Y : Grothendieck F\nf g : X ⟶ Y\nh : f = g\n⊢ f.fiber = eqToHom ⋯ ≫ g.fiber",
"ppTerm": "?m.40",
"assigned": true,
"usedConstants": [
"CategoryTheory.Cat.category",
"CategoryTheory.Grothendieck.fiber",
"CategoryTheory.G... | [] | by
subst h
simp | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.WithTerminal.Basic | {
"line": 456,
"column": 20
} | {
"line": 456,
"column": 30
} | {
"line": 457,
"column": 2
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nJ : Type u_1\nx y✝ : WidePullbackShape J\ny : J\nf : widePullbackShapeEquivObj none ⟶ widePullbackShapeEquivObj (some y)\n⊢ none ⟶ some y",
"ppTerm": "?m.125",
"assigned": true,
"usedConstants": [
"Equiv.instEquivLike",
"CategoryTheory.Cate... | [] | by cases f | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.WithTerminal.Basic | {
"line": 462,
"column": 20
} | {
"line": 462,
"column": 30
} | {
"line": 463,
"column": 2
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nJ : Type u_1\nx y✝ : WidePullbackShape J\ny : J\nf : widePullbackShapeEquivObj none ⟶ widePullbackShapeEquivObj (some y)\n⊢ (fun x ↦\n match some y, none, x with\n | .(none), .(some j), Hom.term j => PUnit.unit\n | y, .(y), Hom.id .(y) => 𝟙 (... | [] | by cases f | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.WithTerminal.Basic | {
"line": 477,
"column": 53
} | {
"line": 477,
"column": 58
} | {
"line": 477,
"column": 58
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nJ : Type u_1\nx : WidePullbackShape J\n⊢ (𝟭 (WidePullbackShape J)).obj x =\n ({ obj := ⇑widePullbackShapeEquivObj, map := fun {X Y} ↦ ⇑(widePullbackShapeEquivMap X Y), map_id := ⋯,\n map_comp := ⋯ } ⋙\n { obj := ⇑widePullbackShapeEquivObj.s... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.WithTerminal.Basic | {
"line": 477,
"column": 53
} | {
"line": 477,
"column": 58
} | {
"line": 477,
"column": 58
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nJ : Type u_1\nx : WidePullbackShape J\n⊢ (𝟭 (WidePullbackShape J)).obj x =\n ({ obj := ⇑widePullbackShapeEquivObj, map := fun {X Y} ↦ ⇑(widePullbackShapeEquivMap X Y), map_id := ⋯,\n map_comp := ⋯ } ⋙\n { obj := ⇑widePullbackShapeEquivObj.s... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.WithTerminal.Basic | {
"line": 477,
"column": 53
} | {
"line": 477,
"column": 58
} | {
"line": 477,
"column": 58
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nJ : Type u_1\nx : WidePullbackShape J\n⊢ (𝟭 (WidePullbackShape J)).obj x =\n ({ obj := ⇑widePullbackShapeEquivObj, map := fun {X Y} ↦ ⇑(widePullbackShapeEquivMap X Y), map_id := ⋯,\n map_comp := ⋯ } ⋙\n { obj := ⇑widePullbackShapeEquivObj.s... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.WithTerminal.Basic | {
"line": 478,
"column": 55
} | {
"line": 478,
"column": 60
} | {
"line": 478,
"column": 60
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nJ : Type u_1\nx : WithTerminal (Discrete J)\n⊢ ({ obj := ⇑widePullbackShapeEquivObj.symm,\n map := fun {X Y} f ↦\n (widePullbackShapeEquivMap (widePullbackShapeEquivObj.symm X) (widePullbackShapeEquivObj.symm Y)).symm\n (eqTo... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.WithTerminal.Basic | {
"line": 478,
"column": 55
} | {
"line": 478,
"column": 60
} | {
"line": 478,
"column": 60
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nJ : Type u_1\nx : WithTerminal (Discrete J)\n⊢ ({ obj := ⇑widePullbackShapeEquivObj.symm,\n map := fun {X Y} f ↦\n (widePullbackShapeEquivMap (widePullbackShapeEquivObj.symm X) (widePullbackShapeEquivObj.symm Y)).symm\n (eqTo... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.WithTerminal.Basic | {
"line": 478,
"column": 55
} | {
"line": 478,
"column": 60
} | {
"line": 478,
"column": 60
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nJ : Type u_1\nx : WithTerminal (Discrete J)\n⊢ ({ obj := ⇑widePullbackShapeEquivObj.symm,\n map := fun {X Y} f ↦\n (widePullbackShapeEquivMap (widePullbackShapeEquivObj.symm X) (widePullbackShapeEquivObj.symm Y)).symm\n (eqTo... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.EffectiveEpi.Basic | {
"line": 244,
"column": 4
} | {
"line": 244,
"column": 14
} | {
"line": 246,
"column": 0
} | [
{
"pp": "C : Type u_1\ninst✝² : Category.{v_1, u_1} C\nB : C\nα : Type u_2\nX : α → C\nπ : (a : α) → X a ⟶ B\ninst✝¹ : HasCoproduct X\ninst✝ : IsIso (Sigma.desc π)\nW✝ : C\ne : (a : α) → X a ⟶ W✝\nh : ∀ {Z : C} (a₁ a₂ : α) (g₁ : Z ⟶ X a₁) (g₂ : Z ⟶ X a₂), g₁ ≫ π a₁ = g₂ ≫ π a₂ → g₁ ≫ e a₁ = g₂ ≫ e a₂\nm : B ⟶ W... | [] | exact hm a | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.CategoryTheory.WithTerminal.Basic | {
"line": 869,
"column": 31
} | {
"line": 869,
"column": 46
} | {
"line": 869,
"column": 47
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nx y z : WithInitial Cᵒᵖ\nf✝ : x ⟶ y\ng✝ : y ⟶ z\nx✝¹ x✝ : WithInitial Cᵒᵖ\nf : WithInitial.star ⟶ x✝¹\ng : x✝¹ ⟶ x✝\n⊢ (match WithInitial.star, x✝, f ≫ g with\n | WithInitial.of (op x), WithInitial.of (op y), f => WithInitial.down f\n | WithInitial.star, Wit... | [] | by subsingleton | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Limits.Final | {
"line": 420,
"column": 4
} | {
"line": 420,
"column": 97
} | {
"line": 421,
"column": 4
} | [
{
"pp": "C : Type u₁\ninst✝⁵ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝⁴ : Category.{v₂, u₂} D\nF : C ⥤ D\ninst✝³ : F.Final\nE : Type u₃\ninst✝² : Category.{v₃, u₃} E\nG : D ⥤ E\nB : Type u₄\ninst✝¹ : Category.{v₄, u₄} B\nH : E ⥤ B\ninst✝ : CreatesColimit (F ⋙ G) H\nc : Cocone (G ⋙ H)\nhc : IsColimit c\ni : H.ma... | [
"C : Type u₁\ninst✝⁵ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝⁴ : Category.{v₂, u₂} D\nF : C ⥤ D\ninst✝³ : F.Final\nE : Type u₃\ninst✝² : Category.{v₃, u₃} E\nG : D ⥤ E\nB : Type u₄\ninst✝¹ : Category.{v₄, u₄} B\nH : E ⥤ B\ninst✝ : CreatesColimit (F ⋙ G) H\nc : Cocone (G ⋙ H)\nhc : IsColimit c\ni : H.mapCocone (lif... | refine ?_ ≪≫ ((extendCocone (F := F)).mapIso i) ≪≫ ((coconesEquiv F (G ⋙ H)).counitIso.app _) | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.CategoryTheory.WithTerminal.Basic | {
"line": 916,
"column": 33
} | {
"line": 916,
"column": 48
} | {
"line": 916,
"column": 49
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nx y z : (WithInitial C)ᵒᵖ\nf✝ : unop y ⟶ unop x\ng✝ : unop z ⟶ unop y\nx✝³ x✝² : (WithInitial C)ᵒᵖ\nf : unop x✝² ⟶ unop x✝³\ng : unop (op star) ⟶ unop x✝²\nx✝¹ : x✝³ ⟶ x✝²\nx✝ : x✝² ⟶ op star\n⊢ (match op f ≫ op g with\n | op f_1 =>\n match x✝³, op star, f... | [] | by subsingleton | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers | {
"line": 393,
"column": 40
} | {
"line": 393,
"column": 59
} | {
"line": 393,
"column": 60
} | [
{
"pp": "case refine_1\nC : Type u₁\ninst✝² : Category.{v₁, u₁} C\nJ : Type u₂\ninst✝¹ : Category.{v₂, u₂} J\nX Y : C\nf : X ⟶ Y\ninst✝ : HasPushout f f\nh : IsColimit (Cofork.ofπ f.op ⋯)\n⊢ (Iso.refl (Opposite.unop (Opposite.op Y))).hom ≫ pushout.inl f f = (pushout.inl f f).op.unop",
"ppTerm": "?refine_1",... | [
"case refine_1\nC : Type u₁\ninst✝² : Category.{v₁, u₁} C\nJ : Type u₂\ninst✝¹ : Category.{v₂, u₂} J\nX Y : C\nf : X ⟶ Y\ninst✝ : HasPushout f f\nh : IsColimit (Cofork.ofπ f.op ⋯)\n⊢ (Iso.refl (Opposite.unop (Opposite.op Y))).hom ≫ pushout.inl f f = pushout.inl f f"
] | Quiver.Hom.unop_op, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers | {
"line": 395,
"column": 40
} | {
"line": 395,
"column": 59
} | {
"line": 395,
"column": 60
} | [
{
"pp": "case refine_2\nC : Type u₁\ninst✝² : Category.{v₁, u₁} C\nJ : Type u₂\ninst✝¹ : Category.{v₂, u₂} J\nX Y : C\nf : X ⟶ Y\ninst✝ : HasPushout f f\nh : IsColimit (Cofork.ofπ f.op ⋯)\n⊢ (Iso.refl (Opposite.unop (Opposite.op Y))).hom ≫ pushout.inr f f = (pushout.inr f f).op.unop",
"ppTerm": "?refine_2",... | [
"case refine_2\nC : Type u₁\ninst✝² : Category.{v₁, u₁} C\nJ : Type u₂\ninst✝¹ : Category.{v₂, u₂} J\nX Y : C\nf : X ⟶ Y\ninst✝ : HasPushout f f\nh : IsColimit (Cofork.ofπ f.op ⋯)\n⊢ (Iso.refl (Opposite.unop (Opposite.op Y))).hom ≫ pushout.inr f f = pushout.inr f f"
] | Quiver.Hom.unop_op, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.RingTheory.FinitePresentation | {
"line": 501,
"column": 4
} | {
"line": 501,
"column": 83
} | {
"line": 502,
"column": 4
} | [
{
"pp": "case succ\nP : (R : Type u) → [inst : CommRing R] → (S : Type u) → [inst_1 : CommRing S] → (R →+* S) → Prop\nQ : (R : Type u) → [inst : CommRing R] → (S : Type v) → [inst_1 : CommRing S] → (R →+* S) → Prop\npolynomial : ∀ (R : Type u) [inst : CommRing R], P R R[X] C\nfg_ker :\n ∀ (R : Type u) [inst : ... | [
"case succ\nP : (R : Type u) → [inst : CommRing R] → (S : Type u) → [inst_1 : CommRing S] → (R →+* S) → Prop\nQ : (R : Type u) → [inst : CommRing R] → (S : Type v) → [inst_1 : CommRing S] → (R →+* S) → Prop\npolynomial : ∀ (R : Type u) [inst : CommRing R], P R R[X] C\nfg_ker :\n ∀ (R : Type u) [inst : CommRing R] ... | have := IH (R := R[X]) (S := S) (g'.comp e.symm) (hg.comp e.symm.surjective) he | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.RingTheory.FinitePresentation | {
"line": 478,
"column": 2
} | {
"line": 505,
"column": 12
} | {
"line": 507,
"column": 0
} | [
{
"pp": "P : (R : Type u) → [inst : CommRing R] → (S : Type u) → [inst_1 : CommRing S] → (R →+* S) → Prop\nQ : (R : Type u) → [inst : CommRing R] → (S : Type v) → [inst_1 : CommRing S] → (R →+* S) → Prop\npolynomial : ∀ (R : Type u) [inst : CommRing R], P R R[X] C\nfg_ker :\n ∀ (R : Type u) [inst : CommRing R]... | [] | letI := f.toAlgebra
obtain ⟨n, g, hg, hg'⟩ := hf
let g' := g.toRingHom
change Surjective g' at hg
change (ker g').FG at hg'
have : g'.comp MvPolynomial.C = f := g.comp_algebraMap
clear_value g'
subst this
clear g
induction n generalizing R S with
| zero =>
refine fg_ker _ _ _ (hg.comp (MvPolynom... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.RingTheory.FinitePresentation | {
"line": 478,
"column": 2
} | {
"line": 505,
"column": 12
} | {
"line": 507,
"column": 0
} | [
{
"pp": "P : (R : Type u) → [inst : CommRing R] → (S : Type u) → [inst_1 : CommRing S] → (R →+* S) → Prop\nQ : (R : Type u) → [inst : CommRing R] → (S : Type v) → [inst_1 : CommRing S] → (R →+* S) → Prop\npolynomial : ∀ (R : Type u) [inst : CommRing R], P R R[X] C\nfg_ker :\n ∀ (R : Type u) [inst : CommRing R]... | [] | letI := f.toAlgebra
obtain ⟨n, g, hg, hg'⟩ := hf
let g' := g.toRingHom
change Surjective g' at hg
change (ker g').FG at hg'
have : g'.comp MvPolynomial.C = f := g.comp_algebraMap
clear_value g'
subst this
clear g
induction n generalizing R S with
| zero =>
refine fg_ker _ _ _ (hg.comp (MvPolynom... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.Assoc | {
"line": 302,
"column": 2
} | {
"line": 303,
"column": 93
} | {
"line": 305,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\nX₁ X₂ X₃ Z₁ Z₂ : C\ng₁ : Z₁ ⟶ X₁\ng₂ : Z₁ ⟶ X₂\ng₃ : Z₂ ⟶ X₂\ng₄ : Z₂ ⟶ X₃\ninst✝² : HasPushout g₁ g₂\ninst✝¹ : HasPushout g₃ g₄\ninst✝ : HasPushout g₁ (g₂ ≫ pushout.inl g₃ g₄)\n⊢ IsColimit\n (PushoutCocone.mk\n (pushout.desc (pushout.inl g₁ (g₂ ≫ pushout... | [] | apply rightSquareIsPushout _ rfl (pushoutIsPushout _ _)
simpa [PushoutCocone.pasteHoriz] using PushoutCocone.mkSelfIsColimit (pushoutIsPushout _ _) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.Assoc | {
"line": 302,
"column": 2
} | {
"line": 303,
"column": 93
} | {
"line": 305,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\nX₁ X₂ X₃ Z₁ Z₂ : C\ng₁ : Z₁ ⟶ X₁\ng₂ : Z₁ ⟶ X₂\ng₃ : Z₂ ⟶ X₂\ng₄ : Z₂ ⟶ X₃\ninst✝² : HasPushout g₁ g₂\ninst✝¹ : HasPushout g₃ g₄\ninst✝ : HasPushout g₁ (g₂ ≫ pushout.inl g₃ g₄)\n⊢ IsColimit\n (PushoutCocone.mk\n (pushout.desc (pushout.inl g₁ (g₂ ≫ pushout... | [] | apply rightSquareIsPushout _ rfl (pushoutIsPushout _ _)
simpa [PushoutCocone.pasteHoriz] using PushoutCocone.mkSelfIsColimit (pushoutIsPushout _ _) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.RingHomProperties | {
"line": 96,
"column": 4
} | {
"line": 96,
"column": 40
} | {
"line": 97,
"column": 2
} | [
{
"pp": "case refine_1\nP Q : {R S : Type u} → [inst : CommRing R] → [inst_1 : CommRing S] → (R →+* S) → Prop\nhP : RespectsIso fun {R S} [CommRing R] [CommRing S] ↦ P\nhQ : RespectsIso fun {R S} [CommRing R] [CommRing S] ↦ Q\nR S T : Type u\ninst✝² : CommRing R\ninst✝¹ : CommRing S\ninst✝ : CommRing T\nf : R →... | [] | exact ⟨hP.1 f e hf.1, hQ.1 f e hf.2⟩ | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.CategoryTheory.Limits.Shapes.Diagonal | {
"line": 63,
"column": 2
} | {
"line": 63,
"column": 57
} | {
"line": 64,
"column": 2
} | [
{
"pp": "C : Type u_1\ninst✝² : Category.{v_1, u_1} C\nX Y Z : C\nf : X ⟶ Y\ninst✝¹ : HasPullback f f\ninst✝ : Mono f\n⊢ IsIso (diagonal f)",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"CategoryTheory.IsIso",
"CategoryTheory.CategoryStruct.toQuiver",
"Q... | [
"C : Type u_1\ninst✝² : Category.{v_1, u_1} C\nX Y Z : C\nf : X ⟶ Y\ninst✝¹ : HasPullback f f\ninst✝ : Mono f\n⊢ IsIso (inv (fst f f))"
] | rw [(IsIso.inv_eq_of_inv_hom_id (diagonal_fst f)).symm] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.RingTheory.RingHomProperties | {
"line": 251,
"column": 2
} | {
"line": 258,
"column": 18
} | {
"line": 260,
"column": 0
} | [
{
"pp": "P Q : {R S : Type u} → [inst : CommRing R] → [inst_1 : CommRing S] → (R →+* S) → Prop\nh₁ : RespectsIso fun {R S} [CommRing R] [CommRing S] ↦ P\nh₂ :\n ∀ ⦃R S T : Type u⦄ [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : CommRing T] [inst_3 : Algebra R S]\n [inst_4 : Algebra R T], Q (algebraMap R... | [] | introv R h hQ H
let e := h.symm.equiv
have : (e.symm : _ →+* _).comp (algebraMap R' S') = algebraMap R' (R' ⊗[R] S) := by
ext r
simp [e]
apply h₂ hQ
rw [← this]
exact h₁.1 _ _ H | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.RingTheory.RingHomProperties | {
"line": 251,
"column": 2
} | {
"line": 258,
"column": 18
} | {
"line": 260,
"column": 0
} | [
{
"pp": "P Q : {R S : Type u} → [inst : CommRing R] → [inst_1 : CommRing S] → (R →+* S) → Prop\nh₁ : RespectsIso fun {R S} [CommRing R] [CommRing S] ↦ P\nh₂ :\n ∀ ⦃R S T : Type u⦄ [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : CommRing T] [inst_3 : Algebra R S]\n [inst_4 : Algebra R T], Q (algebraMap R... | [] | introv R h hQ H
let e := h.symm.equiv
have : (e.symm : _ →+* _).comp (algebraMap R' S') = algebraMap R' (R' ⊗[R] S) := by
ext r
simp [e]
apply h₂ hQ
rw [← this]
exact h₁.1 _ _ H | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Limits.Constructions.FiniteProductsOfBinaryProducts | {
"line": 177,
"column": 6
} | {
"line": 177,
"column": 20
} | {
"line": 178,
"column": 6
} | [
{
"pp": "case refine_1\nJ : Type v\ninst✝² : SmallCategory J\nC : Type u\ninst✝¹ : Category.{v, u} C\nD : Type u'\ninst✝ : Category.{v', u'} D\nn : ℕ\nf : Fin (n + 1) → C\nc₁ : Cofan fun i ↦ f i.succ\nc₂ : BinaryCofan (f 0) c₁.pt\n⊢ f 0 ⟶ c₂.pt",
"ppTerm": "?refine_1",
"assigned": true,
"usedConstan... | [
"case refine_2\nJ : Type v\ninst✝² : SmallCategory J\nC : Type u\ninst✝¹ : Category.{v, u} C\nD : Type u'\ninst✝ : Category.{v', u'} D\nn : ℕ\nf : Fin (n + 1) → C\nc₁ : Cofan fun i ↦ f i.succ\nc₂ : BinaryCofan (f 0) c₁.pt\n⊢ (i : Fin n) → f i.succ ⟶ c₂.pt"
] | · apply c₂.inl | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.CategoryTheory.Limits.Constructions.FiniteProductsOfBinaryProducts | {
"line": 235,
"column": 8
} | {
"line": 235,
"column": 34
} | {
"line": 235,
"column": 34
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : HasBinaryCoproducts C\ninst✝ : HasInitial C\nn : ℕ\nK : Discrete (Fin n) ⥤ C\nthat : K ≅ Discrete.functor fun n_1 ↦ K.obj { as := n_1 } :=\n Discrete.natIso fun x ↦\n match x with\n | { as := as } => Iso.refl (K.obj { as := as })\n⊢ HasColimit K",... | [
"C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : HasBinaryCoproducts C\ninst✝ : HasInitial C\nn : ℕ\nK : Discrete (Fin n) ⥤ C\nthat : K ≅ Discrete.functor fun n_1 ↦ K.obj { as := n_1 } :=\n Discrete.natIso fun x ↦\n match x with\n | { as := as } => Iso.refl (K.obj { as := as })\n⊢ HasColimit (Discrete.funct... | hasColimit_iff_of_iso that | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.CategoryTheory.Limits.Shapes.Diagonal | {
"line": 399,
"column": 2
} | {
"line": 399,
"column": 83
} | {
"line": 400,
"column": 2
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\nX Y : C\ninst✝ : HasPullbacks C\nS : C\ng : Y ⟶ X\nf : X ⟶ S\n⊢ IsPullback g (lift (𝟙 Y) g ⋯) (diagonal f) (map (g ≫ f) f f f g (𝟙 X) (𝟙 S) ⋯ ⋯)",
"ppTerm": "?m.127",
"assigned": true,
"usedConstants": [
"CategoryTheory.Limits.hasPullba... | [
"C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\nX Y : C\ninst✝ : HasPullbacks C\nS : C\ng : Y ⟶ X\nf : X ⟶ S\ni : pullback (g ≫ f) f ≅ pullback (g ≫ f) (𝟙 X ≫ f) := congrHom ⋯ ⋯\n⊢ IsPullback g (lift (𝟙 Y) g ⋯) (diagonal f) (map (g ≫ f) f f f g (𝟙 X) (𝟙 S) ⋯ ⋯)"
] | let i : pullback (g ≫ f) f ≅ pullback (g ≫ f) (𝟙 X ≫ f) := congrHom rfl (by simp) | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticLet___1 | Lean.Parser.Tactic.tacticLet__ |
Mathlib.CategoryTheory.Monoidal.Cartesian.Basic | {
"line": 395,
"column": 33
} | {
"line": 395,
"column": 38
} | {
"line": 397,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : CartesianMonoidalCategory C\nX Y : C\n⊢ (X ◁ toUnit Y ≫ (ρ_ X).hom) ≫ (ρ_ X).inv = fst X Y ≫ (ρ_ X).inv",
"ppTerm": "?m.42",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.Mono... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.Monoidal.Cartesian.Basic | {
"line": 399,
"column": 33
} | {
"line": 399,
"column": 38
} | {
"line": 401,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : CartesianMonoidalCategory C\nX Y : C\n⊢ (toUnit X ▷ Y ≫ (λ_ Y).hom) ≫ (λ_ Y).inv = snd X Y ≫ (λ_ Y).inv",
"ppTerm": "?m.42",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.Semi... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.Monoidal.Cartesian.Basic | {
"line": 466,
"column": 45
} | {
"line": 466,
"column": 50
} | {
"line": 468,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : CartesianMonoidalCategory C\ninst✝ : BraidedCategory C\nT X Y : C\nf : T ⟶ X\ng : T ⟶ Y\n⊢ lift f g ≫ (β_ X Y).hom = lift g f",
"ppTerm": "?m.34",
"assigned": true,
"usedConstants": [
"CategoryTheory.Category.assoc",
"CategoryTheo... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.Monoidal.Cartesian.Basic | {
"line": 466,
"column": 45
} | {
"line": 466,
"column": 50
} | {
"line": 468,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : CartesianMonoidalCategory C\ninst✝ : BraidedCategory C\nT X Y : C\nf : T ⟶ X\ng : T ⟶ Y\n⊢ lift f g ≫ (β_ X Y).hom = lift g f",
"ppTerm": "?m.34",
"assigned": true,
"usedConstants": [
"CategoryTheory.Category.assoc",
"CategoryTheo... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Monoidal.Cartesian.Basic | {
"line": 466,
"column": 45
} | {
"line": 466,
"column": 50
} | {
"line": 468,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : CartesianMonoidalCategory C\ninst✝ : BraidedCategory C\nT X Y : C\nf : T ⟶ X\ng : T ⟶ Y\n⊢ lift f g ≫ (β_ X Y).hom = lift g f",
"ppTerm": "?m.34",
"assigned": true,
"usedConstants": [
"CategoryTheory.Category.assoc",
"CategoryTheo... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Monoidal.Cartesian.Basic | {
"line": 470,
"column": 45
} | {
"line": 470,
"column": 50
} | {
"line": 473,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : CartesianMonoidalCategory C\ninst✝ : BraidedCategory C\nT X Y : C\nf : T ⟶ X\ng : T ⟶ Y\n⊢ lift f g ≫ (β_ Y X).inv = lift g f",
"ppTerm": "?m.34",
"assigned": true,
"usedConstants": [
"CategoryTheory.Category.assoc",
"CategoryTheo... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.Monoidal.Cartesian.Basic | {
"line": 470,
"column": 45
} | {
"line": 470,
"column": 50
} | {
"line": 473,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : CartesianMonoidalCategory C\ninst✝ : BraidedCategory C\nT X Y : C\nf : T ⟶ X\ng : T ⟶ Y\n⊢ lift f g ≫ (β_ Y X).inv = lift g f",
"ppTerm": "?m.34",
"assigned": true,
"usedConstants": [
"CategoryTheory.Category.assoc",
"CategoryTheo... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Monoidal.Cartesian.Basic | {
"line": 470,
"column": 45
} | {
"line": 470,
"column": 50
} | {
"line": 473,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : CartesianMonoidalCategory C\ninst✝ : BraidedCategory C\nT X Y : C\nf : T ⟶ X\ng : T ⟶ Y\n⊢ lift f g ≫ (β_ Y X).inv = lift g f",
"ppTerm": "?m.34",
"assigned": true,
"usedConstants": [
"CategoryTheory.Category.assoc",
"CategoryTheo... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Monoidal.Cartesian.Mon | {
"line": 288,
"column": 18
} | {
"line": 288,
"column": 36
} | {
"line": 290,
"column": 0
} | [
{
"pp": "case zero\nC : Type u_1\ninst✝³ : Category.{v, u_1} C\ninst✝² : CartesianMonoidalCategory C\ninst✝¹ : BraidedCategory C\nM N : Mon C\ninst✝ : IsCommMonObj N.X\nf : M ⟶ N\n⊢ (f ^ 0).hom = f.hom ^ 0",
"ppTerm": "?zero",
"assigned": true,
"usedConstants": [
"MulOne.toOne",
"Categor... | [] | simp [pow_succ, *] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.CategoryTheory.Monoidal.Cartesian.Mon | {
"line": 288,
"column": 18
} | {
"line": 288,
"column": 36
} | {
"line": 290,
"column": 0
} | [
{
"pp": "case succ\nC : Type u_1\ninst✝³ : Category.{v, u_1} C\ninst✝² : CartesianMonoidalCategory C\ninst✝¹ : BraidedCategory C\nM N : Mon C\ninst✝ : IsCommMonObj N.X\nf : M ⟶ N\nn✝ : ℕ\na✝ : (f ^ n✝).hom = f.hom ^ n✝\n⊢ (f ^ (n✝ + 1)).hom = f.hom ^ (n✝ + 1)",
"ppTerm": "?succ",
"assigned": true,
"... | [] | simp [pow_succ, *] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.CategoryTheory.Monoidal.Cartesian.Basic | {
"line": 779,
"column": 2
} | {
"line": 782,
"column": 51
} | {
"line": 784,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝⁴ : Category.{v, u} C\ninst✝³ : CartesianMonoidalCategory C\nD : Type u₁\ninst✝² : Category.{v₁, u₁} D\ninst✝¹ : CartesianMonoidalCategory D\nF : C ⥤ D\ninst✝ : ∀ (A B : C), IsIso (prodComparison F A B)\n⊢ PreservesLimitsOfShape (Discrete WalkingPair) F",
"ppTerm": "?m.28",
"as... | [] | constructor
intro K
refine @preservesLimit_of_iso_diagram _ _ _ _ _ _ _ _ _ (diagramIsoPair K).symm ?_
apply preservesLimit_pair_of_isIso_prodComparison | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Monoidal.Cartesian.Basic | {
"line": 779,
"column": 2
} | {
"line": 782,
"column": 51
} | {
"line": 784,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝⁴ : Category.{v, u} C\ninst✝³ : CartesianMonoidalCategory C\nD : Type u₁\ninst✝² : Category.{v₁, u₁} D\ninst✝¹ : CartesianMonoidalCategory D\nF : C ⥤ D\ninst✝ : ∀ (A B : C), IsIso (prodComparison F A B)\n⊢ PreservesLimitsOfShape (Discrete WalkingPair) F",
"ppTerm": "?m.28",
"as... | [] | constructor
intro K
refine @preservesLimit_of_iso_diagram _ _ _ _ _ _ _ _ _ (diagramIsoPair K).symm ?_
apply preservesLimit_pair_of_isIso_prodComparison | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.HopfAlgebra.Basic | {
"line": 165,
"column": 35
} | {
"line": 165,
"column": 84
} | {
"line": 166,
"column": 2
} | [
{
"pp": "R : Type u_1\nA : Type u_2\ninst✝² : CommSemiring R\ninst✝¹ : Semiring A\ninst✝ : Bialgebra R A\nantipode : A →ₗ[R] A\nantipode_convMul_id : toConv antipode * toConv LinearMap.id = 1\nid_convMul_antipode : toConv LinearMap.id * toConv antipode = 1\n⊢ mul' R A ∘ₗ rTensor A antipode ∘ₗ comul = Algebra.li... | [] | simpa using! congr(($antipode_convMul_id).ofConv) | Lean.Elab.Tactic.Simpa.evalSimpaUsingBang | Lean.Parser.Tactic.simpaUsingBang |
Mathlib.RingTheory.HopfAlgebra.Basic | {
"line": 165,
"column": 35
} | {
"line": 165,
"column": 84
} | {
"line": 166,
"column": 2
} | [
{
"pp": "R : Type u_1\nA : Type u_2\ninst✝² : CommSemiring R\ninst✝¹ : Semiring A\ninst✝ : Bialgebra R A\nantipode : A →ₗ[R] A\nantipode_convMul_id : toConv antipode * toConv LinearMap.id = 1\nid_convMul_antipode : toConv LinearMap.id * toConv antipode = 1\n⊢ mul' R A ∘ₗ rTensor A antipode ∘ₗ comul = Algebra.li... | [] | simpa using! congr(($antipode_convMul_id).ofConv) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.RingTheory.HopfAlgebra.Basic | {
"line": 165,
"column": 35
} | {
"line": 165,
"column": 84
} | {
"line": 166,
"column": 2
} | [
{
"pp": "R : Type u_1\nA : Type u_2\ninst✝² : CommSemiring R\ninst✝¹ : Semiring A\ninst✝ : Bialgebra R A\nantipode : A →ₗ[R] A\nantipode_convMul_id : toConv antipode * toConv LinearMap.id = 1\nid_convMul_antipode : toConv LinearMap.id * toConv antipode = 1\n⊢ mul' R A ∘ₗ rTensor A antipode ∘ₗ comul = Algebra.li... | [] | simpa using! congr(($antipode_convMul_id).ofConv) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.SetTheory.Cardinal.Subfield | {
"line": 83,
"column": 6
} | {
"line": 83,
"column": 58
} | {
"line": 84,
"column": 4
} | [
{
"pp": "case convert_3.inl\nα : Type u\ns : Set α\ninst✝ : DivisionRing α\nn : Fin 6\n⊢ Finite (Operands s (Sum.inl n))",
"ppTerm": "?convert_3.inl",
"assigned": true,
"usedConstants": [
"_private.Mathlib.SetTheory.Cardinal.Subfield.0.Subfield.Operands",
"Fintype.elems",
"Nat.le_r... | [] | fin_cases n <;> (dsimp only [id_eq]; infer_instance) | Lean.Parser.Tactic.«_aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tactic_<;>__1» | Lean.Parser.Tactic.«tactic_<;>_» |
Mathlib.SetTheory.Cardinal.Subfield | {
"line": 83,
"column": 6
} | {
"line": 83,
"column": 58
} | {
"line": 84,
"column": 4
} | [
{
"pp": "case convert_3.inl\nα : Type u\ns : Set α\ninst✝ : DivisionRing α\nn : Fin 6\n⊢ Finite (Operands s (Sum.inl n))",
"ppTerm": "?convert_3.inl",
"assigned": true,
"usedConstants": [
"_private.Mathlib.SetTheory.Cardinal.Subfield.0.Subfield.Operands",
"Fintype.elems",
"Nat.le_r... | [] | fin_cases n <;> (dsimp only [id_eq]; infer_instance) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.SetTheory.Cardinal.Subfield | {
"line": 83,
"column": 6
} | {
"line": 83,
"column": 58
} | {
"line": 84,
"column": 4
} | [
{
"pp": "case convert_3.inl\nα : Type u\ns : Set α\ninst✝ : DivisionRing α\nn : Fin 6\n⊢ Finite (Operands s (Sum.inl n))",
"ppTerm": "?convert_3.inl",
"assigned": true,
"usedConstants": [
"_private.Mathlib.SetTheory.Cardinal.Subfield.0.Subfield.Operands",
"Fintype.elems",
"Nat.le_r... | [] | fin_cases n <;> (dsimp only [id_eq]; infer_instance) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
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