module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.CategoryTheory.Monoidal.Action.End | {
"line": 178,
"column": 4
} | {
"line": 178,
"column": 40
} | {
"line": 179,
"column": 6
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : MonoidalCategory C\ninst✝¹ : Category.{v_2, u_2} D\ninst✝ : MonoidalRightAction C D\nx : C\nt : D\n⊢ (ρ_ ((curriedAction C D).obj x)).inv.app t =\n ((curriedAction C D).map (ρ_ x).inv ≫\n { app := fun x_1 ↦ (αᵣ x_1 x (𝟙_ ... | [
"C : Type u_1\nD : Type u_2\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : MonoidalCategory C\ninst✝¹ : Category.{v_2, u_2} D\ninst✝ : MonoidalRightAction C D\nx : C\nt : D\n⊢ 𝟙 (t ⊙ᵣ x) = t ⊴ᵣ (ρ_ x).inv ≫ (αᵣ t x (𝟙_ C)).hom ≫ (ρᵣ (t ⊙ᵣ x)).hom"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.Action.Basic | {
"line": 259,
"column": 2
} | {
"line": 259,
"column": 61
} | {
"line": 261,
"column": 0
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : Category.{v_2, u_2} D\ninst✝¹ : MonoidalCategory C\ninst✝ : MonoidalLeftAction C D\nx y : C\nf : x ≅ y\nz : D\n⊢ f.hom ⊵ₗ z ≫ f.inv ⊵ₗ z = 𝟙 (x ⊙ₗ z)",
"ppTerm": "?m.45",
"assigned": true,
"usedConstants": [
"Eq.mpr... | [] | rw [← comp_actionHomLeft, Iso.hom_inv_id, id_actionHomLeft] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.CategoryTheory.Monoidal.Action.Basic | {
"line": 259,
"column": 2
} | {
"line": 259,
"column": 61
} | {
"line": 261,
"column": 0
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : Category.{v_2, u_2} D\ninst✝¹ : MonoidalCategory C\ninst✝ : MonoidalLeftAction C D\nx y : C\nf : x ≅ y\nz : D\n⊢ f.hom ⊵ₗ z ≫ f.inv ⊵ₗ z = 𝟙 (x ⊙ₗ z)",
"ppTerm": "?m.45",
"assigned": true,
"usedConstants": [
"Eq.mpr... | [] | rw [← comp_actionHomLeft, Iso.hom_inv_id, id_actionHomLeft] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Monoidal.Action.Basic | {
"line": 259,
"column": 2
} | {
"line": 259,
"column": 61
} | {
"line": 261,
"column": 0
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : Category.{v_2, u_2} D\ninst✝¹ : MonoidalCategory C\ninst✝ : MonoidalLeftAction C D\nx y : C\nf : x ≅ y\nz : D\n⊢ f.hom ⊵ₗ z ≫ f.inv ⊵ₗ z = 𝟙 (x ⊙ₗ z)",
"ppTerm": "?m.45",
"assigned": true,
"usedConstants": [
"Eq.mpr... | [] | rw [← comp_actionHomLeft, Iso.hom_inv_id, id_actionHomLeft] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Monoidal.Action.Opposites | {
"line": 61,
"column": 4
} | {
"line": 62,
"column": 61
} | {
"line": 63,
"column": 6
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : MonoidalCategory C\ninst✝¹ : Category.{v_2, u_2} D\ninst✝ : MonoidalRightAction Cᴹᵒᵖ D\nc₁ c₂ c₃ : C\nd : D\n⊢ d ⊴ᵣ (α_ c₁ c₂ c₃).hom.mop ≫\n (αᵣ d { unmop := c₂ ⊗ c₃ } { unmop := c₁ }).hom ≫ (αᵣ d { unmop := c₃ } { unmop := c₂ }... | [
"C : Type u_1\nD : Type u_2\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : MonoidalCategory C\ninst✝¹ : Category.{v_2, u_2} D\ninst✝ : MonoidalRightAction Cᴹᵒᵖ D\nc₁ c₂ c₃ : C\nd : D\n⊢ d ⊴ᵣ (α_ { unmop := c₃ } { unmop := c₂ } { unmop := c₁ }).inv ≫\n (αᵣ d ({ unmop := c₃ } ⊗ { unmop := c₂ }) { unmop := c₁ }).hom ≫... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.Action.Opposites | {
"line": 133,
"column": 8
} | {
"line": 133,
"column": 56
} | {
"line": 134,
"column": 10
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : MonoidalCategory C\ninst✝¹ : Category.{v_2, u_2} D\ninst✝ : MonoidalLeftAction C D\nc✝ c'✝ : Cᵒᵖ\nd✝ d'✝ : Dᵒᵖ\nf : unop c'✝ ⟶ unop c✝\ng : unop d'✝ ⟶ unop d✝\n⊢ (Quiver.Hom.unop (op f) ⊙ₗₘ Quiver.Hom.unop (op g)).op.unop =\n ((Qui... | [
"C : Type u_1\nD : Type u_2\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : MonoidalCategory C\ninst✝¹ : Category.{v_2, u_2} D\ninst✝ : MonoidalLeftAction C D\nc✝ c'✝ : Cᵒᵖ\nd✝ d'✝ : Dᵒᵖ\nf : unop c'✝ ⟶ unop c✝\ng : unop d'✝ ⟶ unop d✝\n⊢ f ⊙ₗₘ g = f ⊵ₗ unop d'✝ ≫ unop c✝ ⊴ₗ g"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.Action.Basic | {
"line": 569,
"column": 2
} | {
"line": 569,
"column": 61
} | {
"line": 571,
"column": 0
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : Category.{v_2, u_2} D\ninst✝¹ : MonoidalCategory C\ninst✝ : MonoidalRightAction C D\nx y : D\nf : x ≅ y\nz : C\n⊢ f.hom ⊵ᵣ z ≫ f.inv ⊵ᵣ z = 𝟙 (x ⊙ᵣ z)",
"ppTerm": "?m.45",
"assigned": true,
"usedConstants": [
"Eq.mp... | [] | rw [← comp_actionHomLeft, Iso.hom_inv_id, id_actionHomLeft] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.CategoryTheory.Monoidal.Action.Basic | {
"line": 569,
"column": 2
} | {
"line": 569,
"column": 61
} | {
"line": 571,
"column": 0
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : Category.{v_2, u_2} D\ninst✝¹ : MonoidalCategory C\ninst✝ : MonoidalRightAction C D\nx y : D\nf : x ≅ y\nz : C\n⊢ f.hom ⊵ᵣ z ≫ f.inv ⊵ᵣ z = 𝟙 (x ⊙ᵣ z)",
"ppTerm": "?m.45",
"assigned": true,
"usedConstants": [
"Eq.mp... | [] | rw [← comp_actionHomLeft, Iso.hom_inv_id, id_actionHomLeft] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Monoidal.Action.Basic | {
"line": 569,
"column": 2
} | {
"line": 569,
"column": 61
} | {
"line": 571,
"column": 0
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : Category.{v_2, u_2} D\ninst✝¹ : MonoidalCategory C\ninst✝ : MonoidalRightAction C D\nx y : D\nf : x ≅ y\nz : C\n⊢ f.hom ⊵ᵣ z ≫ f.inv ⊵ᵣ z = 𝟙 (x ⊙ᵣ z)",
"ppTerm": "?m.45",
"assigned": true,
"usedConstants": [
"Eq.mp... | [] | rw [← comp_actionHomLeft, Iso.hom_inv_id, id_actionHomLeft] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Monoidal.Action.Opposites | {
"line": 174,
"column": 4
} | {
"line": 174,
"column": 52
} | {
"line": 175,
"column": 6
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : MonoidalCategory C\ninst✝¹ : Category.{v_2, u_2} D\ninst✝ : MonoidalLeftAction Cᵒᵖ Dᵒᵖ\nc✝ c'✝ : C\nd✝ d'✝ : D\nf : c✝ ⟶ c'✝\ng : d✝ ⟶ d'✝\n⊢ (f.op ⊙ₗₘ g.op).unop.op = ((f.op ⊵ₗ op d✝).unop ≫ (op c'✝ ⊴ₗ g.op).unop).op",
"ppTerm": ... | [
"C : Type u_1\nD : Type u_2\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : MonoidalCategory C\ninst✝¹ : Category.{v_2, u_2} D\ninst✝ : MonoidalLeftAction Cᵒᵖ Dᵒᵖ\nc✝ c'✝ : C\nd✝ d'✝ : D\nf : c✝ ⟶ c'✝\ng : d✝ ⟶ d'✝\n⊢ f.op ⊙ₗₘ g.op = f.op ⊵ₗ op d'✝ ≫ op c✝ ⊴ₗ g.op"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.Action.Opposites | {
"line": 275,
"column": 4
} | {
"line": 276,
"column": 59
} | {
"line": 277,
"column": 6
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : MonoidalCategory C\ninst✝¹ : Category.{v_2, u_2} D\ninst✝ : MonoidalLeftAction Cᴹᵒᵖ D\nc₁ c₂ c₃ : C\nd : D\n⊢ (α_ c₁ c₂ c₃).hom.mop ⊵ₗ d ≫\n (αₗ { unmop := c₂ ⊗ c₃ } { unmop := c₁ } d).hom ≫\n (αₗ { unmop := c₃ } { unmop :... | [
"C : Type u_1\nD : Type u_2\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : MonoidalCategory C\ninst✝¹ : Category.{v_2, u_2} D\ninst✝ : MonoidalLeftAction Cᴹᵒᵖ D\nc₁ c₂ c₃ : C\nd : D\n⊢ (α_ { unmop := c₃ } { unmop := c₂ } { unmop := c₁ }).inv ⊵ₗ d ≫\n (αₗ ({ unmop := c₃ } ⊗ { unmop := c₂ }) { unmop := c₁ } d).hom ≫\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.Action.Opposites | {
"line": 345,
"column": 8
} | {
"line": 345,
"column": 57
} | {
"line": 346,
"column": 10
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : MonoidalCategory C\ninst✝¹ : Category.{v_2, u_2} D\ninst✝ : MonoidalRightAction C D\nc✝ c'✝ : Cᵒᵖ\nd✝ d'✝ : Dᵒᵖ\nf : unop d'✝ ⟶ unop d✝\ng : unop c'✝ ⟶ unop c✝\n⊢ (Quiver.Hom.unop (op f) ⊙ᵣₘ Quiver.Hom.unop (op g)).op.unop =\n ((Qu... | [
"C : Type u_1\nD : Type u_2\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : MonoidalCategory C\ninst✝¹ : Category.{v_2, u_2} D\ninst✝ : MonoidalRightAction C D\nc✝ c'✝ : Cᵒᵖ\nd✝ d'✝ : Dᵒᵖ\nf : unop d'✝ ⟶ unop d✝\ng : unop c'✝ ⟶ unop c✝\n⊢ f ⊙ᵣₘ g = f ⊵ᵣ unop c'✝ ≫ unop d✝ ⊴ᵣ g"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.Action.Opposites | {
"line": 386,
"column": 4
} | {
"line": 386,
"column": 53
} | {
"line": 387,
"column": 6
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : MonoidalCategory C\ninst✝¹ : Category.{v_2, u_2} D\ninst✝ : MonoidalRightAction Cᵒᵖ Dᵒᵖ\nc✝ c'✝ : C\nd✝ d'✝ : D\nf : d✝ ⟶ d'✝\ng : c✝ ⟶ c'✝\n⊢ (f.op ⊙ᵣₘ g.op).unop.op = ((f.op ⊵ᵣ op c✝).unop ≫ (op d'✝ ⊴ᵣ g.op).unop).op",
"ppTerm":... | [
"C : Type u_1\nD : Type u_2\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : MonoidalCategory C\ninst✝¹ : Category.{v_2, u_2} D\ninst✝ : MonoidalRightAction Cᵒᵖ Dᵒᵖ\nc✝ c'✝ : C\nd✝ d'✝ : D\nf : d✝ ⟶ d'✝\ng : c✝ ⟶ c'✝\n⊢ f.op ⊙ᵣₘ g.op = f.op ⊵ᵣ op c'✝ ≫ op d✝ ⊴ᵣ g.op"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.Cartesian.CommGrp_ | {
"line": 63,
"column": 8
} | {
"line": 63,
"column": 19
} | {
"line": 63,
"column": 20
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : CartesianMonoidalCategory C\ninst✝ : BraidedCategory C\nX : C\nX₁ X₂ : CommGrp C\nψ : X₁ ⟶ X₂\nY : (Grp C)ᵒᵖ\nf g : unop Y ⟶ X₁.toGrp\n⊢ ((f * g) ≫ ψ.hom).hom.hom = (f ≫ ψ.hom * g ≫ ψ.hom).hom.hom",
"ppTerm": "?m.85",
"assigned": true,
"usedC... | [
"C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : CartesianMonoidalCategory C\ninst✝ : BraidedCategory C\nX : C\nX₁ X₂ : CommGrp C\nψ : X₁ ⟶ X₂\nY : (Grp C)ᵒᵖ\nf g : unop Y ⟶ X₁.toGrp\n⊢ (f.hom.hom * g.hom.hom) ≫ ψ.hom.hom.hom = f.hom.hom ≫ ψ.hom.hom.hom * g.hom.hom ≫ ψ.hom.hom.hom"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.Internal.Limits | {
"line": 95,
"column": 50
} | {
"line": 95,
"column": 61
} | {
"line": 95,
"column": 62
} | [
{
"pp": "J : Type w\ninst✝² : Category.{v_1, w} J\nC : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : MonoidalCategory C\nF : J ⥤ Mon C\nc : Cone (F ⋙ forget C)\nhc : IsLimit c\ns : Cone F\nm : s.pt ⟶ (limitCone F c hc).pt\nw : ∀ (j : J), m ≫ (limitCone F c hc).π.app j = s.π.app j\nj : J\n⊢ m.hom ≫ c.π.app j = { h... | [
"J : Type w\ninst✝² : Category.{v_1, w} J\nC : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : MonoidalCategory C\nF : J ⥤ Mon C\nc : Cone (F ⋙ forget C)\nhc : IsLimit c\ns : Cone F\nm : s.pt ⟶ (limitCone F c hc).pt\nw : ∀ (j : J), m ≫ (limitCone F c hc).π.app j = s.π.app j\nj : J\n⊢ m.hom ≫ c.π.app j = (s.π.app j).hom... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.Mod | {
"line": 395,
"column": 6
} | {
"line": 395,
"column": 17
} | {
"line": 395,
"column": 18
} | [
{
"pp": "C : Type u₁\ninst✝⁹ : Category.{v₁, u₁} C\ninst✝⁸ : MonoidalCategory C\nD : Type u₂\ninst✝⁷ : Category.{v₂, u₂} D\ninst✝⁶ : MonoidalLeftAction C D\nA B : C\ninst✝⁵ : MonObj A\ninst✝⁴ : MonObj B\nf : A ⟶ B\ninst✝³ : IsMonHom f\nM N : D\ninst✝² : ModObj B M\ninst✝¹ : ModObj B N\ng : M ⟶ N\ninst✝ : IsModH... | [
"C : Type u₁\ninst✝⁹ : Category.{v₁, u₁} C\ninst✝⁸ : MonoidalCategory C\nD : Type u₂\ninst✝⁷ : Category.{v₂, u₂} D\ninst✝⁶ : MonoidalLeftAction C D\nA B : C\ninst✝⁵ : MonObj A\ninst✝⁴ : MonObj B\nf : A ⟶ B\ninst✝³ : IsMonHom f\nM N : D\ninst✝² : ModObj B M\ninst✝¹ : ModObj B N\ng : M ⟶ N\ninst✝ : IsModHom B g\nthis... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.Ring | {
"line": 106,
"column": 19
} | {
"line": 106,
"column": 30
} | {
"line": 106,
"column": 31
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : CartesianMonoidalCategory C\ninst✝¹ : BraidedCategory C\nR : C\ninst✝ : RingObj R\nX✝ X : C\na : X ⟶ R\n⊢ 0 * a = 0",
"ppTerm": "?m.37",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"C : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : CartesianMonoidalCategory C\ninst✝¹ : BraidedCategory C\nR : C\ninst✝ : RingObj R\nX✝ X : C\na : X ⟶ R\n⊢ 0 * a = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.Ring | {
"line": 105,
"column": 19
} | {
"line": 105,
"column": 30
} | {
"line": 105,
"column": 31
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : CartesianMonoidalCategory C\ninst✝¹ : BraidedCategory C\nR : C\ninst✝ : RingObj R\nX✝ X : C\na : X ⟶ R\n⊢ a * 0 = 0",
"ppTerm": "?m.58",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"C : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : CartesianMonoidalCategory C\ninst✝¹ : BraidedCategory C\nR : C\ninst✝ : RingObj R\nX✝ X : C\na : X ⟶ R\n⊢ a * 0 = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Subterminal | {
"line": 109,
"column": 2
} | {
"line": 110,
"column": 29
} | {
"line": 112,
"column": 0
} | [
{
"pp": "C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nA : C\nhA : IsSubterminal A\ninst✝ : HasBinaryProduct A A\n⊢ A ⨯ A ≅ A",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"CategoryTheory.IsSubterminal.isIso_diag",
"CategoryTheory.Iso.symm",
"CategoryTheory.Limits.diag",
... | [] | letI := IsSubterminal.isIso_diag hA
apply (asIso (diag A)).symm | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Subterminal | {
"line": 109,
"column": 2
} | {
"line": 110,
"column": 29
} | {
"line": 112,
"column": 0
} | [
{
"pp": "C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nA : C\nhA : IsSubterminal A\ninst✝ : HasBinaryProduct A A\n⊢ A ⨯ A ≅ A",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"CategoryTheory.IsSubterminal.isIso_diag",
"CategoryTheory.Iso.symm",
"CategoryTheory.Limits.diag",
... | [] | letI := IsSubterminal.isIso_diag hA
apply (asIso (diag A)).symm | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Monoidal.DayConvolution.Closed | {
"line": 221,
"column": 4
} | {
"line": 221,
"column": 52
} | {
"line": 222,
"column": 4
} | [
{
"pp": "C : Type u₁\ninst✝⁵ : Category.{v₁, u₁} C\nV : Type u₂\ninst✝⁴ : Category.{v₂, u₂} V\ninst✝³ : MonoidalCategory C\ninst✝² : MonoidalCategory V\ninst✝¹ : MonoidalClosed V\nF G✝ H G : C ⥤ V\ninst✝ : DayConvolution F G\nℌ : DayConvolutionInternalHom F (F ⊛ G) H\nc c' : C\nf : c ⟶ c'\n⊢ G.map f ≫\n We... | [
"C : Type u₁\ninst✝⁵ : Category.{v₁, u₁} C\nV : Type u₂\ninst✝⁴ : Category.{v₂, u₂} V\ninst✝³ : MonoidalCategory C\ninst✝² : MonoidalCategory V\ninst✝¹ : MonoidalClosed V\nF G✝ H G : C ⥤ V\ninst✝ : DayConvolution F G\nℌ : DayConvolutionInternalHom F (F ⊛ G) H\nc c' : C\nf : c ⟶ c'\n⊢ ∀ (j : (multicospanShapeEnd C).... | apply Wedge.IsLimit.hom_ext <| ℌ.isLimitWedge c' | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.CategoryTheory.Monoidal.Hopf_ | {
"line": 115,
"column": 10
} | {
"line": 115,
"column": 24
} | {
"line": 115,
"column": 24
} | [
{
"pp": "case a\nC : Type u₁\ninst✝⁵ : Category.{v₁, u₁} C\ninst✝⁴ : MonoidalCategory C\ninst✝³ : BraidedCategory C\nA B : C\ninst✝² : HopfObj A\ninst✝¹ : HopfObj B\nf : A ⟶ B\ninst✝ : IsBimonHom f\n| Δ ≫ A ◁ 𝒮 ≫ μ",
"ppTerm": "?a",
"assigned": true,
"usedConstants": [
"CategoryTheory.ComonOb... | [
"case a\nC : Type u₁\ninst✝⁵ : Category.{v₁, u₁} C\ninst✝⁴ : MonoidalCategory C\ninst✝³ : BraidedCategory C\nA B : C\ninst✝² : HopfObj A\ninst✝¹ : HopfObj B\nf : A ⟶ B\ninst✝ : IsBimonHom f\n| ε ≫ η",
"case a\nC : Type u₁\ninst✝⁵ : Category.{v₁, u₁} C\ninst✝⁴ : MonoidalCategory C\ninst✝³ : BraidedCategory C\nA B ... | antipode_right | Lean.Elab.Tactic.Conv.evalRewrite | null |
Mathlib.CategoryTheory.Monoidal.Hopf_ | {
"line": 234,
"column": 8
} | {
"line": 234,
"column": 22
} | {
"line": 234,
"column": 22
} | [
{
"pp": "case a.a.a.a.a.a\nC : Type u₁\ninst✝³ : Category.{v₁, u₁} C\ninst✝² : MonoidalCategory C\ninst✝¹ : BraidedCategory C\nA : C\ninst✝ : HopfObj A\n| A ◁ (Δ ≫ A ◁ 𝒮 ≫ μ) ▷ A",
"ppTerm": "?a.a.a.a.a.a",
"assigned": true,
"usedConstants": [
"CategoryTheory.ComonObj.comul",
"CategoryT... | [
"case a.a.a.a.a.a\nC : Type u₁\ninst✝³ : Category.{v₁, u₁} C\ninst✝² : MonoidalCategory C\ninst✝¹ : BraidedCategory C\nA : C\ninst✝ : HopfObj A\n| A ◁ (ε ≫ η) ▷ A",
"case a.a.a.a.a.a\nC : Type u₁\ninst✝³ : Category.{v₁, u₁} C\ninst✝² : MonoidalCategory C\ninst✝¹ : BraidedCategory C\nA : C\ninst✝ : HopfObj A\n| A ... | antipode_right | Lean.Elab.Tactic.Conv.evalRewrite | null |
Mathlib.CategoryTheory.Monoidal.Hopf_ | {
"line": 381,
"column": 8
} | {
"line": 381,
"column": 22
} | {
"line": 381,
"column": 22
} | [
{
"pp": "case a.a.a.a.a.a\nC : Type u₁\ninst✝³ : Category.{v₁, u₁} C\ninst✝² : MonoidalCategory C\ninst✝¹ : BraidedCategory C\nA : C\ninst✝ : HopfObj A\n| A ◁ (Δ ≫ A ◁ 𝒮 ≫ μ) ▷ A",
"ppTerm": "?a.a.a.a.a.a",
"assigned": true,
"usedConstants": [
"CategoryTheory.ComonObj.comul",
"CategoryT... | [
"case a.a.a.a.a.a\nC : Type u₁\ninst✝³ : Category.{v₁, u₁} C\ninst✝² : MonoidalCategory C\ninst✝¹ : BraidedCategory C\nA : C\ninst✝ : HopfObj A\n| A ◁ (ε ≫ η) ▷ A",
"case a.a.a.a.a.a\nC : Type u₁\ninst✝³ : Category.{v₁, u₁} C\ninst✝² : MonoidalCategory C\ninst✝¹ : BraidedCategory C\nA : C\ninst✝ : HopfObj A\n| A ... | antipode_right | Lean.Elab.Tactic.Conv.evalRewrite | null |
Mathlib.CategoryTheory.Monoidal.Hopf_ | {
"line": 410,
"column": 8
} | {
"line": 410,
"column": 22
} | {
"line": 410,
"column": 22
} | [
{
"pp": "case a.a\nC : Type u₁\ninst✝³ : Category.{v₁, u₁} C\ninst✝² : MonoidalCategory C\ninst✝¹ : BraidedCategory C\nA : C\ninst✝ : HopfObj A\n| (Δ ≫ A ◁ 𝒮 ≫ μ) ▷ A",
"ppTerm": "?a.a",
"assigned": true,
"usedConstants": [
"CategoryTheory.ComonObj.comul",
"CategoryTheory.MonoidalCatego... | [
"case a.a\nC : Type u₁\ninst✝³ : Category.{v₁, u₁} C\ninst✝² : MonoidalCategory C\ninst✝¹ : BraidedCategory C\nA : C\ninst✝ : HopfObj A\n| (ε ≫ η) ▷ A",
"case a.a\nC : Type u₁\ninst✝³ : Category.{v₁, u₁} C\ninst✝² : MonoidalCategory C\ninst✝¹ : BraidedCategory C\nA : C\ninst✝ : HopfObj A\n| A ◁ ε",
"case a\nC :... | antipode_right | Lean.Elab.Tactic.Conv.evalRewrite | null |
Mathlib.CategoryTheory.Monoidal.DayConvolution | {
"line": 120,
"column": 2
} | {
"line": 120,
"column": 29
} | {
"line": 120,
"column": 30
} | [
{
"pp": "C : Type u₁\ninst✝⁴ : Category.{v₁, u₁} C\nV : Type u₂\ninst✝³ : Category.{v₂, u₂} V\ninst✝² : MonoidalCategory C\ninst✝¹ : MonoidalCategory V\nF G : C ⥤ V\ninst✝ : DayConvolution F G\nx x' y y' : C\nf : x ⟶ x'\ng : y ⟶ y'\n⊢ (F.map f ⊗ₘ G.map g) ≫ (unit F G).app (x', y') = (unit F G).app (x, y) ≫ (F ⊛... | [
"C : Type u₁\ninst✝⁴ : Category.{v₁, u₁} C\nV : Type u₂\ninst✝³ : Category.{v₂, u₂} V\ninst✝² : MonoidalCategory C\ninst✝¹ : MonoidalCategory V\nF G : C ⥤ V\ninst✝ : DayConvolution F G\nx x' y y' : C\nf : x ⟶ x'\ng : y ⟶ y'\n⊢ F.map f ▷ G.obj y ≫ F.obj x' ◁ G.map g ≫ (unit F G).app (x', y') =\n (unit F G).app (x... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.DayConvolution | {
"line": 129,
"column": 2
} | {
"line": 129,
"column": 29
} | {
"line": 129,
"column": 30
} | [
{
"pp": "C : Type u₁\ninst✝⁴ : Category.{v₁, u₁} C\nV : Type u₂\ninst✝³ : Category.{v₂, u₂} V\ninst✝² : MonoidalCategory C\ninst✝¹ : MonoidalCategory V\nF G : C ⥤ V\ninst✝ : DayConvolution F G\nx x' y : C\nf : x ⟶ x'\n⊢ F.map f ▷ G.obj y ≫ (unit F G).app (x', y) = (unit F G).app (x, y) ≫ (F ⊛ G).map (f ▷ y)",
... | [
"C : Type u₁\ninst✝⁴ : Category.{v₁, u₁} C\nV : Type u₂\ninst✝³ : Category.{v₂, u₂} V\ninst✝² : MonoidalCategory C\ninst✝¹ : MonoidalCategory V\nF G : C ⥤ V\ninst✝ : DayConvolution F G\nx x' y : C\nf : x ⟶ x'\n⊢ F.map f ▷ G.obj y ≫ (unit F G).app (x', y) = (unit F G).app (x, y) ≫ (F ⊛ G).map (f ▷ y)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.DayConvolution | {
"line": 137,
"column": 2
} | {
"line": 137,
"column": 29
} | {
"line": 137,
"column": 30
} | [
{
"pp": "C : Type u₁\ninst✝⁴ : Category.{v₁, u₁} C\nV : Type u₂\ninst✝³ : Category.{v₂, u₂} V\ninst✝² : MonoidalCategory C\ninst✝¹ : MonoidalCategory V\nF G : C ⥤ V\ninst✝ : DayConvolution F G\nx y y' : C\ng : y ⟶ y'\n⊢ F.obj x ◁ G.map g ≫ (unit F G).app (x, y') = (unit F G).app (x, y) ≫ (F ⊛ G).map (x ◁ g)",
... | [
"C : Type u₁\ninst✝⁴ : Category.{v₁, u₁} C\nV : Type u₂\ninst✝³ : Category.{v₂, u₂} V\ninst✝² : MonoidalCategory C\ninst✝¹ : MonoidalCategory V\nF G : C ⥤ V\ninst✝ : DayConvolution F G\nx y y' : C\ng : y ⟶ y'\n⊢ F.obj x ◁ G.map g ≫ (unit F G).app (x, y') = (unit F G).app (x, y) ≫ (F ⊛ G).map (x ◁ g)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.DayConvolution | {
"line": 186,
"column": 64
} | {
"line": 186,
"column": 75
} | {
"line": 186,
"column": 76
} | [
{
"pp": "C : Type u₁\ninst✝⁴ : Category.{v₁, u₁} C\nV : Type u₂\ninst✝³ : Category.{v₂, u₂} V\ninst✝² : MonoidalCategory C\ninst✝¹ : MonoidalCategory V\nF G : C ⥤ V\ninst✝ : DayConvolution F G\nc : C\nv : V\nf g : (F ⊛ G).obj c ⟶ v\nh : ∀ {x y : C} (u : x ⊗ y ⟶ c), (unit F G).app (x, y) ≫ (F ⊛ G).map u ≫ f = (u... | [
"C : Type u₁\ninst✝⁴ : Category.{v₁, u₁} C\nV : Type u₂\ninst✝³ : Category.{v₂, u₂} V\ninst✝² : MonoidalCategory C\ninst✝¹ : MonoidalCategory V\nF G : C ⥤ V\ninst✝ : DayConvolution F G\nc : C\nv : V\nf g : (F ⊛ G).obj c ⟶ v\nh : ∀ {x y : C} (u : x ⊗ y ⟶ c), (unit F G).app (x, y) ≫ (F ⊛ G).map u ≫ f = (unit F G).app... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.Rigid.Braided | {
"line": 43,
"column": 6
} | {
"line": 43,
"column": 17
} | {
"line": 43,
"column": 18
} | [
{
"pp": "case e_g.e_f\nC : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : MonoidalCategory C\ninst✝ : BraidedCategory C\nX Y : C\ninst : ExactPairing X Y\n⊢ ((((((α_ X Y X).inv ≫ (β_ X Y).hom ▷ X) ≫ inv (α_ Y X X).inv) ≫ inv (Y ◁ (β_ X X).inv)) ≫ inv (α_ Y X X).hom) ≫\n inv ((β_ Y X).inv ▷ X)) ≫\n ... | [
"case e_g.e_f\nC : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : MonoidalCategory C\ninst✝ : BraidedCategory C\nX Y : C\ninst : ExactPairing X Y\n⊢ (α_ X Y X).inv ≫\n (β_ X Y).hom ▷ X ≫ (α_ Y X X).hom ≫ Y ◁ (β_ X X).hom ≫ (α_ Y X X).inv ≫ (β_ Y X).hom ▷ X ≫ (α_ X Y X).hom =\n X ◁ (β_ Y X).hom ≫ (α_ X X... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.DayConvolution | {
"line": 451,
"column": 2
} | {
"line": 451,
"column": 13
} | {
"line": 451,
"column": 14
} | [
{
"pp": "C : Type u₁\ninst✝⁴ : Category.{v₁, u₁} C\nV : Type u₂\ninst✝³ : Category.{v₂, u₂} V\ninst✝² : MonoidalCategory C\ninst✝¹ : MonoidalCategory V\nU : C ⥤ V\ninst✝ : DayConvolutionUnit U\nc : C\nv : V\ng h : U.obj c ⟶ v\ne : ∀ (f : 𝟙_ C ⟶ c), can ≫ U.map f ≫ g = can ≫ U.map f ≫ h\nj : CostructuredArrow (... | [
"C : Type u₁\ninst✝⁴ : Category.{v₁, u₁} C\nV : Type u₂\ninst✝³ : Category.{v₂, u₂} V\ninst✝² : MonoidalCategory C\ninst✝¹ : MonoidalCategory V\nU : C ⥤ V\ninst✝ : DayConvolutionUnit U\nc : C\nv : V\ng h : U.obj c ⟶ v\ne : ∀ (f : 𝟙_ C ⟶ c), can ≫ U.map f ≫ g = can ≫ U.map f ≫ h\nj : CostructuredArrow (fromPUnit (�... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.Rigid.Braided | {
"line": 69,
"column": 6
} | {
"line": 69,
"column": 17
} | {
"line": 69,
"column": 18
} | [
{
"pp": "case e_g.e_a\nC : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : MonoidalCategory C\ninst✝ : BraidedCategory C\nX Y : C\ninst : ExactPairing X Y\n⊢ (((Y ◁ (β_ X Y).hom ≫ inv (α_ Y Y X).hom) ≫ inv ((β_ Y Y).inv ▷ X)) ≫ inv (α_ Y Y X).inv) ≫ inv (Y ◁ (β_ Y X).inv) =\n (((((inv (α_ Y X Y).hom ≫ inv... | [
"case e_g.e_a\nC : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : MonoidalCategory C\ninst✝ : BraidedCategory C\nX Y : C\ninst : ExactPairing X Y\n⊢ Y ◁ (β_ X Y).hom ≫ (α_ Y Y X).inv ≫ (β_ Y Y).hom ▷ X ≫ (α_ Y Y X).hom ≫ Y ◁ (β_ Y X).hom =\n (α_ Y X Y).inv ≫\n (β_ Y X).hom ▷ Y ≫ (α_ X Y Y).hom ≫ X ◁ (β_... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Presentable.ColimitPresentation | {
"line": 61,
"column": 4
} | {
"line": 62,
"column": 23
} | {
"line": 64,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\nJ : Type u_1\nI : J → Type u_2\ninst✝¹ : Category.{v_1, u_1} J\ninst✝ : (j : J) → Category.{?u.14, u_2} (I j)\nD : J ⥤ C\nP : (j : J) → ColimitPresentation (I j) (D.obj j)\nk l m : Total P\nf : k.Hom l\ng : l.Hom m\n⊢ (P k.fst).ι.app k.snd ≫ D.map (f.base ≫ g.bas... | [] | simp only [Functor.map_comp, Category.assoc]
rw [f.w_assoc, g.w] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Presentable.ColimitPresentation | {
"line": 61,
"column": 4
} | {
"line": 62,
"column": 23
} | {
"line": 64,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\nJ : Type u_1\nI : J → Type u_2\ninst✝¹ : Category.{v_1, u_1} J\ninst✝ : (j : J) → Category.{?u.14, u_2} (I j)\nD : J ⥤ C\nP : (j : J) → ColimitPresentation (I j) (D.obj j)\nk l m : Total P\nf : k.Hom l\ng : l.Hom m\n⊢ (P k.fst).ι.app k.snd ≫ D.map (f.base ≫ g.bas... | [] | simp only [Functor.map_comp, Category.assoc]
rw [f.w_assoc, g.w] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Presentable.Dense | {
"line": 40,
"column": 2
} | {
"line": 40,
"column": 35
} | {
"line": 42,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\nκ : Cardinal.{w}\ninst✝¹ : Fact κ.IsRegular\ninst✝ : IsCardinalAccessibleCategory C κ\nP : ObjectProperty C\nw✝ : ObjectProperty.EssentiallySmall.{w, v, u} P\nhP : P.IsCardinalFilteredGenerator κ\n⊢ P ≤ isCardinalPresentable C κ",
"ppTerm": "?m.43",
"assi... | [] | exact hP.le_isCardinalPresentable | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.CategoryTheory.Presentable.ColimitPresentation | {
"line": 143,
"column": 12
} | {
"line": 143,
"column": 23
} | {
"line": 143,
"column": 24
} | [
{
"pp": "C : Type u\ninst✝⁶ : Category.{v, u} C\nJ✝ : Type u_1\nI✝ : J✝ → Type u_2\ninst✝⁵ : Category.{v_1, u_1} J✝\ninst✝⁴ : (j : J✝) → Category.{?u.14, u_2} (I✝ j)\nD✝ : J✝ ⥤ C\nP✝¹ : (j : J✝) → ColimitPresentation (I✝ j) (D✝.obj j)\nJ : Type w\nI : J → Type w\ninst✝³ : SmallCategory J\ninst✝² : (j : J) → Sma... | [
"C : Type u\ninst✝⁶ : Category.{v, u} C\nJ✝ : Type u_1\nI✝ : J✝ → Type u_2\ninst✝⁵ : Category.{v_1, u_1} J✝\ninst✝⁴ : (j : J✝) → Category.{?u.14, u_2} (I✝ j)\nD✝ : J✝ ⥤ C\nP✝¹ : (j : J✝) → ColimitPresentation (I✝ j) (D✝.obj j)\nJ : Type w\nI : J → Type w\ninst✝³ : SmallCategory J\ninst✝² : (j : J) → SmallCategory (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Presentable.ColimitPresentation | {
"line": 150,
"column": 8
} | {
"line": 150,
"column": 19
} | {
"line": 150,
"column": 20
} | [
{
"pp": "C : Type u\ninst✝⁶ : Category.{v, u} C\nJ✝ : Type u_1\nI✝ : J✝ → Type u_2\ninst✝⁵ : Category.{v_1, u_1} J✝\ninst✝⁴ : (j : J✝) → Category.{?u.14, u_2} (I✝ j)\nD✝ : J✝ ⥤ C\nP✝¹ : (j : J✝) → ColimitPresentation (I✝ j) (D✝.obj j)\nJ : Type w\nI : J → Type w\ninst✝³ : SmallCategory J\ninst✝² : (j : J) → Sma... | [
"C : Type u\ninst✝⁶ : Category.{v, u} C\nJ✝ : Type u_1\nI✝ : J✝ → Type u_2\ninst✝⁵ : Category.{v_1, u_1} J✝\ninst✝⁴ : (j : J✝) → Category.{?u.14, u_2} (I✝ j)\nD✝ : J✝ ⥤ C\nP✝¹ : (j : J✝) → ColimitPresentation (I✝ j) (D✝.obj j)\nJ : Type w\nI : J → Type w\ninst✝³ : SmallCategory J\ninst✝² : (j : J) → SmallCategory (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Presentable.ColimitPresentation | {
"line": 156,
"column": 4
} | {
"line": 156,
"column": 37
} | {
"line": 156,
"column": 38
} | [
{
"pp": "C : Type u\ninst✝⁶ : Category.{v, u} C\nJ✝ : Type u_1\nI✝ : J✝ → Type u_2\ninst✝⁵ : Category.{v_1, u_1} J✝\ninst✝⁴ : (j : J✝) → Category.{?u.14, u_2} (I✝ j)\nD✝ : J✝ ⥤ C\nP✝¹ : (j : J✝) → ColimitPresentation (I✝ j) (D✝.obj j)\nJ : Type w\nI : J → Type w\ninst✝³ : SmallCategory J\ninst✝² : (j : J) → Sma... | [
"C : Type u\ninst✝⁶ : Category.{v, u} C\nJ✝ : Type u_1\nI✝ : J✝ → Type u_2\ninst✝⁵ : Category.{v_1, u_1} J✝\ninst✝⁴ : (j : J✝) → Category.{?u.14, u_2} (I✝ j)\nD✝ : J✝ ⥤ C\nP✝¹ : (j : J✝) → ColimitPresentation (I✝ j) (D✝.obj j)\nJ : Type w\nI : J → Type w\ninst✝³ : SmallCategory J\ninst✝² : (j : J) → SmallCategory (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.MorphismProperty.LocalClosure | {
"line": 87,
"column": 6
} | {
"line": 87,
"column": 24
} | {
"line": 87,
"column": 25
} | [
{
"pp": "case comp\nC : Type u\ninst✝³ : Category.{v, u} C\nK : Precoverage C\nP Q : MorphismProperty C\nX✝¹ Y✝¹ : C\ninst✝² : P.IsStableUnderBaseChange\ninst✝¹ : K.IsStableUnderBaseChange\ninst✝ : HasPullbacks C\nY X Z : C\nf : X ⟶ Z\nX✝ Y✝ : C\nf' : X✝ ⟶ Y✝\nhf' : sourceLocalClosure K P f'\nR : Presieve X✝\nh... | [
"case comp\nC : Type u\ninst✝³ : Category.{v, u} C\nK : Precoverage C\nP Q : MorphismProperty C\nX✝¹ Y✝¹ : C\ninst✝² : P.IsStableUnderBaseChange\ninst✝¹ : K.IsStableUnderBaseChange\ninst✝ : HasPullbacks C\nY X Z : C\nf : X ⟶ Z\nX✝ Y✝ : C\nf' : X✝ ⟶ Y✝\nhf' : sourceLocalClosure K P f'\nR : Presieve X✝\nhR : R ∈ K.co... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.MorphismProperty.LocalClosure | {
"line": 102,
"column": 17
} | {
"line": 102,
"column": 92
} | {
"line": 103,
"column": 4
} | [
{
"pp": "case refine_1.of\nC : Type u\ninst✝⁶ : Category.{v, u} C\nK : Precoverage C\nP : MorphismProperty C\ninst✝⁵ : P.RespectsIso\ninst✝⁴ : P.RespectsLeft K.morphismProperty\ninst✝³ : K.HasIsos\ninst✝² : K.IsStableUnderBaseChange\ninst✝¹ : K.IsStableUnderComposition\ninst✝ : K.HasPullbacks\nX Y : C\nf✝ : X ⟶... | [] | exact ⟨.singleton (𝟙 _), K.mem_coverings_of_isIso _, fun U g ⟨⟩ ↦ by simpa⟩ | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.CategoryTheory.MorphismProperty.LocalClosure | {
"line": 102,
"column": 17
} | {
"line": 102,
"column": 92
} | {
"line": 103,
"column": 4
} | [
{
"pp": "case refine_1.of\nC : Type u\ninst✝⁶ : Category.{v, u} C\nK : Precoverage C\nP : MorphismProperty C\ninst✝⁵ : P.RespectsIso\ninst✝⁴ : P.RespectsLeft K.morphismProperty\ninst✝³ : K.HasIsos\ninst✝² : K.IsStableUnderBaseChange\ninst✝¹ : K.IsStableUnderComposition\ninst✝ : K.HasPullbacks\nX Y : C\nf✝ : X ⟶... | [] | exact ⟨.singleton (𝟙 _), K.mem_coverings_of_isIso _, fun U g ⟨⟩ ↦ by simpa⟩ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.MorphismProperty.LocalClosure | {
"line": 102,
"column": 17
} | {
"line": 102,
"column": 92
} | {
"line": 103,
"column": 4
} | [
{
"pp": "case refine_1.of\nC : Type u\ninst✝⁶ : Category.{v, u} C\nK : Precoverage C\nP : MorphismProperty C\ninst✝⁵ : P.RespectsIso\ninst✝⁴ : P.RespectsLeft K.morphismProperty\ninst✝³ : K.HasIsos\ninst✝² : K.IsStableUnderBaseChange\ninst✝¹ : K.IsStableUnderComposition\ninst✝ : K.HasPullbacks\nX Y : C\nf✝ : X ⟶... | [] | exact ⟨.singleton (𝟙 _), K.mem_coverings_of_isIso _, fun U g ⟨⟩ ↦ by simpa⟩ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Monoidal.DayConvolution | {
"line": 993,
"column": 8
} | {
"line": 993,
"column": 46
} | {
"line": 993,
"column": 46
} | [
{
"pp": "C✝ : Type u₁\ninst✝¹⁶ : Category.{v₁, u₁} C✝\nV✝ : Type u₂\ninst✝¹⁵ : Category.{v₂, u₂} V✝\ninst✝¹⁴ : MonoidalCategory C✝\ninst✝¹³ : MonoidalCategory V✝\nC : Type u₁\ninst✝¹² : Category.{v₁, u₁} C\nV : Type u₂\ninst✝¹¹ : Category.{v₂, u₂} V\ninst✝¹⁰ : MonoidalCategory C\ninst✝⁹ : MonoidalCategory V\nD ... | [
"C✝ : Type u₁\ninst✝¹⁶ : Category.{v₁, u₁} C✝\nV✝ : Type u₂\ninst✝¹⁵ : Category.{v₂, u₂} V✝\ninst✝¹⁴ : MonoidalCategory C✝\ninst✝¹³ : MonoidalCategory V✝\nC : Type u₁\ninst✝¹² : Category.{v₁, u₁} C\nV : Type u₂\ninst✝¹¹ : Category.{v₂, u₂} V\ninst✝¹⁰ : MonoidalCategory C\ninst✝⁹ : MonoidalCategory V\nD : Type u₃\ni... | ι_map_leftUnitor_hom_eq_leftUnitor_hom | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.CategoryTheory.MorphismProperty.Ind | {
"line": 139,
"column": 2
} | {
"line": 140,
"column": 42
} | {
"line": 140,
"column": 43
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nP : MorphismProperty C\nhp : P ≤ isFinitelyPresentable C\ninst✝ : LocallySmall.{w, v, u} C\nX Y : C\nf : X ⟶ Y\nhf : P.ind.ind f\nthis : P.underObj ≤ ObjectProperty.isFinitelyPresentable (Under X)\n⊢ P.ind f",
"ppTerm": "?m.47",
"assigned": true,
"use... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\nP : MorphismProperty C\nhp : P ≤ isFinitelyPresentable C\ninst✝ : LocallySmall.{w, v, u} C\nX Y : C\nf : X ⟶ Y\nhf : P.ind.ind f\nthis : P.underObj ≤ ObjectProperty.isFinitelyPresentable (Under X)\n⊢ P.underObj.ind (CategoryTheory.Under.mk f)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.MorphismProperty.LocalEpi | {
"line": 51,
"column": 56
} | {
"line": 51,
"column": 67
} | {
"line": 51,
"column": 68
} | [
{
"pp": "C : Type u_1\ninst✝ : Category.{v_1, u_1} C\nP : ObjectProperty C\nX✝ Y✝ Z✝ : C\nf : X✝ ⟶ Y✝\ng : Y✝ ⟶ Z✝\nhf : P.localEpi f\nhg : P.localEpi g\nT : C\nhT : P T\nx✝¹ x✝ : Z✝ ⟶ T\nhuv : (fun g_1 ↦ (f ≫ g) ≫ g_1) x✝¹ = (fun g_1 ↦ (f ≫ g) ≫ g_1) x✝\n⊢ (fun g ↦ f ≫ g) ((fun g_1 ↦ g ≫ g_1) x✝¹) = (fun g ↦ f... | [
"C : Type u_1\ninst✝ : Category.{v_1, u_1} C\nP : ObjectProperty C\nX✝ Y✝ Z✝ : C\nf : X✝ ⟶ Y✝\ng : Y✝ ⟶ Z✝\nhf : P.localEpi f\nhg : P.localEpi g\nT : C\nhT : P T\nx✝¹ x✝ : Z✝ ⟶ T\nhuv : (fun g_1 ↦ (f ≫ g) ≫ g_1) x✝¹ = (fun g_1 ↦ (f ≫ g) ≫ g_1) x✝\n⊢ f ≫ g ≫ x✝¹ = f ≫ g ≫ x✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.MorphismProperty.LocalEpi | {
"line": 83,
"column": 58
} | {
"line": 83,
"column": 68
} | {
"line": 83,
"column": 68
} | [
{
"pp": "C : Type u_1\ninst✝ : Category.{v_1, u_1} C\nP : ObjectProperty C\nW : MorphismProperty C\nX Y Z : C\nf : X ⟶ Y\ng : Y ⟶ Z\nx✝ : W f\nhfg : P.localEpi (f ≫ g)\nT : C\nhT : P T\nu v : Z ⟶ T\nhuv : (fun g_1 ↦ g ≫ g_1) u = (fun g_1 ↦ g ≫ g_1) v\n⊢ (fun g_1 ↦ (f ≫ g) ≫ g_1) u = (fun g_1 ↦ (f ≫ g) ≫ g_1) v"... | [] | simp [huv] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.CategoryTheory.MorphismProperty.LocalEpi | {
"line": 83,
"column": 58
} | {
"line": 83,
"column": 68
} | {
"line": 83,
"column": 68
} | [
{
"pp": "C : Type u_1\ninst✝ : Category.{v_1, u_1} C\nP : ObjectProperty C\nW : MorphismProperty C\nX Y Z : C\nf : X ⟶ Y\ng : Y ⟶ Z\nx✝ : W f\nhfg : P.localEpi (f ≫ g)\nT : C\nhT : P T\nu v : Z ⟶ T\nhuv : (fun g_1 ↦ g ≫ g_1) u = (fun g_1 ↦ g ≫ g_1) v\n⊢ (fun g_1 ↦ (f ≫ g) ≫ g_1) u = (fun g_1 ↦ (f ≫ g) ≫ g_1) v"... | [] | simp [huv] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.MorphismProperty.LocalEpi | {
"line": 83,
"column": 58
} | {
"line": 83,
"column": 68
} | {
"line": 83,
"column": 68
} | [
{
"pp": "C : Type u_1\ninst✝ : Category.{v_1, u_1} C\nP : ObjectProperty C\nW : MorphismProperty C\nX Y Z : C\nf : X ⟶ Y\ng : Y ⟶ Z\nx✝ : W f\nhfg : P.localEpi (f ≫ g)\nT : C\nhT : P T\nu v : Z ⟶ T\nhuv : (fun g_1 ↦ g ≫ g_1) u = (fun g_1 ↦ g ≫ g_1) v\n⊢ (fun g_1 ↦ (f ≫ g) ≫ g_1) u = (fun g_1 ↦ (f ≫ g) ≫ g_1) v"... | [] | simp [huv] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.MorphismProperty.LocalEpi | {
"line": 89,
"column": 21
} | {
"line": 89,
"column": 32
} | {
"line": 89,
"column": 33
} | [
{
"pp": "C : Type u_1\ninst✝ : Category.{v_1, u_1} C\nP : ObjectProperty C\nX Y Z : C\nf : X ⟶ Y\ng : Y ⟶ Z\nhg : P.isLocal g\nhfg : P.localEpi (f ≫ g)\nT : C\nhT : P T\nu v : Z ⟶ T\nhuv : (fun g ↦ f ≫ g) ((fun g_1 ↦ g ≫ g_1) u) = (fun g ↦ f ≫ g) ((fun g_1 ↦ g ≫ g_1) v)\n⊢ (fun g_1 ↦ (f ≫ g) ≫ g_1) ?m.71 = (fun... | [
"C : Type u_1\ninst✝ : Category.{v_1, u_1} C\nP : ObjectProperty C\nX Y Z : C\nf : X ⟶ Y\ng : Y ⟶ Z\nhg : P.isLocal g\nhfg : P.localEpi (f ≫ g)\nT : C\nhT : P T\nu v : Z ⟶ T\nhuv : (fun g ↦ f ≫ g) ((fun g_1 ↦ g ≫ g_1) u) = (fun g ↦ f ≫ g) ((fun g_1 ↦ g ≫ g_1) v)\n⊢ f ≫ g ≫ ?m.71 = f ≫ g ≫ ?m.72"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Subobject.ArtinianObject | {
"line": 103,
"column": 4
} | {
"line": 104,
"column": 11
} | {
"line": 104,
"column": 12
} | [
{
"pp": "case refine_2\nC : Type u\ninst✝ : Category.{v, u} C\nX : C\nh : ∀ (F : ℕ ⥤ (MonoOver X)ᵒᵖ), IsFiltered.IsEventuallyConstant F\nF : ℕ →o (Subobject X)ᵒᵈ\nn : ℕ\nhn : (⋯.functor ⋙ (orderDualEquivalence (Subobject X)).functor ⋙ Subobject.representative.op).IsEventuallyConstantFrom n\nm : ℕ\nhm : n ≤ m\n⊢... | [
"case refine_2\nC : Type u\ninst✝ : Category.{v, u} C\nX : C\nh : ∀ (F : ℕ ⥤ (MonoOver X)ᵒᵖ), IsFiltered.IsEventuallyConstant F\nF : ℕ →o (Subobject X)ᵒᵈ\nn : ℕ\nhn : (⋯.functor ⋙ (orderDualEquivalence (Subobject X)).functor ⋙ Subobject.representative.op).IsEventuallyConstantFrom n\nm : ℕ\nhm : n ≤ m\n⊢ F m = F n"
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Subobject.ArtinianObject | {
"line": 136,
"column": 4
} | {
"line": 136,
"column": 36
} | {
"line": 138,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nX Y X✝ Y✝ : C\nf : X✝ ⟶ Y✝\nx✝ : Mono f\nhY : isArtinianObject.Is Y✝\n⊢ isArtinianObject.Is X✝",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"CategoryTheory.isArtinianObject_of_mono"
],
"usedFVars": [
"C",
"inst✝",... | [] | exact isArtinianObject_of_mono f | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.CategoryTheory.Subobject.NoetherianObject | {
"line": 99,
"column": 4
} | {
"line": 100,
"column": 38
} | {
"line": 100,
"column": 39
} | [
{
"pp": "case refine_2\nC : Type u\ninst✝ : Category.{v, u} C\nX : C\nh : ∀ (F : ℕ ⥤ MonoOver X), IsFiltered.IsEventuallyConstant F\nF : ℕ →o Subobject X\nn : ℕ\nhn : (⋯.functor ⋙ Subobject.representative).IsEventuallyConstantFrom n\nm : ℕ\nhm : n ≤ m\n⊢ F n = F m",
"ppTerm": "?refine_2",
"assigned": fa... | [
"case refine_2\nC : Type u\ninst✝ : Category.{v, u} C\nX : C\nh : ∀ (F : ℕ ⥤ MonoOver X), IsFiltered.IsEventuallyConstant F\nF : ℕ →o Subobject X\nn : ℕ\nhn : (⋯.functor ⋙ Subobject.representative).IsEventuallyConstantFrom n\nm : ℕ\nhm : n ≤ m\n⊢ F n = F m"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Preadditive.FreydCategory.RightFreyd | {
"line": 88,
"column": 33
} | {
"line": 88,
"column": 44
} | {
"line": 88,
"column": 45
} | [
{
"pp": "V : Type u_1\ninst✝¹ : Category.{v_1, u_1} V\ninst✝ : Preadditive V\nu v : Arrow V\nf g : u ⟶ v\nh : (quotient V).map f = (quotient V).map g\n⊢ (quotient V).map f = (quotient V).map g",
"ppTerm": "?m.41",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"V : Type u_1\ninst✝¹ : Category.{v_1, u_1} V\ninst✝ : Preadditive V\nu v : Arrow V\nf g : u ⟶ v\nh : (quotient V).map f = (quotient V).map g\n⊢ (quotient V).map f = (quotient V).map g"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Preadditive.FreydCategory.RightFreyd | {
"line": 89,
"column": 17
} | {
"line": 89,
"column": 28
} | {
"line": 89,
"column": 29
} | [
{
"pp": "V : Type u_1\ninst✝¹ : Category.{v_1, u_1} V\ninst✝ : Preadditive V\nu v : Arrow V\nf g : u ⟶ v\nx✝ : Nonempty (RightHomotopy f g)\nh : RightHomotopy f g\n⊢ (quotient V).map f = (quotient V).map g",
"ppTerm": "?m.46",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoa... | [
"V : Type u_1\ninst✝¹ : Category.{v_1, u_1} V\ninst✝ : Preadditive V\nu v : Arrow V\nf g : u ⟶ v\nx✝ : Nonempty (RightHomotopy f g)\nh : RightHomotopy f g\n⊢ (quotient V).map f = (quotient V).map g"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Preadditive.FreydCategory.RightFreyd | {
"line": 94,
"column": 33
} | {
"line": 94,
"column": 44
} | {
"line": 94,
"column": 45
} | [
{
"pp": "V : Type u_1\ninst✝¹ : Category.{v_1, u_1} V\ninst✝ : Preadditive V\nu v : Arrow V\nf : u ⟶ v\nh : (quotient V).map f = 0\n⊢ (quotient V).map f = (quotient V).map 0",
"ppTerm": "?m.37",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"CategoryTheory.Preadditive.RightFreyd",
... | [
"V : Type u_1\ninst✝¹ : Category.{v_1, u_1} V\ninst✝ : Preadditive V\nu v : Arrow V\nf : u ⟶ v\nh : (quotient V).map f = 0\n⊢ (quotient V).map f = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Preadditive.FreydCategory.RightFreyd | {
"line": 95,
"column": 17
} | {
"line": 95,
"column": 28
} | {
"line": 95,
"column": 29
} | [
{
"pp": "V : Type u_1\ninst✝¹ : Category.{v_1, u_1} V\ninst✝ : Preadditive V\nu v : Arrow V\nf : u ⟶ v\nx✝ : Nonempty (RightHomotopy f 0)\nh : RightHomotopy f 0\n⊢ (quotient V).map f = 0",
"ppTerm": "?m.42",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"V : Type u_1\ninst✝¹ : Category.{v_1, u_1} V\ninst✝ : Preadditive V\nu v : Arrow V\nf : u ⟶ v\nx✝ : Nonempty (RightHomotopy f 0)\nh : RightHomotopy f 0\n⊢ (quotient V).map f = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Preadditive.Comma | {
"line": 75,
"column": 20
} | {
"line": 77,
"column": 49
} | {
"line": 79,
"column": 0
} | [
{
"pp": "A : Type u₁\ninst✝⁷ : Category.{v₁, u₁} A\ninst✝⁶ : Preadditive A\nB : Type u₂\ninst✝⁵ : Category.{v₂, u₂} B\ninst✝⁴ : Preadditive B\nT : Type u₃\ninst✝³ : Category.{v₃, u₃} T\ninst✝² : Preadditive T\nL : A ⥤ T\ninst✝¹ : L.Additive\nR : B ⥤ T\ninst✝ : R.Additive\nu v : Comma L R\nx✝¹ : ℕ\nx✝ : u ⟶ v\n⊢... | [] | by
simp_rw [HSMul.hSMul, SMul.smul]
ext <;> dsimp <;> simp [add_nsmul, add_zsmul] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Preadditive.HomOrthogonal | {
"line": 143,
"column": 4
} | {
"line": 143,
"column": 15
} | {
"line": 143,
"column": 16
} | [
{
"pp": "case e'_2.e'_7\nC : Type u\ninst✝³ : Category.{v, u} C\nι : Type u_1\ns : ι → C\ninst✝² : Preadditive C\ninst✝¹ : HasFiniteBiproducts C\no : HomOrthogonal s\nα : Type\ninst✝ : Finite α\nf : α → ι\nb a : α\nj_property✝ : a ∈ f ⁻¹' {f b}\nj_property : f a = f b\nh : ¬b = a\n⊢ biproduct.ι (fun a ↦ s (f a)... | [
"case e'_2.e'_7\nC : Type u\ninst✝³ : Category.{v, u} C\nι : Type u_1\ns : ι → C\ninst✝² : Preadditive C\ninst✝¹ : HasFiniteBiproducts C\no : HomOrthogonal s\nα : Type\ninst✝ : Finite α\nf : α → ι\nb a : α\nj_property✝ : a ∈ f ⁻¹' {f b}\nj_property : f a = f b\nh : ¬b = a\n⊢ biproduct.ι (fun a ↦ s (f a)) a ≫ biprod... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Pi.Monoidal | {
"line": 259,
"column": 20
} | {
"line": 259,
"column": 31
} | {
"line": 259,
"column": 32
} | [
{
"pp": "I : Type w₁\nC : I → Type u₁\ninst✝⁶ : (i : I) → Category.{v₁, u₁} (C i)\ninst✝⁵ : (i : I) → MonoidalCategory (C i)\nD : Type u_1\ninst✝⁴ : Category.{v_1, u_1} D\ninst✝³ : MonoidalCategory D\nF G : D ⥤ ((i : I) → C i)\ninst✝² : F.LaxMonoidal\ninst✝¹ : G.LaxMonoidal\nτ : (i : I) → F ⋙ eval C i ⟶ G ⋙ eva... | [
"I : Type w₁\nC : I → Type u₁\ninst✝⁶ : (i : I) → Category.{v₁, u₁} (C i)\ninst✝⁵ : (i : I) → MonoidalCategory (C i)\nD : Type u_1\ninst✝⁴ : Category.{v_1, u_1} D\ninst✝³ : MonoidalCategory D\nF G : D ⥤ ((i : I) → C i)\ninst✝² : F.LaxMonoidal\ninst✝¹ : G.LaxMonoidal\nτ : (i : I) → F ⋙ eval C i ⟶ G ⋙ eval C i\ninst✝... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Pi.Monoidal | {
"line": 260,
"column": 26
} | {
"line": 260,
"column": 37
} | {
"line": 260,
"column": 38
} | [
{
"pp": "I : Type w₁\nC : I → Type u₁\ninst✝⁶ : (i : I) → Category.{v₁, u₁} (C i)\ninst✝⁵ : (i : I) → MonoidalCategory (C i)\nD : Type u_1\ninst✝⁴ : Category.{v_1, u_1} D\ninst✝³ : MonoidalCategory D\nF G : D ⥤ ((i : I) → C i)\ninst✝² : F.LaxMonoidal\ninst✝¹ : G.LaxMonoidal\nτ : (i : I) → F ⋙ eval C i ⟶ G ⋙ eva... | [
"I : Type w₁\nC : I → Type u₁\ninst✝⁶ : (i : I) → Category.{v₁, u₁} (C i)\ninst✝⁵ : (i : I) → MonoidalCategory (C i)\nD : Type u_1\ninst✝⁴ : Category.{v_1, u_1} D\ninst✝³ : MonoidalCategory D\nF G : D ⥤ ((i : I) → C i)\ninst✝² : F.LaxMonoidal\ninst✝¹ : G.LaxMonoidal\nτ : (i : I) → F ⋙ eval C i ⟶ G ⋙ eval C i\ninst✝... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.EckmannHilton | {
"line": 58,
"column": 2
} | {
"line": 58,
"column": 69
} | {
"line": 58,
"column": 70
} | [
{
"pp": "X : Type u\nm₁ m₂ : X → X → X\ne₁ e₂ : X\nh₁ : IsUnital m₁ e₁\nh₂ : IsUnital m₂ e₂\ndistrib : ∀ (a b c d : X), m₁ (m₂ a b) (m₂ c d) = m₂ (m₁ a c) (m₁ b d)\n⊢ e₁ = e₂",
"ppTerm": "?m.9",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"X : Type u\nm₁ m₂ : X → X → X\ne₁ e₂ : X\nh₁ : IsUnital m₁ e₁\nh₂ : IsUnital m₂ e₂\ndistrib : ∀ (a b c d : X), m₁ (m₂ a b) (m₂ c d) = m₂ (m₁ a c) (m₁ b d)\n⊢ e₁ = e₂"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.EckmannHilton | {
"line": 76,
"column": 17
} | {
"line": 76,
"column": 73
} | {
"line": 76,
"column": 74
} | [
{
"pp": "X : Type u\nm₁ m₂ : X → X → X\ne₁ e₂ : X\nh₁ : IsUnital m₁ e₁\nh₂ : IsUnital m₂ e₂\ndistrib : ∀ (a b c d : X), m₁ (m₂ a b) (m₂ c d) = m₂ (m₁ a c) (m₁ b d)\na b : X\n⊢ m₂ a b = m₂ b a",
"ppTerm": "?m.13",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"X : Type u\nm₁ m₂ : X → X → X\ne₁ e₂ : X\nh₁ : IsUnital m₁ e₁\nh₂ : IsUnital m₂ e₂\ndistrib : ∀ (a b c d : X), m₁ (m₂ a b) (m₂ c d) = m₂ (m₁ a c) (m₁ b d)\na b : X\n⊢ m₂ a b = m₂ b a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.EckmannHilton | {
"line": 83,
"column": 19
} | {
"line": 83,
"column": 75
} | {
"line": 83,
"column": 76
} | [
{
"pp": "X : Type u\nm₁ m₂ : X → X → X\ne₁ e₂ : X\nh₁ : IsUnital m₁ e₁\nh₂ : IsUnital m₂ e₂\ndistrib : ∀ (a b c d : X), m₁ (m₂ a b) (m₂ c d) = m₂ (m₁ a c) (m₁ b d)\na b c : X\n⊢ m₂ (m₂ a b) c = m₂ a (m₂ b c)",
"ppTerm": "?m.14",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedG... | [
"X : Type u\nm₁ m₂ : X → X → X\ne₁ e₂ : X\nh₁ : IsUnital m₁ e₁\nh₂ : IsUnital m₂ e₂\ndistrib : ∀ (a b c d : X), m₁ (m₂ a b) (m₂ c d) = m₂ (m₁ a c) (m₁ b d)\na b c : X\n⊢ m₂ (m₂ a b) c = m₂ a (m₂ b c)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Presentable.Adjunction | {
"line": 62,
"column": 4
} | {
"line": 62,
"column": 65
} | {
"line": 63,
"column": 4
} | [
{
"pp": "C : Type u\nD : Type u'\ninst✝⁵ : Category.{v, u} C\ninst✝⁴ : Category.{v', u'} D\nF : C ⥤ D\nG : D ⥤ C\nadj : F ⊣ G\nκ : Cardinal.{w}\ninst✝³ : Fact κ.IsRegular\nP : ObjectProperty C\nhP : P.IsCardinalFilteredGenerator κ\ninst✝² : G.IsCardinalAccessible κ\ninst✝¹ : G.Full\ninst✝ : G.Faithful\nY : D\nt... | [
"C : Type u\nD : Type u'\ninst✝⁵ : Category.{v, u} C\ninst✝⁴ : Category.{v', u'} D\nF : C ⥤ D\nG : D ⥤ C\nadj : F ⊣ G\nκ : Cardinal.{w}\ninst✝³ : Fact κ.IsRegular\nP : ObjectProperty C\nhP : P.IsCardinalFilteredGenerator κ\ninst✝² : G.IsCardinalAccessible κ\ninst✝¹ : G.Full\ninst✝ : G.Faithful\nY : D\nthis : F.IsLe... | obtain ⟨J, _, _, ⟨hY⟩⟩ := hP.exists_colimitsOfShape (G.obj Y) | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.CategoryTheory.Preadditive.Schur | {
"line": 167,
"column": 17
} | {
"line": 167,
"column": 28
} | {
"line": 167,
"column": 29
} | [
{
"pp": "C : Type u_1\ninst✝⁸ : Category.{v_1, u_1} C\ninst✝⁷ : Preadditive C\n𝕜 : Type u_2\ninst✝⁶ : Field 𝕜\ninst✝⁵ : IsAlgClosed 𝕜\ninst✝⁴ : Linear 𝕜 C\ninst✝³ : HasKernels C\nX Y : C\ninst✝² : FiniteDimensional 𝕜 (X ⟶ X)\ninst✝¹ : Simple X\ninst✝ : Simple Y\nh : Nontrivial (X ⟶ Y)\nf : X ⟶ Y\nnz : f ≠ ... | [
"C : Type u_1\ninst✝⁸ : Category.{v_1, u_1} C\ninst✝⁷ : Preadditive C\n𝕜 : Type u_2\ninst✝⁶ : Field 𝕜\ninst✝⁵ : IsAlgClosed 𝕜\ninst✝⁴ : Linear 𝕜 C\ninst✝³ : HasKernels C\nX Y : C\ninst✝² : FiniteDimensional 𝕜 (X ⟶ X)\ninst✝¹ : Simple X\ninst✝ : Simple Y\nh : Nontrivial (X ⟶ Y)\nf : X ⟶ Y\nnz : f ≠ 0\nfi : IsIs... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Preadditive.Schur | {
"line": 196,
"column": 2
} | {
"line": 196,
"column": 81
} | {
"line": 198,
"column": 0
} | [
{
"pp": "case neg\nC : Type u_1\ninst✝⁸ : Category.{v_1, u_1} C\ninst✝⁷ : Preadditive C\n𝕜 : Type u_2\ninst✝⁶ : Field 𝕜\ninst✝⁵ : IsAlgClosed 𝕜\ninst✝⁴ : Linear 𝕜 C\ninst✝³ : HasKernels C\nX Y : C\ninst✝² : ∀ (X Y : C), FiniteDimensional 𝕜 (X ⟶ Y)\ninst✝¹ : Simple X\ninst✝ : Simple Y\nh : ¬Nonempty (X ≅ Y)... | [] | · exact (finrank_hom_simple_simple_eq_zero_iff 𝕜 X Y).2 (not_nonempty_iff.mp h) | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.CategoryTheory.Presentable.CardinalDirectedPoset | {
"line": 209,
"column": 6
} | {
"line": 209,
"column": 22
} | {
"line": 209,
"column": 23
} | [
{
"pp": "κ : Cardinal.{u}\ninst✝ : Fact κ.IsRegular\nX : Type u\nhX : Cardinal.mk X = κ\nα : Type u := (S : Set X) × (x : PartialOrder ↑S) × ULift.{u, 0} (PLift (IsCardinalFiltered (↑S) κ))\nthis : (a : α) → PartialOrder ↑a.fst := fun a ↦ a.snd.fst\nι : α → CardinalDirectedPoset κ := fun a ↦ { obj := { carrier ... | [
"κ : Cardinal.{u}\ninst✝ : Fact κ.IsRegular\nX : Type u\nhX : Cardinal.mk X = κ\nα : Type u := (S : Set X) × (x : PartialOrder ↑S) × ULift.{u, 0} (PLift (IsCardinalFiltered (↑S) κ))\nthis : (a : α) → PartialOrder ↑a.fst := fun a ↦ a.snd.fst\nι : α → CardinalDirectedPoset κ := fun a ↦ { obj := { carrier := ↑a.fst, s... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Category.PartOrdEmb | {
"line": 257,
"column": 12
} | {
"line": 257,
"column": 37
} | {
"line": 257,
"column": 38
} | [
{
"pp": "J : Type u\ninst✝¹ : SmallCategory J\ninst✝ : IsFiltered J\nF : J ⥤ PartOrdEmb\nc : Cocone (F ⋙ forget PartOrdEmb)\nhc : IsColimit c\nx y : CoconePt hc\nj : J\nx₁ y₁ : ↑(F.obj j)\nhx₁ : (ConcreteCategory.hom (c.ι.app j)) x₁ = x\nhy₁ : (ConcreteCategory.hom (c.ι.app j)) y₁ = y\nh₁ : x₁ ≤ y₁\nk : J\ny₂ x... | [
"J : Type u\ninst✝¹ : SmallCategory J\ninst✝ : IsFiltered J\nF : J ⥤ PartOrdEmb\nc : Cocone (F ⋙ forget PartOrdEmb)\nhc : IsColimit c\nx y : CoconePt hc\nj : J\nx₁ y₁ : ↑(F.obj j)\nhx₁ : (ConcreteCategory.hom (c.ι.app j)) x₁ = x\nhy₁ : (ConcreteCategory.hom (c.ι.app j)) y₁ = y\nh₁ : x₁ ≤ y₁\nk : J\ny₂ x₂ : ↑(F.obj ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Category.PartOrdEmb | {
"line": 258,
"column": 12
} | {
"line": 258,
"column": 37
} | {
"line": 258,
"column": 38
} | [
{
"pp": "J : Type u\ninst✝¹ : SmallCategory J\ninst✝ : IsFiltered J\nF : J ⥤ PartOrdEmb\nc : Cocone (F ⋙ forget PartOrdEmb)\nhc : IsColimit c\nx y : CoconePt hc\nj : J\nx₁ y₁ : ↑(F.obj j)\nhx₁ : (ConcreteCategory.hom (c.ι.app j)) x₁ = x\nhy₁ : (ConcreteCategory.hom (c.ι.app j)) y₁ = y\nh₁ : x₁ ≤ y₁\nk : J\ny₂ x... | [
"J : Type u\ninst✝¹ : SmallCategory J\ninst✝ : IsFiltered J\nF : J ⥤ PartOrdEmb\nc : Cocone (F ⋙ forget PartOrdEmb)\nhc : IsColimit c\nx y : CoconePt hc\nj : J\nx₁ y₁ : ↑(F.obj j)\nhx₁ : (ConcreteCategory.hom (c.ι.app j)) x₁ = x\nhy₁ : (ConcreteCategory.hom (c.ι.app j)) y₁ = y\nh₁ : x₁ ≤ y₁\nk : J\ny₂ x₂ : ↑(F.obj ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.Bimod | {
"line": 963,
"column": 2
} | {
"line": 963,
"column": 34
} | {
"line": 964,
"column": 2
} | [
{
"pp": "C : Type u₁\ninst✝⁴ : Category.{v₁, u₁} C\ninst✝³ : MonoidalCategory C\ninst✝² : HasCoequalizers C\ninst✝¹ : ∀ (X : C), PreservesColimitsOfSize.{0, 0, v₁, v₁, u₁, u₁} (tensorLeft X)\ninst✝ : ∀ (X : C), PreservesColimitsOfSize.{0, 0, v₁, v₁, u₁, u₁} (tensorRight X)\nV W X Y Z : Mon C\nM : Bimod V W\nN :... | [
"C : Type u₁\ninst✝⁴ : Category.{v₁, u₁} C\ninst✝³ : MonoidalCategory C\ninst✝² : HasCoequalizers C\ninst✝¹ : ∀ (X : C), PreservesColimitsOfSize.{0, 0, v₁, v₁, u₁, u₁} (tensorLeft X)\ninst✝ : ∀ (X : C), PreservesColimitsOfSize.{0, 0, v₁, v₁, u₁, u₁} (tensorRight X)\nV W X Y Z : Mon C\nM : Bimod V W\nN : Bimod W X\n... | dsimp only [AssociatorBimod.hom] | Lean.Elab.Tactic.evalDSimp | Lean.Parser.Tactic.dsimp |
Mathlib.Order.Category.PartOrdEmb | {
"line": 285,
"column": 8
} | {
"line": 285,
"column": 34
} | {
"line": 285,
"column": 35
} | [
{
"pp": "J : Type u\ninst✝¹ : SmallCategory J\ninst✝ : IsFiltered J\nF : J ⥤ PartOrdEmb\nc : Cocone (F ⋙ forget PartOrdEmb)\nhc : IsColimit c\nj : J\nx y : ↑(F.1 j)\nk : J\nx' y' : ↑(F.obj k)\nhx : (ConcreteCategory.hom (c.ι.app k)) x' = (ConcreteCategory.hom (c.ι.app j)) x\nhy : (ConcreteCategory.hom (c.ι.app ... | [
"J : Type u\ninst✝¹ : SmallCategory J\ninst✝ : IsFiltered J\nF : J ⥤ PartOrdEmb\nc : Cocone (F ⋙ forget PartOrdEmb)\nhc : IsColimit c\nj : J\nx y : ↑(F.1 j)\nk : J\nx' y' : ↑(F.obj k)\nhx : (ConcreteCategory.hom (c.ι.app k)) x' = (ConcreteCategory.hom (c.ι.app j)) x\nhy : (ConcreteCategory.hom (c.ι.app k)) y' = (Co... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Presentable.CardinalDirectedPoset | {
"line": 256,
"column": 21
} | {
"line": 256,
"column": 36
} | {
"line": 256,
"column": 37
} | [
{
"pp": "κ : Cardinal.{u}\ninst✝¹ : Fact κ.IsRegular\nJ : CardinalDirectedPoset κ\nκ' : Cardinal.{u}\ninst✝ : Fact κ'.IsRegular\nhJ : HasCardinalLT (↑J.obj) κ'\nh✝ : κ ≤ κ'\nA : Type u\nx✝¹ : SmallCategory A\nx✝ : IsCardinalFiltered A κ'\nF : A ⥤ CardinalDirectedPoset κ\nc : Cocone F\nthis✝ : IsFiltered A\nthis... | [
"κ : Cardinal.{u}\ninst✝¹ : Fact κ.IsRegular\nJ : CardinalDirectedPoset κ\nκ' : Cardinal.{u}\ninst✝ : Fact κ'.IsRegular\nhJ : HasCardinalLT (↑J.obj) κ'\nh✝ : κ ≤ κ'\nA : Type u\nx✝¹ : SmallCategory A\nx✝ : IsCardinalFiltered A κ'\nF : A ⥤ CardinalDirectedPoset κ\nc : Cocone F\nthis✝ : IsFiltered A\nthis : IsCardina... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Presentable.OrthogonalReflection | {
"line": 268,
"column": 2
} | {
"line": 268,
"column": 13
} | {
"line": 268,
"column": 14
} | [
{
"pp": "C : Type u\ninst✝⁴ : Category.{v, u} C\nW : MorphismProperty C\nZ : C\ninst✝³ : HasCoproduct D₁.obj₁\ninst✝² : HasCoproduct D₁.obj₂\ninst✝¹ : HasPushouts C\ninst✝ : HasMulticoequalizer (D₂.multispanIndex W Z)\nX Y : C\nf : X ⟶ Y\nhf : W f\ng₁ g₂ : Y ⟶ Z\nhg : f ≫ g₁ = f ≫ g₂\n⊢ g₁ ≫ toSucc W Z = g₂ ≫ t... | [
"C : Type u\ninst✝⁴ : Category.{v, u} C\nW : MorphismProperty C\nZ : C\ninst✝³ : HasCoproduct D₁.obj₁\ninst✝² : HasCoproduct D₁.obj₂\ninst✝¹ : HasPushouts C\ninst✝ : HasMulticoequalizer (D₂.multispanIndex W Z)\nX Y : C\nf : X ⟶ Y\nhf : W f\ng₁ g₂ : Y ⟶ Z\nhg : f ≫ g₁ = f ≫ g₂\n⊢ g₁ ≫ toSucc W Z = g₂ ≫ toSucc W Z"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Presentable.OrthogonalReflection | {
"line": 287,
"column": 4
} | {
"line": 288,
"column": 65
} | {
"line": 289,
"column": 4
} | [
{
"pp": "case refine_1.h₀\nC : Type u\ninst✝⁴ : Category.{v, u} C\nW : MorphismProperty C\nZ : C\ninst✝³ : HasCoproduct D₁.obj₁\ninst✝² : HasCoproduct D₁.obj₂\ninst✝¹ : HasPushouts C\ninst✝ : HasMulticoequalizer (D₂.multispanIndex W Z)\nT : C\nhT : W.isLocal T\nφ₁ φ₂ : succ W Z ⟶ T\nh : toStep W Z ≫ fromStep W ... | [
"case h₁\nC : Type u\ninst✝⁴ : Category.{v, u} C\nW : MorphismProperty C\nZ : C\ninst✝³ : HasCoproduct D₁.obj₁\ninst✝² : HasCoproduct D₁.obj₂\ninst✝¹ : HasPushouts C\ninst✝ : HasMulticoequalizer (D₂.multispanIndex W Z)\nT : C\nhT : W.isLocal T\nφ₁ φ₂ : succ W Z ⟶ T\nh : toStep W Z ≫ fromStep W Z ≫ φ₁ = toStep W Z ≫... | · apply (hT d.1.1.hom d.1.2).1
simp only [← D₁.ι_comp_t_assoc, pushout.condition_assoc, h] | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.CategoryTheory.Presentable.Directed | {
"line": 303,
"column": 30
} | {
"line": 303,
"column": 41
} | {
"line": 303,
"column": 42
} | [
{
"pp": "J : Type w\ninst✝² : SmallCategory J\nκ : Cardinal.{w}\ninst✝¹ : Fact κ.IsRegular\ninst✝ : IsCardinalFiltered J κ\nhJ : ∀ (e : J), ∃ m x, IsEmpty (m ⟶ e)\nι : Type w\nD : ι → DiagramWithUniqueTerminal J κ\nhι : HasCardinalLT ι κ\nm₀ : ι → J\nt₀ : (i : ι) → (D i).top ⟶ m₀ i\nhm₀ : ∀ (i : ι), IsEmpty (m₀... | [
"J : Type w\ninst✝² : SmallCategory J\nκ : Cardinal.{w}\ninst✝¹ : Fact κ.IsRegular\ninst✝ : IsCardinalFiltered J κ\nhJ : ∀ (e : J), ∃ m x, IsEmpty (m ⟶ e)\nι : Type w\nD : ι → DiagramWithUniqueTerminal J κ\nhι : HasCardinalLT ι κ\nm₀ : ι → J\nt₀ : (i : ι) → (D i).top ⟶ m₀ i\nhm₀ : ∀ (i : ι), IsEmpty (m₀ i ⟶ (D i).t... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Presentable.OrthogonalReflection | {
"line": 303,
"column": 6
} | {
"line": 303,
"column": 46
} | {
"line": 304,
"column": 8
} | [
{
"pp": "case refine_1.refine_1\nC : Type u\ninst✝⁴ : Category.{v, u} C\nW : MorphismProperty C\nZ : C\ninst✝³ : HasCoproduct D₁.obj₁\ninst✝² : HasCoproduct D₁.obj₂\ninst✝¹ : HasPushouts C\ninst✝ : HasMulticoequalizer (D₂.multispanIndex W Z)\nx✝ : IsIso (toSucc W Z)\nX Y : C\nf : X ⟶ Y\nhf : W f\ng₁ g₂ : Y ⟶ Z\... | [
"case refine_1.refine_1\nC : Type u\ninst✝⁴ : Category.{v, u} C\nW : MorphismProperty C\nZ : C\ninst✝³ : HasCoproduct D₁.obj₁\ninst✝² : HasCoproduct D₁.obj₂\ninst✝¹ : HasPushouts C\ninst✝ : HasMulticoequalizer (D₂.multispanIndex W Z)\nx✝ : IsIso (toSucc W Z)\nX Y : C\nf : X ⟶ Y\nhf : W f\ng₁ g₂ : Y ⟶ Z\nh : (fun g ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Preadditive.Mat | {
"line": 456,
"column": 6
} | {
"line": 456,
"column": 17
} | {
"line": 456,
"column": 18
} | [
{
"pp": "case e_a.e_a\nC : Type u₁\ninst✝⁶ : Category.{v₁, u₁} C\ninst✝⁵ : Preadditive C\nD : Type u₁\ninst✝⁴ : Category.{v₁, u₁} D\ninst✝³ : Preadditive D\ninst✝² : HasFiniteBiproducts D\nF : C ⥤ D\ninst✝¹ : F.Additive\nL : Mat_ C ⥤ D\ninst✝ : L.Additive\nα : embedding C ⋙ L ≅ F\nX✝ Y✝ : Mat_ C\nf : X✝ ⟶ Y✝\nj... | [
"case e_a.e_a\nC : Type u₁\ninst✝⁶ : Category.{v₁, u₁} C\ninst✝⁵ : Preadditive C\nD : Type u₁\ninst✝⁴ : Category.{v₁, u₁} D\ninst✝³ : Preadditive D\ninst✝² : HasFiniteBiproducts D\nF : C ⥤ D\ninst✝¹ : F.Additive\nL : Mat_ C ⥤ D\ninst✝ : L.Additive\nα : embedding C ⋙ L ≅ F\nX✝ Y✝ : Mat_ C\nf : X✝ ⟶ Y✝\nj : X✝.ι\nk :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Presentable.Directed | {
"line": 315,
"column": 27
} | {
"line": 315,
"column": 53
} | {
"line": 315,
"column": 54
} | [
{
"pp": "J : Type w\ninst✝² : SmallCategory J\nκ : Cardinal.{w}\ninst✝¹ : Fact κ.IsRegular\ninst✝ : IsCardinalFiltered J κ\nhJ : ∀ (e : J), ∃ m x, IsEmpty (m ⟶ e)\nι : Type w\nD : ι → DiagramWithUniqueTerminal J κ\nhι : HasCardinalLT ι κ\nm₀ : ι → J\nt₀ : (i : ι) → (D i).top ⟶ m₀ i\nhm₀ : ∀ (i : ι), IsEmpty (m₀... | [
"J : Type w\ninst✝² : SmallCategory J\nκ : Cardinal.{w}\ninst✝¹ : Fact κ.IsRegular\ninst✝ : IsCardinalFiltered J κ\nhJ : ∀ (e : J), ∃ m x, IsEmpty (m ⟶ e)\nι : Type w\nD : ι → DiagramWithUniqueTerminal J κ\nhι : HasCardinalLT ι κ\nm₀ : ι → J\nt₀ : (i : ι) → (D i).top ⟶ m₀ i\nhm₀ : ∀ (i : ι), IsEmpty (m₀ i ⟶ (D i).t... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Presentable.OrthogonalReflection | {
"line": 316,
"column": 6
} | {
"line": 321,
"column": 47
} | {
"line": 322,
"column": 4
} | [
{
"pp": "case refine_2.h₀\nC : Type u\ninst✝⁴ : Category.{v, u} C\nW : MorphismProperty C\nZ : C\ninst✝³ : HasCoproduct D₁.obj₁\ninst✝² : HasCoproduct D₁.obj₂\ninst✝¹ : HasPushouts C\ninst✝ : HasMulticoequalizer (D₂.multispanIndex W Z)\nhZ : W.isLocal Z\nf : succ W Z ⟶ Z\nhf : toSucc W Z ≫ f = 𝟙 Z\nd : D₁ W Z\... | [] | simp only [Category.assoc] at hf
simp only [Category.comp_id, ← Category.assoc]
refine D₂.condition _ d.1.2 ?_
rw [Category.assoc, Category.assoc, Category.assoc,
← D₁.ι_comp_t_assoc, pushout.condition_assoc, reassoc_of% hf,
← D₁.ι_comp_t_assoc, pushout.condition] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Presentable.OrthogonalReflection | {
"line": 316,
"column": 6
} | {
"line": 321,
"column": 47
} | {
"line": 322,
"column": 4
} | [
{
"pp": "case refine_2.h₀\nC : Type u\ninst✝⁴ : Category.{v, u} C\nW : MorphismProperty C\nZ : C\ninst✝³ : HasCoproduct D₁.obj₁\ninst✝² : HasCoproduct D₁.obj₂\ninst✝¹ : HasPushouts C\ninst✝ : HasMulticoequalizer (D₂.multispanIndex W Z)\nhZ : W.isLocal Z\nf : succ W Z ⟶ Z\nhf : toSucc W Z ≫ f = 𝟙 Z\nd : D₁ W Z\... | [] | simp only [Category.assoc] at hf
simp only [Category.comp_id, ← Category.assoc]
refine D₂.condition _ d.1.2 ?_
rw [Category.assoc, Category.assoc, Category.assoc,
← D₁.ι_comp_t_assoc, pushout.condition_assoc, reassoc_of% hf,
← D₁.ι_comp_t_assoc, pushout.condition] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Presentable.Directed | {
"line": 313,
"column": 2
} | {
"line": 315,
"column": 88
} | {
"line": 317,
"column": 0
} | [
{
"pp": "J : Type w\ninst✝² : SmallCategory J\nκ : Cardinal.{w}\ninst✝¹ : Fact κ.IsRegular\ninst✝ : IsCardinalFiltered J κ\nhJ : ∀ (e : J), ∃ m x, IsEmpty (m ⟶ e)\nι : Type w\nD : ι → DiagramWithUniqueTerminal J κ\nhι : HasCardinalLT ι κ\nm₀ : ι → J\nt₀ : (i : ι) → (D i).top ⟶ m₀ i\nhm₀ : ∀ (i : ι), IsEmpty (m₀... | [] | exact ⟨c.pt, fun i ↦ u i ≫ c.π ⟨⟩,
fun i ↦ ⟨fun hi ↦ (hm₀ i).false (t₁ i ≫ c.π ⟨⟩ ≫ hi)⟩,
fun i₁ i₂ j h₁ h₂ ↦ by simpa [index, shape] using c.condition ⟨⟨i₁, i₂, j⟩, h₁, h₂⟩⟩ | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.CategoryTheory.Presentable.Directed | {
"line": 364,
"column": 4
} | {
"line": 364,
"column": 33
} | {
"line": 365,
"column": 4
} | [
{
"pp": "case inr\nJ : Type w\ninst✝¹ : SmallCategory J\nκ : Cardinal.{w}\ninst✝ : Fact κ.IsRegular\nι : Type w\nD : ι → DiagramWithUniqueTerminal J κ\nhι : HasCardinalLT ι κ\nm : J\nu : (i : ι) → (D i).top ⟶ m\nhD : ∀ {i : ι}, ¬(D i).P m\nf : m ⟶ m\nhf : ∃ i, Arrow.mk f = Arrow.mk ((D i.fst).isTerminal.lift ⋯ ... | [
"case inr\nJ : Type w\ninst✝¹ : SmallCategory J\nκ : Cardinal.{w}\ninst✝ : Fact κ.IsRegular\nι : Type w\nD : ι → DiagramWithUniqueTerminal J κ\nhι : HasCardinalLT ι κ\nm : J\nu : (i : ι) → (D i).top ⟶ m\nhD : ∀ {i : ι}, ¬(D i).P m\nf : m ⟶ m\ni : ι\nj : J\nhj : (D i).P j\nhi : Arrow.mk f = Arrow.mk ((D ⟨i, ⟨j, hj⟩⟩... | obtain ⟨⟨i, j, hj⟩, hi⟩ := hf | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.CategoryTheory.Presentable.SharplyLT.Basic | {
"line": 189,
"column": 6
} | {
"line": 189,
"column": 40
} | {
"line": 189,
"column": 41
} | [
{
"pp": "case succ.refine_2\nκ₁ κ₂ : Cardinal.{w}\ninst✝¹ : Fact κ₁.IsRegular\ninst✝ : Fact κ₂.IsRegular\nh₀ : κ₁ < κ₂\nX : Type w\nY : (B : Set X) → HasCardinalLT (↑B) κ₂ → Set (SetCardinalLT κ₁ ↑B)\nhY : ∀ (B : Set X) (hB : HasCardinalLT (↑B) κ₂), HasCardinalLT (↑(Y B hB)) κ₂\nm : (B : Set X) → (hB : HasCardi... | [
"case succ.refine_2\nκ₁ κ₂ : Cardinal.{w}\ninst✝¹ : Fact κ₁.IsRegular\ninst✝ : Fact κ₂.IsRegular\nh₀ : κ₁ < κ₂\nX : Type w\nY : (B : Set X) → HasCardinalLT (↑B) κ₂ → Set (SetCardinalLT κ₁ ↑B)\nhY : ∀ (B : Set X) (hB : HasCardinalLT (↑B) κ₂), HasCardinalLT (↑(Y B hB)) κ₂\nm : (B : Set X) → (hB : HasCardinalLT (↑B) κ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Presentable.OrthogonalReflection | {
"line": 429,
"column": 44
} | {
"line": 429,
"column": 55
} | {
"line": 429,
"column": 56
} | [
{
"pp": "C : Type u\ninst✝⁷ : Category.{v, u} C\nW : MorphismProperty C\nZ : C\ninst✝⁶ : HasPushouts C\ninst✝⁵ : ∀ (Z : C), HasCoproduct D₁.obj₁\ninst✝⁴ : ∀ (Z : C), HasCoproduct D₁.obj₂\ninst✝³ : ∀ (Z : C), HasMulticoequalizer (D₂.multispanIndex W Z)\nκ : Cardinal.{w}\ninst✝² : OrderBot κ.ord.ToType\ninst✝¹ : ... | [
"C : Type u\ninst✝⁷ : Category.{v, u} C\nW : MorphismProperty C\nZ : C\ninst✝⁶ : HasPushouts C\ninst✝⁵ : ∀ (Z : C), HasCoproduct D₁.obj₁\ninst✝⁴ : ∀ (Z : C), HasCoproduct D₁.obj₂\ninst✝³ : ∀ (Z : C), HasMulticoequalizer (D₂.multispanIndex W Z)\nκ : Cardinal.{w}\ninst✝² : OrderBot κ.ord.ToType\ninst✝¹ : HasIteration... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Presentable.SharplyLT.Basic | {
"line": 220,
"column": 6
} | {
"line": 220,
"column": 39
} | {
"line": 220,
"column": 40
} | [
{
"pp": "κ₁ κ₂ : Cardinal.{w}\ninst✝² : Fact κ₁.IsRegular\ninst✝¹ : Fact κ₂.IsRegular\nh₀ : κ₁ < κ₂\nX : Type w\ninst✝ : PartialOrder X\nY : (B : Set X) → HasCardinalLT (↑B) κ₂ → Set (SetCardinalLT κ₁ ↑B)\nhY : ∀ (B : Set X) (hB : HasCardinalLT (↑B) κ₂), HasCardinalLT (↑(Y B hB)) κ₂\nhY' : ∀ (B : Set X) (hB : H... | [
"κ₁ κ₂ : Cardinal.{w}\ninst✝² : Fact κ₁.IsRegular\ninst✝¹ : Fact κ₂.IsRegular\nh₀ : κ₁ < κ₂\nX : Type w\ninst✝ : PartialOrder X\nY : (B : Set X) → HasCardinalLT (↑B) κ₂ → Set (SetCardinalLT κ₁ ↑B)\nhY : ∀ (B : Set X) (hB : HasCardinalLT (↑B) κ₂), HasCardinalLT (↑(Y B hB)) κ₂\nhY' : ∀ (B : Set X) (hB : HasCardinalLT... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Presentable.OrthogonalReflection | {
"line": 468,
"column": 37
} | {
"line": 468,
"column": 48
} | {
"line": 468,
"column": 49
} | [
{
"pp": "C : Type u\ninst✝⁴ : Category.{v, u} C\nW : MorphismProperty C\nκ : Cardinal.{w}\ninst✝³ : Fact κ.IsRegular\ninst✝² : IsSmall.{w, v, u} W\ninst✝¹ : LocallySmall.{w, v, u} C\nhW : ∀ ⦃X Y : C⦄ (f : X ⟶ Y), W f → IsCardinalPresentable X κ ∧ IsCardinalPresentable Y κ\ninst✝ : HasColimitsOfSize.{w, w, v, u}... | [
"C : Type u\ninst✝⁴ : Category.{v, u} C\nW : MorphismProperty C\nκ : Cardinal.{w}\ninst✝³ : Fact κ.IsRegular\ninst✝² : IsSmall.{w, v, u} W\ninst✝¹ : LocallySmall.{w, v, u} C\nhW : ∀ ⦃X Y : C⦄ (f : X ⟶ Y), W f → IsCardinalPresentable X κ ∧ IsCardinalPresentable Y κ\ninst✝ : HasColimitsOfSize.{w, w, v, u} C\n⊢ ¬κ = 0... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Presentable.Type | {
"line": 60,
"column": 23
} | {
"line": 60,
"column": 38
} | {
"line": 60,
"column": 39
} | [
{
"pp": "X : Type u\nκ : Cardinal.{u}\nhX : HasCardinalLT X κ\ninst✝ : Fact κ.IsRegular\nJ : Type u\nx✝¹ : SmallCategory J\nx✝ : IsCardinalFiltered J κ\nF : J ⥤ Type u\nc : Cocone F\nhc : IsColimit c\nthis : IsFiltered J\nj : J\nf g : X ⟶ F.obj j\nh : f ≫ c.ι.app j = g ≫ c.ι.app j\nk : ToType X → J\na : (x : To... | [
"X : Type u\nκ : Cardinal.{u}\nhX : HasCardinalLT X κ\ninst✝ : Fact κ.IsRegular\nJ : Type u\nx✝¹ : SmallCategory J\nx✝ : IsCardinalFiltered J κ\nF : J ⥤ Type u\nc : Cocone F\nhc : IsColimit c\nthis : IsFiltered J\nj : J\nf g : X ⟶ F.obj j\nh : f ≫ c.ι.app j = g ≫ c.ι.app j\nk : ToType X → J\na : (x : ToType X) → j ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.RegularCategory.Basic | {
"line": 119,
"column": 6
} | {
"line": 119,
"column": 70
} | {
"line": 119,
"column": 71
} | [
{
"pp": "case refine_1\nC : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Regular C\nX Y : C\nf : X ⟶ Y\nm : coequalizer (pullback.fst f f) (pullback.snd f f) ⟶ Y := coequalizer.desc f ⋯\ne : X ⟶ coequalizer (pullback.fst f f) (pullback.snd f f) := coequalizer.π (pullback.fst f f) (pullback.snd f f)\nk₁ : pullbac... | [
"case refine_1\nC : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Regular C\nX Y : C\nf : X ⟶ Y\nm : coequalizer (pullback.fst f f) (pullback.snd f f) ⟶ Y := coequalizer.desc f ⋯\ne : X ⟶ coequalizer (pullback.fst f f) (pullback.snd f f) := coequalizer.π (pullback.fst f f) (pullback.snd f f)\nk₁ : pullback m m ⟶ coeq... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.RepresentedBy | {
"line": 95,
"column": 2
} | {
"line": 95,
"column": 32
} | {
"line": 95,
"column": 33
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF : Cᵒᵖ ⥤ Type w\nX : C\nR : F.RepresentableBy X\nx✝¹ : Cᵒᵖ\nx✝ : (uliftYoneda.{w, v, u}.obj X).obj x✝¹\n⊢ (ConcreteCategory.hom ((uliftYonedaEquiv.symm { down := R.homEquiv (𝟙 X) }).app x✝¹)).toFun x✝ =\n (ConcreteCategory.hom\n (((equivUliftYonedaIs... | [
"C : Type u\ninst✝ : Category.{v, u} C\nF : Cᵒᵖ ⥤ Type w\nX : C\nR : F.RepresentableBy X\nx✝¹ : Cᵒᵖ\nx✝ : (uliftYoneda.{w, v, u}.obj X).obj x✝¹\n⊢ (ConcreteCategory.hom (F.map x✝.down.op)) (R.homEquiv (𝟙 X)) = R.homEquiv x✝.down"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.RepresentedBy | {
"line": 110,
"column": 14
} | {
"line": 110,
"column": 25
} | {
"line": 110,
"column": 26
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF : Cᵒᵖ ⥤ Type w\nX : C\nx : F.obj (op X)\nF' : Cᵒᵖ ⥤ Type w\ne : F ≅ F'\nh : F'.IsRepresentedBy ((ConcreteCategory.hom (e.hom.app (op X))) x)\n⊢ F.IsRepresentedBy x",
"ppTerm": "?m.33",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
... | [
"C : Type u\ninst✝ : Category.{v, u} C\nF : Cᵒᵖ ⥤ Type w\nX : C\nx : F.obj (op X)\nF' : Cᵒᵖ ⥤ Type w\ne : F ≅ F'\nh : F'.IsRepresentedBy ((ConcreteCategory.hom (e.hom.app (op X))) x)\n⊢ F.IsRepresentedBy x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Presentable.Directed | {
"line": 463,
"column": 9
} | {
"line": 463,
"column": 20
} | {
"line": 463,
"column": 21
} | [
{
"pp": "J : Type w\ninst✝² : SmallCategory J\nκ : Cardinal.{w}\ninst✝¹ : Fact κ.IsRegular\ninst✝ : IsCardinalFiltered J κ\nhJ : ∀ (e : J), ∃ m x, IsEmpty (m ⟶ e)\nthis✝¹ : IsCardinalFiltered (DiagramWithUniqueTerminal J κ) κ\nthis✝ : IsFiltered J\nthis : IsFiltered (DiagramWithUniqueTerminal J κ)\nj : J\nD : D... | [
"J : Type w\ninst✝² : SmallCategory J\nκ : Cardinal.{w}\ninst✝¹ : Fact κ.IsRegular\ninst✝ : IsCardinalFiltered J κ\nhJ : ∀ (e : J), ∃ m x, IsEmpty (m ⟶ e)\nthis✝¹ : IsCardinalFiltered (DiagramWithUniqueTerminal J κ) κ\nthis✝ : IsFiltered J\nthis : IsFiltered (DiagramWithUniqueTerminal J κ)\nj : J\nD : DiagramWithUn... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.RegularCategory.Basic | {
"line": 198,
"column": 2
} | {
"line": 199,
"column": 44
} | {
"line": 200,
"column": 4
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Regular C\nA B : C\nf : A ⟶ B\nA' : Subobject A\nB' : Subobject B\n⊢ IsPullback (frobeniusMorphism f A' B' ≫ ((«exists» f).obj A' ⊓ B').ofLE B' ⋯)\n ((A' ⊓ (Subobject.pullback f).obj B').ofLE A' ⋯) B'.arrow\n ((imageFactorisation f A').F.e ≫ ((«exis... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Regular C\nA B : C\nf : A ⟶ B\nA' : Subobject A\nB' : Subobject B\n⊢ IsPullback ((A' ⊓ (Subobject.pullback f).obj B').ofLE ((Subobject.pullback f).obj B') ⋯)\n ((A' ⊓ (Subobject.pullback f).obj B').ofLE A' ⋯) ((Subobject.pullback f).obj B').arrow A'.arrow"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.Coherent.CoherentTopology | {
"line": 95,
"column": 6
} | {
"line": 95,
"column": 39
} | {
"line": 96,
"column": 6
} | [
{
"pp": "case mp.of\nC : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Precoherent C\nX : C\nS : Sieve X\nY : C\nT : Presieve Y\nhS : T ∈ (coherentCoverage C).coverings Y\n⊢ ∃ α, ∃ (_ : Finite α), ∃ Y_1 π, EffectiveEpiFamily Y_1 π ∧ ∀ (a : α), (Sieve.generate T).arrows (π a)",
"ppTerm": "?mp.of",
"a... | [
"case mp.of\nC : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Precoherent C\nX : C\nS : Sieve X\nY : C\nT : Presieve Y\na : Type\nh : Finite a\nY' : a → C\nπ : (a : a) → Y' a ⟶ Y\nh' : T = Presieve.ofArrows Y' π\nright✝ : EffectiveEpiFamily Y' π\n⊢ ∃ α, ∃ (_ : Finite α), ∃ Y_1 π, EffectiveEpiFamily Y_1 π ∧ ∀ (... | obtain ⟨a, h, Y', π, h', _⟩ := hS | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.CategoryTheory.Sites.Coherent.RegularTopology | {
"line": 82,
"column": 44
} | {
"line": 82,
"column": 55
} | {
"line": 82,
"column": 56
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Preregular C\nX : C\nS✝ : Sieve X\nY : C\nR S : Sieve Y\na✝¹ : (regularCoverage C).Saturate Y R\na✝ : ∀ ⦃Y_1 : C⦄ ⦃f : Y_1 ⟶ Y⦄, R.arrows f → (regularCoverage C).Saturate Y_1 (Sieve.pullback f S)\nb : ∀ ⦃Y_1 : C⦄ ⦃f : Y_1 ⟶ Y⦄, R.arrows f → ∃ Y_2 π,... | [
"C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Preregular C\nX : C\nS✝ : Sieve X\nY : C\nR S : Sieve Y\na✝¹ : (regularCoverage C).Saturate Y R\na✝ : ∀ ⦃Y_1 : C⦄ ⦃f : Y_1 ⟶ Y⦄, R.arrows f → (regularCoverage C).Saturate Y_1 (Sieve.pullback f S)\nb : ∀ ⦃Y_1 : C⦄ ⦃f : Y_1 ⟶ Y⦄, R.arrows f → ∃ Y_2 π, EffectiveEp... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.Coherent.Comparison | {
"line": 42,
"column": 4
} | {
"line": 42,
"column": 15
} | {
"line": 42,
"column": 16
} | [
{
"pp": "C : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Precoherent C\ninst✝ : HasFiniteCoproducts C\nX Y Z : C\nf : X ⟶ Y\ng : Z ⟶ Y\nx✝ : EffectiveEpi g\nhp : EffectiveEpi g → ∃ β, ∃ (_ : Finite β), ∃ X₂ π₂, EffectiveEpiFamily X₂ π₂ ∧ ∃ ι, ∀ (b : β), ι b ≫ g = π₂ b ≫ f\nβ : Type\nw✝ : Finite β\nX₂ : β... | [
"C : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Precoherent C\ninst✝ : HasFiniteCoproducts C\nX Y Z : C\nf : X ⟶ Y\ng : Z ⟶ Y\nx✝ : EffectiveEpi g\nhp : EffectiveEpi g → ∃ β, ∃ (_ : Finite β), ∃ X₂ π₂, EffectiveEpiFamily X₂ π₂ ∧ ∃ ι, ∀ (b : β), ι b ≫ g = π₂ b ≫ f\nβ : Type\nw✝ : Finite β\nX₂ : β → C\nπ₂ : (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.Coherent.Comparison | {
"line": 94,
"column": 56
} | {
"line": 94,
"column": 67
} | {
"line": 94,
"column": 68
} | [
{
"pp": "case mk\nC : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Preregular C\ninst✝ : FinitaryPreExtensive C\nB : C\nS : Sieve B\nY✝ : C\nI : Type\nw✝ : Finite I\nX : I → C\nf : (a : I) → X a ⟶ Y✝\nhT : EffectiveEpiFamily X f\nR Y : C\ni✝¹ : Unit\nψ : R ⟶ ∐ fun i ↦ X i\nQ : C\ni✝ : I\ne : Q ⟶ X i✝\n⊢ P... | [
"case mk\nC : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Preregular C\ninst✝ : FinitaryPreExtensive C\nB : C\nS : Sieve B\nY✝ : C\nI : Type\nw✝ : Finite I\nX : I → C\nf : (a : I) → X a ⟶ Y✝\nhT : EffectiveEpiFamily X f\nR Y : C\ni✝¹ : Unit\nψ : R ⟶ ∐ fun i ↦ X i\nQ : C\ni✝ : I\ne : Q ⟶ X i✝\n⊢ Presieve.ofAr... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.Coherent.RegularSheaves | {
"line": 110,
"column": 4
} | {
"line": 110,
"column": 32
} | {
"line": 110,
"column": 33
} | [
{
"pp": "case refine_2\nC : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\nP : Cᵒᵖ ⥤ Type u_4\nX B : C\nπ : X ⟶ B\ninst✝ : EffectiveEpi π\nc : PullbackCone π π\nhP :\n ∀ (y : P.obj (op X)),\n (ConcreteCategory.hom (P.map c.fst.op)) y = (ConcreteCategory.hom (P.map c.snd.op)) y →\n ∃! x, (ConcreteCategory.ho... | [
"case refine_2\nC : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\nP : Cᵒᵖ ⥤ Type u_4\nX B : C\nπ : X ⟶ B\ninst✝ : EffectiveEpi π\nc : PullbackCone π π\nhP :\n ∀ (y : P.obj (op X)),\n (ConcreteCategory.hom (P.map c.fst.op)) y = (ConcreteCategory.hom (P.map c.snd.op)) y →\n ∃! x, (ConcreteCategory.hom (P.map π.o... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.Coherent.RegularSheaves | {
"line": 129,
"column": 4
} | {
"line": 129,
"column": 32
} | {
"line": 129,
"column": 33
} | [
{
"pp": "case refine_1\nC : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\nP : Cᵒᵖ ⥤ Type u_4\nX B : C\nπ : X ⟶ B\ninst✝ : EffectiveEpi π\nc : PullbackCone π π\nhP :\n ∀ (b : (fun X ↦ X) ↑{x | (ConcreteCategory.hom (P.map c.fst.op)) x = (ConcreteCategory.hom (P.map c.snd.op)) x}),\n ∃! a, (ConcreteCategory.hom (... | [
"case refine_1\nC : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\nP : Cᵒᵖ ⥤ Type u_4\nX B : C\nπ : X ⟶ B\ninst✝ : EffectiveEpi π\nc : PullbackCone π π\nhP :\n ∀ (b : (fun X ↦ X) ↑{x | (ConcreteCategory.hom (P.map c.fst.op)) x = (ConcreteCategory.hom (P.map c.snd.op)) x}),\n ∃! a, (ConcreteCategory.hom (mapToEqualiz... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.Coherent.RegularSheaves | {
"line": 133,
"column": 4
} | {
"line": 133,
"column": 32
} | {
"line": 133,
"column": 33
} | [
{
"pp": "case refine_2\nC : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\nP : Cᵒᵖ ⥤ Type u_4\nX B : C\nπ : X ⟶ B\ninst✝ : EffectiveEpi π\nc : PullbackCone π π\nhP :\n ∀ (b : (fun X ↦ X) ↑{x | (ConcreteCategory.hom (P.map c.fst.op)) x = (ConcreteCategory.hom (P.map c.snd.op)) x}),\n ∃! a, (ConcreteCategory.hom (... | [
"case refine_2\nC : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\nP : Cᵒᵖ ⥤ Type u_4\nX B : C\nπ : X ⟶ B\ninst✝ : EffectiveEpi π\nc : PullbackCone π π\nhP :\n ∀ (b : (fun X ↦ X) ↑{x | (ConcreteCategory.hom (P.map c.fst.op)) x = (ConcreteCategory.hom (P.map c.snd.op)) x}),\n ∃! a, (ConcreteCategory.hom (mapToEqualiz... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.Coherent.RegularSheaves | {
"line": 153,
"column": 4
} | {
"line": 153,
"column": 32
} | {
"line": 153,
"column": 33
} | [
{
"pp": "case refine_1\nC : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\nP : Cᵒᵖ ⥤ Type u_4\nX B : C\nπ : X ⟶ B\ninst✝ : EffectiveEpi π\nc : PullbackCone π π\nhc : IsLimit c\nthis : HasPullback π π\nhP :\n ∀\n (b :\n (fun X ↦ X)\n ↑{x |\n (ConcreteCategory.hom (P.map (pullback.fst π π).o... | [
"case refine_1\nC : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\nP : Cᵒᵖ ⥤ Type u_4\nX B : C\nπ : X ⟶ B\ninst✝ : EffectiveEpi π\nc : PullbackCone π π\nhc : IsLimit c\nthis : HasPullback π π\nhP :\n ∀\n (b :\n (fun X ↦ X)\n ↑{x |\n (ConcreteCategory.hom (P.map (pullback.fst π π).op)) x =\n ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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