module stringlengths 16 90 | startPos dict | endPos dict | goals listlengths 0 96 | ppTac stringlengths 1 14.5k | elaborator stringclasses 366
values | kind stringclasses 370
values |
|---|---|---|---|---|---|---|
Mathlib.CategoryTheory.Category.Cat.Adjunction | {
"line": 68,
"column": 28
} | {
"line": 68,
"column": 39
} | [
{
"pp": "case h.toFun.h\nX : Type u\nC : Cat\nX✝ Y✝ Z✝ : Cat\nx✝¹ : X✝ ⟶ Y✝\nx✝ : Y✝ ⟶ Z✝\nx : ConnectedComponents ↑X✝\n⊢ (ConcreteCategory.hom (↾(x✝¹ ≫ x✝).toFunctor.mapConnectedComponents)).toFun x =\n (ConcreteCategory.hom (↾x✝¹.toFunctor.mapConnectedComponents ≫ ↾x✝.toFunctor.mapConnectedComponents)).toF... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Category.PartialFun | {
"line": 149,
"column": 54
} | {
"line": 153,
"column": 54
} | [
{
"pp": "X Y : Pointed\nf : X ⟶ Y\na : ((pointedToPartialFun ⋙ partialFunToPointed).obj X).X\n⊢ ((pointedToPartialFun ⋙ partialFunToPointed).map f ≫\n ((fun X ↦ Pointed.Iso.mk (Equiv.optionSubtypeNe X.point) ⋯) Y).hom).toFun\n a =\n (((fun X ↦ Pointed.Iso.mk (Equiv.optionSubtypeNe X.point) ⋯) X... | by
obtain _ | ⟨a, ha⟩ := a
· exact f.map_point.symm
simp_all [Equiv.optionSubtypeNe, Equiv.optionSubtype,
Option.casesOn'_eq_elim, Part.elim_toOption] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Category.PartialFun | {
"line": 176,
"column": 8
} | {
"line": 176,
"column": 19
} | [
{
"pp": "case h.e'_2\nX✝ Y✝ : Type ?u.29563\nf : X✝ ⟶ Y✝\na✝ : ((typeToPartialFun ⋙ partialFunToPointed).obj X✝).X\na : typeToPartialFun.obj X✝\n⊢ ((typeToPartialFun ⋙ partialFunToPointed).map f ≫\n ((fun x ↦\n { hom := { toFun := id, map_point := ⋯ }, inv := { toFun := id, map_point := ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.Cartesian.Comon_ | {
"line": 46,
"column": 4
} | {
"line": 46,
"column": 19
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : CartesianMonoidalCategory C\nX✝ Y✝ : C\nf : X✝ ⟶ Y✝\n⊢ f ≫ Δ = Δ ≫ (f ⊗ₘ f)",
"usedConstants": [
"CategoryTheory.ComonObj.comul",
"CategoryTheory.cartesianComon._proof_6",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",... | simp +instances | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.CategoryTheory.Monoidal.Cartesian.Comon_ | {
"line": 54,
"column": 4
} | {
"line": 54,
"column": 15
} | [
{
"pp": "case h_fst\nC : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : CartesianMonoidalCategory C\nA : C\ninst✝ : ComonObj A\n⊢ Δ ≫ fst A A = lift (𝟙 A) (𝟙 A) ≫ fst A A",
"usedConstants": [
"CategoryTheory.ComonObj.comul",
"Eq.mpr",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.Cartesian.Comon_ | {
"line": 55,
"column": 4
} | {
"line": 55,
"column": 15
} | [
{
"pp": "case h_snd\nC : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : CartesianMonoidalCategory C\nA : C\ninst✝ : ComonObj A\n⊢ Δ ≫ snd A A = lift (𝟙 A) (𝟙 A) ≫ snd A A",
"usedConstants": [
"CategoryTheory.ComonObj.comul",
"Eq.mpr",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Localization.Prod | {
"line": 58,
"column": 2
} | {
"line": 58,
"column": 60
} | [
{
"pp": "case h.h.h.h.h.h\nC₁ : Type u₁\nC₂ : Type u₂\ninst✝² : Category.{v₁, u₁} C₁\ninst✝¹ : Category.{v₂, u₂} C₂\nW₁ : MorphismProperty C₁\nW₂ : MorphismProperty C₂\nE : Type u₅\ninst✝ : Category.{v₅, u₅} E\nF₁ F₂ : W₁.Localization × W₂.Localization ⥤ E\nh : W₁.Q.prod W₂.Q ⋙ F₁ = W₁.Q.prod W₂.Q ⋙ F₂\n⊢ uncur... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Localization.Monoidal.Basic | {
"line": 53,
"column": 31
} | {
"line": 53,
"column": 42
} | [
{
"pp": "C : Type u_1\ninst✝² : Category.{v_1, u_1} C\nW : MorphismProperty C\ninst✝¹ : MonoidalCategory C\ninst✝ : W.IsMultiplicative\nh : ∀ {X₁ X₂ Y₁ Y₂ : C} (f : X₁ ⟶ X₂) (g : Y₁ ⟶ Y₂), W f → W g → W (f ⊗ₘ g)\nX x✝¹ x✝ : C\ng : x✝¹ ⟶ x✝\nhg : W g\n⊢ W (X ◁ g)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Localization.Monoidal.Basic | {
"line": 54,
"column": 28
} | {
"line": 54,
"column": 39
} | [
{
"pp": "C : Type u_1\ninst✝² : Category.{v_1, u_1} C\nW : MorphismProperty C\ninst✝¹ : MonoidalCategory C\ninst✝ : W.IsMultiplicative\nh : ∀ {X₁ X₂ Y₁ Y₂ : C} (f : X₁ ⟶ X₂) (g : Y₁ ⟶ Y₂), W f → W g → W (f ⊗ₘ g)\nX₁✝ X₂✝ : C\nf : X₁✝ ⟶ X₂✝\nhf : W f\nY : C\n⊢ W (f ▷ Y)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Distributive.Cartesian | {
"line": 79,
"column": 6
} | {
"line": 79,
"column": 33
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : CartesianMonoidalCategory C\ninst✝¹ : HasBinaryCoproducts C\ninst✝ : IsCartesianDistributive C\nA B Z : C\nf g : Z ⟶ (pair A B).obj { as := WalkingPair.left }\nhe : f ≫ (BinaryCofan.mk coprod.inl coprod.inr).inl = g ≫ (BinaryCofan.mk coprod.inl coprod.in... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Localization.Monoidal.Basic | {
"line": 289,
"column": 2
} | {
"line": 289,
"column": 67
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝⁴ : Category.{v_1, u_1} C\ninst✝³ : Category.{v_2, u_2} D\nL : C ⥤ D\nW : MorphismProperty C\ninst✝² : MonoidalCategory C\ninst✝¹ : W.IsMonoidal\ninst✝ : L.IsLocalization W\nunit : D\nε : L.obj (𝟙_ C) ≅ unit\nX₁ X₂ X₃ Y₁ Y₂ Y₃ : LocalizedMonoidal L W ε\nf₁ : X₁ ⟶ Y₁\nf... | have h₁ := (((associator L W ε).hom.app Y₁).app Y₂).naturality f₃ | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.CategoryTheory.EffectiveEpi.Coproduct | {
"line": 91,
"column": 2
} | {
"line": 91,
"column": 13
} | [
{
"pp": "case h.h.a\nC : Type u_1\ninst✝⁴ : Category.{v_1, u_1} C\nB : C\nα : Type u_2\nX : α → C\nπ : (a : α) → X a ⟶ B\ninst✝³ : HasCoproduct X\ninst✝² : ∀ {Z : C} (g : Z ⟶ ∐ X) (a : α), HasPullback g (Sigma.ι X a)\ninst✝¹ : ∀ {Z : C} (g : Z ⟶ ∐ X), HasCoproduct fun a ↦ pullback g (Sigma.ι X a)\ninst✝ : ∀ {Z ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.EffectiveEpi.Coproduct | {
"line": 116,
"column": 4
} | {
"line": 116,
"column": 15
} | [
{
"pp": "case hm.h\nC : Type u_1\ninst✝⁵ : Category.{v_1, u_1} C\nB : C\nα : Type u_2\nX : α → C\nπ : (a : α) → X a ⟶ B\ninst✝⁴ : HasCoproduct X\ninst✝³ : EffectiveEpi (Sigma.desc π)\ninst✝² : ∀ {Z : C} (g : Z ⟶ ∐ X) (a : α), HasPullback g (Sigma.ι X a)\ninst✝¹ : ∀ {Z : C} (g : Z ⟶ ∐ X), HasCoproduct fun a ↦ pu... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sums.Basic | {
"line": 217,
"column": 8
} | {
"line": 217,
"column": 19
} | [
{
"pp": "case inl\nA : Type u₁\ninst✝³ : Category.{v₁, u₁} A\nB : Type u₂\ninst✝² : Category.{v₂, u₂} B\nC : Type u₃\ninst✝¹ : Category.{v₃, u₃} C\nD : Type u₄\ninst✝ : Category.{v₄, u₄} D\nF G : A ⊕ B ⥤ C\ne₁ : Sum.inl_ A B ⋙ F ≅ Sum.inl_ A B ⋙ G\ne₂ : Sum.inr_ A B ⋙ F ≅ Sum.inr_ A B ⋙ G\nx✝ y✝ : A\nf✝ : x✝ ⟶ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sums.Basic | {
"line": 218,
"column": 8
} | {
"line": 218,
"column": 19
} | [
{
"pp": "case inr\nA : Type u₁\ninst✝³ : Category.{v₁, u₁} A\nB : Type u₂\ninst✝² : Category.{v₂, u₂} B\nC : Type u₃\ninst✝¹ : Category.{v₃, u₃} C\nD : Type u₄\ninst✝ : Category.{v₄, u₄} D\nF G : A ⊕ B ⥤ C\ne₁ : Sum.inl_ A B ⋙ F ≅ Sum.inl_ A B ⋙ G\ne₂ : Sum.inr_ A B ⋙ F ≅ Sum.inr_ A B ⋙ G\nx✝ y✝ : B\nf✝ : x✝ ⟶ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.End | {
"line": 91,
"column": 21
} | {
"line": 91,
"column": 32
} | [
{
"pp": "J : Type u\ninst✝¹ : Category.{v, u} J\nC : Type u'\ninst✝ : Category.{v', u'} C\nF : Jᵒᵖ ⥤ J ⥤ C\nW₁ W₂ : Wedge F\ne : W₁.pt ≅ W₂.pt\nhe : ∀ (j : J), Multifork.ι W₁ j = e.hom ≫ Multifork.ι W₂ j\nj : WalkingMulticospan (multicospanShapeEnd J)\nf : (multicospanShapeEnd J).R\n⊢ W₁.π.app (WalkingMulticosp... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.End | {
"line": 155,
"column": 20
} | {
"line": 155,
"column": 31
} | [
{
"pp": "J : Type u\ninst✝¹ : Category.{v, u} J\nC : Type u'\ninst✝ : Category.{v', u'} C\nF : Jᵒᵖ ⥤ J ⥤ C\nW₁ W₂ : Cowedge F\ne : W₁.pt ≅ W₂.pt\nhe : ∀ (j : J), Multicofork.π W₁ j ≫ e.hom = Multicofork.π W₂ j\nj : WalkingMultispan (multispanShapeCoend J)\nf : (multispanShapeCoend J).L\n⊢ W₁.ι.app (WalkingMulti... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.FiberedCategory.HomLift | {
"line": 109,
"column": 33
} | {
"line": 109,
"column": 44
} | [
{
"pp": "𝒮 : Type u₁\n𝒳 : Type u₂\ninst✝¹ : Category.{v₁, u₂} 𝒳\ninst✝ : Category.{v₂, u₁} 𝒮\np : 𝒳 ⥤ 𝒮\na b : 𝒳\nφ : a ⟶ b\nf : p.obj a ⟶ p.obj b\nh : p.map φ = eqToHom ⋯ ≫ f ≫ eqToHom ⋯\n⊢ f = p.map φ",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.FiberedCategory.HomLift | {
"line": 115,
"column": 33
} | {
"line": 115,
"column": 44
} | [
{
"pp": "𝒮 : Type u₁\n𝒳 : Type u₂\ninst✝¹ : Category.{v₁, u₂} 𝒳\ninst✝ : Category.{v₂, u₁} 𝒮\np : 𝒳 ⥤ 𝒮\na b : 𝒳\nφ : a ⟶ b\nf : p.obj a ⟶ p.obj b\nh : p.map φ ≫ eqToHom ⋯ = eqToHom ⋯ ≫ f\n⊢ f = p.map φ",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.FiberedCategory.HomLift | {
"line": 136,
"column": 2
} | {
"line": 136,
"column": 13
} | [
{
"pp": "𝒮 : Type u₁\n𝒳 : Type u₂\ninst✝³ : Category.{v₁, u₂} 𝒳\ninst✝² : Category.{v₂, u₁} 𝒮\np : 𝒳 ⥤ 𝒮\na b c : 𝒳\nS T : 𝒮\nf : S ⟶ T\nφ : a ⟶ b\ninst✝¹ : p.IsHomLift f φ\nψ : b ⟶ c\ninst✝ : p.IsHomLift (𝟙 T) ψ\n⊢ p.IsHomLift f (φ ≫ ψ)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.FiberedCategory.HomLift | {
"line": 146,
"column": 2
} | {
"line": 146,
"column": 13
} | [
{
"pp": "𝒮 : Type u₁\n𝒳 : Type u₂\ninst✝³ : Category.{v₁, u₂} 𝒳\ninst✝² : Category.{v₂, u₁} 𝒮\np : 𝒳 ⥤ 𝒮\na b c : 𝒳\nS T : 𝒮\nf : S ⟶ T\nψ : b ⟶ c\ninst✝¹ : p.IsHomLift f ψ\nφ : a ⟶ b\ninst✝ : p.IsHomLift (𝟙 S) φ\n⊢ p.IsHomLift f (φ ≫ ψ)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.FiberedCategory.HomLift | {
"line": 164,
"column": 2
} | {
"line": 164,
"column": 20
} | [
{
"pp": "𝒮 : Type u₁\n𝒳 : Type u₂\ninst✝¹ : Category.{v₁, u₂} 𝒳\ninst✝ : Category.{v₂, u₁} 𝒮\np : 𝒳 ⥤ 𝒮\nR S : 𝒮\nhRS : R = S\na : 𝒳\nha : p.obj a = R\n⊢ p.IsHomLift (eqToHom hRS) (𝟙 a)",
"usedConstants": [
"CategoryTheory.IsHomLift.instIsHomLiftIdObj._simp_1",
"CategoryTheory.eqToHom",... | subst hRS ha; simp | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.FiberedCategory.HomLift | {
"line": 164,
"column": 2
} | {
"line": 164,
"column": 20
} | [
{
"pp": "𝒮 : Type u₁\n𝒳 : Type u₂\ninst✝¹ : Category.{v₁, u₂} 𝒳\ninst✝ : Category.{v₂, u₁} 𝒮\np : 𝒳 ⥤ 𝒮\nR S : 𝒮\nhRS : R = S\na : 𝒳\nha : p.obj a = R\n⊢ p.IsHomLift (eqToHom hRS) (𝟙 a)",
"usedConstants": [
"CategoryTheory.IsHomLift.instIsHomLiftIdObj._simp_1",
"CategoryTheory.eqToHom",... | subst hRS ha; simp | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.FiberedCategory.HomLift | {
"line": 204,
"column": 24
} | {
"line": 204,
"column": 35
} | [
{
"pp": "𝒮 : Type u₁\n𝒳 : Type u₂\ninst✝¹ : Category.{v₁, u₂} 𝒳\ninst✝ : Category.{v₂, u₁} 𝒮\np : 𝒳 ⥤ 𝒮\nR S : 𝒮\na' b : 𝒳\nf : R ⟶ S\nφ : a' ⟶ b\nhφ' : p.IsHomLift f (eqToHom ⋯ ≫ φ)\n⊢ p.IsHomLift f φ",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.FiberedCategory.HomLift | {
"line": 210,
"column": 24
} | {
"line": 210,
"column": 35
} | [
{
"pp": "𝒮 : Type u₁\n𝒳 : Type u₂\ninst✝¹ : Category.{v₁, u₂} 𝒳\ninst✝ : Category.{v₂, u₁} 𝒮\np : 𝒳 ⥤ 𝒮\nR S : 𝒮\na b : 𝒳\nf : R ⟶ S\nφ : a ⟶ b\nhφ' : p.IsHomLift f (φ ≫ eqToHom ⋯)\n⊢ p.IsHomLift f φ",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.FiberedCategory.HomLift | {
"line": 216,
"column": 24
} | {
"line": 216,
"column": 35
} | [
{
"pp": "𝒮 : Type u₁\n𝒳 : Type u₂\ninst✝¹ : Category.{v₁, u₂} 𝒳\ninst✝ : Category.{v₂, u₁} 𝒮\np : 𝒳 ⥤ 𝒮\nR' S : 𝒮\na b : 𝒳\nφ : a ⟶ b\nf : R' ⟶ S\nhφ' : p.IsHomLift (eqToHom ⋯ ≫ f) φ\n⊢ p.IsHomLift f φ",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.FiberedCategory.HomLift | {
"line": 222,
"column": 31
} | {
"line": 222,
"column": 42
} | [
{
"pp": "𝒮 : Type u₁\n𝒳 : Type u₂\ninst✝¹ : Category.{v₁, u₂} 𝒳\ninst✝ : Category.{v₂, u₁} 𝒮\np : 𝒳 ⥤ 𝒮\nR S : 𝒮\na b : 𝒳\nf : R ⟶ S\nφ : a ⟶ b\nhφ' : p.IsHomLift (f ≫ eqToHom ⋯) φ\n⊢ p.IsHomLift f φ",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Enriched.Opposite | {
"line": 50,
"column": 4
} | {
"line": 51,
"column": 43
} | [
{
"pp": "V : Type u₁\ninst✝³ : Category.{v₁, u₁} V\ninst✝² : MonoidalCategory V\ninst✝¹ : BraidedCategory V\nC : Type u\ninst✝ : EnrichedCategory V C\nx✝¹ x✝ : Cᵒᵖ\n⊢ (λ_ (Opposite.unop x✝ ⟶[V] Opposite.unop x✝¹)).inv ≫\n (id (Opposite.unop x✝¹) ▷ Opposite.unop x✝ ⟶[V] Opposite.unop x✝¹) ≫\n (β_ (Op... | simp only [braiding_naturality_left_assoc, braiding_tensorUnit_left,
Category.assoc, Iso.inv_hom_id_assoc] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.CategoryTheory.FiberedCategory.Cartesian | {
"line": 124,
"column": 2
} | {
"line": 124,
"column": 16
} | [
{
"pp": "𝒮 : Type u₁\n𝒳 : Type u₂\ninst✝² : Category.{v₁, u₁} 𝒮\ninst✝¹ : Category.{v₂, u₂} 𝒳\np : 𝒳 ⥤ 𝒮\na✝ b✝ : 𝒳\nφ : a✝ ⟶ b✝\nR S : 𝒮\na b : 𝒳\ninst✝ : p.IsCartesian (p.map φ) φ\n⊢ 𝟙 a✝ = IsCartesian.map p (p.map φ) φ φ",
"usedConstants": [
"CategoryTheory.CategoryStruct.id",
"Cate... | apply map_uniq | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.CategoryTheory.FiberedCategory.Cartesian | {
"line": 134,
"column": 4
} | {
"line": 134,
"column": 18
} | [
{
"pp": "case h\n𝒮 : Type u₁\n𝒳 : Type u₂\ninst✝³ : Category.{v₁, u₁} 𝒮\ninst✝² : Category.{v₂, u₂} 𝒳\np : 𝒳 ⥤ 𝒮\nR S : 𝒮\na b : 𝒳\nf : R ⟶ S\nφ : a ⟶ b\ninst✝¹ : p.IsCartesian f φ\nb' : 𝒳\nφ' : b ≅ b'\ninst✝ : p.IsHomLift (𝟙 S) φ'.hom\nc : 𝒳\nψ : c ⟶ b'\nhψ : p.IsHomLift f ψ\nτ : c ⟶ a\nhτ₁ : p.IsHo... | apply map_uniq | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.CategoryTheory.FiberedCategory.Cocartesian | {
"line": 119,
"column": 2
} | {
"line": 119,
"column": 16
} | [
{
"pp": "𝒮 : Type u₁\n𝒳 : Type u₂\ninst✝² : Category.{v₁, u₁} 𝒮\ninst✝¹ : Category.{v₂, u₂} 𝒳\np : 𝒳 ⥤ 𝒮\na✝ b✝ : 𝒳\nφ : a✝ ⟶ b✝\nR S : 𝒮\na b : 𝒳\ninst✝ : p.IsCocartesian (p.map φ) φ\n⊢ 𝟙 b✝ = IsCocartesian.map p (p.map φ) φ φ",
"usedConstants": [
"CategoryTheory.Functor.IsCocartesian.toIsH... | apply map_uniq | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.CategoryTheory.FiberedCategory.Cocartesian | {
"line": 147,
"column": 4
} | {
"line": 147,
"column": 18
} | [
{
"pp": "case h\n𝒮 : Type u₁\n𝒳 : Type u₂\ninst✝³ : Category.{v₁, u₁} 𝒮\ninst✝² : Category.{v₂, u₂} 𝒳\np : 𝒳 ⥤ 𝒮\nR S : 𝒮\na b : 𝒳\nf : R ⟶ S\nφ : a ⟶ b\ninst✝¹ : p.IsCocartesian f φ\nb' : 𝒳\nφ' : b ≅ b'\ninst✝ : p.IsHomLift (𝟙 S) φ'.hom\nc : 𝒳\nψ : a ⟶ c\nhψ : p.IsHomLift f ψ\nτ : b' ⟶ c\nhτ₁ : p.Is... | apply map_uniq | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.CategoryTheory.FiberedCategory.Cartesian | {
"line": 170,
"column": 4
} | {
"line": 170,
"column": 18
} | [
{
"pp": "case h\n𝒮 : Type u₁\n𝒳 : Type u₂\ninst✝³ : Category.{v₁, u₁} 𝒮\ninst✝² : Category.{v₂, u₂} 𝒳\np : 𝒳 ⥤ 𝒮\nR S : 𝒮\na b : 𝒳\nf : R ⟶ S\nφ : a ⟶ b\ninst✝¹ : p.IsCartesian f φ\na' : 𝒳\nφ' : a' ≅ a\ninst✝ : p.IsHomLift (𝟙 R) φ'.hom\nc : 𝒳\nψ : c ⟶ b\nhψ : p.IsHomLift f ψ\nτ : c ⟶ a'\nhτ₁ : p.IsHo... | apply map_uniq | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.CategoryTheory.FiberedCategory.Cocartesian | {
"line": 159,
"column": 4
} | {
"line": 159,
"column": 18
} | [
{
"pp": "case h\n𝒮 : Type u₁\n𝒳 : Type u₂\ninst✝³ : Category.{v₁, u₁} 𝒮\ninst✝² : Category.{v₂, u₂} 𝒳\np : 𝒳 ⥤ 𝒮\nR S : 𝒮\na b : 𝒳\nf : R ⟶ S\nφ : a ⟶ b\ninst✝¹ : p.IsCocartesian f φ\na' : 𝒳\nφ' : a' ≅ a\ninst✝ : p.IsHomLift (𝟙 R) φ'.hom\nc : 𝒳\nψ : a' ⟶ c\nhψ : p.IsHomLift f ψ\nτ : b ⟶ c\nhτ₁ : p.Is... | apply map_uniq | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.CategoryTheory.FiberedCategory.Cartesian | {
"line": 248,
"column": 2
} | {
"line": 248,
"column": 16
} | [
{
"pp": "𝒮 : Type u₁\n𝒳 : Type u₂\ninst✝² : Category.{v₁, u₁} 𝒮\ninst✝¹ : Category.{v₂, u₂} 𝒳\np : 𝒳 ⥤ 𝒮\na✝ b✝ : 𝒳\nφ : a✝ ⟶ b✝\nR S : 𝒮\na b : 𝒳\ninst✝ : p.IsStronglyCartesian (p.map φ) φ\n⊢ 𝟙 a✝ = map p (p.map φ) φ ⋯ φ",
"usedConstants": [
"CategoryTheory.CategoryStruct.toQuiver",
"... | apply map_uniq | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.CategoryTheory.FiberedCategory.Cocartesian | {
"line": 238,
"column": 2
} | {
"line": 238,
"column": 16
} | [
{
"pp": "𝒮 : Type u₁\n𝒳 : Type u₂\ninst✝² : Category.{v₁, u₁} 𝒮\ninst✝¹ : Category.{v₂, u₂} 𝒳\np : 𝒳 ⥤ 𝒮\na✝ b✝ : 𝒳\nφ : a✝ ⟶ b✝\nR S : 𝒮\na b : 𝒳\ninst✝ : p.IsStronglyCocartesian (p.map φ) φ\n⊢ 𝟙 b✝ = map p (p.map φ) φ ⋯ φ",
"usedConstants": [
"CategoryTheory.CategoryStruct.toQuiver",
... | apply map_uniq | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.CategoryTheory.FiberedCategory.Cartesian | {
"line": 307,
"column": 6
} | {
"line": 307,
"column": 20
} | [
{
"pp": "case h.refine_2\n𝒮 : Type u₁\n𝒳 : Type u₂\ninst✝³ : Category.{v₁, u₁} 𝒮\ninst✝² : Category.{v₂, u₂} 𝒳\np : 𝒳 ⥤ 𝒮\nR S T : 𝒮\na b c : 𝒳\nf : R ⟶ S\ng : S ⟶ T\nφ : a ⟶ b\nψ : b ⟶ c\ninst✝¹ : p.IsStronglyCartesian f φ\ninst✝ : p.IsStronglyCartesian g ψ\na' : 𝒳\nh : p.obj a' ⟶ R\nτ : a' ⟶ c\nhτ : ... | apply map_uniq | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.CategoryTheory.FiberedCategory.Cartesian | {
"line": 308,
"column": 6
} | {
"line": 308,
"column": 20
} | [
{
"pp": "case h.refine_2.hψ\n𝒮 : Type u₁\n𝒳 : Type u₂\ninst✝³ : Category.{v₁, u₁} 𝒮\ninst✝² : Category.{v₂, u₂} 𝒳\np : 𝒳 ⥤ 𝒮\nR S T : 𝒮\na b c : 𝒳\nf : R ⟶ S\ng : S ⟶ T\nφ : a ⟶ b\nψ : b ⟶ c\ninst✝¹ : p.IsStronglyCartesian f φ\ninst✝ : p.IsStronglyCartesian g ψ\na' : 𝒳\nh : p.obj a' ⟶ R\nτ : a' ⟶ c\nhτ... | apply map_uniq | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.CategoryTheory.FiberedCategory.Cartesian | {
"line": 323,
"column": 52
} | {
"line": 323,
"column": 63
} | [
{
"pp": "𝒮 : Type u₁\n𝒳 : Type u₂\ninst✝⁴ : Category.{v₁, u₁} 𝒮\ninst✝³ : Category.{v₂, u₂} 𝒳\np : 𝒳 ⥤ 𝒮\nR S T : 𝒮\na b c : 𝒳\nf : R ⟶ S\ng : S ⟶ T\nφ : a ⟶ b\nψ : b ⟶ c\ninst✝² : p.IsStronglyCartesian g ψ\ninst✝¹ : p.IsStronglyCartesian (f ≫ g) (φ ≫ ψ)\ninst✝ : p.IsHomLift f φ\na' : 𝒳\nh : p.obj a' ⟶... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.FiberedCategory.BasedCategory | {
"line": 118,
"column": 2
} | {
"line": 118,
"column": 13
} | [
{
"pp": "𝒮 : Type u₁\ninst✝¹ : Category.{v₁, u₁} 𝒮\n𝒳 : BasedCategory 𝒮\n𝒴 : BasedCategory 𝒮\nF : 𝒳 ⥤ᵇ 𝒴\nR S : 𝒮\na b : 𝒳.obj\nf : R ⟶ S\nφ : a ⟶ b\ninst✝ : 𝒳.p.IsHomLift f φ\n⊢ f = eqToHom ⋯ ≫ (eqToHom ⋯ ≫ 𝒳.p.map φ ≫ eqToHom ⋯) ≫ eqToHom ⋯",
"usedConstants": [
"Eq.mpr",
"CategoryT... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.FiberedCategory.Cartesian | {
"line": 333,
"column": 6
} | {
"line": 333,
"column": 20
} | [
{
"pp": "case h.refine_2\n𝒮 : Type u₁\n𝒳 : Type u₂\ninst✝⁴ : Category.{v₁, u₁} 𝒮\ninst✝³ : Category.{v₂, u₂} 𝒳\np : 𝒳 ⥤ 𝒮\nR S T : 𝒮\na b c : 𝒳\nf : R ⟶ S\ng : S ⟶ T\nφ : a ⟶ b\nψ : b ⟶ c\ninst✝² : p.IsStronglyCartesian g ψ\ninst✝¹ : p.IsStronglyCartesian (f ≫ g) (φ ≫ ψ)\ninst✝ : p.IsHomLift f φ\na' : �... | apply map_uniq | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.CategoryTheory.FiberedCategory.Cocartesian | {
"line": 298,
"column": 6
} | {
"line": 298,
"column": 20
} | [
{
"pp": "case h.refine_2\n𝒮 : Type u₁\n𝒳 : Type u₂\ninst✝³ : Category.{v₁, u₁} 𝒮\ninst✝² : Category.{v₂, u₂} 𝒳\np : 𝒳 ⥤ 𝒮\nR S T : 𝒮\na b c : 𝒳\nf : R ⟶ S\ng : S ⟶ T\nφ : a ⟶ b\nψ : b ⟶ c\ninst✝¹ : p.IsStronglyCocartesian f φ\ninst✝ : p.IsStronglyCocartesian g ψ\nc' : 𝒳\nh : T ⟶ p.obj c'\nτ : a ⟶ c'\nh... | apply map_uniq | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.CategoryTheory.FiberedCategory.Cocartesian | {
"line": 299,
"column": 6
} | {
"line": 299,
"column": 20
} | [
{
"pp": "case h.refine_2.hψ\n𝒮 : Type u₁\n𝒳 : Type u₂\ninst✝³ : Category.{v₁, u₁} 𝒮\ninst✝² : Category.{v₂, u₂} 𝒳\np : 𝒳 ⥤ 𝒮\nR S T : 𝒮\na b c : 𝒳\nf : R ⟶ S\ng : S ⟶ T\nφ : a ⟶ b\nψ : b ⟶ c\ninst✝¹ : p.IsStronglyCocartesian f φ\ninst✝ : p.IsStronglyCocartesian g ψ\nc' : 𝒳\nh : T ⟶ p.obj c'\nτ : a ⟶ c'... | apply map_uniq | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.CategoryTheory.FiberedCategory.Cartesian | {
"line": 347,
"column": 4
} | {
"line": 347,
"column": 15
} | [
{
"pp": "case h\n𝒮 : Type u₁\n𝒳 : Type u₂\ninst✝² : Category.{v₁, u₁} 𝒮\ninst✝¹ : Category.{v₂, u₂} 𝒳\np : 𝒳 ⥤ 𝒮\nR S : 𝒮\na b : 𝒳\nf : R ⟶ S\nφ : a ≅ b\ninst✝ : p.IsHomLift f φ.hom\na' : 𝒳\ng : p.obj a' ⟶ R\nτ : a' ⟶ b\nhτ : p.IsHomLift (g ≫ f) τ\n⊢ (fun χ ↦ p.IsHomLift g χ ∧ χ ≫ φ.hom = τ) (τ ≫ φ.inv... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.FiberedCategory.Cartesian | {
"line": 382,
"column": 6
} | {
"line": 382,
"column": 17
} | [
{
"pp": "𝒮 : Type u₁\n𝒳 : Type u₂\ninst✝³ : Category.{v₁, u₁} 𝒮\ninst✝² : Category.{v₂, u₂} 𝒳\np : 𝒳 ⥤ 𝒮\nR R' S : 𝒮\na a' b : 𝒳\nf : R ⟶ S\nf' : R' ⟶ S\ng : R' ≅ R\nh : f' = g.hom ≫ f\nφ : a ⟶ b\nφ' : a' ⟶ b\ninst✝¹ : p.IsStronglyCartesian f φ\ninst✝ : p.IsStronglyCartesian f' φ'\n⊢ p.IsHomLift ((fun x... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.FiberedCategory.Cartesian | {
"line": 394,
"column": 4
} | {
"line": 394,
"column": 15
} | [
{
"pp": "𝒮 : Type u₁\n𝒳 : Type u₂\ninst✝³ : Category.{v₁, u₁} 𝒮\ninst✝² : Category.{v₂, u₂} 𝒳\np : 𝒳 ⥤ 𝒮\nR R' S : 𝒮\na a' b : 𝒳\nf : R ⟶ S\nf' : R' ⟶ S\ng : R' ≅ R\nh : f' = g.hom ≫ f\nφ : a ⟶ b\nφ' : a' ⟶ b\ninst✝¹ : p.IsStronglyCartesian f φ\ninst✝ : p.IsStronglyCartesian f' φ'\n⊢ p.IsHomLift ((fun x... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.FiberedCategory.Cartesian | {
"line": 395,
"column": 2
} | {
"line": 395,
"column": 13
} | [
{
"pp": "𝒮 : Type u₁\n𝒳 : Type u₂\ninst✝³ : Category.{v₁, u₁} 𝒮\ninst✝² : Category.{v₂, u₂} 𝒳\np : 𝒳 ⥤ 𝒮\nR R' S : 𝒮\na a' b : 𝒳\nf : R ⟶ S\nf' : R' ⟶ S\ng : R' ≅ R\nh : f' = g.hom ≫ f\nφ : a ⟶ b\nφ' : a' ⟶ b\ninst✝¹ : p.IsStronglyCartesian f φ\ninst✝ : p.IsStronglyCartesian f' φ'\nthis : p.IsHomLift ((... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.FiberedCategory.Fiber | {
"line": 115,
"column": 7
} | {
"line": 115,
"column": 18
} | [
{
"pp": "𝒮 : Type u₁\n𝒳 : Type u₂\ninst✝² : Category.{v₁, u₁} 𝒮\ninst✝¹ : Category.{v₂, u₂} 𝒳\np✝ : 𝒳 ⥤ 𝒮\nS✝ : 𝒮\np : 𝒳 ⥤ 𝒮\nS : 𝒮\nC : Type u₃\ninst✝ : Category.{v₃, u₃} C\nF : C ⥤ 𝒳\nhF : F ⋙ p = (const C).obj S\nX✝ Y✝ : C\nφ : X✝ ⟶ Y✝\n⊢ p.map (F.map φ) ≫ eqToHom ⋯ = eqToHom ⋯ ≫ 𝟙 S",
"usedC... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.FiberedCategory.Cocartesian | {
"line": 323,
"column": 6
} | {
"line": 323,
"column": 20
} | [
{
"pp": "case h.refine_2\n𝒮 : Type u₁\n𝒳 : Type u₂\ninst✝⁴ : Category.{v₁, u₁} 𝒮\ninst✝³ : Category.{v₂, u₂} 𝒳\np : 𝒳 ⥤ 𝒮\nR S T : 𝒮\na b c : 𝒳\nf : R ⟶ S\ng : S ⟶ T\nφ : a ⟶ b\nψ : b ⟶ c\ninst✝² : p.IsStronglyCocartesian f φ\ninst✝¹ : p.IsStronglyCocartesian (f ≫ g) (φ ≫ ψ)\ninst✝ : p.IsHomLift g ψ\nc'... | apply map_uniq | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.CategoryTheory.FiberedCategory.Fibered | {
"line": 118,
"column": 4
} | {
"line": 118,
"column": 18
} | [
{
"pp": "case h.e_a\n𝒮 : Type u₁\n𝒳 : Type u₂\ninst✝³ : Category.{v₁, u₁} 𝒮\ninst✝² : Category.{v₂, u₂} 𝒳\np : 𝒳 ⥤ 𝒮\ninst✝¹ : p.IsFibered\nR S : 𝒮\nf : R ⟶ S\na b : 𝒳\nφ : a ⟶ b\ninst✝ : p.IsCartesian f φ\na'✝ : 𝒳\ng : p.obj a'✝ ⟶ R\nφ' : a'✝ ⟶ b\nhφ' : p.IsHomLift (g ≫ f) φ'\nψ : pullbackObj ⋯ g ⟶ a ... | apply map_uniq | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.CategoryTheory.FiberedCategory.Cocartesian | {
"line": 337,
"column": 4
} | {
"line": 337,
"column": 25
} | [
{
"pp": "case h\n𝒮 : Type u₁\n𝒳 : Type u₂\ninst✝² : Category.{v₁, u₁} 𝒮\ninst✝¹ : Category.{v₂, u₂} 𝒳\np : 𝒳 ⥤ 𝒮\nR S : 𝒮\na b : 𝒳\nf : R ⟶ S\nφ : a ≅ b\ninst✝ : p.IsHomLift f φ.hom\nb' : 𝒳\ng : S ⟶ p.obj b'\nτ : a ⟶ b'\nhτ : p.IsHomLift (f ≫ g) τ\n⊢ (fun χ ↦ p.IsHomLift g χ ∧ φ.hom ≫ χ = τ) (φ.inv ≫ τ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Enriched.FunctorCategory | {
"line": 385,
"column": 4
} | {
"line": 385,
"column": 15
} | [
{
"pp": "case h\nV : Type u₁\ninst✝⁷ : Category.{v₁, u₁} V\ninst✝⁶ : MonoidalCategory V\nC : Type u₂\ninst✝⁵ : Category.{v₂, u₂} C\nJ : Type u₃\ninst✝⁴ : Category.{v₃, u₃} J\nK : Type u₄\ninst✝³ : Category.{v₄, u₄} K\ninst✝² : EnrichedOrdinaryCategory V C\nF₁ F₂ F₃ F₄ : J ⥤ C\ninst✝¹ : HasFunctorEnrichedHom V F... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.FiberedCategory.HasFibers | {
"line": 143,
"column": 2
} | {
"line": 143,
"column": 55
} | [
{
"pp": "𝒮 : Type u₁\n𝒳 : Type u₂\ninst✝³ : Category.{v₁, u₁} 𝒮\ninst✝² : Category.{v₂, u₂} 𝒳\np : 𝒳 ⥤ 𝒮\ninst✝¹ : HasFibers p\nS : 𝒮\na b : Fib p S\nφ : (ι S).obj a ⟶ (ι S).obj b\ninst✝ : p.IsHomLift (𝟙 S) φ\n⊢ (ι S).map (homMk φ) = φ",
"usedConstants": [
"CategoryTheory.Functor.preimage",
... | simp [Fib.homMk, congr_hom (inducedFunctor_comp p S)] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.CategoryTheory.FiberedCategory.HasFibers | {
"line": 143,
"column": 2
} | {
"line": 143,
"column": 55
} | [
{
"pp": "𝒮 : Type u₁\n𝒳 : Type u₂\ninst✝³ : Category.{v₁, u₁} 𝒮\ninst✝² : Category.{v₂, u₂} 𝒳\np : 𝒳 ⥤ 𝒮\ninst✝¹ : HasFibers p\nS : 𝒮\na b : Fib p S\nφ : (ι S).obj a ⟶ (ι S).obj b\ninst✝ : p.IsHomLift (𝟙 S) φ\n⊢ (ι S).map (homMk φ) = φ",
"usedConstants": [
"CategoryTheory.Functor.preimage",
... | simp [Fib.homMk, congr_hom (inducedFunctor_comp p S)] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.FiberedCategory.HasFibers | {
"line": 143,
"column": 2
} | {
"line": 143,
"column": 55
} | [
{
"pp": "𝒮 : Type u₁\n𝒳 : Type u₂\ninst✝³ : Category.{v₁, u₁} 𝒮\ninst✝² : Category.{v₂, u₂} 𝒳\np : 𝒳 ⥤ 𝒮\ninst✝¹ : HasFibers p\nS : 𝒮\na b : Fib p S\nφ : (ι S).obj a ⟶ (ι S).obj b\ninst✝ : p.IsHomLift (𝟙 S) φ\n⊢ (ι S).map (homMk φ) = φ",
"usedConstants": [
"CategoryTheory.Functor.preimage",
... | simp [Fib.homMk, congr_hom (inducedFunctor_comp p S)] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Functor.Derived.LeftDerived | {
"line": 184,
"column": 2
} | {
"line": 184,
"column": 52
} | [
{
"pp": "C : Type u_1\nD : Type u_2\nH : Type u_3\ninst✝⁴ : Category.{v_1, u_1} C\ninst✝³ : Category.{v_3, u_2} D\ninst✝² : Category.{v_5, u_3} H\nLF : D ⥤ H\nF : C ⥤ H\nL : C ⥤ D\nα : L ⋙ LF ⟶ F\nW : MorphismProperty C\ninst✝¹ : L.IsLocalization W\ninst✝ : LF.IsLeftDerivedFunctor α W\nthis : LF.IsRightKanExten... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Localization.StructuredArrow | {
"line": 86,
"column": 8
} | {
"line": 86,
"column": 67
} | [
{
"pp": "case cons.inr\nC : Type u_1\ninst✝ : Category.{v_1, u_1} C\nW : MorphismProperty C\nX : C\nP : StructuredArrow (W.Q.obj X) W.Q → Prop\nhP₀ : P (StructuredArrow.mk (𝟙 (W.Q.obj X)))\nhP₁ :\n ∀ ⦃Y₁ Y₂ : C⦄ (f : Y₁ ⟶ Y₂) (φ : W.Q.obj X ⟶ W.Q.obj Y₁),\n P (StructuredArrow.mk φ) → P (StructuredArrow.mk ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Functor.Derived.RightDerived | {
"line": 188,
"column": 2
} | {
"line": 188,
"column": 53
} | [
{
"pp": "C : Type u_1\nD : Type u_2\nH : Type u_3\ninst✝⁴ : Category.{v_1, u_1} C\ninst✝³ : Category.{v_3, u_2} D\ninst✝² : Category.{v_5, u_3} H\nRF : D ⥤ H\nF : C ⥤ H\nL : C ⥤ D\nα : F ⟶ L ⋙ RF\nW : MorphismProperty C\ninst✝¹ : L.IsLocalization W\ninst✝ : RF.IsRightDerivedFunctor α W\nthis : RF.IsLeftKanExten... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Functor.Derived.Adjunction | {
"line": 63,
"column": 18
} | {
"line": 63,
"column": 29
} | [
{
"pp": "C₁ : Type u_1\nC₂ : Type u_2\nD₁ : Type u_3\nD₂ : Type u_4\ninst✝⁷ : Category.{v_1, u_1} C₁\ninst✝⁶ : Category.{v_2, u_2} C₂\ninst✝⁵ : Category.{v_3, u_3} D₁\ninst✝⁴ : Category.{v_4, u_4} D₂\nG : C₁ ⥤ C₂\nF : C₂ ⥤ C₁\nadj : G ⊣ F\nL₁ : C₁ ⥤ D₁\nL₂ : C₂ ⥤ D₂\nW₁ : MorphismProperty C₁\nW₂ : MorphismPrope... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.FiberedCategory.Grothendieck | {
"line": 54,
"column": 33
} | {
"line": 54,
"column": 44
} | [
{
"pp": "𝒮 : Type u_1\ninst✝¹ : Category.{v_1, u_1} 𝒮\nF : LocallyDiscrete 𝒮ᵒᵖ ⥤ᵖ Cat\nR S : 𝒮\na : ↑(F.obj { as := op S })\nf : R ⟶ S\na' : ∫ᶜ F\ng : a'.base ⟶ R\nφ' : a' ⟶ { base := S, fiber := a }\ninst✝ : (forget F).IsHomLift (g ≫ f) φ'\n⊢ φ'.base = g ≫ f",
"usedConstants": [
"CategoryTheory.C... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.FiberedCategory.Grothendieck | {
"line": 66,
"column": 28
} | {
"line": 66,
"column": 39
} | [
{
"pp": "𝒮 : Type u_1\ninst✝ : Category.{v_1, u_1} 𝒮\nF : LocallyDiscrete 𝒮ᵒᵖ ⥤ᵖ Cat\nR S : 𝒮\na : ↑(F.obj { as := op S })\nf : R ⟶ S\na' : ∫ᶜ F\ng : (forget F).obj a' ⟶ R\nφ' : a' ⟶ { base := S, fiber := a }\nhφ' : (forget F).IsHomLift (g ≫ f) φ'\n⊢ (homCartesianLift f g φ' ≫ cartesianLift a f).base = φ'.b... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.FiberedCategory.Grothendieck | {
"line": 69,
"column": 34
} | {
"line": 69,
"column": 45
} | [
{
"pp": "𝒮 : Type u_1\ninst✝ : Category.{v_1, u_1} 𝒮\nF : LocallyDiscrete 𝒮ᵒᵖ ⥤ᵖ Cat\nR S : 𝒮\na : ↑(F.obj { as := op S })\nf : R ⟶ S\na' : ∫ᶜ F\ng : (forget F).obj a' ⟶ R\nχ' : a' ⟶ domainCartesianLift a f\nhχ'.symm : (forget F).IsHomLift g χ'\nhφ' : (forget F).IsHomLift (g ≫ f) (χ' ≫ cartesianLift a f)\n⊢... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Localization.StructuredArrow | {
"line": 138,
"column": 21
} | {
"line": 138,
"column": 59
} | [
{
"pp": "case hP₂\nC : Type u_1\nD : Type u_2\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Category.{v_2, u_2} D\nL : C ⥤ D\nW : MorphismProperty C\ninst✝ : L.IsLocalization W\nY : C\nP : CostructuredArrow L (L.obj Y) → Prop\nhP₀ : P (CostructuredArrow.mk (𝟙 (L.obj Y)))\nhP₁ :\n ∀ ⦃X₁ X₂ : C⦄ (f : X₁ ⟶ X₂) (φ : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.FiberedCategory.Grothendieck | {
"line": 106,
"column": 6
} | {
"line": 106,
"column": 17
} | [
{
"pp": "𝒮 : Type u_1\ninst✝ : Category.{v_1, u_1} 𝒮\nF : LocallyDiscrete 𝒮ᵒᵖ ⥤ᵖ Cat\nS : 𝒮\nX Y : ↑(F.obj { as := op S })\nf : (Fiber.inducedFunctor ⋯).obj X ⟶ (Fiber.inducedFunctor ⋯).obj Y\n⊢ (fiberInclusion.map f).base = 𝟙 S",
"usedConstants": [
"Opposite",
"CategoryTheory.LocallyDiscre... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.FiberedCategory.Grothendieck | {
"line": 107,
"column": 4
} | {
"line": 108,
"column": 43
} | [
{
"pp": "𝒮 : Type u_1\ninst✝ : Category.{v_1, u_1} 𝒮\nF : LocallyDiscrete 𝒮ᵒᵖ ⥤ᵖ Cat\nS : 𝒮\nX Y : ↑(F.obj { as := op S })\nf : (Fiber.inducedFunctor ⋯).obj X ⟶ (Fiber.inducedFunctor ⋯).obj Y\nhf : (fiberInclusion.map f).base = 𝟙 S\n⊢ ∃ a, (Fiber.inducedFunctor ⋯).map a = f",
"usedConstants": [
"... | use (fiberInclusion.map f).fiber ≫ eqToHom (by simp [hf]) ≫
(F.mapId ⟨op S⟩).hom.toNatTrans.app Y | Mathlib.Tactic._aux_Mathlib_Tactic_Use___elabRules_Mathlib_Tactic_useSyntax_1 | Mathlib.Tactic.useSyntax |
Mathlib.CategoryTheory.FiberedCategory.Grothendieck | {
"line": 116,
"column": 4
} | {
"line": 117,
"column": 35
} | [
{
"pp": "𝒮 : Type u_1\ninst✝ : Category.{v_1, u_1} 𝒮\nF : LocallyDiscrete 𝒮ᵒᵖ ⥤ᵖ Cat\nS : 𝒮\na b : ↑(F.obj { as := op S })\nf g : a ⟶ b\nheq : fiberInclusion.map ((Fiber.inducedFunctor ⋯).map f) = fiberInclusion.map ((Fiber.inducedFunctor ⋯).map g)\n⊢ f = g",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.FiberedCategory.Grothendieck | {
"line": 122,
"column": 51
} | {
"line": 122,
"column": 62
} | [
{
"pp": "𝒮 : Type u_1\ninst✝ : Category.{v_1, u_1} 𝒮\nF : LocallyDiscrete 𝒮ᵒᵖ ⥤ᵖ Cat\nS : 𝒮\nY : (forget F).Fiber S\n⊢ (fiberInclusion.obj Y).base = S",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Functor.Derived.Adjunction | {
"line": 78,
"column": 20
} | {
"line": 78,
"column": 31
} | [
{
"pp": "C₁ : Type u_1\nC₂ : Type u_2\nD₁ : Type u_3\nD₂ : Type u_4\ninst✝⁷ : Category.{v_1, u_1} C₁\ninst✝⁶ : Category.{v_2, u_2} C₂\ninst✝⁵ : Category.{v_3, u_3} D₁\ninst✝⁴ : Category.{v_4, u_4} D₂\nG : C₁ ⥤ C₂\nF : C₂ ⥤ C₁\nadj : G ⊣ F\nL₁ : C₁ ⥤ D₁\nL₂ : C₂ ⥤ D₂\nW₁ : MorphismProperty C₁\nW₂ : MorphismPrope... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Functor.Derived.PointwiseRightDerived | {
"line": 58,
"column": 2
} | {
"line": 60,
"column": 51
} | [
{
"pp": "C : Type u₁\nD : Type u₂\nH : Type u₃\ninst✝³ : Category.{v₁, u₁} C\ninst✝² : Category.{v₂, u₂} D\ninst✝¹ : Category.{v₃, u₃} H\nF : C ⥤ H\nL : C ⥤ D\nW : MorphismProperty C\ninst✝ : L.IsLocalization W\nX : C\n⊢ F.HasPointwiseRightDerivedFunctorAt W X ↔ L.HasPointwiseLeftKanExtensionAt F (L.obj X)",
... | rw [← hasPointwiseLeftKanExtensionAt_iff_of_equivalence W.Q L F
(Localization.uniq W.Q L W) (Localization.compUniqFunctor W.Q L W) (W.Q.obj X) (L.obj X)
((Localization.compUniqFunctor W.Q L W).app X)] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.CategoryTheory.Functor.Derived.Adjunction | {
"line": 105,
"column": 2
} | {
"line": 105,
"column": 13
} | [
{
"pp": "C₁ : Type u_1\nC₂ : Type u_2\nD₁ : Type u_3\nD₂ : Type u_4\ninst✝⁵ : Category.{v_1, u_1} C₁\ninst✝⁴ : Category.{v_2, u_2} C₂\ninst✝³ : Category.{v_3, u_3} D₁\ninst✝² : Category.{v_4, u_4} D₂\nG : C₁ ⥤ C₂\nF : C₂ ⥤ C₁\nadj : G ⊣ F\nL₁ : C₁ ⥤ D₁\nL₂ : C₂ ⥤ D₂\nW₁ : MorphismProperty C₁\ninst✝¹ : L₁.IsLoca... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Functor.Derived.Adjunction | {
"line": 126,
"column": 2
} | {
"line": 126,
"column": 13
} | [
{
"pp": "C₁ : Type u_1\nC₂ : Type u_2\nD₁ : Type u_3\nD₂ : Type u_4\ninst✝⁵ : Category.{v_1, u_1} C₁\ninst✝⁴ : Category.{v_2, u_2} C₂\ninst✝³ : Category.{v_3, u_3} D₁\ninst✝² : Category.{v_4, u_4} D₂\nG : C₁ ⥤ C₂\nF : C₂ ⥤ C₁\nadj : G ⊣ F\nL₁ : C₁ ⥤ D₁\nL₂ : C₂ ⥤ D₂\nW₂ : MorphismProperty C₂\ninst✝¹ : L₂.IsLoca... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.EpiMono | {
"line": 46,
"column": 4
} | {
"line": 46,
"column": 38
} | [
{
"pp": "case mp\nC : Type u_1\ninst✝ : Category.{v_1, u_1} C\nX Y : C\nf : X ⟶ Y\nc : PullbackCone f f\nhc : IsLimit c\nhf : Mono f\n⊢ c.fst = c.snd",
"usedConstants": [
"Eq.mpr",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.WidePullbackShape.catego... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.EpiMono | {
"line": 88,
"column": 4
} | {
"line": 88,
"column": 37
} | [
{
"pp": "case mp\nC : Type u_1\ninst✝ : Category.{v_1, u_1} C\nX Y : C\nf : X ⟶ Y\nc : PushoutCocone f f\nhc : IsColimit c\nhf : Epi f\n⊢ c.inl = c.inr",
"usedConstants": [
"Eq.mpr",
"CategoryTheory.Limits.WalkingSpan",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"C... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Functor.ReflectsIso.Jointly | {
"line": 62,
"column": 58
} | {
"line": 62,
"column": 69
} | [
{
"pp": "C : Type u_1\ninst✝³ : Category.{u_4, u_1} C\nI : Type u_2\nD : I → Type u_3\ninst✝² : (i : I) → Category.{u_5, u_3} (D i)\nF : (i : I) → C ⥤ D i\ninst✝¹ : HasEqualizers C\ninst✝ : ∀ (i : I), PreservesLimitsOfShape WalkingParallelPair (F i)\nhF : ∀ ⦃X Y : C⦄ (f : X ⟶ Y) [Mono f], (∀ (i : I), IsIso ((F ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Functor.ReflectsIso.Jointly | {
"line": 61,
"column": 8
} | {
"line": 63,
"column": 71
} | [
{
"pp": "C : Type u_1\ninst✝³ : Category.{u_4, u_1} C\nI : Type u_2\nD : I → Type u_3\ninst✝² : (i : I) → Category.{u_5, u_3} (D i)\nF : (i : I) → C ⥤ D i\ninst✝¹ : HasEqualizers C\ninst✝ : ∀ (i : I), PreservesLimitsOfShape WalkingParallelPair (F i)\nhF : ∀ ⦃X Y : C⦄ (f : X ⟶ Y) [Mono f], (∀ (i : I), IsIso ((F ... | let hc := isLimitForkMapOfIsLimit (F i) _ (equalizerIsEqualizer f g)
obtain ⟨l, hl⟩ := Fork.IsLimit.lift' hc (𝟙 _) (by simpa using hfg i)
exact ⟨l, Fork.IsLimit.hom_ext hc (by cat_disch), by cat_disch⟩ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Functor.ReflectsIso.Jointly | {
"line": 61,
"column": 8
} | {
"line": 63,
"column": 71
} | [
{
"pp": "C : Type u_1\ninst✝³ : Category.{u_4, u_1} C\nI : Type u_2\nD : I → Type u_3\ninst✝² : (i : I) → Category.{u_5, u_3} (D i)\nF : (i : I) → C ⥤ D i\ninst✝¹ : HasEqualizers C\ninst✝ : ∀ (i : I), PreservesLimitsOfShape WalkingParallelPair (F i)\nhF : ∀ ⦃X Y : C⦄ (f : X ⟶ Y) [Mono f], (∀ (i : I), IsIso ((F ... | let hc := isLimitForkMapOfIsLimit (F i) _ (equalizerIsEqualizer f g)
obtain ⟨l, hl⟩ := Fork.IsLimit.lift' hc (𝟙 _) (by simpa using hfg i)
exact ⟨l, Fork.IsLimit.hom_ext hc (by cat_disch), by cat_disch⟩ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Functor.ReflectsIso.Limits | {
"line": 48,
"column": 6
} | {
"line": 48,
"column": 38
} | [
{
"pp": "C : Type u_1\ninst✝⁴ : Category.{?u.400, u_1} C\nI : Type u_2\nD : I → Type u_3\ninst✝³ : (i : I) → Category.{?u.414, u_3} (D i)\nF : (i : I) → C ⥤ D i\nhF : JointlyReflectIsomorphisms F\nJ : Type u_4\ninst✝² : Category.{v_1, u_4} J\nG : J ⥤ C\nc : Cone G\nhc : (i : I) → IsLimit ((F i).mapCone c)\ninst... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Functor.ReflectsIso.Limits | {
"line": 72,
"column": 6
} | {
"line": 72,
"column": 38
} | [
{
"pp": "C : Type u_1\ninst✝⁴ : Category.{?u.7363, u_1} C\nI : Type u_2\nD : I → Type u_3\ninst✝³ : (i : I) → Category.{?u.7377, u_3} (D i)\nF : (i : I) → C ⥤ D i\nhF : JointlyReflectIsomorphisms F\nJ : Type u_4\ninst✝² : Category.{v_1, u_4} J\nG : J ⥤ C\nc : Cocone G\nhc : (i : I) → IsColimit ((F i).mapCocone ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Functor.ReflectsIso.Exact | {
"line": 111,
"column": 2
} | {
"line": 111,
"column": 52
} | [
{
"pp": "C : Type u_1\ninst✝⁶ : Category.{v_1, u_1} C\nI : Type u_2\nD : I → Type u_3\ninst✝⁵ : (i : I) → Category.{v_2, u_3} (D i)\nF : (i : I) → C ⥤ D i\nhP : JointlyReflectIsomorphisms F\ninst✝⁴ : Abelian C\ninst✝³ : (i : I) → Abelian (D i)\ninst✝² : CategoryWithHomology C\ninst✝¹ : ∀ (i : I), PreservesFinit... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.FintypeCat | {
"line": 87,
"column": 2
} | {
"line": 87,
"column": 69
} | [
{
"pp": "ι : Type u_1\ninst✝ : Finite ι\nX : ι → FintypeCat\nx : (∏ᶜ X).obj\ni : ι\n⊢ (productEquiv X) x i = (ConcreteCategory.hom (Pi.π X i)) x",
"usedConstants": [
"CategoryTheory.Limits.Types.Small.productIso_hom_comp_eval_apply",
"CategoryTheory.Limits.FintypeCat.productEquiv._proof_6",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Galois.Basic | {
"line": 209,
"column": 75
} | {
"line": 211,
"column": 44
} | [
{
"pp": "C : Type u₁\ninst✝ : Category.{u₂, u₁} C\nX : C\nhc : ¬IsConnected X\nhi : ∀ (a : IsInitial X), False\n⊢ ∃ Y v, (∀ (a : IsInitial Y), False) ∧ Mono v ∧ ¬IsIso v",
"usedConstants": [
"Mathlib.Tactic.Push.not_exists._simp_1",
"Eq.mpr",
"Mathlib.Tactic.Push.not_and_eq",
"False"... | by
contrapose! hc
exact ⟨hi, fun Y i hm hni ↦ hc Y i hni hm⟩ | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Galois.GaloisObjects | {
"line": 150,
"column": 4
} | {
"line": 150,
"column": 15
} | [
{
"pp": "case refine_3.a\nC : Type u₁\ninst✝³ : Category.{u₂, u₁} C\ninst✝² : GaloisCategory C\nA B : C\nf : A ⟶ B\ninst✝¹ : IsConnected A\ninst✝ : IsGalois B\nσ : Aut A\nF : C ⥤ FintypeCat := ⋯\na : (F.obj A).obj\nτ : Aut B\nhτ : f ≫ τ.hom = σ.hom ≫ f\n⊢ (fun f_1 ↦ (ConcreteCategory.hom (F.map f_1.hom)) ((Conc... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Galois.Basic | {
"line": 337,
"column": 2
} | {
"line": 337,
"column": 13
} | [
{
"pp": "case a\nC : Type u₁\ninst✝³ : Category.{u₂, u₁} C\nF : C ⥤ FintypeCat\ninst✝² : PreGaloisCategory C\ninst✝¹ : FiberFunctor F\nX A : C\ninst✝ : IsConnected A\nh : Nonempty (F.obj X).obj\nf : X ⟶ A\nZ : C\nu v : A ⟶ Z\nhuv : f ≫ u = f ≫ v\n⊢ (fun f_1 ↦\n (ConcreteCategory.hom (F.map f_1))\n ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Galois.GaloisObjects | {
"line": 167,
"column": 2
} | {
"line": 167,
"column": 28
} | [
{
"pp": "C : Type u₁\ninst✝³ : Category.{u₂, u₁} C\ninst✝² : GaloisCategory C\nF : C ⥤ FintypeCat\nA B : C\ninst✝¹ : IsConnected A\ninst✝ : IsGalois B\nf : A ⟶ B\nσ : Aut A\na : (F.obj A).obj\n⊢ (ConcreteCategory.hom (F.map (autMap f σ).hom)) ((ConcreteCategory.hom (F.map f)) a) =\n (ConcreteCategory.hom (F.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Galois.Decomposition | {
"line": 162,
"column": 2
} | {
"line": 162,
"column": 42
} | [
{
"pp": "case h\nC : Type u₁\ninst✝⁶ : Category.{u₂, u₁} C\ninst✝⁵ : GaloisCategory C\nF : C ⥤ FintypeCat\ninst✝⁴ : FiberFunctor F\nX A B : C\ninst✝³ : IsConnected A\ninst✝² : IsConnected B\na : (F.obj A).obj\nb : (F.obj B).obj\ni : A ⟶ X\nj : B ⟶ X\nh : (ConcreteCategory.hom (F.map i)) a = (ConcreteCategory.ho... | change (F.map u ≫ F.map _) y = F.map v y | Lean.Elab.Tactic.evalChange | Lean.Parser.Tactic.change |
Mathlib.CategoryTheory.Galois.Topology | {
"line": 98,
"column": 9
} | {
"line": 98,
"column": 20
} | [
{
"pp": "case h\nC : Type u₁\ninst✝ : Category.{u₂, u₁} C\nF : C ⥤ FintypeCat\na : (X : C) → Aut (F.obj X)\nh : ∀ (i : Arrow C), F.map i.hom ≫ (a i.right).hom = (a i.left).hom ≫ F.map i.hom\nX Y : C\nf : X ⟶ Y\nx✝ : (F.obj X).obj\n⊢ (ConcreteCategory.hom (F.map f ≫ (a Y).hom)) x✝ = (ConcreteCategory.hom ((a X).... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.GradedObject.Braiding | {
"line": 45,
"column": 29
} | {
"line": 45,
"column": 60
} | [
{
"pp": "I : Type u_1\ninst✝⁵ : AddCommMonoid I\nC : Type u_2\ninst✝⁴ : Category.{v_1, u_2} C\ninst✝³ : MonoidalCategory C\nX Y Z : GradedObject I C\ninst✝² : BraidedCategory C\ninst✝¹ : X.HasTensor Y\ninst✝ : Y.HasTensor X\nk i j : I\nhij : i + j = k\n⊢ j + i = k",
"usedConstants": [
"Eq.mpr",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.GradedObject.Braiding | {
"line": 47,
"column": 29
} | {
"line": 47,
"column": 60
} | [
{
"pp": "I : Type u_1\ninst✝⁵ : AddCommMonoid I\nC : Type u_2\ninst✝⁴ : Category.{v_1, u_2} C\ninst✝³ : MonoidalCategory C\nX Y Z : GradedObject I C\ninst✝² : BraidedCategory C\ninst✝¹ : X.HasTensor Y\ninst✝ : Y.HasTensor X\nk i j : I\nhij : i + j = k\n⊢ j + i = k",
"usedConstants": [
"Eq.mpr",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Groupoid.FreeGroupoid | {
"line": 81,
"column": 2
} | {
"line": 83,
"column": 33
} | [
{
"pp": "V : Type u\ninst✝ : Quiver V\nX✝² Y✝¹ X✝¹ Y✝ X Y : Paths (Symmetrify V)\nX✝ Z✝ : Symmetrify V\nf : X✝ ⟶ Z✝\nXW : X✝² ⟶ (Paths.of (Symmetrify V)).obj X✝\nWY : (Paths.of (Symmetrify V)).obj X✝ ⟶ Y✝¹\nthis :\n HomRel.CompClosure redStep (Path.reverse WY ≫ 𝟙 ((Paths.of (Symmetrify V)).obj X✝) ≫ Path.reve... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Groupoid.FreeGroupoidOfCategory | {
"line": 125,
"column": 2
} | {
"line": 125,
"column": 13
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nE : Type u₂\ninst✝ : Groupoid E\nφ : C ⥤ E\nX Y : C\nf : X ⟶ Y\n⊢ (lift φ).map (homMk f) = φ.map f",
"usedConstants": [
"CategoryTheory.FreeGroupoid",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.instGroupoid... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Groupoid.FreeGroupoidOfCategory | {
"line": 134,
"column": 2
} | {
"line": 136,
"column": 22
} | [
{
"pp": "G : Type u₁\ninst✝ : Groupoid G\n⊢ lift (𝟭 G) ⋙ of G = 𝟭 (FreeGroupoid G)",
"usedConstants": [
"CategoryTheory.FreeGroupoid",
"Eq.mpr",
"CategoryTheory.Functor",
"congrArg",
"CategoryTheory.Functor.assoc",
"CategoryTheory.Functor.comp_id",
"CategoryTheory... | rw [lift_unique (of G) (lift (𝟭 G) ⋙ of G) (by rw [← Functor.assoc, lift_spec, Functor.id_comp])]
symm; apply lift_unique
rw [Functor.comp_id] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Groupoid.FreeGroupoidOfCategory | {
"line": 134,
"column": 2
} | {
"line": 136,
"column": 22
} | [
{
"pp": "G : Type u₁\ninst✝ : Groupoid G\n⊢ lift (𝟭 G) ⋙ of G = 𝟭 (FreeGroupoid G)",
"usedConstants": [
"CategoryTheory.FreeGroupoid",
"Eq.mpr",
"CategoryTheory.Functor",
"congrArg",
"CategoryTheory.Functor.assoc",
"CategoryTheory.Functor.comp_id",
"CategoryTheory... | rw [lift_unique (of G) (lift (𝟭 G) ⋙ of G) (by rw [← Functor.assoc, lift_spec, Functor.id_comp])]
symm; apply lift_unique
rw [Functor.comp_id] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Groupoid.Subgroupoid | {
"line": 87,
"column": 4
} | {
"line": 87,
"column": 48
} | [
{
"pp": "case mp\nC : Type u\ninst✝ : Groupoid C\nS : Subgroupoid C\nc d : C\nf : c ⟶ d\nh : Groupoid.inv f ∈ S.arrows d c\n⊢ f ∈ S.arrows c d",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Groupoid.Subgroupoid | {
"line": 95,
"column": 6
} | {
"line": 95,
"column": 59
} | [
{
"pp": "C : Type u\ninst✝ : Groupoid C\nS : Subgroupoid C\nc d e : C\nf : c ⟶ d\ng : d ⟶ e\nhf : f ∈ S.arrows c d\nh : f ≫ g ∈ S.arrows c e\nthis : Groupoid.inv f ≫ f ≫ g ∈ S.arrows d e\n⊢ g ∈ S.arrows d e",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Groupoid.Subgroupoid | {
"line": 104,
"column": 6
} | {
"line": 104,
"column": 87
} | [
{
"pp": "C : Type u\ninst✝ : Groupoid C\nS : Subgroupoid C\nc d e : C\nf : c ⟶ d\ng : d ⟶ e\nhg : g ∈ S.arrows d e\nh : f ≫ g ∈ S.arrows c e\nthis : (f ≫ g) ≫ Groupoid.inv g ∈ S.arrows c d\n⊢ f ∈ S.arrows c d",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Groupoid.Subgroupoid | {
"line": 251,
"column": 2
} | {
"line": 251,
"column": 48
} | [
{
"pp": "C : Type u\ninst✝ : Groupoid C\nS T : Subgroupoid C\nh : S ≤ T\nx✝¹ x✝ : ↑S.objs\ns : C\nhs : s ∈ S.objs\nt : C\nht : t ∈ S.objs\n⊢ (inclusion h).obj ⟨s, hs⟩ = (inclusion h).obj ⟨t, ht⟩ → ⟨s, hs⟩ = ⟨t, ht⟩",
"usedConstants": [
"Eq.mpr",
"Membership.mem",
"Set.Elem",
"id",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.GuitartExact.Over | {
"line": 71,
"column": 10
} | {
"line": 71,
"column": 45
} | [
{
"pp": "case h.h.h₁\nC : Type u₁\ninst✝³ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝² : Category.{v₂, u₂} D\nF : C ⥤ D\nX : C\ninst✝¹ : ∀ (Y : C), HasBinaryProduct X Y\ninst✝ : ∀ (Y : C), PreservesLimit (pair X Y) F\nW : Over (F.obj X)\nZ : C\ng : (Over.forget (F.obj X)).obj W ⟶ F.obj Z\nP : (TwoSquare.overPost ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.GuitartExact.Over | {
"line": 72,
"column": 10
} | {
"line": 72,
"column": 45
} | [
{
"pp": "case h.h.h₂\nC : Type u₁\ninst✝³ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝² : Category.{v₂, u₂} D\nF : C ⥤ D\nX : C\ninst✝¹ : ∀ (Y : C), HasBinaryProduct X Y\ninst✝ : ∀ (Y : C), PreservesLimit (pair X Y) F\nW : Over (F.obj X)\nZ : C\ng : (Over.forget (F.obj X)).obj W ⟶ F.obj Z\nP : (TwoSquare.overPost ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Groupoid.Subgroupoid | {
"line": 314,
"column": 4
} | {
"line": 315,
"column": 35
} | [
{
"pp": "case refine_1\nC : Type u\ninst✝ : Groupoid C\nS : Subgroupoid C\nSn : S.IsNormal\nc d : C\np : c ⟶ d\nγ₁ : c ⟶ c\nx✝¹ : γ₁ ∈ S.arrows c c\nγ₂ : c ⟶ c\nx✝ : γ₂ ∈ S.arrows c c\nh : (fun γ ↦ Groupoid.inv p ≫ γ ≫ p) γ₁ = (fun γ ↦ Groupoid.inv p ≫ γ ≫ p) γ₂\n⊢ γ₁ = γ₂",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Groupoid.Subgroupoid | {
"line": 428,
"column": 4
} | {
"line": 428,
"column": 39
} | [
{
"pp": "case mpr\nC : Type u\ninst✝¹ : Groupoid C\nD : Type u_1\ninst✝ : Groupoid D\nφ : C ⥤ D\nhφ : Function.Injective φ.obj\nS : Subgroupoid C\nc d : D\nf : c ⟶ d\n⊢ (∃ a b g, ∃ (ha : φ.obj a = c) (hb : φ.obj b = d) (_ : g ∈ S.arrows a b), f = eqToHom ⋯ ≫ φ.map g ≫ eqToHom hb) →\n Arrows φ hφ S c d f",
... | rintro ⟨a, b, g, rfl, rfl, hg, rfl⟩ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRIntro | Lean.Parser.Tactic.rintro |
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