module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.LinearAlgebra.ExteriorPower.Basic | {
"line": 294,
"column": 2
} | {
"line": 294,
"column": 7
} | {
"line": 296,
"column": 0
} | [
{
"pp": "R : Type u\ninst✝² : CommRing R\nn : ℕ\nM : Type u_1\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\n⊢ map n LinearMap.id = LinearMap.id",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"LinearMap.id",
"AlternatingMap",
"Submodule",
"Semiring.toModule",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.ExteriorPower.Basic | {
"line": 294,
"column": 2
} | {
"line": 294,
"column": 7
} | {
"line": 296,
"column": 0
} | [
{
"pp": "R : Type u\ninst✝² : CommRing R\nn : ℕ\nM : Type u_1\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\n⊢ map n LinearMap.id = LinearMap.id",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"LinearMap.id",
"AlternatingMap",
"Submodule",
"Semiring.toModule",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.ExteriorPower.Basic | {
"line": 299,
"column": 2
} | {
"line": 299,
"column": 7
} | {
"line": 301,
"column": 0
} | [
{
"pp": "R : Type u\ninst✝⁶ : CommRing R\nn : ℕ\nM : Type u_1\nN : Type u_2\nN' : Type u_3\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module R M\ninst✝³ : AddCommGroup N\ninst✝² : Module R N\ninst✝¹ : AddCommGroup N'\ninst✝ : Module R N'\nf : M →ₗ[R] N\ng : N →ₗ[R] N'\n⊢ map n (g ∘ₗ f) = map n g ∘ₗ map n f",
"ppTer... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.LinearAlgebra.ExteriorPower.Basic | {
"line": 299,
"column": 2
} | {
"line": 299,
"column": 7
} | {
"line": 301,
"column": 0
} | [
{
"pp": "R : Type u\ninst✝⁶ : CommRing R\nn : ℕ\nM : Type u_1\nN : Type u_2\nN' : Type u_3\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module R M\ninst✝³ : AddCommGroup N\ninst✝² : Module R N\ninst✝¹ : AddCommGroup N'\ninst✝ : Module R N'\nf : M →ₗ[R] N\ng : N →ₗ[R] N'\n⊢ map n (g ∘ₗ f) = map n g ∘ₗ map n f",
"ppTer... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.ExteriorPower.Basic | {
"line": 299,
"column": 2
} | {
"line": 299,
"column": 7
} | {
"line": 301,
"column": 0
} | [
{
"pp": "R : Type u\ninst✝⁶ : CommRing R\nn : ℕ\nM : Type u_1\nN : Type u_2\nN' : Type u_3\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module R M\ninst✝³ : AddCommGroup N\ninst✝² : Module R N\ninst✝¹ : AddCommGroup N'\ninst✝ : Module R N'\nf : M →ₗ[R] N\ng : N →ₗ[R] N'\n⊢ map n (g ∘ₗ f) = map n g ∘ₗ map n f",
"ppTer... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.ExteriorPower.Basic | {
"line": 369,
"column": 4
} | {
"line": 372,
"column": 29
} | {
"line": 373,
"column": 2
} | [
{
"pp": "case a\nR : Type u\ninst✝³ : CommRing R\nn : ℕ\nM : Type u_1\ninst✝² : AddCommGroup M\ninst✝¹ : Module R M\nI : Type u_4\ninst✝ : LinearOrder I\nv : I → M\nhv : Submodule.span R (Set.range v) = ⊤\n⊢ Submodule.span R (Set.range (ExteriorAlgebra.ιMulti_family R n v)) ≤ ⋀[R]^n M",
"ppTerm": "?a✝",
... | [] | rw [Submodule.span_le, Set.range_subset_iff]
intro
rw [SetLike.mem_coe, ιMulti_family_eq_coe_comp, comp_apply]
exact Submodule.coe_mem _ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.ExteriorPower.Basic | {
"line": 369,
"column": 4
} | {
"line": 372,
"column": 29
} | {
"line": 373,
"column": 2
} | [
{
"pp": "case a\nR : Type u\ninst✝³ : CommRing R\nn : ℕ\nM : Type u_1\ninst✝² : AddCommGroup M\ninst✝¹ : Module R M\nI : Type u_4\ninst✝ : LinearOrder I\nv : I → M\nhv : Submodule.span R (Set.range v) = ⊤\n⊢ Submodule.span R (Set.range (ExteriorAlgebra.ιMulti_family R n v)) ≤ ⋀[R]^n M",
"ppTerm": "?a✝",
... | [] | rw [Submodule.span_le, Set.range_subset_iff]
intro
rw [SetLike.mem_coe, ιMulti_family_eq_coe_comp, comp_apply]
exact Submodule.coe_mem _ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.ExteriorPower.Basic | {
"line": 419,
"column": 8
} | {
"line": 419,
"column": 13
} | {
"line": 419,
"column": 13
} | [
{
"pp": "R : Type u\ninst✝⁶ : CommRing R\nn : ℕ\nM : Type u_1\nN : Type u_2\nN' : Type u_3\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module R M\ninst✝³ : AddCommGroup N\ninst✝² : Module R N\ninst✝¹ : AddCommGroup N'\ninst✝ : Module R N'\n⊢ alternatingMapLinearEquiv (AlternatingMap.constOfIsEmpty R M (Fin 0) 1) ∘ₗ\n ... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.LinearAlgebra.ExteriorPower.Basic | {
"line": 419,
"column": 8
} | {
"line": 419,
"column": 13
} | {
"line": 419,
"column": 13
} | [
{
"pp": "R : Type u\ninst✝⁶ : CommRing R\nn : ℕ\nM : Type u_1\nN : Type u_2\nN' : Type u_3\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module R M\ninst✝³ : AddCommGroup N\ninst✝² : Module R N\ninst✝¹ : AddCommGroup N'\ninst✝ : Module R N'\n⊢ alternatingMapLinearEquiv (AlternatingMap.constOfIsEmpty R M (Fin 0) 1) ∘ₗ\n ... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.ExteriorPower.Basic | {
"line": 419,
"column": 8
} | {
"line": 419,
"column": 13
} | {
"line": 419,
"column": 13
} | [
{
"pp": "R : Type u\ninst✝⁶ : CommRing R\nn : ℕ\nM : Type u_1\nN : Type u_2\nN' : Type u_3\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module R M\ninst✝³ : AddCommGroup N\ninst✝² : Module R N\ninst✝¹ : AddCommGroup N'\ninst✝ : Module R N'\n⊢ alternatingMapLinearEquiv (AlternatingMap.constOfIsEmpty R M (Fin 0) 1) ∘ₗ\n ... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.ExteriorPower.Basic | {
"line": 419,
"column": 19
} | {
"line": 419,
"column": 24
} | {
"line": 419,
"column": 24
} | [
{
"pp": "R : Type u\ninst✝⁶ : CommRing R\nn : ℕ\nM : Type u_1\nN : Type u_2\nN' : Type u_3\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module R M\ninst✝³ : AddCommGroup N\ninst✝² : Module R N\ninst✝¹ : AddCommGroup N'\ninst✝ : Module R N'\n⊢ { toFun := fun r ↦ r • (ιMulti R 0) fun a ↦ Fin.casesOn a fun i hi ↦ ⋯.elim, ma... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.LinearAlgebra.ExteriorPower.Basic | {
"line": 419,
"column": 19
} | {
"line": 419,
"column": 24
} | {
"line": 419,
"column": 24
} | [
{
"pp": "R : Type u\ninst✝⁶ : CommRing R\nn : ℕ\nM : Type u_1\nN : Type u_2\nN' : Type u_3\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module R M\ninst✝³ : AddCommGroup N\ninst✝² : Module R N\ninst✝¹ : AddCommGroup N'\ninst✝ : Module R N'\n⊢ { toFun := fun r ↦ r • (ιMulti R 0) fun a ↦ Fin.casesOn a fun i hi ↦ ⋯.elim, ma... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.ExteriorPower.Basic | {
"line": 419,
"column": 19
} | {
"line": 419,
"column": 24
} | {
"line": 419,
"column": 24
} | [
{
"pp": "R : Type u\ninst✝⁶ : CommRing R\nn : ℕ\nM : Type u_1\nN : Type u_2\nN' : Type u_3\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module R M\ninst✝³ : AddCommGroup N\ninst✝² : Module R N\ninst✝¹ : AddCommGroup N'\ninst✝ : Module R N'\n⊢ { toFun := fun r ↦ r • (ιMulti R 0) fun a ↦ Fin.casesOn a fun i hi ↦ ⋯.elim, ma... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.ExteriorPower.Basic | {
"line": 427,
"column": 57
} | {
"line": 427,
"column": 62
} | {
"line": 429,
"column": 0
} | [
{
"pp": "R : Type u\ninst✝⁴ : CommRing R\nM : Type u_1\nN : Type u_2\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : AddCommGroup N\ninst✝ : Module R N\nf : M →ₗ[R] N\n⊢ ↑(zeroEquiv R N) ∘ₗ map 0 f = ↑(zeroEquiv R M)",
"ppTerm": "?m.52",
"assigned": true,
"usedConstants": [
"Alternatin... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.LinearAlgebra.ExteriorPower.Basic | {
"line": 427,
"column": 57
} | {
"line": 427,
"column": 62
} | {
"line": 429,
"column": 0
} | [
{
"pp": "R : Type u\ninst✝⁴ : CommRing R\nM : Type u_1\nN : Type u_2\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : AddCommGroup N\ninst✝ : Module R N\nf : M →ₗ[R] N\n⊢ ↑(zeroEquiv R N) ∘ₗ map 0 f = ↑(zeroEquiv R M)",
"ppTerm": "?m.52",
"assigned": true,
"usedConstants": [
"Alternatin... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.ExteriorPower.Basic | {
"line": 427,
"column": 57
} | {
"line": 427,
"column": 62
} | {
"line": 429,
"column": 0
} | [
{
"pp": "R : Type u\ninst✝⁴ : CommRing R\nM : Type u_1\nN : Type u_2\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : AddCommGroup N\ninst✝ : Module R N\nf : M →ₗ[R] N\n⊢ ↑(zeroEquiv R N) ∘ₗ map 0 f = ↑(zeroEquiv R M)",
"ppTerm": "?m.52",
"assigned": true,
"usedConstants": [
"Alternatin... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.ExteriorPower.Basic | {
"line": 448,
"column": 8
} | {
"line": 448,
"column": 13
} | {
"line": 448,
"column": 13
} | [
{
"pp": "R : Type u\ninst✝⁶ : CommRing R\nn : ℕ\nM : Type u_1\nN : Type u_2\nN' : Type u_3\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module R M\ninst✝³ : AddCommGroup N\ninst✝² : Module R N\ninst✝¹ : AddCommGroup N'\ninst✝ : Module R N'\n⊢ (alternatingMapLinearEquiv ((AlternatingMap.ofSubsingleton R M M 0) LinearMap.i... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.LinearAlgebra.ExteriorPower.Basic | {
"line": 448,
"column": 8
} | {
"line": 448,
"column": 13
} | {
"line": 448,
"column": 13
} | [
{
"pp": "R : Type u\ninst✝⁶ : CommRing R\nn : ℕ\nM : Type u_1\nN : Type u_2\nN' : Type u_3\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module R M\ninst✝³ : AddCommGroup N\ninst✝² : Module R N\ninst✝¹ : AddCommGroup N'\ninst✝ : Module R N'\n⊢ (alternatingMapLinearEquiv ((AlternatingMap.ofSubsingleton R M M 0) LinearMap.i... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.ExteriorPower.Basic | {
"line": 448,
"column": 8
} | {
"line": 448,
"column": 13
} | {
"line": 448,
"column": 13
} | [
{
"pp": "R : Type u\ninst✝⁶ : CommRing R\nn : ℕ\nM : Type u_1\nN : Type u_2\nN' : Type u_3\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module R M\ninst✝³ : AddCommGroup N\ninst✝² : Module R N\ninst✝¹ : AddCommGroup N'\ninst✝ : Module R N'\n⊢ (alternatingMapLinearEquiv ((AlternatingMap.ofSubsingleton R M M 0) LinearMap.i... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.ExteriorPower.Basic | {
"line": 448,
"column": 19
} | {
"line": 448,
"column": 24
} | {
"line": 448,
"column": 24
} | [
{
"pp": "R : Type u\ninst✝⁶ : CommRing R\nn : ℕ\nM : Type u_1\nN : Type u_2\nN' : Type u_3\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module R M\ninst✝³ : AddCommGroup N\ninst✝² : Module R N\ninst✝¹ : AddCommGroup N'\ninst✝ : Module R N'\n⊢ (have h := ⋯;\n { toFun := fun m ↦ (ιMulti R 1) fun x ↦ m, map_add' := ⋯, ... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.LinearAlgebra.ExteriorPower.Basic | {
"line": 448,
"column": 19
} | {
"line": 448,
"column": 24
} | {
"line": 448,
"column": 24
} | [
{
"pp": "R : Type u\ninst✝⁶ : CommRing R\nn : ℕ\nM : Type u_1\nN : Type u_2\nN' : Type u_3\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module R M\ninst✝³ : AddCommGroup N\ninst✝² : Module R N\ninst✝¹ : AddCommGroup N'\ninst✝ : Module R N'\n⊢ (have h := ⋯;\n { toFun := fun m ↦ (ιMulti R 1) fun x ↦ m, map_add' := ⋯, ... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.ExteriorPower.Basic | {
"line": 448,
"column": 19
} | {
"line": 448,
"column": 24
} | {
"line": 448,
"column": 24
} | [
{
"pp": "R : Type u\ninst✝⁶ : CommRing R\nn : ℕ\nM : Type u_1\nN : Type u_2\nN' : Type u_3\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module R M\ninst✝³ : AddCommGroup N\ninst✝² : Module R N\ninst✝¹ : AddCommGroup N'\ninst✝ : Module R N'\n⊢ (have h := ⋯;\n { toFun := fun m ↦ (ιMulti R 1) fun x ↦ m, map_add' := ⋯, ... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.ExteriorPower.Basic | {
"line": 456,
"column": 76
} | {
"line": 456,
"column": 81
} | {
"line": 458,
"column": 0
} | [
{
"pp": "R : Type u\ninst✝⁴ : CommRing R\nM : Type u_1\nN : Type u_2\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : AddCommGroup N\ninst✝ : Module R N\nf : M →ₗ[R] N\n⊢ ↑(oneEquiv R N) ∘ₗ map 1 f = f ∘ₗ ↑(oneEquiv R M)",
"ppTerm": "?m.85",
"assigned": true,
"usedConstants": [
"Alterna... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.LinearAlgebra.ExteriorPower.Basic | {
"line": 456,
"column": 76
} | {
"line": 456,
"column": 81
} | {
"line": 458,
"column": 0
} | [
{
"pp": "R : Type u\ninst✝⁴ : CommRing R\nM : Type u_1\nN : Type u_2\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : AddCommGroup N\ninst✝ : Module R N\nf : M →ₗ[R] N\n⊢ ↑(oneEquiv R N) ∘ₗ map 1 f = f ∘ₗ ↑(oneEquiv R M)",
"ppTerm": "?m.85",
"assigned": true,
"usedConstants": [
"Alterna... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.ExteriorPower.Basic | {
"line": 456,
"column": 76
} | {
"line": 456,
"column": 81
} | {
"line": 458,
"column": 0
} | [
{
"pp": "R : Type u\ninst✝⁴ : CommRing R\nM : Type u_1\nN : Type u_2\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : AddCommGroup N\ninst✝ : Module R N\nf : M →ₗ[R] N\n⊢ ↑(oneEquiv R N) ∘ₗ map 1 f = f ∘ₗ ↑(oneEquiv R M)",
"ppTerm": "?m.85",
"assigned": true,
"usedConstants": [
"Alterna... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Discrete.StructuredArrow | {
"line": 39,
"column": 57
} | {
"line": 39,
"column": 72
} | {
"line": 39,
"column": 72
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nT : Type w\nF : C ⥤ Discrete T\nt : T\ninst✝ : Subsingleton T\nX : C\n⊢ { as := t } = F.obj X",
"ppTerm": "?m.77",
"assigned": true,
"usedConstants": [
"CategoryTheory.Discrete.mk",
"CategoryTheory.Discrete.instSubsingleton",
"Catego... | [] | by subsingleton | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Discrete.StructuredArrow | {
"line": 52,
"column": 59
} | {
"line": 52,
"column": 74
} | {
"line": 52,
"column": 74
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nT : Type w\nF : C ⥤ Discrete T\nt : T\ninst✝ : Subsingleton T\nX : C\n⊢ F.obj X = { as := t }",
"ppTerm": "?m.76",
"assigned": true,
"usedConstants": [
"CategoryTheory.Discrete.mk",
"CategoryTheory.Discrete.instSubsingleton",
"Catego... | [] | by subsingleton | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Monoidal.Closed.Types | {
"line": 51,
"column": 4
} | {
"line": 51,
"column": 80
} | {
"line": 52,
"column": 4
} | [
{
"pp": "C✝ : Type v₂\ninst✝¹ : Category.{v₁, v₂} C✝\nC : Type v₁\ninst✝ : SmallCategory C\nF : C ⥤ Type v₁\n⊢ Closed F",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"CategoryTheory.instMonoidalClosedFunctorType._proof_1"
],
"usedFVars": [],
"usedGoals": [
{
... | [
"C✝ : Type v₂\ninst✝¹ : Category.{v₁, v₂} C✝\nC : Type v₁\ninst✝ : SmallCategory C\nF : C ⥤ Type v₁\nthis : ∀ (X : Type v₁), PreservesColimits (tensorLeft X)\n⊢ Closed F"
] | haveI : ∀ X : Type v₁, PreservesColimits (tensorLeft X) := by infer_instance | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHaveI___1 | Lean.Parser.Tactic.tacticHaveI__ |
Mathlib.CategoryTheory.Limits.IsConnected | {
"line": 100,
"column": 2
} | {
"line": 100,
"column": 20
} | {
"line": 100,
"column": 21
} | [
{
"pp": "case symm\nC : Type u\ninst✝ : Category.{v, u} C\nF : C ⥤ Type w\nc d x✝ y✝ : (j : C) × F.obj j\na✝ : Relation.EqvGen F.ColimitTypeRel x✝ y✝\nih : Zigzag x✝.fst y✝.fst\n⊢ Zigzag y✝.fst x✝.fst",
"ppTerm": "?symm",
"assigned": true,
"usedConstants": [
"Sigma.fst",
"CategoryTheory.... | [] | | symm _ _ _ ih => | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | null |
Mathlib.CategoryTheory.Monoidal.FunctorCategory | {
"line": 218,
"column": 29
} | {
"line": 218,
"column": 34
} | {
"line": 219,
"column": 2
} | [
{
"pp": "C✝ : Type u₁\ninst✝⁸ : Category.{v₁, u₁} C✝\nD✝ : Type u₂\ninst✝⁷ : Category.{v₂, u₂} D✝\ninst✝⁶ : MonoidalCategory D✝\nC : Type u_1\nD : Type u_2\nE : Type u_3\ninst✝⁵ : Category.{v_1, u_1} C\ninst✝⁴ : Category.{v_2, u_2} D\ninst✝³ : Category.{v_3, u_3} E\ninst✝² : MonoidalCategory D\ninst✝¹ : Monoida... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.Monoidal.FunctorCategory | {
"line": 218,
"column": 29
} | {
"line": 218,
"column": 34
} | {
"line": 219,
"column": 2
} | [
{
"pp": "C✝ : Type u₁\ninst✝⁸ : Category.{v₁, u₁} C✝\nD✝ : Type u₂\ninst✝⁷ : Category.{v₂, u₂} D✝\ninst✝⁶ : MonoidalCategory D✝\nC : Type u_1\nD : Type u_2\nE : Type u_3\ninst✝⁵ : Category.{v_1, u_1} C\ninst✝⁴ : Category.{v_2, u_2} D\ninst✝³ : Category.{v_3, u_3} E\ninst✝² : MonoidalCategory D\ninst✝¹ : Monoida... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Monoidal.FunctorCategory | {
"line": 218,
"column": 29
} | {
"line": 218,
"column": 34
} | {
"line": 219,
"column": 2
} | [
{
"pp": "C✝ : Type u₁\ninst✝⁸ : Category.{v₁, u₁} C✝\nD✝ : Type u₂\ninst✝⁷ : Category.{v₂, u₂} D✝\ninst✝⁶ : MonoidalCategory D✝\nC : Type u_1\nD : Type u_2\nE : Type u_3\ninst✝⁵ : Category.{v_1, u_1} C\ninst✝⁴ : Category.{v_2, u_2} D\ninst✝³ : Category.{v_3, u_3} E\ninst✝² : MonoidalCategory D\ninst✝¹ : Monoida... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Monoidal.FunctorCategory | {
"line": 219,
"column": 30
} | {
"line": 219,
"column": 35
} | {
"line": 221,
"column": 0
} | [
{
"pp": "C✝ : Type u₁\ninst✝⁸ : Category.{v₁, u₁} C✝\nD✝ : Type u₂\ninst✝⁷ : Category.{v₂, u₂} D✝\ninst✝⁶ : MonoidalCategory D✝\nC : Type u_1\nD : Type u_2\nE : Type u_3\ninst✝⁵ : Category.{v_1, u_1} C\ninst✝⁴ : Category.{v_2, u_2} D\ninst✝³ : Category.{v_3, u_3} E\ninst✝² : MonoidalCategory D\ninst✝¹ : Monoida... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.Monoidal.FunctorCategory | {
"line": 219,
"column": 30
} | {
"line": 219,
"column": 35
} | {
"line": 221,
"column": 0
} | [
{
"pp": "C✝ : Type u₁\ninst✝⁸ : Category.{v₁, u₁} C✝\nD✝ : Type u₂\ninst✝⁷ : Category.{v₂, u₂} D✝\ninst✝⁶ : MonoidalCategory D✝\nC : Type u_1\nD : Type u_2\nE : Type u_3\ninst✝⁵ : Category.{v_1, u_1} C\ninst✝⁴ : Category.{v_2, u_2} D\ninst✝³ : Category.{v_3, u_3} E\ninst✝² : MonoidalCategory D\ninst✝¹ : Monoida... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Monoidal.FunctorCategory | {
"line": 219,
"column": 30
} | {
"line": 219,
"column": 35
} | {
"line": 221,
"column": 0
} | [
{
"pp": "C✝ : Type u₁\ninst✝⁸ : Category.{v₁, u₁} C✝\nD✝ : Type u₂\ninst✝⁷ : Category.{v₂, u₂} D✝\ninst✝⁶ : MonoidalCategory D✝\nC : Type u_1\nD : Type u_2\nE : Type u_3\ninst✝⁵ : Category.{v_1, u_1} C\ninst✝⁴ : Category.{v_2, u_2} D\ninst✝³ : Category.{v_3, u_3} E\ninst✝² : MonoidalCategory D\ninst✝¹ : Monoida... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Category.ModuleCat.Presheaf.Free | {
"line": 45,
"column": 15
} | {
"line": 45,
"column": 20
} | {
"line": 47,
"column": 0
} | [
{
"pp": "C : Type u₁\ninst✝ : Category.{v₁, u₁} C\nR : Cᵒᵖ ⥤ RingCat\nF : Cᵒᵖ ⥤ Type u\n⊢ ∀ (X : Cᵒᵖ),\n ModuleCat.freeDesc (↾fun x ↦ ModuleCat.freeMk ((ConcreteCategory.hom (F.map (𝟙 X))) x)) =\n (ModuleCat.restrictScalarsId' (RingCat.Hom.hom (R.map (𝟙 X))) ⋯).inv.app\n ((ModuleCat.free ↑(R.ob... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Algebra.Category.ModuleCat.Presheaf.Free | {
"line": 45,
"column": 15
} | {
"line": 45,
"column": 20
} | {
"line": 47,
"column": 0
} | [
{
"pp": "C : Type u₁\ninst✝ : Category.{v₁, u₁} C\nR : Cᵒᵖ ⥤ RingCat\nF : Cᵒᵖ ⥤ Type u\n⊢ ∀ (X : Cᵒᵖ),\n ModuleCat.freeDesc (↾fun x ↦ ModuleCat.freeMk ((ConcreteCategory.hom (F.map (𝟙 X))) x)) =\n (ModuleCat.restrictScalarsId' (RingCat.Hom.hom (R.map (𝟙 X))) ⋯).inv.app\n ((ModuleCat.free ↑(R.ob... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Category.ModuleCat.Presheaf.Free | {
"line": 45,
"column": 15
} | {
"line": 45,
"column": 20
} | {
"line": 47,
"column": 0
} | [
{
"pp": "C : Type u₁\ninst✝ : Category.{v₁, u₁} C\nR : Cᵒᵖ ⥤ RingCat\nF : Cᵒᵖ ⥤ Type u\n⊢ ∀ (X : Cᵒᵖ),\n ModuleCat.freeDesc (↾fun x ↦ ModuleCat.freeMk ((ConcreteCategory.hom (F.map (𝟙 X))) x)) =\n (ModuleCat.restrictScalarsId' (RingCat.Hom.hom (R.map (𝟙 X))) ⋯).inv.app\n ((ModuleCat.free ↑(R.ob... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Limits.Fubini | {
"line": 412,
"column": 2
} | {
"line": 412,
"column": 41
} | {
"line": 413,
"column": 2
} | [
{
"pp": "J : Type u_1\nK : Type u_2\ninst✝⁵ : Category.{v_1, u_1} J\ninst✝⁴ : Category.{v_2, u_2} K\nC : Type u_3\ninst✝³ : Category.{v_3, u_3} C\nF : J ⥤ K ⥤ C\nG✝ : J × K ⥤ C\ninst✝² : HasLimitsOfShape K C\ninst✝¹ : HasLimit (uncurry.obj F)\ninst✝ : HasLimit (F ⋙ lim)\nc : Cone (uncurry.obj F) := limit.cone (... | [
"J : Type u_1\nK : Type u_2\ninst✝⁵ : Category.{v_1, u_1} J\ninst✝⁴ : Category.{v_2, u_2} K\nC : Type u_3\ninst✝³ : Category.{v_3, u_3} C\nF : J ⥤ K ⥤ C\nG✝ : J × K ⥤ C\ninst✝² : HasLimitsOfShape K C\ninst✝¹ : HasLimit (uncurry.obj F)\ninst✝ : HasLimit (F ⋙ lim)\nc : Cone (uncurry.obj F) := limit.cone (uncurry.obj ... | have Q' := coneOfConeUncurryIsLimit Q P | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.CategoryTheory.Adjunction.PartialAdjoint | {
"line": 86,
"column": 2
} | {
"line": 86,
"column": 39
} | {
"line": 88,
"column": 0
} | [
{
"pp": "C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝ : Category.{v₂, u₂} D\nF : D ⥤ C\nX : F.PartialLeftAdjointSource\nY Y' : D\nf : F.partialLeftAdjointObj X ⟶ Y\ng : Y ⟶ Y'\n⊢ F.partialLeftAdjointHomEquiv (f ≫ g) = F.partialLeftAdjointHomEquiv f ≫ F.map g",
"ppTerm": "?m.46",
"assign... | [] | apply CorepresentableBy.homEquiv_comp | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.CategoryTheory.Adjunction.PartialAdjoint | {
"line": 86,
"column": 2
} | {
"line": 86,
"column": 39
} | {
"line": 88,
"column": 0
} | [
{
"pp": "C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝ : Category.{v₂, u₂} D\nF : D ⥤ C\nX : F.PartialLeftAdjointSource\nY Y' : D\nf : F.partialLeftAdjointObj X ⟶ Y\ng : Y ⟶ Y'\n⊢ F.partialLeftAdjointHomEquiv (f ≫ g) = F.partialLeftAdjointHomEquiv f ≫ F.map g",
"ppTerm": "?m.46",
"assign... | [] | apply CorepresentableBy.homEquiv_comp | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Adjunction.PartialAdjoint | {
"line": 86,
"column": 2
} | {
"line": 86,
"column": 39
} | {
"line": 88,
"column": 0
} | [
{
"pp": "C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝ : Category.{v₂, u₂} D\nF : D ⥤ C\nX : F.PartialLeftAdjointSource\nY Y' : D\nf : F.partialLeftAdjointObj X ⟶ Y\ng : Y ⟶ Y'\n⊢ F.partialLeftAdjointHomEquiv (f ≫ g) = F.partialLeftAdjointHomEquiv f ≫ F.map g",
"ppTerm": "?m.46",
"assign... | [] | apply CorepresentableBy.homEquiv_comp | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Adjunction.PartialAdjoint | {
"line": 141,
"column": 25
} | {
"line": 141,
"column": 62
} | {
"line": 141,
"column": 62
} | [
{
"pp": "C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝ : Category.{v₂, u₂} D\nF : D ⥤ C\nh : ∀ (X : C), (F ⋙ coyoneda.obj (op X)).IsCorepresentable\nX : C\nY Y' : D\ng : Y ⟶ Y'\nf : (F ⋙ coyoneda.obj (op X)).coreprX ⟶ Y\n⊢ (F ⋙ coyoneda.obj (op X)).corepresentableBy.homEquiv (f ≫ g) =\n (F ⋙ ... | [] | apply CorepresentableBy.homEquiv_comp | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.CategoryTheory.Adjunction.PartialAdjoint | {
"line": 141,
"column": 25
} | {
"line": 141,
"column": 62
} | {
"line": 141,
"column": 62
} | [
{
"pp": "C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝ : Category.{v₂, u₂} D\nF : D ⥤ C\nh : ∀ (X : C), (F ⋙ coyoneda.obj (op X)).IsCorepresentable\nX : C\nY Y' : D\ng : Y ⟶ Y'\nf : (F ⋙ coyoneda.obj (op X)).coreprX ⟶ Y\n⊢ (F ⋙ coyoneda.obj (op X)).corepresentableBy.homEquiv (f ≫ g) =\n (F ⋙ ... | [] | apply CorepresentableBy.homEquiv_comp | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Adjunction.PartialAdjoint | {
"line": 141,
"column": 25
} | {
"line": 141,
"column": 62
} | {
"line": 141,
"column": 62
} | [
{
"pp": "C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝ : Category.{v₂, u₂} D\nF : D ⥤ C\nh : ∀ (X : C), (F ⋙ coyoneda.obj (op X)).IsCorepresentable\nX : C\nY Y' : D\ng : Y ⟶ Y'\nf : (F ⋙ coyoneda.obj (op X)).coreprX ⟶ Y\n⊢ (F ⋙ coyoneda.obj (op X)).corepresentableBy.homEquiv (f ≫ g) =\n (F ⋙ ... | [] | apply CorepresentableBy.homEquiv_comp | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Adjunction.CompositionIso | {
"line": 181,
"column": 2
} | {
"line": 182,
"column": 40
} | {
"line": 184,
"column": 0
} | [
{
"pp": "C₀ : Type u_1\nC₁ : Type u_2\nC₂ : Type u_3\nC₃ : Type u_4\ninst✝³ : Category.{v_1, u_1} C₀\ninst✝² : Category.{v_2, u_2} C₁\ninst✝¹ : Category.{v_3, u_3} C₂\ninst✝ : Category.{v_4, u_4} C₃\nF₀₁ : C₀ ⥤ C₁\nF₁₂ : C₁ ⥤ C₂\nF₂₃ : C₂ ⥤ C₃\nF₀₂ : C₀ ⥤ C₂\nF₁₃ : C₁ ⥤ C₃\nF₀₃ : C₀ ⥤ C₃\nG₁₀ : C₁ ⥤ C₀\nG₂₁ : C... | [] | exact leftAdjointCompNatTrans_assoc _ _ _ _ _ _ _ _ _ _
(by simpa using congr_arg Iso.inv h) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.CategoryTheory.Subfunctor.Basic | {
"line": 79,
"column": 36
} | {
"line": 79,
"column": 41
} | {
"line": 79,
"column": 41
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF F' F'' : C ⥤ Type w\nG G' : Subfunctor F\nx✝⁴ : Set (Subfunctor F)\nx✝³ : Subfunctor F\nx✝² : x✝³ ∈ x✝⁴\nx✝¹ : C\nx✝ : F.obj x✝¹\n⊢ x✝ ∈ x✝³.obj x✝¹ → x✝ ∈ { obj := fun U ↦ sSup ((fun T ↦ T.obj U) '' x✝⁴), map := ⋯ }.obj x✝¹",
"ppTerm": "?m.331",
"assign... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.Subfunctor.Basic | {
"line": 79,
"column": 36
} | {
"line": 79,
"column": 41
} | {
"line": 79,
"column": 41
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF F' F'' : C ⥤ Type w\nG G' : Subfunctor F\nx✝⁴ : Set (Subfunctor F)\nx✝³ : Subfunctor F\nx✝² : x✝³ ∈ x✝⁴\nx✝¹ : C\nx✝ : F.obj x✝¹\n⊢ x✝ ∈ x✝³.obj x✝¹ → x✝ ∈ { obj := fun U ↦ sSup ((fun T ↦ T.obj U) '' x✝⁴), map := ⋯ }.obj x✝¹",
"ppTerm": "?m.331",
"assign... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Subfunctor.Basic | {
"line": 79,
"column": 36
} | {
"line": 79,
"column": 41
} | {
"line": 79,
"column": 41
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF F' F'' : C ⥤ Type w\nG G' : Subfunctor F\nx✝⁴ : Set (Subfunctor F)\nx✝³ : Subfunctor F\nx✝² : x✝³ ∈ x✝⁴\nx✝¹ : C\nx✝ : F.obj x✝¹\n⊢ x✝ ∈ x✝³.obj x✝¹ → x✝ ∈ { obj := fun U ↦ sSup ((fun T ↦ T.obj U) '' x✝⁴), map := ⋯ }.obj x✝¹",
"ppTerm": "?m.331",
"assign... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Subfunctor.Basic | {
"line": 79,
"column": 58
} | {
"line": 79,
"column": 63
} | {
"line": 79,
"column": 63
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF F' F'' : C ⥤ Type w\nG G' : Subfunctor F\nx✝³ : Set (Subfunctor F)\nx✝² : Subfunctor F\nx✝¹ : x✝² ∈ upperBounds x✝³\nx✝ : C\n⊢ { obj := fun U ↦ sSup ((fun T ↦ T.obj U) '' x✝³), map := ⋯ }.obj x✝ ⊆ x✝².obj x✝",
"ppTerm": "?m.332",
"assigned": true,
"u... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.Subfunctor.Basic | {
"line": 79,
"column": 58
} | {
"line": 79,
"column": 63
} | {
"line": 79,
"column": 63
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF F' F'' : C ⥤ Type w\nG G' : Subfunctor F\nx✝³ : Set (Subfunctor F)\nx✝² : Subfunctor F\nx✝¹ : x✝² ∈ upperBounds x✝³\nx✝ : C\n⊢ { obj := fun U ↦ sSup ((fun T ↦ T.obj U) '' x✝³), map := ⋯ }.obj x✝ ⊆ x✝².obj x✝",
"ppTerm": "?m.332",
"assigned": true,
"u... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Subfunctor.Basic | {
"line": 79,
"column": 58
} | {
"line": 79,
"column": 63
} | {
"line": 79,
"column": 63
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF F' F'' : C ⥤ Type w\nG G' : Subfunctor F\nx✝³ : Set (Subfunctor F)\nx✝² : Subfunctor F\nx✝¹ : x✝² ∈ upperBounds x✝³\nx✝ : C\n⊢ { obj := fun U ↦ sSup ((fun T ↦ T.obj U) '' x✝³), map := ⋯ }.obj x✝ ⊆ x✝².obj x✝",
"ppTerm": "?m.332",
"assigned": true,
"u... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Subfunctor.Basic | {
"line": 85,
"column": 36
} | {
"line": 85,
"column": 41
} | {
"line": 85,
"column": 41
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF F' F'' : C ⥤ Type w\nG G' : Subfunctor F\nx✝⁴ : Set (Subfunctor F)\nx✝³ : Subfunctor F\nx✝² : x✝³ ∈ x✝⁴\nx✝¹ : C\nx✝ : F.obj x✝¹\n⊢ x✝ ∈ { obj := fun U ↦ sInf ((fun T ↦ T.obj U) '' x✝⁴), map := ⋯ }.obj x✝¹ → x✝ ∈ x✝³.obj x✝¹",
"ppTerm": "?m.372",
"assign... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.Subfunctor.Basic | {
"line": 85,
"column": 36
} | {
"line": 85,
"column": 41
} | {
"line": 85,
"column": 41
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF F' F'' : C ⥤ Type w\nG G' : Subfunctor F\nx✝⁴ : Set (Subfunctor F)\nx✝³ : Subfunctor F\nx✝² : x✝³ ∈ x✝⁴\nx✝¹ : C\nx✝ : F.obj x✝¹\n⊢ x✝ ∈ { obj := fun U ↦ sInf ((fun T ↦ T.obj U) '' x✝⁴), map := ⋯ }.obj x✝¹ → x✝ ∈ x✝³.obj x✝¹",
"ppTerm": "?m.372",
"assign... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Subfunctor.Basic | {
"line": 85,
"column": 36
} | {
"line": 85,
"column": 41
} | {
"line": 85,
"column": 41
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF F' F'' : C ⥤ Type w\nG G' : Subfunctor F\nx✝⁴ : Set (Subfunctor F)\nx✝³ : Subfunctor F\nx✝² : x✝³ ∈ x✝⁴\nx✝¹ : C\nx✝ : F.obj x✝¹\n⊢ x✝ ∈ { obj := fun U ↦ sInf ((fun T ↦ T.obj U) '' x✝⁴), map := ⋯ }.obj x✝¹ → x✝ ∈ x✝³.obj x✝¹",
"ppTerm": "?m.372",
"assign... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Subfunctor.Basic | {
"line": 85,
"column": 58
} | {
"line": 85,
"column": 63
} | {
"line": 85,
"column": 63
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF F' F'' : C ⥤ Type w\nG G' : Subfunctor F\nx✝³ : Set (Subfunctor F)\nx✝² : Subfunctor F\nx✝¹ : x✝² ∈ lowerBounds x✝³\nx✝ : C\n⊢ x✝².obj x✝ ⊆ { obj := fun U ↦ sInf ((fun T ↦ T.obj U) '' x✝³), map := ⋯ }.obj x✝",
"ppTerm": "?m.373",
"assigned": true,
"u... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.Subfunctor.Basic | {
"line": 85,
"column": 58
} | {
"line": 85,
"column": 63
} | {
"line": 85,
"column": 63
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF F' F'' : C ⥤ Type w\nG G' : Subfunctor F\nx✝³ : Set (Subfunctor F)\nx✝² : Subfunctor F\nx✝¹ : x✝² ∈ lowerBounds x✝³\nx✝ : C\n⊢ x✝².obj x✝ ⊆ { obj := fun U ↦ sInf ((fun T ↦ T.obj U) '' x✝³), map := ⋯ }.obj x✝",
"ppTerm": "?m.373",
"assigned": true,
"u... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Subfunctor.Basic | {
"line": 85,
"column": 58
} | {
"line": 85,
"column": 63
} | {
"line": 85,
"column": 63
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF F' F'' : C ⥤ Type w\nG G' : Subfunctor F\nx✝³ : Set (Subfunctor F)\nx✝² : Subfunctor F\nx✝¹ : x✝² ∈ lowerBounds x✝³\nx✝ : C\n⊢ x✝².obj x✝ ⊆ { obj := fun U ↦ sInf ((fun T ↦ T.obj U) '' x✝³), map := ⋯ }.obj x✝",
"ppTerm": "?m.373",
"assigned": true,
"u... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Subfunctor.Basic | {
"line": 132,
"column": 2
} | {
"line": 132,
"column": 7
} | {
"line": 134,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF : C ⥤ Type w\nS₁ S₂ T : Subfunctor F\n⊢ (S₁ ⊔ S₂) ⊓ T = S₁ ⊓ T ⊔ S₂ ⊓ T",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"Lattice.toSemilatticeSup",
"and_true",
"CompleteLattice.toLattice",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.Subfunctor.Basic | {
"line": 132,
"column": 2
} | {
"line": 132,
"column": 7
} | {
"line": 134,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF : C ⥤ Type w\nS₁ S₂ T : Subfunctor F\n⊢ (S₁ ⊔ S₂) ⊓ T = S₁ ⊓ T ⊔ S₂ ⊓ T",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"Lattice.toSemilatticeSup",
"and_true",
"CompleteLattice.toLattice",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Subfunctor.Basic | {
"line": 132,
"column": 2
} | {
"line": 132,
"column": 7
} | {
"line": 134,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF : C ⥤ Type w\nS₁ S₂ T : Subfunctor F\n⊢ (S₁ ⊔ S₂) ⊓ T = S₁ ⊓ T ⊔ S₂ ⊓ T",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"Lattice.toSemilatticeSup",
"and_true",
"CompleteLattice.toLattice",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Subfunctor.Basic | {
"line": 136,
"column": 2
} | {
"line": 136,
"column": 7
} | {
"line": 138,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF : C ⥤ Type w\nι : Sort u_1\nS : ι → Subfunctor F\nT : Subfunctor F\n⊢ (⨆ i, S i) ⊓ T = ⨆ i, S i ⊓ T",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Set.ext",
"CompleteLattice.toLattice",
"congrArg",
"iSup",
"S... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.Subfunctor.Basic | {
"line": 136,
"column": 2
} | {
"line": 136,
"column": 7
} | {
"line": 138,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF : C ⥤ Type w\nι : Sort u_1\nS : ι → Subfunctor F\nT : Subfunctor F\n⊢ (⨆ i, S i) ⊓ T = ⨆ i, S i ⊓ T",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Set.ext",
"CompleteLattice.toLattice",
"congrArg",
"iSup",
"S... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Subfunctor.Basic | {
"line": 136,
"column": 2
} | {
"line": 136,
"column": 7
} | {
"line": 138,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF : C ⥤ Type w\nι : Sort u_1\nS : ι → Subfunctor F\nT : Subfunctor F\n⊢ (⨆ i, S i) ⊓ T = ⨆ i, S i ⊓ T",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Set.ext",
"CompleteLattice.toLattice",
"congrArg",
"iSup",
"S... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Sites.Pretopology | {
"line": 192,
"column": 4
} | {
"line": 192,
"column": 54
} | {
"line": 193,
"column": 4
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : HasPullbacks C\nX Z : C\ng : Z ⟶ X\ni : IsIso g\nTi : ⦃Y : C⦄ → (f : Y ⟶ X) → Presieve.singleton g f → Presieve Y\nhS :\n ∀ ⦃Y : C⦄ (f : Y ⟶ X) (H : Presieve.singleton g f), Ti f H ∈ {S | ∃ Y_1 f, ∃ (_ : IsIso f), S = Presieve.singleton f}\n⊢ (Presieve.s... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : HasPullbacks C\nX Z : C\ng : Z ⟶ X\ni✝ : IsIso g\nTi : ⦃Y : C⦄ → (f : Y ⟶ X) → Presieve.singleton g f → Presieve Y\nhS :\n ∀ ⦃Y : C⦄ (f : Y ⟶ X) (H : Presieve.singleton g f), Ti f H ∈ {S | ∃ Y_1 f, ∃ (_ : IsIso f), S = Presieve.singleton f}\nY : C\nf : Y ⟶ Z\ni : Is... | rcases hS g (singleton_self g) with ⟨Y, f, i, hTi⟩ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRCases | Lean.Parser.Tactic.rcases |
Mathlib.CategoryTheory.Sites.Sieves | {
"line": 656,
"column": 4
} | {
"line": 658,
"column": 19
} | {
"line": 659,
"column": 2
} | [
{
"pp": "C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝ : Category.{v₂, u₂} D\nF : C ⥤ D\nX Y Z : C\nf✝ : Y ⟶ X\nS R x✝³ x✝² x✝¹ : Sieve X\nh₁ : ∀ ⦃Y : C⦄ (f : Y ⟶ X), x✝³.arrows f → x✝¹.arrows f\nh₂ : ∀ ⦃Y : C⦄ (f : Y ⟶ X), x✝².arrows f → x✝¹.arrows f\nx✝ : C\nf : x✝ ⟶ X\n⊢ (x✝³.union x✝²).arrow... | [] | rintro (hf | hf)
· exact h₁ _ hf
· exact h₂ _ hf | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Sites.Sieves | {
"line": 656,
"column": 4
} | {
"line": 658,
"column": 19
} | {
"line": 659,
"column": 2
} | [
{
"pp": "C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝ : Category.{v₂, u₂} D\nF : C ⥤ D\nX Y Z : C\nf✝ : Y ⟶ X\nS R x✝³ x✝² x✝¹ : Sieve X\nh₁ : ∀ ⦃Y : C⦄ (f : Y ⟶ X), x✝³.arrows f → x✝¹.arrows f\nh₂ : ∀ ⦃Y : C⦄ (f : Y ⟶ X), x✝².arrows f → x✝¹.arrows f\nx✝ : C\nf : x✝ ⟶ X\n⊢ (x✝³.union x✝²).arrow... | [] | rintro (hf | hf)
· exact h₁ _ hf
· exact h₂ _ hf | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Sites.Sieves | {
"line": 796,
"column": 2
} | {
"line": 798,
"column": 6
} | {
"line": 800,
"column": 0
} | [
{
"pp": "C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nX Y Z : C\ni : X ⟶ Y\nf : Y ⟶ Z\ninst✝ : IsIso i\nS : Sieve Z\n⊢ S.arrows (i ≫ f) ↔ S.arrows f",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"cong... | [] | refine ⟨fun H ↦ ?_, fun H ↦ S.downward_closed H _⟩
convert! S.downward_closed H (inv i)
simp | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Sites.Sieves | {
"line": 796,
"column": 2
} | {
"line": 798,
"column": 6
} | {
"line": 800,
"column": 0
} | [
{
"pp": "C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nX Y Z : C\ni : X ⟶ Y\nf : Y ⟶ Z\ninst✝ : IsIso i\nS : Sieve Z\n⊢ S.arrows (i ≫ f) ↔ S.arrows f",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"cong... | [] | refine ⟨fun H ↦ ?_, fun H ↦ S.downward_closed H _⟩
convert! S.downward_closed H (inv i)
simp | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Sites.Plus | {
"line": 156,
"column": 4
} | {
"line": 157,
"column": 39
} | {
"line": 158,
"column": 4
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\nJ : GrothendieckTopology C\nD : Type w\ninst✝² : Category.{w', w} D\ninst✝¹ : ∀ (P : Cᵒᵖ ⥤ D) (X : C) (S : J.Cover X), HasMultiequalizer (S.index P)\nP✝ : Cᵒᵖ ⥤ D\ninst✝ : ∀ (X : C), HasColimitsOfShape (J.Cover X)ᵒᵖ D\nP Q : Cᵒᵖ ⥤ D\nη : P ⟶ Q\nX Y : Cᵒᵖ\nf : X ⟶... | [
"C : Type u\ninst✝³ : Category.{v, u} C\nJ : GrothendieckTopology C\nD : Type w\ninst✝² : Category.{w', w} D\ninst✝¹ : ∀ (P : Cᵒᵖ ⥤ D) (X : C) (S : J.Cover X), HasMultiequalizer (S.index P)\nP✝ : Cᵒᵖ ⥤ D\ninst✝ : ∀ (X : C), HasColimitsOfShape (J.Cover X)ᵒᵖ D\nP Q : Cᵒᵖ ⥤ D\nη : P ⟶ Q\nX Y : Cᵒᵖ\nf : X ⟶ Y\nj✝ : (J.... | simp only [diagramPullback_app, ι_colimMap, colimit.ι_pre_assoc, colimit.ι_pre,
ι_colimMap_assoc, Category.assoc] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.CategoryTheory.Sites.Sheaf | {
"line": 679,
"column": 8
} | {
"line": 679,
"column": 42
} | {
"line": 679,
"column": 42
} | [
{
"pp": "case mp\nC : Type u₁\ninst✝³ : Category.{v₁, u₁} C\nA' : Type u₂\ninst✝² : Category.{max v₁ u₁, u₂} A'\nJ : GrothendieckTopology C\nP' : Cᵒᵖ ⥤ A'\ninst✝¹ : HasProducts A'\ninst✝ : HasPullbacks C\nh : IsSheaf J P'\nU : C\nR : Presieve U\nhR : generate R ∈ J U\nX : A'ᵒᵖ\nq : Presieve.IsSheafFor (P' ⋙ coy... | [
"case mp\nC : Type u₁\ninst✝³ : Category.{v₁, u₁} C\nA' : Type u₂\ninst✝² : Category.{max v₁ u₁, u₂} A'\nJ : GrothendieckTopology C\nP' : Cᵒᵖ ⥤ A'\ninst✝¹ : HasProducts A'\ninst✝ : HasPullbacks C\nh : IsSheaf J P'\nU : C\nR : Presieve U\nhR : generate R ∈ J U\nX : A'ᵒᵖ\nq : Presieve.IsSheafFor (P' ⋙ coyoneda.obj X)... | ← Presieve.isSheafFor_iff_generate | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.CategoryTheory.Subfunctor.Image | {
"line": 43,
"column": 39
} | {
"line": 43,
"column": 44
} | {
"line": 45,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF : C ⥤ Type w\n⊢ range (𝟙 F) = ⊤",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Set.ext",
"CategoryTheory.Functor",
"Lattice.toSemilatticeSup",
"CompleteLattice.toLattice",
"congrArg",
"CategoryTheory.C... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.Subfunctor.Image | {
"line": 43,
"column": 39
} | {
"line": 43,
"column": 44
} | {
"line": 45,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF : C ⥤ Type w\n⊢ range (𝟙 F) = ⊤",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Set.ext",
"CategoryTheory.Functor",
"Lattice.toSemilatticeSup",
"CompleteLattice.toLattice",
"congrArg",
"CategoryTheory.C... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Subfunctor.Image | {
"line": 43,
"column": 39
} | {
"line": 43,
"column": 44
} | {
"line": 45,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF : C ⥤ Type w\n⊢ range (𝟙 F) = ⊤",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Set.ext",
"CategoryTheory.Functor",
"Lattice.toSemilatticeSup",
"CompleteLattice.toLattice",
"congrArg",
"CategoryTheory.C... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Subfunctor.Image | {
"line": 47,
"column": 55
} | {
"line": 47,
"column": 60
} | {
"line": 49,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF : C ⥤ Type w\nG : Subfunctor F\n⊢ range G.ι = G",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"congrArg",
"CategoryTheory.Subfunctor.ext",
"TypeCat.instFunLikeFun",
"TypeCat.Fun.mk"... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.Subfunctor.Image | {
"line": 47,
"column": 55
} | {
"line": 47,
"column": 60
} | {
"line": 49,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF : C ⥤ Type w\nG : Subfunctor F\n⊢ range G.ι = G",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"congrArg",
"CategoryTheory.Subfunctor.ext",
"TypeCat.instFunLikeFun",
"TypeCat.Fun.mk"... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Subfunctor.Image | {
"line": 47,
"column": 55
} | {
"line": 47,
"column": 60
} | {
"line": 49,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF : C ⥤ Type w\nG : Subfunctor F\n⊢ range G.ι = G",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"congrArg",
"CategoryTheory.Subfunctor.ext",
"TypeCat.instFunLikeFun",
"TypeCat.Fun.mk"... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Subfunctor.Image | {
"line": 115,
"column": 4
} | {
"line": 115,
"column": 29
} | {
"line": 116,
"column": 4
} | [
{
"pp": "case right\nC : Type u\ninst✝¹ : Category.{v, u} C\nF F' F'' : C ⥤ Type w\np : F' ⟶ F\ninst✝ : Mono p\nthis : Mono (toRange p)\ni : C\n⊢ Function.Surjective ⇑(ConcreteCategory.hom ((toRange p).app i))",
"ppTerm": "?right",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Category... | [
"case right\nC : Type u\ninst✝¹ : Category.{v, u} C\nF F' F'' : C ⥤ Type w\np : F' ⟶ F\ninst✝ : Mono p\nthis : Mono (toRange p)\ni : C\n⊢ Epi ((toRange p).app i)"
] | rw [← epi_iff_surjective] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.CategoryTheory.Subfunctor.Image | {
"line": 119,
"column": 46
} | {
"line": 119,
"column": 51
} | {
"line": 121,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF F' F'' : C ⥤ Type w\nf : F ⟶ F'\ng : F' ⟶ F''\nx✝² : C\nx✝¹ : F''.obj x✝²\nx✝ : x✝¹ ∈ (range (f ≫ g)).obj x✝²\n⊢ x✝¹ ∈ (range g).obj x✝²",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"CategoryTheory.Functor",
"... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.Subfunctor.Image | {
"line": 119,
"column": 46
} | {
"line": 119,
"column": 51
} | {
"line": 121,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF F' F'' : C ⥤ Type w\nf : F ⟶ F'\ng : F' ⟶ F''\nx✝² : C\nx✝¹ : F''.obj x✝²\nx✝ : x✝¹ ∈ (range (f ≫ g)).obj x✝²\n⊢ x✝¹ ∈ (range g).obj x✝²",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"CategoryTheory.Functor",
"... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Subfunctor.Image | {
"line": 119,
"column": 46
} | {
"line": 119,
"column": 51
} | {
"line": 121,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF F' F'' : C ⥤ Type w\nf : F ⟶ F'\ng : F' ⟶ F''\nx✝² : C\nx✝¹ : F''.obj x✝²\nx✝ : x✝¹ ∈ (range (f ≫ g)).obj x✝²\n⊢ x✝¹ ∈ (range g).obj x✝²",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"CategoryTheory.Functor",
"... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Subfunctor.Image | {
"line": 135,
"column": 61
} | {
"line": 135,
"column": 66
} | {
"line": 137,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF F' : C ⥤ Type w\nf : F ⟶ F'\n⊢ ⊤.image f = range f",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"Set.ext",
"Set.image_univ",
"CategoryTheory.Subfunctor.image",
"Lattice.toSemilatticeSup",
"CompleteLattice.to... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.Subfunctor.Image | {
"line": 135,
"column": 61
} | {
"line": 135,
"column": 66
} | {
"line": 137,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF F' : C ⥤ Type w\nf : F ⟶ F'\n⊢ ⊤.image f = range f",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"Set.ext",
"Set.image_univ",
"CategoryTheory.Subfunctor.image",
"Lattice.toSemilatticeSup",
"CompleteLattice.to... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Subfunctor.Image | {
"line": 135,
"column": 61
} | {
"line": 135,
"column": 66
} | {
"line": 137,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF F' : C ⥤ Type w\nf : F ⟶ F'\n⊢ ⊤.image f = range f",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"Set.ext",
"Set.image_univ",
"CategoryTheory.Subfunctor.image",
"Lattice.toSemilatticeSup",
"CompleteLattice.to... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Subfunctor.Image | {
"line": 139,
"column": 50
} | {
"line": 139,
"column": 55
} | {
"line": 141,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF F' : C ⥤ Type w\nι : Type u_1\nG : ι → Subfunctor F\nf : F ⟶ F'\n⊢ (⨆ i, G i).image f = ⨆ i, (G i).image f",
"ppTerm": "?m.33",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"CategoryTheory.Subfunctor.image",
"cong... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.Subfunctor.Image | {
"line": 139,
"column": 50
} | {
"line": 139,
"column": 55
} | {
"line": 141,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF F' : C ⥤ Type w\nι : Type u_1\nG : ι → Subfunctor F\nf : F ⟶ F'\n⊢ (⨆ i, G i).image f = ⨆ i, (G i).image f",
"ppTerm": "?m.33",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"CategoryTheory.Subfunctor.image",
"cong... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Subfunctor.Image | {
"line": 139,
"column": 50
} | {
"line": 139,
"column": 55
} | {
"line": 141,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF F' : C ⥤ Type w\nι : Type u_1\nG : ι → Subfunctor F\nf : F ⟶ F'\n⊢ (⨆ i, G i).image f = ⨆ i, (G i).image f",
"ppTerm": "?m.33",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"CategoryTheory.Subfunctor.image",
"cong... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Subfunctor.Image | {
"line": 142,
"column": 48
} | {
"line": 142,
"column": 53
} | {
"line": 144,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF F' F'' : C ⥤ Type w\nG : Subfunctor F\nf : F ⟶ F'\ng : F' ⟶ F''\n⊢ G.image (f ≫ g) = (G.image f).image g",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"Set.ext",
"CategoryTheory.Subfunctor.image",
"CategoryTheory.Functor... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.Subfunctor.Image | {
"line": 142,
"column": 48
} | {
"line": 142,
"column": 53
} | {
"line": 144,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF F' F'' : C ⥤ Type w\nG : Subfunctor F\nf : F ⟶ F'\ng : F' ⟶ F''\n⊢ G.image (f ≫ g) = (G.image f).image g",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"Set.ext",
"CategoryTheory.Subfunctor.image",
"CategoryTheory.Functor... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Subfunctor.Image | {
"line": 142,
"column": 48
} | {
"line": 142,
"column": 53
} | {
"line": 144,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF F' F'' : C ⥤ Type w\nG : Subfunctor F\nf : F ⟶ F'\ng : F' ⟶ F''\n⊢ G.image (f ≫ g) = (G.image f).image g",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"Set.ext",
"CategoryTheory.Subfunctor.image",
"CategoryTheory.Functor... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Subfunctor.Image | {
"line": 145,
"column": 44
} | {
"line": 145,
"column": 49
} | {
"line": 147,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF F' F'' : C ⥤ Type w\nf : F ⟶ F'\ng : F' ⟶ F''\n⊢ range (f ≫ g) = (range f).image g",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"Set.ext",
"CategoryTheory.Subfunctor.image",
"CategoryTheory.Functor",
"congrArg",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.Subfunctor.Image | {
"line": 145,
"column": 44
} | {
"line": 145,
"column": 49
} | {
"line": 147,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF F' F'' : C ⥤ Type w\nf : F ⟶ F'\ng : F' ⟶ F''\n⊢ range (f ≫ g) = (range f).image g",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"Set.ext",
"CategoryTheory.Subfunctor.image",
"CategoryTheory.Functor",
"congrArg",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Subfunctor.Image | {
"line": 145,
"column": 44
} | {
"line": 145,
"column": 49
} | {
"line": 147,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF F' F'' : C ⥤ Type w\nf : F ⟶ F'\ng : F' ⟶ F''\n⊢ range (f ≫ g) = (range f).image g",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"Set.ext",
"CategoryTheory.Subfunctor.image",
"CategoryTheory.Functor",
"congrArg",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Subfunctor.Image | {
"line": 161,
"column": 31
} | {
"line": 161,
"column": 36
} | {
"line": 163,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF : C ⥤ Type w\nG : Subfunctor F\n⊢ G.preimage (𝟙 F) = G",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"CategoryTheory.Functor",
"CategoryTheory.Functor.category",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.Subfunctor.Image | {
"line": 161,
"column": 31
} | {
"line": 161,
"column": 36
} | {
"line": 163,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF : C ⥤ Type w\nG : Subfunctor F\n⊢ G.preimage (𝟙 F) = G",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"CategoryTheory.Functor",
"CategoryTheory.Functor.category",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Subfunctor.Image | {
"line": 161,
"column": 31
} | {
"line": 161,
"column": 36
} | {
"line": 163,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF : C ⥤ Type w\nG : Subfunctor F\n⊢ G.preimage (𝟙 F) = G",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"CategoryTheory.Functor",
"CategoryTheory.Functor.category",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Subfunctor.Image | {
"line": 164,
"column": 57
} | {
"line": 164,
"column": 62
} | {
"line": 166,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF F' F'' : C ⥤ Type w\nG : Subfunctor F\nf : F'' ⟶ F'\ng : F' ⟶ F\n⊢ G.preimage (f ≫ g) = (G.preimage g).preimage f",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"CategoryTheory.Functor",
"CategoryTheory.Functor.category",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.Subfunctor.Image | {
"line": 164,
"column": 57
} | {
"line": 164,
"column": 62
} | {
"line": 166,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF F' F'' : C ⥤ Type w\nG : Subfunctor F\nf : F'' ⟶ F'\ng : F' ⟶ F\n⊢ G.preimage (f ≫ g) = (G.preimage g).preimage f",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"CategoryTheory.Functor",
"CategoryTheory.Functor.category",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Subfunctor.Image | {
"line": 164,
"column": 57
} | {
"line": 164,
"column": 62
} | {
"line": 166,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF F' F'' : C ⥤ Type w\nG : Subfunctor F\nf : F'' ⟶ F'\ng : F' ⟶ F\n⊢ G.preimage (f ≫ g) = (G.preimage g).preimage f",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"CategoryTheory.Functor",
"CategoryTheory.Functor.category",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Sites.IsSheafFor | {
"line": 979,
"column": 2
} | {
"line": 979,
"column": 7
} | {
"line": 981,
"column": 0
} | [
{
"pp": "C : Type u₁\ninst✝ : Category.{v₁, u₁} C\nP : Cᵒᵖ ⥤ Type w\nX Y : C\nf : X ⟶ Y\n⊢ (∀ (b : P.obj (op X)) (t₁ t₂ : P.obj (op Y)),\n (ConcreteCategory.hom (P.map f.op)) t₁ = b → (ConcreteCategory.hom (P.map f.op)) t₂ = b → t₁ = t₂) ↔\n ∀ ⦃a₁ a₂ : P.obj (op Y)⦄, (ConcreteCategory.hom (P.map f.op)) ... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
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