module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Analysis.SumIntegralComparisons | {
"line": 69,
"column": 18
} | {
"line": 69,
"column": 29
} | {
"line": 69,
"column": 30
} | [
{
"pp": "a b : ℕ\nf g : ℝ → ℝ\nhab : a ≤ b\nh : ∀ i ∈ Ico a b, ∀ x ∈ Ico ↑i ↑(i + 1), f ↑i ≤ g x\nhg : IntegrableOn g (Ico ↑a ↑b) volume\nA : ∀ i ∈ Finset.Ico a b, IntervalIntegrable g volume ↑i ↑(i + 1)\ni : ℕ\nhi : i ∈ Finset.Ico a b\nx : ℝ\nhx : x ∈ Ioo ↑i ↑(i + 1)\n⊢ i ∈ Ico a b",
"ppTerm": "?m.200",
... | [
"a b : ℕ\nf g : ℝ → ℝ\nhab : a ≤ b\nh : ∀ i ∈ Ico a b, ∀ x ∈ Ico ↑i ↑(i + 1), f ↑i ≤ g x\nhg : IntegrableOn g (Ico ↑a ↑b) volume\nA : ∀ i ∈ Finset.Ico a b, IntervalIntegrable g volume ↑i ↑(i + 1)\ni : ℕ\nhi : i ∈ Finset.Ico a b\nx : ℝ\nhx : x ∈ Ioo ↑i ↑(i + 1)\n⊢ a ≤ i ∧ i < b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecificLimits.FloorPow | {
"line": 63,
"column": 10
} | {
"line": 63,
"column": 21
} | {
"line": 63,
"column": 22
} | [
{
"pp": "case hbc\nu : ℕ → ℝ\nl : ℝ\nhmono : Monotone u\nhlim :\n ∀ (a : ℝ),\n 1 < a →\n ∃ c,\n (∀ᶠ (n : ℕ) in atTop, ↑(c (n + 1)) ≤ a * ↑(c n)) ∧\n Tendsto c atTop atTop ∧ Tendsto (fun n ↦ u (c n) / ↑(c n)) atTop (𝓝 l)\nlnonneg : 0 ≤ l\nε : ℝ\nεpos : 0 < ε\nc : ℕ → ℕ\ncgrowth : ∀ᶠ (n ... | [
"case hbc\nu : ℕ → ℝ\nl : ℝ\nhmono : Monotone u\nhlim :\n ∀ (a : ℝ),\n 1 < a →\n ∃ c,\n (∀ᶠ (n : ℕ) in atTop, ↑(c (n + 1)) ≤ a * ↑(c n)) ∧\n Tendsto c atTop atTop ∧ Tendsto (fun n ↦ u (c n) / ↑(c n)) atTop (𝓝 l)\nlnonneg : 0 ≤ l\nε : ℝ\nεpos : 0 < ε\nc : ℕ → ℕ\ncgrowth : ∀ᶠ (n : ℕ) in atTo... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecificLimits.FloorPow | {
"line": 64,
"column": 4
} | {
"line": 66,
"column": 40
} | {
"line": 67,
"column": 4
} | [
{
"pp": "u : ℕ → ℝ\nl : ℝ\nhmono : Monotone u\nhlim :\n ∀ (a : ℝ),\n 1 < a →\n ∃ c,\n (∀ᶠ (n : ℕ) in atTop, ↑(c (n + 1)) ≤ a * ↑(c n)) ∧\n Tendsto c atTop atTop ∧ Tendsto (fun n ↦ u (c n) / ↑(c n)) atTop (𝓝 l)\nlnonneg : 0 ≤ l\nε : ℝ\nεpos : 0 < ε\nc : ℕ → ℕ\ncgrowth : ∀ᶠ (n : ℕ) in at... | [
"u : ℕ → ℝ\nl : ℝ\nhmono : Monotone u\nhlim :\n ∀ (a : ℝ),\n 1 < a →\n ∃ c,\n (∀ᶠ (n : ℕ) in atTop, ↑(c (n + 1)) ≤ a * ↑(c n)) ∧\n Tendsto c atTop atTop ∧ Tendsto (fun n ↦ u (c n) / ↑(c n)) atTop (𝓝 l)\nlnonneg : 0 ≤ l\nε : ℝ\nεpos : 0 < ε\nc : ℕ → ℕ\ncgrowth : ∀ᶠ (n : ℕ) in atTop, ↑(c (n ... | obtain ⟨a, ha⟩ :
∃ a : ℕ, ∀ b : ℕ, a ≤ b → (c (b + 1) : ℝ) ≤ (1 + ε) * c b ∧ u (c b) - c b * l ≤ ε * c b :=
eventually_atTop.1 (cgrowth.and L) | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.Analysis.SumIntegralComparisons | {
"line": 100,
"column": 28
} | {
"line": 100,
"column": 49
} | {
"line": 100,
"column": 49
} | [
{
"pp": "a b : ℕ\nf : ℝ → ℝ\nhab : a ≤ b\nhf : AntitoneOn f (Icc ↑a ↑b)\n⊢ ∫ (x : ℝ) in ↑a..↑a + ↑(b - a), f x ≤ ∑ x ∈ Finset.Ico 0 (b - a), f ↑(a + x)",
"ppTerm": "?m.81",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"Real.instLE",
"Real"... | [
"a b : ℕ\nf : ℝ → ℝ\nhab : a ≤ b\nhf : AntitoneOn f (Icc ↑a ↑b)\n⊢ ∫ (x : ℝ) in ↑a..↑a + ↑(b - a), f x ≤ ∑ x ∈ Finset.range (b - a), f ↑(a + x)"
] | Nat.Ico_zero_eq_range | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.SpecificLimits.FloorPow | {
"line": 84,
"column": 6
} | {
"line": 84,
"column": 31
} | {
"line": 84,
"column": 32
} | [
{
"pp": "u : ℕ → ℝ\nl : ℝ\nhmono : Monotone u\nhlim :\n ∀ (a : ℝ),\n 1 < a →\n ∃ c,\n (∀ᶠ (n : ℕ) in atTop, ↑(c (n + 1)) ≤ a * ↑(c n)) ∧\n Tendsto c atTop atTop ∧ Tendsto (fun n ↦ u (c n) / ↑(c n)) atTop (𝓝 l)\nlnonneg : 0 ≤ l\nε : ℝ\nεpos : 0 < ε\nc : ℕ → ℕ\ncgrowth : ∀ᶠ (n : ℕ) in at... | [
"u : ℕ → ℝ\nl : ℝ\nhmono : Monotone u\nhlim :\n ∀ (a : ℝ),\n 1 < a →\n ∃ c,\n (∀ᶠ (n : ℕ) in atTop, ↑(c (n + 1)) ≤ a * ↑(c n)) ∧\n Tendsto c atTop atTop ∧ Tendsto (fun n ↦ u (c n) / ↑(c n)) atTop (𝓝 l)\nlnonneg : 0 ≤ l\nε : ℝ\nεpos : 0 < ε\nc : ℕ → ℕ\ncgrowth : ∀ᶠ (n : ℕ) in atTop, ↑(c (n ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Generator.Preadditive | {
"line": 33,
"column": 33
} | {
"line": 33,
"column": 68
} | {
"line": 33,
"column": 69
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Preadditive C\nP : ObjectProperty C\nh𝒢 : P.IsSeparating\nX Y : C\nf : X ⟶ Y\nhf : ∀ (G : C), P G → ∀ (h : G ⟶ X), h ≫ f = 0\n⊢ ∀ (G : C), P G → ∀ (h : G ⟶ X), h ≫ f = h ≫ 0",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"Eq.... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Preadditive C\nP : ObjectProperty C\nh𝒢 : P.IsSeparating\nX Y : C\nf : X ⟶ Y\nhf : ∀ (G : C), P G → ∀ (h : G ⟶ X), h ≫ f = 0\n⊢ ∀ (G : C), P G → ∀ (h : G ⟶ X), h ≫ f = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Generator.Preadditive | {
"line": 34,
"column": 30
} | {
"line": 34,
"column": 82
} | {
"line": 34,
"column": 83
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Preadditive C\nP : ObjectProperty C\nh𝒢 : ∀ ⦃X Y : C⦄ (f : X ⟶ Y), (∀ (G : C), P G → ∀ (h : G ⟶ X), h ≫ f = 0) → f = 0\nX Y : C\nf g : X ⟶ Y\nhfg : ∀ (G : C), P G → ∀ (h : G ⟶ X), h ≫ f = h ≫ g\n⊢ ∀ (G : C), P G → ∀ (h : G ⟶ X), h ≫ (f - g) = 0",
"pp... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Preadditive C\nP : ObjectProperty C\nh𝒢 : ∀ ⦃X Y : C⦄ (f : X ⟶ Y), (∀ (G : C), P G → ∀ (h : G ⟶ X), h ≫ f = 0) → f = 0\nX Y : C\nf g : X ⟶ Y\nhfg : ∀ (G : C), P G → ∀ (h : G ⟶ X), h ≫ f = h ≫ g\n⊢ ∀ (G : C), P G → ∀ (h : G ⟶ X), h ≫ f = h ≫ g"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Generator.Preadditive | {
"line": 39,
"column": 33
} | {
"line": 39,
"column": 68
} | {
"line": 39,
"column": 69
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Preadditive C\nP : ObjectProperty C\nh𝒢 : P.IsCoseparating\nX Y : C\nf : X ⟶ Y\nhf : ∀ (G : C), P G → ∀ (h : Y ⟶ G), f ≫ h = 0\n⊢ ∀ (G : C), P G → ∀ (h : Y ⟶ G), f ≫ h = 0 ≫ h",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"E... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Preadditive C\nP : ObjectProperty C\nh𝒢 : P.IsCoseparating\nX Y : C\nf : X ⟶ Y\nhf : ∀ (G : C), P G → ∀ (h : Y ⟶ G), f ≫ h = 0\n⊢ ∀ (G : C), P G → ∀ (h : Y ⟶ G), f ≫ h = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Generator.Preadditive | {
"line": 40,
"column": 30
} | {
"line": 40,
"column": 82
} | {
"line": 40,
"column": 83
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Preadditive C\nP : ObjectProperty C\nh𝒢 : ∀ ⦃X Y : C⦄ (f : X ⟶ Y), (∀ (G : C), P G → ∀ (h : Y ⟶ G), f ≫ h = 0) → f = 0\nX Y : C\nf g : X ⟶ Y\nhfg : ∀ (G : C), P G → ∀ (h : Y ⟶ G), f ≫ h = g ≫ h\n⊢ ∀ (G : C), P G → ∀ (h : Y ⟶ G), (f - g) ≫ h = 0",
"pp... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Preadditive C\nP : ObjectProperty C\nh𝒢 : ∀ ⦃X Y : C⦄ (f : X ⟶ Y), (∀ (G : C), P G → ∀ (h : Y ⟶ G), f ≫ h = 0) → f = 0\nX Y : C\nf g : X ⟶ Y\nhfg : ∀ (G : C), P G → ∀ (h : Y ⟶ G), f ≫ h = g ≫ h\n⊢ ∀ (G : C), P G → ∀ (h : Y ⟶ G), f ≫ h = g ≫ h"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Generator.Preadditive | {
"line": 44,
"column": 37
} | {
"line": 44,
"column": 72
} | {
"line": 44,
"column": 73
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Preadditive C\nG : C\nhG : IsSeparator G\nX Y : C\nf : X ⟶ Y\nhf : ∀ (h : G ⟶ X), h ≫ f = 0\n⊢ ∀ (h : G ⟶ X), h ≫ f = h ≫ 0",
"ppTerm": "?m.33",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"CategoryTheory.CategoryStruct.toQuiver... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Preadditive C\nG : C\nhG : IsSeparator G\nX Y : C\nf : X ⟶ Y\nhf : ∀ (h : G ⟶ X), h ≫ f = 0\n⊢ ∀ (h : G ⟶ X), h ≫ f = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Generator.Preadditive | {
"line": 46,
"column": 32
} | {
"line": 46,
"column": 84
} | {
"line": 46,
"column": 85
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Preadditive C\nG : C\nhG : ∀ ⦃X Y : C⦄ (f : X ⟶ Y), (∀ (h : G ⟶ X), h ≫ f = 0) → f = 0\nX Y : C\nf g : X ⟶ Y\nhfg : ∀ (h : G ⟶ X), h ≫ f = h ≫ g\n⊢ ∀ (h : G ⟶ X), h ≫ (f - g) = 0",
"ppTerm": "?m.55",
"assigned": true,
"usedConstants": [
... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Preadditive C\nG : C\nhG : ∀ ⦃X Y : C⦄ (f : X ⟶ Y), (∀ (h : G ⟶ X), h ≫ f = 0) → f = 0\nX Y : C\nf g : X ⟶ Y\nhfg : ∀ (h : G ⟶ X), h ≫ f = h ≫ g\n⊢ ∀ (h : G ⟶ X), h ≫ f = h ≫ g"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Generator.Preadditive | {
"line": 50,
"column": 37
} | {
"line": 50,
"column": 72
} | {
"line": 50,
"column": 73
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Preadditive C\nG : C\nhG : IsCoseparator G\nX Y : C\nf : X ⟶ Y\nhf : ∀ (h : Y ⟶ G), f ≫ h = 0\n⊢ ∀ (h : Y ⟶ G), f ≫ h = 0 ≫ h",
"ppTerm": "?m.33",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"CategoryTheory.CategoryStruct.toQuiv... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Preadditive C\nG : C\nhG : IsCoseparator G\nX Y : C\nf : X ⟶ Y\nhf : ∀ (h : Y ⟶ G), f ≫ h = 0\n⊢ ∀ (h : Y ⟶ G), f ≫ h = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Generator.Preadditive | {
"line": 52,
"column": 32
} | {
"line": 52,
"column": 84
} | {
"line": 52,
"column": 85
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Preadditive C\nG : C\nhG : ∀ ⦃X Y : C⦄ (f : X ⟶ Y), (∀ (h : Y ⟶ G), f ≫ h = 0) → f = 0\nX Y : C\nf g : X ⟶ Y\nhfg : ∀ (h : Y ⟶ G), f ≫ h = g ≫ h\n⊢ ∀ (h : Y ⟶ G), (f - g) ≫ h = 0",
"ppTerm": "?m.55",
"assigned": true,
"usedConstants": [
... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Preadditive C\nG : C\nhG : ∀ ⦃X Y : C⦄ (f : X ⟶ Y), (∀ (h : Y ⟶ G), f ≫ h = 0) → f = 0\nX Y : C\nf g : X ⟶ Y\nhfg : ∀ (h : Y ⟶ G), f ≫ h = g ≫ h\n⊢ ∀ (h : Y ⟶ G), f ≫ h = g ≫ h"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecificLimits.FloorPow | {
"line": 113,
"column": 10
} | {
"line": 113,
"column": 21
} | {
"line": 113,
"column": 22
} | [
{
"pp": "case hbc\nu : ℕ → ℝ\nl : ℝ\nhmono : Monotone u\nhlim :\n ∀ (a : ℝ),\n 1 < a →\n ∃ c,\n (∀ᶠ (n : ℕ) in atTop, ↑(c (n + 1)) ≤ a * ↑(c n)) ∧\n Tendsto c atTop atTop ∧ Tendsto (fun n ↦ u (c n) / ↑(c n)) atTop (𝓝 l)\nlnonneg : 0 ≤ l\nA : ∀ (ε : ℝ), 0 < ε → ∀ᶠ (n : ℕ) in atTop, u n ... | [
"case hbc\nu : ℕ → ℝ\nl : ℝ\nhmono : Monotone u\nhlim :\n ∀ (a : ℝ),\n 1 < a →\n ∃ c,\n (∀ᶠ (n : ℕ) in atTop, ↑(c (n + 1)) ≤ a * ↑(c n)) ∧\n Tendsto c atTop atTop ∧ Tendsto (fun n ↦ u (c n) / ↑(c n)) atTop (𝓝 l)\nlnonneg : 0 ≤ l\nA : ∀ (ε : ℝ), 0 < ε → ∀ᶠ (n : ℕ) in atTop, u n - ↑n * l ≤ ε... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecificLimits.FloorPow | {
"line": 136,
"column": 6
} | {
"line": 136,
"column": 31
} | {
"line": 136,
"column": 32
} | [
{
"pp": "u : ℕ → ℝ\nl : ℝ\nhmono : Monotone u\nhlim :\n ∀ (a : ℝ),\n 1 < a →\n ∃ c,\n (∀ᶠ (n : ℕ) in atTop, ↑(c (n + 1)) ≤ a * ↑(c n)) ∧\n Tendsto c atTop atTop ∧ Tendsto (fun n ↦ u (c n) / ↑(c n)) atTop (𝓝 l)\nlnonneg : 0 ≤ l\nA : ∀ (ε : ℝ), 0 < ε → ∀ᶠ (n : ℕ) in atTop, u n - ↑n * l ≤... | [
"u : ℕ → ℝ\nl : ℝ\nhmono : Monotone u\nhlim :\n ∀ (a : ℝ),\n 1 < a →\n ∃ c,\n (∀ᶠ (n : ℕ) in atTop, ↑(c (n + 1)) ≤ a * ↑(c n)) ∧\n Tendsto c atTop atTop ∧ Tendsto (fun n ↦ u (c n) / ↑(c n)) atTop (𝓝 l)\nlnonneg : 0 ≤ l\nA : ∀ (ε : ℝ), 0 < ε → ∀ᶠ (n : ℕ) in atTop, u n - ↑n * l ≤ ε * (1 + ε ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecificLimits.FloorPow | {
"line": 144,
"column": 8
} | {
"line": 144,
"column": 23
} | {
"line": 144,
"column": 24
} | [
{
"pp": "case hbc\nu : ℕ → ℝ\nl : ℝ\nhmono : Monotone u\nhlim :\n ∀ (a : ℝ),\n 1 < a →\n ∃ c,\n (∀ᶠ (n : ℕ) in atTop, ↑(c (n + 1)) ≤ a * ↑(c n)) ∧\n Tendsto c atTop atTop ∧ Tendsto (fun n ↦ u (c n) / ↑(c n)) atTop (𝓝 l)\nlnonneg : 0 ≤ l\nA : ∀ (ε : ℝ), 0 < ε → ∀ᶠ (n : ℕ) in atTop, u n ... | [
"case hbc\nu : ℕ → ℝ\nl : ℝ\nhmono : Monotone u\nhlim :\n ∀ (a : ℝ),\n 1 < a →\n ∃ c,\n (∀ᶠ (n : ℕ) in atTop, ↑(c (n + 1)) ≤ a * ↑(c n)) ∧\n Tendsto c atTop atTop ∧ Tendsto (fun n ↦ u (c n) / ↑(c n)) atTop (𝓝 l)\nlnonneg : 0 ≤ l\nA : ∀ (ε : ℝ), 0 < ε → ∀ᶠ (n : ℕ) in atTop, u n - ↑n * l ≤ ε... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SumIntegralComparisons | {
"line": 190,
"column": 4
} | {
"line": 190,
"column": 50
} | {
"line": 190,
"column": 51
} | [
{
"pp": "case pos\nf : ℝ → ℝ\na b : ℕ\nanti : AntitoneOn f (Icc ↑a ↑b)\nintegrable : IntegrableOn f (Ioi ↑a) volume\nnonneg : ∀ t ∈ Ioi ↑a, 0 ≤ f t\nhab : b < a\n⊢ ∑ n ∈ Finset.Ico a b, f ↑(n + 1) ≤ ∫ (x : ℝ) in Ioi ↑a, f x",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
... | [
"case pos\nf : ℝ → ℝ\na b : ℕ\nanti : AntitoneOn f (Icc ↑a ↑b)\nintegrable : IntegrableOn f (Ioi ↑a) volume\nnonneg : ∀ t ∈ Ioi ↑a, 0 ≤ f t\nhab : b < a\n⊢ 0 ≤ ∫ (x : ℝ) in Ioi ↑a, f x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecificLimits.FloorPow | {
"line": 225,
"column": 4
} | {
"line": 225,
"column": 15
} | {
"line": 225,
"column": 16
} | [
{
"pp": "N : ℕ\nj : ℝ\nhj : 0 < j\nc : ℝ\nhc : 1 < c\ncpos : 0 < c\nA : 0 < c⁻¹ ^ 2\nthis : c ^ 3 = c ^ 2 * c\n⊢ c ≤ c ^ 2",
"ppTerm": "?m.335",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real.partialOrder",
"Real",
"PartialOrder.toPreorder",
"Preorder.toLE",
... | [
"N : ℕ\nj : ℝ\nhj : 0 < j\nc : ℝ\nhc : 1 < c\ncpos : 0 < c\nA : 0 < c⁻¹ ^ 2\nthis : c ^ 3 = c ^ 2 * c\n⊢ c ≤ c ^ 2"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecificLimits.FloorPow | {
"line": 266,
"column": 6
} | {
"line": 266,
"column": 67
} | {
"line": 266,
"column": 68
} | [
{
"pp": "case h\nc : ℝ\nhc : 1 < c\ni : ℕ\ncpos : 0 < c\nhi : i ≠ 0\n⊢ 1 ≤ c ^ i * c⁻¹",
"ppTerm": "?h",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Real.partialOrder",
"Real.instLE",
"Real",
"instHDiv",
"HMul.h... | [
"case h\nc : ℝ\nhc : 1 < c\ni : ℕ\ncpos : 0 < c\nhi : i ≠ 0\n⊢ c ≤ c ^ i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecificLimits.FloorPow | {
"line": 281,
"column": 6
} | {
"line": 290,
"column": 41
} | {
"line": 291,
"column": 4
} | [
{
"pp": "N : ℕ\nj : ℝ\nhj : 0 < j\nc : ℝ\nhc : 1 < c\ncpos : 0 < c\nA : 0 < 1 - c⁻¹\n⊢ ∑ i ∈ range N with j < c ^ i, 1 / ↑⌊c ^ i⌋₊ ^ 2 ≤ ∑ i ∈ range N with j < c ^ i, (1 - c⁻¹)⁻¹ ^ 2 * (1 / (c ^ i) ^ 2)",
"ppTerm": "?m.317",
"assigned": true,
"usedConstants": [
"NonUnitalNonAssocCommRing.toNon... | [] | gcongr with i
rw [mul_div_assoc', mul_one, div_le_div_iff₀]; rotate_left
· apply sq_pos_of_pos
refine zero_lt_one.trans_le ?_
simp only [Nat.le_floor, one_le_pow₀, hc.le, Nat.one_le_cast, Nat.cast_one]
· exact sq_pos_of_pos (pow_pos cpos _)
rw [one_mul, ← mul_pow]
gcongr
... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.SpecificLimits.FloorPow | {
"line": 281,
"column": 6
} | {
"line": 290,
"column": 41
} | {
"line": 291,
"column": 4
} | [
{
"pp": "N : ℕ\nj : ℝ\nhj : 0 < j\nc : ℝ\nhc : 1 < c\ncpos : 0 < c\nA : 0 < 1 - c⁻¹\n⊢ ∑ i ∈ range N with j < c ^ i, 1 / ↑⌊c ^ i⌋₊ ^ 2 ≤ ∑ i ∈ range N with j < c ^ i, (1 - c⁻¹)⁻¹ ^ 2 * (1 / (c ^ i) ^ 2)",
"ppTerm": "?m.317",
"assigned": true,
"usedConstants": [
"NonUnitalNonAssocCommRing.toNon... | [] | gcongr with i
rw [mul_div_assoc', mul_one, div_le_div_iff₀]; rotate_left
· apply sq_pos_of_pos
refine zero_lt_one.trans_le ?_
simp only [Nat.le_floor, one_le_pow₀, hc.le, Nat.one_le_cast, Nat.cast_one]
· exact sq_pos_of_pos (pow_pos cpos _)
rw [one_mul, ← mul_pow]
gcongr
... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.SpecificLimits.FloorPow | {
"line": 276,
"column": 2
} | {
"line": 297,
"column": 11
} | {
"line": 298,
"column": 0
} | [
{
"pp": "N : ℕ\nj : ℝ\nhj : 0 < j\nc : ℝ\nhc : 1 < c\ncpos : 0 < c\nA : 0 < 1 - c⁻¹\n⊢ ∑ i ∈ range N with j < ↑⌊c ^ i⌋₊, 1 / ↑⌊c ^ i⌋₊ ^ 2 ≤ c ^ 5 * (c - 1)⁻¹ ^ 3 / j ^ 2",
"ppTerm": "?m.159",
"assigned": true,
"usedConstants": [
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"NonUnitalNonAss... | [] | calc
(∑ i ∈ range N with j < ⌊c ^ i⌋₊, (1 : ℝ) / (⌊c ^ i⌋₊ : ℝ) ^ 2) ≤
∑ i ∈ range N with j < c ^ i, (1 : ℝ) / (⌊c ^ i⌋₊ : ℝ) ^ 2 := by
gcongr with k hk; exact Nat.floor_le (by positivity)
_ ≤ ∑ i ∈ range N with j < c ^ i, (1 - c⁻¹)⁻¹ ^ 2 * ((1 : ℝ) / (c ^ i) ^ 2) := by
gcongr with i
r... | Lean.Elab.Tactic._aux_Mathlib_Tactic_Widget_Calc___elabRules_Lean_calcTactic_1 | Lean.calcTactic |
Mathlib.CategoryTheory.Comma.Final | {
"line": 71,
"column": 6
} | {
"line": 72,
"column": 82
} | {
"line": 74,
"column": 0
} | [
{
"pp": "case refine_2\nA : Type u₁\ninst✝⁵ : Category.{v₁, u₁} A\nB : Type u₂\ninst✝⁴ : Category.{v₂, u₂} B\nT : Type u₃\ninst✝³ : Category.{v₃, u₃} T\nL : A ⥤ T\nR : B ⥤ T\ninst✝² : IsCofiltered A\ninst✝¹ : IsCofiltered B\ninst✝ : ∀ (b : B), IsCofiltered (CostructuredArrow L (R.obj b))\nj₁ j₂ : Comma L R\nu v... | [] | exact ⟨⟨i₀, IsCofiltered.eq u.right v.right, L.map (β ≫ va₁) ≫ Q.hom⟩,
⟨β ≫ va₂, IsCofiltered.eqHom u.right v.right, by cat_disch⟩, by cat_disch⟩ | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.CategoryTheory.Limits.Indization.FilteredColimits | {
"line": 73,
"column": 2
} | {
"line": 73,
"column": 17
} | {
"line": 74,
"column": 2
} | [
{
"pp": "C : Type u\ninst✝⁵ : Category.{v, u} C\nI : Type v\ninst✝⁴ : SmallCategory I\nF : I ⥤ Cᵒᵖ ⥤ Type v\nJ : Type v\ninst✝³ : SmallCategory J\ninst✝² : FinCategory J\nG : J ⥤ CostructuredArrow yoneda (colimit F)\nK : Type v\ninst✝¹ : SmallCategory K\nH : K ⥤ Over (colimit F)\ninst✝ : IsFiltered K\nh : Nonem... | [
"C : Type u\ninst✝⁵ : Category.{v, u} C\nI : Type v\ninst✝⁴ : SmallCategory I\nF : I ⥤ Cᵒᵖ ⥤ Type v\nJ : Type v\ninst✝³ : SmallCategory J\ninst✝² : FinCategory J\nG : J ⥤ CostructuredArrow yoneda (colimit F)\nK : Type v\ninst✝¹ : SmallCategory K\nH : K ⥤ Over (colimit F)\ninst✝ : IsFiltered K\nt : limit ((G.op ⋙ (C... | obtain ⟨t⟩ := h | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.CategoryTheory.Comma.Final | {
"line": 161,
"column": 2
} | {
"line": 176,
"column": 16
} | {
"line": 176,
"column": 16
} | [
{
"pp": "A : Type u₁\ninst✝¹⁰ : Category.{v₁, u₁} A\nB : Type u₂\ninst✝⁹ : Category.{v₂, u₂} B\nT : Type u₃\ninst✝⁸ : Category.{v₃, u₃} T\nL : A ⥤ T\nR : B ⥤ T\nA' : Type u₄\ninst✝⁷ : Category.{v₄, u₄} A'\nB' : Type u₅\ninst✝⁶ : Category.{v₅, u₅} B'\nT' : Type u₆\ninst✝⁵ : Category.{v₆, u₆} T'\nL' : A' ⥤ T'\nR'... | [] | haveI := final_of_natIso iR
rw [isConnected_iff_of_equivalence (StructuredArrow.commaMapEquivalence iL.hom iR.inv _)]
have : StructuredArrow.map₂ u₂ iR.hom ≅ StructuredArrow.post j₂ G R' ⋙
StructuredArrow.map₂ (G := 𝟭 _) (F := 𝟭 _) (R' := R ⋙ H) u₂ iR.hom ⋙
StructuredArrow.pre _ R H :=
eqToIso (by... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Comma.Final | {
"line": 161,
"column": 2
} | {
"line": 176,
"column": 16
} | {
"line": 176,
"column": 16
} | [
{
"pp": "A : Type u₁\ninst✝¹⁰ : Category.{v₁, u₁} A\nB : Type u₂\ninst✝⁹ : Category.{v₂, u₂} B\nT : Type u₃\ninst✝⁸ : Category.{v₃, u₃} T\nL : A ⥤ T\nR : B ⥤ T\nA' : Type u₄\ninst✝⁷ : Category.{v₄, u₄} A'\nB' : Type u₅\ninst✝⁶ : Category.{v₅, u₅} B'\nT' : Type u₆\ninst✝⁵ : Category.{v₆, u₆} T'\nL' : A' ⥤ T'\nR'... | [] | haveI := final_of_natIso iR
rw [isConnected_iff_of_equivalence (StructuredArrow.commaMapEquivalence iL.hom iR.inv _)]
have : StructuredArrow.map₂ u₂ iR.hom ≅ StructuredArrow.post j₂ G R' ⋙
StructuredArrow.map₂ (G := 𝟭 _) (F := 𝟭 _) (R' := R ⋙ H) u₂ iR.hom ⋙
StructuredArrow.pre _ R H :=
eqToIso (by... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Comma.StructuredArrow.CommaMap | {
"line": 40,
"column": 10
} | {
"line": 43,
"column": 49
} | {
"line": 44,
"column": 8
} | [
{
"pp": "C : Type u₁\ninst✝⁶ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝⁵ : Category.{v₂, u₂} D\nT : Type u₃\ninst✝⁴ : Category.{v₃, u₃} T\nL : C ⥤ T\nR : D ⥤ T\nC' : Type u₄\ninst✝³ : Category.{v₄, u₄} C'\nD' : Type u₅\ninst✝² : Category.{v₅, u₅} D'\nT' : Type u₆\ninst✝¹ : Category.{v₆, u₆} T'\nL' : C' ⥤ T'\nR' ... | [
"C : Type u₁\ninst✝⁶ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝⁵ : Category.{v₂, u₂} D\nT : Type u₃\ninst✝⁴ : Category.{v₃, u₃} T\nL : C ⥤ T\nR : D ⥤ T\nC' : Type u₄\ninst✝³ : Category.{v₄, u₄} C'\nD' : Type u₅\ninst✝² : Category.{v₅, u₅} D'\nT' : Type u₆\ninst✝¹ : Category.{v₆, u₆} T'\nL' : C' ⥤ T'\nR' : D' ⥤ T'\nF... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Comma.StructuredArrow.CommaMap | {
"line": 57,
"column": 6
} | {
"line": 57,
"column": 17
} | {
"line": 57,
"column": 18
} | [
{
"pp": "C : Type u₁\ninst✝⁶ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝⁵ : Category.{v₂, u₂} D\nT : Type u₃\ninst✝⁴ : Category.{v₃, u₃} T\nL : C ⥤ T\nR : D ⥤ T\nC' : Type u₄\ninst✝³ : Category.{v₄, u₄} C'\nD' : Type u₅\ninst✝² : Category.{v₅, u₅} D'\nT' : Type u₆\ninst✝¹ : Category.{v₆, u₆} T'\nL' : C' ⥤ T'\nR' ... | [
"C : Type u₁\ninst✝⁶ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝⁵ : Category.{v₂, u₂} D\nT : Type u₃\ninst✝⁴ : Category.{v₃, u₃} T\nL : C ⥤ T\nR : D ⥤ T\nC' : Type u₄\ninst✝³ : Category.{v₄, u₄} C'\nD' : Type u₅\ninst✝² : Category.{v₅, u₅} D'\nT' : Type u₆\ninst✝¹ : Category.{v₆, u₆} T'\nL' : C' ⥤ T'\nR' : D' ⥤ T'\nF... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.FilteredColimitCommutesProduct | {
"line": 248,
"column": 4
} | {
"line": 249,
"column": 66
} | {
"line": 250,
"column": 4
} | [
{
"pp": "case refine_1\nα : Type u\nI : α → Type u\ninst✝¹ : (i : α) → SmallCategory (I i)\ninst✝ : ∀ (i : α), IsFiltered (I i)\nF : (i : α) → I i ⥤ Type u\ny y' : (fun X ↦ X) (colimit (pointwiseProduct F))\nhy : (hom (colimitPointwiseProductToProductColimit F)) y = (hom (colimitPointwiseProductToProductColimit... | [
"case refine_1\nα : Type u\nI : α → Type u\ninst✝¹ : (i : α) → SmallCategory (I i)\ninst✝ : ∀ (i : α), IsFiltered (I i)\nF : (i : α) → I i ⥤ Type u\ny y' : (fun X ↦ X) (colimit (pointwiseProduct F))\nhy : (hom (colimitPointwiseProductToProductColimit F)) y = (hom (colimitPointwiseProductToProductColimit F)) y'\nky ... | let yk' : (pointwiseProduct F).obj k :=
(pointwiseProduct F).map (IsFiltered.rightToMax ky ky') yk₀' | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticLet___1 | Lean.Parser.Tactic.tacticLet__ |
Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Connected | {
"line": 73,
"column": 32
} | {
"line": 73,
"column": 43
} | {
"line": 73,
"column": 44
} | [
{
"pp": "J : Type w\ninst✝⁶ : Category.{w', w} J\ninst✝⁵ : IsConnected J\nC : Type u\ninst✝⁴ : Category.{v, u} C\ninst✝³ : HasZeroMorphisms C\ninst✝² : HasPullbacks C\ninst✝¹ : HasColimitsOfShape J C\ninst✝ : HasExactColimitsOfShape J C\nF : J ⥤ C\nc : Cocone F\nhc : IsColimit c\nX Y : C\nf : X ⟶ c.pt\ng : c.pt... | [
"J : Type w\ninst✝⁶ : Category.{w', w} J\ninst✝⁵ : IsConnected J\nC : Type u\ninst✝⁴ : Category.{v, u} C\ninst✝³ : HasZeroMorphisms C\ninst✝² : HasPullbacks C\ninst✝¹ : HasColimitsOfShape J C\ninst✝ : HasExactColimitsOfShape J C\nF : J ⥤ C\nc : Cocone F\nhc : IsColimit c\nX Y : C\nf : X ⟶ c.pt\ng : c.pt ⟶ Y\nhf : ∀... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Connected | {
"line": 111,
"column": 31
} | {
"line": 111,
"column": 42
} | {
"line": 111,
"column": 43
} | [
{
"pp": "J : Type w\ninst✝⁶ : Category.{w', w} J\ninst✝⁵ : IsConnected J\nC : Type u\ninst✝⁴ : Category.{v, u} C\ninst✝³ : HasZeroMorphisms C\ninst✝² : HasPushouts C\ninst✝¹ : HasLimitsOfShape J C\ninst✝ : HasExactLimitsOfShape J C\nF : J ⥤ C\nc : Cone F\nhc : IsLimit c\nX Y : C\ng : Y ⟶ c.pt\nf : c.pt ⟶ X\nhf ... | [
"J : Type w\ninst✝⁶ : Category.{w', w} J\ninst✝⁵ : IsConnected J\nC : Type u\ninst✝⁴ : Category.{v, u} C\ninst✝³ : HasZeroMorphisms C\ninst✝² : HasPushouts C\ninst✝¹ : HasLimitsOfShape J C\ninst✝ : HasExactLimitsOfShape J C\nF : J ⥤ C\nc : Cone F\nhc : IsLimit c\nX Y : C\ng : Y ⟶ c.pt\nf : c.pt ⟶ X\nhf : ∀ (j : J),... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.FilteredColimitCommutesProduct | {
"line": 270,
"column": 48
} | {
"line": 270,
"column": 88
} | {
"line": 270,
"column": 89
} | [
{
"pp": "α : Type u\nI : α → Type u\ninst✝¹ : (i : α) → SmallCategory (I i)\ninst✝ : ∀ (i : α), IsFiltered (I i)\nF : (i : α) → I i ⥤ Type u\nky : (i : α) → I i\nyk₀ : (pointwiseProduct F).obj ky\nky' : (i : α) → I i\nyk₀' : (pointwiseProduct F).obj ky'\nk : (i : α) → I i := IsFiltered.max ky ky'\nyk : ∏ᶜ (Func... | [
"α : Type u\nI : α → Type u\ninst✝¹ : (i : α) → SmallCategory (I i)\ninst✝ : ∀ (i : α), IsFiltered (I i)\nF : (i : α) → I i ⥤ Type u\nky : (i : α) → I i\nyk₀ : (pointwiseProduct F).obj ky\nky' : (i : α) → I i\nyk₀' : (pointwiseProduct F).obj ky'\nk : (i : α) → I i := IsFiltered.max ky ky'\nyk : ∏ᶜ (Functor.pi F).ob... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.FilteredColimitCommutesProduct | {
"line": 278,
"column": 25
} | {
"line": 278,
"column": 49
} | {
"line": 278,
"column": 50
} | [
{
"pp": "α : Type u\nI : α → Type u\ninst✝¹ : (i : α) → SmallCategory (I i)\ninst✝ : ∀ (i : α), IsFiltered (I i)\nF : (i : α) → I i ⥤ Type u\nx : (fun X ↦ X) (∏ᶜ fun s ↦ colimit (F s))\nk : (s : α) → I s\np : (s : α) → (F s).obj (k s)\nhk : ∀ (s : α), (hom (colimit.ι (F s) (k s))) (p s) = (hom (Pi.π (fun s ↦ co... | [
"α : Type u\nI : α → Type u\ninst✝¹ : (i : α) → SmallCategory (I i)\ninst✝ : ∀ (i : α), IsFiltered (I i)\nF : (i : α) → I i ⥤ Type u\nx : (fun X ↦ X) (∏ᶜ fun s ↦ colimit (F s))\nk : (s : α) → I s\np : (s : α) → (F s).obj (k s)\nhk : ∀ (s : α), (hom (colimit.ι (F s) (k s))) (p s) = (hom (Pi.π (fun s ↦ colimit (F s))... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.Injective.Dimension | {
"line": 105,
"column": 2
} | {
"line": 106,
"column": 9
} | {
"line": 106,
"column": 10
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : Abelian C\nX : C\ninst✝ : HasInjectiveDimensionLT X 0\nthis : HasExt C := ⋯\n⊢ Ext.homEquiv₀.symm (𝟙 X) = Ext.homEquiv₀.symm 0",
"ppTerm": "?m.32",
"assigned": true,
"usedConstants": [
"CategoryTheory.Abelian.toPreadditive",
"Eq.... | [
"C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : Abelian C\nX : C\ninst✝ : HasInjectiveDimensionLT X 0\nthis : HasExt C := HasExt.standard C\n⊢ Ext.mk₀ (𝟙 X) = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.Injective.Dimension | {
"line": 147,
"column": 45
} | {
"line": 147,
"column": 56
} | {
"line": 147,
"column": 57
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : Abelian C\nX : C\ninst✝ : HasExt C\nh : ∀ ⦃Y : C⦄, Subsingleton (Ext Y X 1)\nX✝ Y✝ : C\nf : X✝ ⟶ X\ng : X✝ ⟶ Y✝\nx✝ : Mono g\nφ : { X₁ := X✝, X₂ := Y✝, X₃ := cokernel g, f := g, g := cokernel.π g, zero := ⋯ }.X₂ ⟶ X\nhφ :\n (Ext.mk₀ { X₁ := X✝, X₂ := Y✝... | [
"C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : Abelian C\nX : C\ninst✝ : HasExt C\nh : ∀ ⦃Y : C⦄, Subsingleton (Ext Y X 1)\nX✝ Y✝ : C\nf : X✝ ⟶ X\ng : X✝ ⟶ Y✝\nx✝ : Mono g\nφ : { X₁ := X✝, X₂ := Y✝, X₃ := cokernel g, f := g, g := cokernel.π g, zero := ⋯ }.X₂ ⟶ X\nhφ :\n (Ext.mk₀ { X₁ := X✝, X₂ := Y✝, X₃ := coke... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.Injective.Dimension | {
"line": 240,
"column": 29
} | {
"line": 240,
"column": 40
} | {
"line": 240,
"column": 41
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : Abelian C\ninst✝¹ : HasExt C\ninst✝ : EnoughProjectives C\nX : C\nn : ℕ\nhX : ∀ (Y : C), Subsingleton (Ext Y X n)\nd : ℕ\nY : C\ne : Ext Y X d\nhd : d = n + 0\n⊢ d = n",
"ppTerm": "?m.85",
"assigned": false,
"usedConstants": [],
"usedFVar... | [
"C : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : Abelian C\ninst✝¹ : HasExt C\ninst✝ : EnoughProjectives C\nX : C\nn : ℕ\nhX : ∀ (Y : C), Subsingleton (Ext Y X n)\nd : ℕ\nY : C\ne : Ext Y X d\nhd : d = n + 0\n⊢ d = n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.GrothendieckCategory.ModuleEmbedding.GabrielPopescu | {
"line": 92,
"column": 53
} | {
"line": 92,
"column": 83
} | {
"line": 92,
"column": 84
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : Abelian C\ninst✝ : IsGrothendieckAbelian.{v, v, u} C\nG : C\nhG : IsSeparator G\nA B : C\nM : ModuleCat (End G)ᵐᵒᵖ\ng : M ⟶ ModuleCat.of (End G)ᵐᵒᵖ (G ⟶ A)\nhg : Mono g\nf : M ⟶ ModuleCat.of (End G)ᵐᵒᵖ (G ⟶ B)\nF : Finset (Discrete ↑M)\nh : G ⟶ pullback ... | [
"C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : Abelian C\ninst✝ : IsGrothendieckAbelian.{v, v, u} C\nG : C\nhG : IsSeparator G\nA B : C\nM : ModuleCat (End G)ᵐᵒᵖ\ng : M ⟶ ModuleCat.of (End G)ᵐᵒᵖ (G ⟶ A)\nhg : Mono g\nf : M ⟶ ModuleCat.of (End G)ᵐᵒᵖ (G ⟶ B)\nF : Finset (Discrete ↑M)\nh : G ⟶ pullback (∑ a ∈ F.att... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.Injective.Dimension | {
"line": 287,
"column": 73
} | {
"line": 287,
"column": 84
} | {
"line": 287,
"column": 85
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Abelian C\nX : C\nn : ℕ\nh : HasInjectiveDimensionLT X (n + 1)\ni : ℕ\nhi : ↑n < ↑i\n⊢ n + 1 ≤ i",
"ppTerm": "?m.95",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"Nat.instOne",
"Order.add_one_le_iff.... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Abelian C\nX : C\nn : ℕ\nh : HasInjectiveDimensionLT X (n + 1)\ni : ℕ\nhi : ↑n < ↑i\n⊢ n < i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.GrothendieckCategory.ModuleEmbedding.GabrielPopescu | {
"line": 131,
"column": 4
} | {
"line": 142,
"column": 15
} | {
"line": 144,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : Abelian C\ninst✝ : IsGrothendieckAbelian.{v, v, u} C\nG : C\nhG : IsSeparator G\nB : C\nhB : Injective B\n⊢ Injective ((preadditiveCoyonedaObj G).obj B)",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"CategoryTheory.IsGrothen... | [] | rw [← Module.injective_iff_injective_object]
simp only [preadditiveCoyonedaObj_obj_carrier]
refine Module.Baer.injective (fun M g => ?_)
have h := exists_d_comp_eq_d hG B (ModuleCat.ofHom
⟨⟨fun i => i.1.unop, by cat_disch⟩, by cat_disch⟩) ?_ (ModuleCat.ofHom g)
· obtain ⟨l, hl⟩ := h
refine ⟨... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Abelian.GrothendieckCategory.ModuleEmbedding.GabrielPopescu | {
"line": 131,
"column": 4
} | {
"line": 142,
"column": 15
} | {
"line": 144,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : Abelian C\ninst✝ : IsGrothendieckAbelian.{v, v, u} C\nG : C\nhG : IsSeparator G\nB : C\nhB : Injective B\n⊢ Injective ((preadditiveCoyonedaObj G).obj B)",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"CategoryTheory.IsGrothen... | [] | rw [← Module.injective_iff_injective_object]
simp only [preadditiveCoyonedaObj_obj_carrier]
refine Module.Baer.injective (fun M g => ?_)
have h := exists_d_comp_eq_d hG B (ModuleCat.ofHom
⟨⟨fun i => i.1.unop, by cat_disch⟩, by cat_disch⟩) ?_ (ModuleCat.ofHom g)
· obtain ⟨l, hl⟩ := h
refine ⟨... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Abelian.Injective.Ext | {
"line": 204,
"column": 9
} | {
"line": 204,
"column": 89
} | {
"line": 204,
"column": 89
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : Abelian C\ninst✝ : HasExt C\nX Y : C\nR : InjectiveResolution Y\nn : ℕ\nf : X ⟶ R.cocomplex.X n\nm : ℕ\nhm : n + 1 = m\nhf : f ≫ R.cocomplex.d n m = 0\np : ℕ\nhp : p + 1 = n\nx✝ :\n ∃ g,\n g ≫ (R.cochainComplexXIso (↑p) p ⋯).hom ≫ R.cocomplex.d p n ≫... | [] | simp only [← cancel_mono (R.cochainComplexXIso n n rfl).inv, Category.assoc, hg] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.CategoryTheory.Abelian.Injective.Ext | {
"line": 204,
"column": 9
} | {
"line": 204,
"column": 89
} | {
"line": 204,
"column": 89
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : Abelian C\ninst✝ : HasExt C\nX Y : C\nR : InjectiveResolution Y\nn : ℕ\nf : X ⟶ R.cocomplex.X n\nm : ℕ\nhm : n + 1 = m\nhf : f ≫ R.cocomplex.d n m = 0\np : ℕ\nhp : p + 1 = n\nx✝ :\n ∃ g,\n g ≫ (R.cochainComplexXIso (↑p) p ⋯).hom ≫ R.cocomplex.d p n ≫... | [] | simp only [← cancel_mono (R.cochainComplexXIso n n rfl).inv, Category.assoc, hg] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Abelian.Injective.Ext | {
"line": 204,
"column": 9
} | {
"line": 204,
"column": 89
} | {
"line": 204,
"column": 89
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : Abelian C\ninst✝ : HasExt C\nX Y : C\nR : InjectiveResolution Y\nn : ℕ\nf : X ⟶ R.cocomplex.X n\nm : ℕ\nhm : n + 1 = m\nhf : f ≫ R.cocomplex.d n m = 0\np : ℕ\nhp : p + 1 = n\nx✝ :\n ∃ g,\n g ≫ (R.cochainComplexXIso (↑p) p ⋯).hom ≫ R.cocomplex.d p n ≫... | [] | simp only [← cancel_mono (R.cochainComplexXIso n n rfl).inv, Category.assoc, hg] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Abelian.Injective.Ext | {
"line": 214,
"column": 7
} | {
"line": 215,
"column": 61
} | {
"line": 215,
"column": 62
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : Abelian C\ninst✝ : HasExt C\nX Y : C\nR : InjectiveResolution Y\nn m : ℕ\nhm : n + 1 = m\nf : X ⟶ R.cochainComplex.X ↑n\nhf : f ≫ R.cochainComplex.d ↑n ↑m = 0\n⊢ (f ≫ (R.cochainComplexXIso (↑n) n ⋯).hom) ≫ R.cocomplex.d n m = 0",
"ppTerm": "?m.163",
... | [
"C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : Abelian C\ninst✝ : HasExt C\nX Y : C\nR : InjectiveResolution Y\nn m : ℕ\nhm : n + 1 = m\nf : X ⟶ R.cochainComplex.X ↑n\nhf : f ≫ R.cochainComplex.d ↑n ↑m = 0\n⊢ f ≫ (R.cochainComplexXIso (↑n) n ⋯).hom ≫ R.cocomplex.d n m ≫ (R.cochainComplexXIso (↑m) m ⋯).inv = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.Injective.Resolution | {
"line": 191,
"column": 4
} | {
"line": 191,
"column": 25
} | {
"line": 191,
"column": 26
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Abelian C\nX : C\nI J : InjectiveResolution X\n⊢ Homotopy (desc (𝟙 X ≫ 𝟙 X) I I) (𝟙 I.cocomplex)",
"ppTerm": "?m.75",
"assigned": true,
"usedConstants": [
"CategoryTheory.Abelian.toPreadditive",
"Eq.mpr",
"HomologicalCompl... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Abelian C\nX : C\nI J : InjectiveResolution X\n⊢ Homotopy (desc (𝟙 X) I I) (𝟙 I.cocomplex)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square | {
"line": 106,
"column": 4
} | {
"line": 106,
"column": 46
} | {
"line": 106,
"column": 47
} | [
{
"pp": "case refine_1\nsq₁ : Square (Type v)\nsq₂ : Square (Type u)\ne₁ : sq₁.X₁ ≃ sq₂.X₁\ne₂ : sq₁.X₂ ≃ sq₂.X₂\ne₃ : sq₁.X₃ ≃ sq₂.X₃\ne₄ : sq₁.X₄ ≃ sq₂.X₄\ncomm₁₂ : ⇑e₂ ∘ ⇑(ConcreteCategory.hom sq₁.f₁₂) = ⇑(ConcreteCategory.hom sq₂.f₁₂) ∘ ⇑e₁\ncomm₁₃ : ⇑e₃ ∘ ⇑(ConcreteCategory.hom sq₁.f₁₃) = ⇑(ConcreteCategor... | [
"case refine_1\nsq₁ : Square (Type v)\nsq₂ : Square (Type u)\ne₁ : sq₁.X₁ ≃ sq₂.X₁\ne₂ : sq₁.X₂ ≃ sq₂.X₂\ne₃ : sq₁.X₃ ≃ sq₂.X₃\ne₄ : sq₁.X₄ ≃ sq₂.X₄\ncomm₁₂ : ⇑e₂ ∘ ⇑(ConcreteCategory.hom sq₁.f₁₂) = ⇑(ConcreteCategory.hom sq₂.f₁₂) ∘ ⇑e₁\ncomm₁₃ : ⇑e₃ ∘ ⇑(ConcreteCategory.hom sq₁.f₁₃) = ⇑(ConcreteCategory.hom sq₂.f₁... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.Injective.Resolution | {
"line": 193,
"column": 4
} | {
"line": 193,
"column": 25
} | {
"line": 193,
"column": 26
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Abelian C\nX : C\nI J : InjectiveResolution X\n⊢ Homotopy (desc (𝟙 X ≫ 𝟙 X) J J) (𝟙 J.cocomplex)",
"ppTerm": "?m.105",
"assigned": true,
"usedConstants": [
"CategoryTheory.Abelian.toPreadditive",
"Eq.mpr",
"HomologicalComp... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Abelian C\nX : C\nI J : InjectiveResolution X\n⊢ Homotopy (desc (𝟙 X) J J) (𝟙 J.cocomplex)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.Injective.Resolution | {
"line": 251,
"column": 2
} | {
"line": 251,
"column": 17
} | {
"line": 253,
"column": 0
} | [
{
"pp": "case g_comm\nC : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : Abelian C\ninst✝ : HasInjectiveResolutions C\nX Y : C\nf : X ⟶ Y\nI : InjectiveResolution X\nJ : InjectiveResolution Y\nφ : I.cocomplex ⟶ J.cocomplex\ncomm : I.ι.f 0 ≫ φ.f 0 = f ≫ J.ι.f 0\n⊢ (injectiveResolution X).ι ≫\n desc f (injecti... | [] | all_goals aesop | Lean.Elab.Tactic.evalAllGoals | Lean.Parser.Tactic.allGoals |
Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square | {
"line": 107,
"column": 4
} | {
"line": 107,
"column": 46
} | {
"line": 107,
"column": 47
} | [
{
"pp": "case refine_2\nsq₁ : Square (Type v)\nsq₂ : Square (Type u)\ne₁ : sq₁.X₁ ≃ sq₂.X₁\ne₂ : sq₁.X₂ ≃ sq₂.X₂\ne₃ : sq₁.X₃ ≃ sq₂.X₃\ne₄ : sq₁.X₄ ≃ sq₂.X₄\ncomm₁₂ : ⇑e₂ ∘ ⇑(ConcreteCategory.hom sq₁.f₁₂) = ⇑(ConcreteCategory.hom sq₂.f₁₂) ∘ ⇑e₁\ncomm₁₃ : ⇑e₃ ∘ ⇑(ConcreteCategory.hom sq₁.f₁₃) = ⇑(ConcreteCategor... | [
"case refine_2\nsq₁ : Square (Type v)\nsq₂ : Square (Type u)\ne₁ : sq₁.X₁ ≃ sq₂.X₁\ne₂ : sq₁.X₂ ≃ sq₂.X₂\ne₃ : sq₁.X₃ ≃ sq₂.X₃\ne₄ : sq₁.X₄ ≃ sq₂.X₄\ncomm₁₂ : ⇑e₂ ∘ ⇑(ConcreteCategory.hom sq₁.f₁₂) = ⇑(ConcreteCategory.hom sq₂.f₁₂) ∘ ⇑e₁\ncomm₁₃ : ⇑e₃ ∘ ⇑(ConcreteCategory.hom sq₁.f₁₃) = ⇑(ConcreteCategory.hom sq₂.f₁... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square | {
"line": 108,
"column": 4
} | {
"line": 108,
"column": 46
} | {
"line": 108,
"column": 47
} | [
{
"pp": "case refine_3\nsq₁ : Square (Type v)\nsq₂ : Square (Type u)\ne₁ : sq₁.X₁ ≃ sq₂.X₁\ne₂ : sq₁.X₂ ≃ sq₂.X₂\ne₃ : sq₁.X₃ ≃ sq₂.X₃\ne₄ : sq₁.X₄ ≃ sq₂.X₄\ncomm₁₂ : ⇑e₂ ∘ ⇑(ConcreteCategory.hom sq₁.f₁₂) = ⇑(ConcreteCategory.hom sq₂.f₁₂) ∘ ⇑e₁\ncomm₁₃ : ⇑e₃ ∘ ⇑(ConcreteCategory.hom sq₁.f₁₃) = ⇑(ConcreteCategor... | [
"case refine_3\nsq₁ : Square (Type v)\nsq₂ : Square (Type u)\ne₁ : sq₁.X₁ ≃ sq₂.X₁\ne₂ : sq₁.X₂ ≃ sq₂.X₂\ne₃ : sq₁.X₃ ≃ sq₂.X₃\ne₄ : sq₁.X₄ ≃ sq₂.X₄\ncomm₁₂ : ⇑e₂ ∘ ⇑(ConcreteCategory.hom sq₁.f₁₂) = ⇑(ConcreteCategory.hom sq₂.f₁₂) ∘ ⇑e₁\ncomm₁₃ : ⇑e₃ ∘ ⇑(ConcreteCategory.hom sq₁.f₁₃) = ⇑(ConcreteCategory.hom sq₂.f₁... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.Preradical.Colon | {
"line": 150,
"column": 2
} | {
"line": 150,
"column": 13
} | {
"line": 150,
"column": 14
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{u_2, u_1} C\ninst✝ : Abelian C\nΦ Ψ : Preradical C\nX : C\n⊢ IsPullback ((Φ.colon Ψ).ι.app X) ((Φ.colonπ Ψ).app X) (Φ.π.app X) (Ψ.ι.app (Φ.quotient.obj X))",
"ppTerm": "?m.56",
"assigned": true,
"usedConstants": [
"CategoryTheory.Abelian.Preradical.col... | [
"C : Type u_1\ninst✝¹ : Category.{u_2, u_1} C\ninst✝ : Abelian C\nΦ Ψ : Preradical C\nX : C\n⊢ IsPullback ((Φ.colon Ψ).ι.app X) ((Φ.colonπ Ψ).app X) (Φ.π.app X) (Ψ.ι.app (Φ.quotient.obj X))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square | {
"line": 109,
"column": 4
} | {
"line": 109,
"column": 46
} | {
"line": 109,
"column": 47
} | [
{
"pp": "case refine_4\nsq₁ : Square (Type v)\nsq₂ : Square (Type u)\ne₁ : sq₁.X₁ ≃ sq₂.X₁\ne₂ : sq₁.X₂ ≃ sq₂.X₂\ne₃ : sq₁.X₃ ≃ sq₂.X₃\ne₄ : sq₁.X₄ ≃ sq₂.X₄\ncomm₁₂ : ⇑e₂ ∘ ⇑(ConcreteCategory.hom sq₁.f₁₂) = ⇑(ConcreteCategory.hom sq₂.f₁₂) ∘ ⇑e₁\ncomm₁₃ : ⇑e₃ ∘ ⇑(ConcreteCategory.hom sq₁.f₁₃) = ⇑(ConcreteCategor... | [
"case refine_4\nsq₁ : Square (Type v)\nsq₂ : Square (Type u)\ne₁ : sq₁.X₁ ≃ sq₂.X₁\ne₂ : sq₁.X₂ ≃ sq₂.X₂\ne₃ : sq₁.X₃ ≃ sq₂.X₃\ne₄ : sq₁.X₄ ≃ sq₂.X₄\ncomm₁₂ : ⇑e₂ ∘ ⇑(ConcreteCategory.hom sq₁.f₁₂) = ⇑(ConcreteCategory.hom sq₂.f₁₂) ∘ ⇑e₁\ncomm₁₃ : ⇑e₃ ∘ ⇑(ConcreteCategory.hom sq₁.f₁₃) = ⇑(ConcreteCategory.hom sq₂.f₁... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.Preradical.Colon | {
"line": 197,
"column": 2
} | {
"line": 198,
"column": 39
} | {
"line": 198,
"column": 40
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{u_2, u_1} C\ninst✝ : Abelian C\nΦ Ψ : Preradical C\n⊢ IsIso (Φ.toColon Ψ) ↔ IsZero (Φ.quotient ⋙ Ψ.r)",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"CategoryTheory.Over",
"CategoryTheory.Functor",
"_private.Mathl... | [
"C : Type u_1\ninst✝¹ : Category.{u_2, u_1} C\ninst✝ : Abelian C\nΦ Ψ : Preradical C\n⊢ (∀ (X : C), IsIso ((Over.Hom.left (Φ.toColon Ψ).hom).app X)) ↔ ∀ (X : C), IsZero (Ψ.r.obj (Φ.quotient.obj X))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.Projective.Ext | {
"line": 213,
"column": 2
} | {
"line": 213,
"column": 30
} | {
"line": 213,
"column": 31
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : Abelian C\ninst✝ : HasExt C\nX Y : C\nR : ProjectiveResolution X\nn : ℕ\nf : R.complex.X n ⟶ Y\nm : ℕ\nhm : n + 1 = m\nhf : R.complex.d m n ≫ f = 0\np : ℕ\nhp : p + 1 = n\nx✝ :\n ∃ g,\n ((R.cochainComplexXIso (-↑n) n ⋯).hom ≫ R.complex.d n p ≫ (R.coc... | [
"C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : Abelian C\ninst✝ : HasExt C\nX Y : C\nR : ProjectiveResolution X\nn : ℕ\nf : R.complex.X n ⟶ Y\nm : ℕ\nhm : n + 1 = m\nhf : R.complex.d m n ≫ f = 0\np : ℕ\nhp : p + 1 = n\nx✝ :\n ∃ g,\n ((R.cochainComplexXIso (-↑n) n ⋯).hom ≫ R.complex.d n p ≫ (R.cochainComplexX... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.Projective.Ext | {
"line": 223,
"column": 2
} | {
"line": 223,
"column": 50
} | {
"line": 223,
"column": 51
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : Abelian C\ninst✝ : HasExt C\nX Y : C\nR : ProjectiveResolution X\nn m : ℕ\nhm : n + 1 = m\nf : R.cochainComplex.X (-↑n) ⟶ Y\nhf : R.cochainComplex.d (-↑m) (-↑n) ≫ f = 0\n⊢ (R.cochainComplexXIso (-↑m) m ⋯).hom ≫ R.complex.d m n ≫ (R.cochainComplexXIso (-↑... | [
"C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : Abelian C\ninst✝ : HasExt C\nX Y : C\nR : ProjectiveResolution X\nn m : ℕ\nhm : n + 1 = m\nf : R.cochainComplex.X (-↑n) ⟶ Y\nhf : R.cochainComplex.d (-↑m) (-↑n) ≫ f = 0\n⊢ R.complex.d m n ≫ (R.cochainComplexXIso (-↑n) n ⋯).inv ≫ f = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.Pseudoelements | {
"line": 415,
"column": 12
} | {
"line": 415,
"column": 23
} | {
"line": 415,
"column": 24
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Abelian C\nP Q : C\nf : P ⟶ Q\nx y : Pseudoelement P\na a' : Over P\nh : pseudoApply f ⟦a⟧ = pseudoApply f ⟦a'⟧\nR : C\np : R ⟶ ((fun g ↦ app f g) a).left\nq : R ⟶ ((fun g ↦ app f g) a').left\nep : Epi p\nw✝¹ : Epi q\ncomm : p ≫ ((fun g ↦ app f g) a).hom ... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Abelian C\nP Q : C\nf : P ⟶ Q\nx y : Pseudoelement P\na a' : Over P\nh : pseudoApply f ⟦a⟧ = pseudoApply f ⟦a'⟧\nR : C\np : R ⟶ ((fun g ↦ app f g) a).left\nq : R ⟶ ((fun g ↦ app f g) a').left\nep : Epi p\nw✝¹ : Epi q\ncomm : p ≫ ((fun g ↦ app f g) a).hom = q ≫ ((fun ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.Pseudoelements | {
"line": 448,
"column": 2
} | {
"line": 453,
"column": 58
} | {
"line": 454,
"column": 2
} | [
{
"pp": "case refine_1\nR : Type u_1\ninst✝ : Ring R\nG : ModuleCat R\nx y : Over G\nP : ModuleCat R\np : P ⟶ x.left\nq : P ⟶ y.left\nhp : Epi p\nhq : Epi q\nH : p ≫ x.hom = q ≫ y.hom\na : ↑G\nha : a ∈ (ModuleCat.Hom.hom x.hom).range\n⊢ a ∈ (ModuleCat.Hom.hom y.hom).range",
"ppTerm": "?refine_1",
"assig... | [
"case refine_2\nR : Type u_1\ninst✝ : Ring R\nG : ModuleCat R\nx y : Over G\nP : ModuleCat R\np : P ⟶ x.left\nq : P ⟶ y.left\nhp : Epi p\nhq : Epi q\nH : p ≫ x.hom = q ≫ y.hom\na : ↑G\nha : a ∈ (ModuleCat.Hom.hom y.hom).range\n⊢ a ∈ (ModuleCat.Hom.hom x.hom).range"
] | · obtain ⟨a', ha'⟩ := ha
obtain ⟨a'', ha''⟩ := (ModuleCat.epi_iff_surjective p).1 hp a'
refine ⟨q a'', ?_⟩
dsimp at ha' ⊢
rw [← LinearMap.comp_apply, ← ModuleCat.hom_comp, ← H,
ModuleCat.hom_comp, LinearMap.comp_apply, ha'', ha'] | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.CategoryTheory.Abelian.SerreClass.Localization | {
"line": 111,
"column": 6
} | {
"line": 111,
"column": 58
} | {
"line": 111,
"column": 59
} | [
{
"pp": "case refine_2\nC : Type u\ninst✝⁵ : Category.{v, u} C\ninst✝⁴ : Abelian C\nD : Type u'\ninst✝³ : Category.{v', u'} D\nL : C ⥤ D\nP : ObjectProperty C\ninst✝² : P.IsSerreClass\nE : Type u''\ninst✝¹ : Category.{v'', u''} E\ninst✝ : Abelian E\nX' X Y : C\nf₁ f₂ : X ⟶ Y\ns : X' ⟶ X\nhs : P.isoModSerre s\ne... | [
"case refine_2\nC : Type u\ninst✝⁵ : Category.{v, u} C\ninst✝⁴ : Abelian C\nD : Type u'\ninst✝³ : Category.{v', u'} D\nL : C ⥤ D\nP : ObjectProperty C\ninst✝² : P.IsSerreClass\nE : Type u''\ninst✝¹ : Category.{v'', u''} E\ninst✝ : Abelian E\nX' X Y : C\nf₁ f₂ : X ⟶ Y\ns : X' ⟶ X\nhs : P.isoModSerre s\neq : s ≫ f₁ =... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.SerreClass.Localization | {
"line": 123,
"column": 6
} | {
"line": 123,
"column": 58
} | {
"line": 123,
"column": 59
} | [
{
"pp": "case refine_2\nC : Type u\ninst✝⁵ : Category.{v, u} C\ninst✝⁴ : Abelian C\nD : Type u'\ninst✝³ : Category.{v', u'} D\nL : C ⥤ D\nP : ObjectProperty C\ninst✝² : P.IsSerreClass\nE : Type u''\ninst✝¹ : Category.{v'', u''} E\ninst✝ : Abelian E\nX Y Y' : C\nf₁ f₂ : X ⟶ Y\ns : Y ⟶ Y'\nhs : P.isoModSerre s\ne... | [
"case refine_2\nC : Type u\ninst✝⁵ : Category.{v, u} C\ninst✝⁴ : Abelian C\nD : Type u'\ninst✝³ : Category.{v', u'} D\nL : C ⥤ D\nP : ObjectProperty C\ninst✝² : P.IsSerreClass\nE : Type u''\ninst✝¹ : Category.{v'', u''} E\ninst✝ : Abelian E\nX Y Y' : C\nf₁ f₂ : X ⟶ Y\ns : Y ⟶ Y'\nhs : P.isoModSerre s\neq : f₁ ≫ s =... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.SerreClass.Localization | {
"line": 139,
"column": 2
} | {
"line": 139,
"column": 13
} | {
"line": 139,
"column": 14
} | [
{
"pp": "C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : Abelian C\nD : Type u'\ninst✝⁴ : Category.{v', u'} D\nL : C ⥤ D\nP : ObjectProperty C\ninst✝³ : P.IsSerreClass\ninst✝² : L.IsLocalization P.isoModSerre\ninst✝¹ : Preadditive D\ninst✝ : L.Additive\nX Y : C\nh : P.isoModSerre 0\n⊢ P X",
"ppTerm": "?m.4... | [
"C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : Abelian C\nD : Type u'\ninst✝⁴ : Category.{v', u'} D\nL : C ⥤ D\nP : ObjectProperty C\ninst✝³ : P.IsSerreClass\ninst✝² : L.IsLocalization P.isoModSerre\ninst✝¹ : Preadditive D\ninst✝ : L.Additive\nX Y : C\nh : P.isoModSerre 0\n⊢ P X"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.SerreClass.Localization | {
"line": 231,
"column": 22
} | {
"line": 231,
"column": 57
} | {
"line": 231,
"column": 58
} | [
{
"pp": "C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : Abelian C\nD : Type u'\ninst✝⁴ : Category.{v', u'} D\nL : C ⥤ D\nP : ObjectProperty C\ninst✝³ : P.IsSerreClass\ninst✝² : L.IsLocalization P.isoModSerre\ninst✝¹ : Preadditive D\ninst✝ : L.Additive\nX✝ Y✝ : C\nf : X✝ ⟶ Y✝\nx✝ : Mono f\n⊢ Mono (L.map f)",
... | [
"C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : Abelian C\nD : Type u'\ninst✝⁴ : Category.{v', u'} D\nL : C ⥤ D\nP : ObjectProperty C\ninst✝³ : P.IsSerreClass\ninst✝² : L.IsLocalization P.isoModSerre\ninst✝¹ : Preadditive D\ninst✝ : L.Additive\nX✝ Y✝ : C\nf : X✝ ⟶ Y✝\nx✝ : Mono f\n⊢ P.monoModSerre f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.SerreClass.Localization | {
"line": 234,
"column": 22
} | {
"line": 234,
"column": 56
} | {
"line": 234,
"column": 57
} | [
{
"pp": "C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : Abelian C\nD : Type u'\ninst✝⁴ : Category.{v', u'} D\nL : C ⥤ D\nP : ObjectProperty C\ninst✝³ : P.IsSerreClass\ninst✝² : L.IsLocalization P.isoModSerre\ninst✝¹ : Preadditive D\ninst✝ : L.Additive\nX✝ Y✝ : C\nf : X✝ ⟶ Y✝\nx✝ : Epi f\n⊢ Epi (L.map f)",
... | [
"C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : Abelian C\nD : Type u'\ninst✝⁴ : Category.{v', u'} D\nL : C ⥤ D\nP : ObjectProperty C\ninst✝³ : P.IsSerreClass\ninst✝² : L.IsLocalization P.isoModSerre\ninst✝¹ : Preadditive D\ninst✝ : L.Additive\nX✝ Y✝ : C\nf : X✝ ⟶ Y✝\nx✝ : Epi f\n⊢ P.epiModSerre f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.RightDerived | {
"line": 318,
"column": 22
} | {
"line": 320,
"column": 49
} | {
"line": 321,
"column": 6
} | [
{
"pp": "C : Type u\ninst✝⁵ : Category.{v, u} C\nD : Type u_1\ninst✝⁴ : Category.{v_1, u_1} D\ninst✝³ : Abelian C\ninst✝² : HasInjectiveResolutions C\ninst✝¹ : Abelian D\nF : C ⥤ D\ninst✝ : F.Additive\nX Y : C\nf : X ⟶ Y\n⊢ F.map f ≫\n (injectiveResolution Y).toRightDerivedZero' F ≫\n ((F.mapHomolog... | [
"C : Type u\ninst✝⁵ : Category.{v, u} C\nD : Type u_1\ninst✝⁴ : Category.{v_1, u_1} D\ninst✝³ : Abelian C\ninst✝² : HasInjectiveResolutions C\ninst✝¹ : Abelian D\nF : C ⥤ D\ninst✝ : F.Additive\nX Y : C\nf : X ⟶ Y\n⊢ (injectiveResolution X).toRightDerivedZero' F ≫\n HomologicalComplex.cyclesMap\n ((F.m... | InjectiveResolution.toRightDerivedZero'_naturality_assoc f
(injectiveResolution X) (injectiveResolution Y)
(InjectiveResolution.desc f _ _) (by simp), | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.CategoryTheory.Abelian.SerreClass.Localization | {
"line": 258,
"column": 10
} | {
"line": 258,
"column": 21
} | {
"line": 258,
"column": 22
} | [
{
"pp": "C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : Abelian C\nD : Type u'\ninst✝⁴ : Category.{v', u'} D\nL : C ⥤ D\nP : ObjectProperty C\ninst✝³ : P.IsSerreClass\ninst✝² : L.IsLocalization P.isoModSerre\ninst✝¹ : Preadditive D\ninst✝ : L.Additive\nX Y : D\nf : X ⟶ Y\nthis✝ : L.PreservesMonomorphisms\nthi... | [
"C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : Abelian C\nD : Type u'\ninst✝⁴ : Category.{v', u'} D\nL : C ⥤ D\nP : ObjectProperty C\ninst✝³ : P.IsSerreClass\ninst✝² : L.IsLocalization P.isoModSerre\ninst✝¹ : Preadditive D\ninst✝ : L.Additive\nX Y : D\nf : X ⟶ Y\nthis✝ : L.PreservesMonomorphisms\nthis : L.mapArr... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.SerreClass.Localization | {
"line": 276,
"column": 4
} | {
"line": 276,
"column": 65
} | {
"line": 277,
"column": 4
} | [
{
"pp": "case refine_1\nC : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : Abelian C\nD : Type u'\ninst✝⁴ : Category.{v', u'} D\nL : C ⥤ D\nP : ObjectProperty C\ninst✝³ : P.IsSerreClass\ninst✝² : L.IsLocalization P.isoModSerre\ninst✝¹ : Preadditive D\ninst✝ : L.Additive\nX✝ Y✝ : D\nf✝ : X✝ ⟶ Y✝\nthis✝ : L.Preserv... | [
"case refine_1\nC : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : Abelian C\nD : Type u'\ninst✝⁴ : Category.{v', u'} D\nL : C ⥤ D\nP : ObjectProperty C\ninst✝³ : P.IsSerreClass\ninst✝² : L.IsLocalization P.isoModSerre\ninst✝¹ : Preadditive D\ninst✝ : L.Additive\nX✝ Y✝ : D\nf✝ : X✝ ⟶ Y✝\nthis✝ : L.PreservesEpimorphis... | refine ⟨_, _, Abelian.factorThruImage f, inferInstance, ⟨?_⟩⟩ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.CategoryTheory.Abelian.SerreClass.Localization | {
"line": 281,
"column": 10
} | {
"line": 281,
"column": 21
} | {
"line": 281,
"column": 22
} | [
{
"pp": "C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : Abelian C\nD : Type u'\ninst✝⁴ : Category.{v', u'} D\nL : C ⥤ D\nP : ObjectProperty C\ninst✝³ : P.IsSerreClass\ninst✝² : L.IsLocalization P.isoModSerre\ninst✝¹ : Preadditive D\ninst✝ : L.Additive\nX Y : D\nf : X ⟶ Y\nthis✝ : L.PreservesEpimorphisms\nthis... | [
"C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : Abelian C\nD : Type u'\ninst✝⁴ : Category.{v', u'} D\nL : C ⥤ D\nP : ObjectProperty C\ninst✝³ : P.IsSerreClass\ninst✝² : L.IsLocalization P.isoModSerre\ninst✝¹ : Preadditive D\ninst✝ : L.Additive\nX Y : D\nf : X ⟶ Y\nthis✝ : L.PreservesEpimorphisms\nthis : L.mapArro... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.SerreClass.Localization | {
"line": 295,
"column": 32
} | {
"line": 295,
"column": 57
} | {
"line": 295,
"column": 58
} | [
{
"pp": "C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : Abelian C\nD : Type u'\ninst✝⁴ : Category.{v', u'} D\nL : C ⥤ D\nP : ObjectProperty C\ninst✝³ : P.IsSerreClass\ninst✝² : L.IsLocalization P.isoModSerre\ninst✝¹ : Preadditive D\ninst✝ : L.Additive\nX Y : C\nf : X ⟶ Y\nthis✝¹ : L.PreservesMonomorphisms\nth... | [
"C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : Abelian C\nD : Type u'\ninst✝⁴ : Category.{v', u'} D\nL : C ⥤ D\nP : ObjectProperty C\ninst✝³ : P.IsSerreClass\ninst✝² : L.IsLocalization P.isoModSerre\ninst✝¹ : Preadditive D\ninst✝ : L.Additive\nX Y : C\nf : X ⟶ Y\nthis✝¹ : L.PreservesMonomorphisms\nthis✝ : L.EssS... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Action.Concrete | {
"line": 144,
"column": 6
} | {
"line": 144,
"column": 29
} | {
"line": 144,
"column": 30
} | [
{
"pp": "G : Type u_1\ninst✝² : Group G\nH N : Subgroup G\ninst✝¹ : Fintype (G ⧸ N)\ninst✝ : N.Normal\nv a b : G\nh : a ≈ b\n⊢ (a * v⁻¹)⁻¹ * (b * v⁻¹) ∈ N",
"ppTerm": "?m.68",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Semigroup.toMul",
"DivInvMonoid.toInv",
"HMul.hMul",... | [
"G : Type u_1\ninst✝² : Group G\nH N : Subgroup G\ninst✝¹ : Fintype (G ⧸ N)\ninst✝ : N.Normal\nv a b : G\nh : a ≈ b\n⊢ v * (a⁻¹ * (b * v⁻¹)) ∈ N"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.SerreClass.Localization | {
"line": 326,
"column": 32
} | {
"line": 326,
"column": 56
} | {
"line": 326,
"column": 57
} | [
{
"pp": "C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : Abelian C\nD : Type u'\ninst✝⁴ : Category.{v', u'} D\nL : C ⥤ D\nP : ObjectProperty C\ninst✝³ : P.IsSerreClass\ninst✝² : L.IsLocalization P.isoModSerre\ninst✝¹ : Preadditive D\ninst✝ : L.Additive\nX Y : C\nf : X ⟶ Y\nthis✝¹ : L.PreservesEpimorphisms\nthi... | [
"C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : Abelian C\nD : Type u'\ninst✝⁴ : Category.{v', u'} D\nL : C ⥤ D\nP : ObjectProperty C\ninst✝³ : P.IsSerreClass\ninst✝² : L.IsLocalization P.isoModSerre\ninst✝¹ : Preadditive D\ninst✝ : L.Additive\nX Y : C\nf : X ⟶ Y\nthis✝¹ : L.PreservesEpimorphisms\nthis✝ : L.EssSu... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Action.Basic | {
"line": 269,
"column": 4
} | {
"line": 269,
"column": 15
} | {
"line": 269,
"column": 16
} | [
{
"pp": "V : Type u_1\ninst✝³ : Category.{v_1, u_1} V\nG : Type u_2\ninst✝² : Monoid G\nFV : V → V → Type u_3\nCV : V → Type u_4\ninst✝¹ : (X Y : V) → FunLike (FV X Y) (CV X) (CV Y)\ninst✝ : ConcreteCategory V FV\nX✝ Y✝ : Action V G\nf : X✝ ⟶ Y✝\ng : G\nx✝ : CV X✝.V\n⊢ (⇑(ConcreteCategory.hom f.hom) ∘ ⇑(Concret... | [
"V : Type u_1\ninst✝³ : Category.{v_1, u_1} V\nG : Type u_2\ninst✝² : Monoid G\nFV : V → V → Type u_3\nCV : V → Type u_4\ninst✝¹ : (X Y : V) → FunLike (FV X Y) (CV X) (CV Y)\ninst✝ : ConcreteCategory V FV\nX✝ Y✝ : Action V G\nf : X✝ ⟶ Y✝\ng : G\nx✝ : CV X✝.V\n⊢ (ConcreteCategory.hom f.hom) ((ConcreteCategory.hom (X... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Action.Basic | {
"line": 271,
"column": 4
} | {
"line": 271,
"column": 44
} | {
"line": 271,
"column": 45
} | [
{
"pp": "V : Type u_1\ninst✝³ : Category.{v_1, u_1} V\nG : Type u_2\ninst✝² : Monoid G\nFV : V → V → Type u_3\nCV : V → Type u_4\ninst✝¹ : (X Y : V) → FunLike (FV X Y) (CV X) (CV Y)\ninst✝ : ConcreteCategory V FV\nX✝ Y✝ : Action V G\nf : HomSubtype V G X✝ Y✝\ng : G\nx : CV X✝.V\n⊢ (ConcreteCategory.hom (X✝.ρ g ... | [
"V : Type u_1\ninst✝³ : Category.{v_1, u_1} V\nG : Type u_2\ninst✝² : Monoid G\nFV : V → V → Type u_3\nCV : V → Type u_4\ninst✝¹ : (X Y : V) → FunLike (FV X Y) (CV X) (CV Y)\ninst✝ : ConcreteCategory V FV\nX✝ Y✝ : Action V G\nf : HomSubtype V G X✝ Y✝\ng : G\nx : CV X✝.V\n⊢ ↑f ((ConcreteCategory.hom (X✝.ρ g)) x) = (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.SerreClass.Localization | {
"line": 516,
"column": 6
} | {
"line": 516,
"column": 50
} | {
"line": 516,
"column": 51
} | [
{
"pp": "C : Type u\ninst✝⁸ : Category.{v, u} C\ninst✝⁷ : Abelian C\nD : Type u'\ninst✝⁶ : Category.{v', u'} D\nL : C ⥤ D\nP : ObjectProperty C\ninst✝⁵ : P.IsSerreClass\nE : Type u''\ninst✝⁴ : Category.{v'', u''} E\ninst✝³ : Abelian E\ninst✝² : L.IsLocalization P.isoModSerre\ninst✝¹ : Preadditive D\ninst✝ : L.A... | [
"C : Type u\ninst✝⁸ : Category.{v, u} C\ninst✝⁷ : Abelian C\nD : Type u'\ninst✝⁶ : Category.{v', u'} D\nL : C ⥤ D\nP : ObjectProperty C\ninst✝⁵ : P.IsSerreClass\nE : Type u''\ninst✝⁴ : Category.{v'', u''} E\ninst✝³ : Abelian E\ninst✝² : L.IsLocalization P.isoModSerre\ninst✝¹ : Preadditive D\ninst✝ : L.Additive\nG✝ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monad.Coequalizer | {
"line": 73,
"column": 4
} | {
"line": 73,
"column": 36
} | {
"line": 74,
"column": 2
} | [
{
"pp": "C : Type u₁\ninst✝ : Category.{v₁, u₁} C\nT : Monad C\nX : T.Algebra\n⊢ T.free.obj X.A ⟶ T.free.obj (T.obj X.A)",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"CategoryTheory.Functor.id",
"CategoryTheory.Monad.Algebra.A",
"CategoryTheory.Functor.map",
"Cat... | [] | apply (free T).map (T.η.app X.A) | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.CategoryTheory.Monad.Coequalizer | {
"line": 73,
"column": 4
} | {
"line": 73,
"column": 36
} | {
"line": 74,
"column": 2
} | [
{
"pp": "C : Type u₁\ninst✝ : Category.{v₁, u₁} C\nT : Monad C\nX : T.Algebra\n⊢ T.free.obj X.A ⟶ T.free.obj (T.obj X.A)",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"CategoryTheory.Functor.id",
"CategoryTheory.Monad.Algebra.A",
"CategoryTheory.Functor.map",
"Cat... | [] | apply (free T).map (T.η.app X.A) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Monad.Coequalizer | {
"line": 73,
"column": 4
} | {
"line": 73,
"column": 36
} | {
"line": 74,
"column": 2
} | [
{
"pp": "C : Type u₁\ninst✝ : Category.{v₁, u₁} C\nT : Monad C\nX : T.Algebra\n⊢ T.free.obj X.A ⟶ T.free.obj (T.obj X.A)",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"CategoryTheory.Functor.id",
"CategoryTheory.Monad.Algebra.A",
"CategoryTheory.Functor.map",
"Cat... | [] | apply (free T).map (T.η.app X.A) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Adjunction.Triple | {
"line": 92,
"column": 6
} | {
"line": 93,
"column": 20
} | {
"line": 94,
"column": 4
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Category.{v_2, u_2} D\nF : C ⥤ D\nG : D ⥤ C\nH : C ⥤ D\nt : Triple F G H\nh : H.FullyFaithful\nthis✝ : H.Full\nthis : H.Faithful\n⊢ IsIso t.adj₁.unit",
"ppTerm": "?m.138",
"assigned": true,
"usedConstants": [
"Categor... | [] | rw [t.isIso_unit_iff_isIso_counit]
infer_instance | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Adjunction.Triple | {
"line": 92,
"column": 6
} | {
"line": 93,
"column": 20
} | {
"line": 94,
"column": 4
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Category.{v_2, u_2} D\nF : C ⥤ D\nG : D ⥤ C\nH : C ⥤ D\nt : Triple F G H\nh : H.FullyFaithful\nthis✝ : H.Full\nthis : H.Faithful\n⊢ IsIso t.adj₁.unit",
"ppTerm": "?m.138",
"assigned": true,
"usedConstants": [
"Categor... | [] | rw [t.isIso_unit_iff_isIso_counit]
infer_instance | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Adjunction.Triple | {
"line": 195,
"column": 2
} | {
"line": 195,
"column": 13
} | {
"line": 195,
"column": 14
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝⁴ : Category.{v_1, u_1} C\ninst✝³ : Category.{v_2, u_2} D\nF : C ⥤ D\nG : D ⥤ C\nH : C ⥤ D\nt : Triple F G H\ninst✝² : G.Full\ninst✝¹ : G.Faithful\ninst✝ : H.PreservesEpimorphisms\nX : C\nx✝ : G.IsLeftAdjoint\nh : Epi (t.adj₂.counit.app X ≫ t.adj₁.unit.app X)\n⊢ Epi (H.... | [
"C : Type u_1\nD : Type u_2\ninst✝⁴ : Category.{v_1, u_1} C\ninst✝³ : Category.{v_2, u_2} D\nF : C ⥤ D\nG : D ⥤ C\nH : C ⥤ D\nt : Triple F G H\ninst✝² : G.Full\ninst✝¹ : G.Faithful\ninst✝ : H.PreservesEpimorphisms\nX : C\nx✝ : G.IsLeftAdjoint\nh : Epi (t.adj₂.counit.app X ≫ t.adj₁.unit.app X)\n⊢ Epi (H.map (t.adj₁.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Adjunction.Triple | {
"line": 245,
"column": 2
} | {
"line": 245,
"column": 13
} | {
"line": 245,
"column": 14
} | [
{
"pp": "case e_a\nC : Type u_1\nD : Type u_2\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : Category.{v_2, u_2} D\nF : C ⥤ D\nG : D ⥤ C\nH : C ⥤ D\nt : Triple F G H\ninst✝¹ : F.Full\ninst✝ : F.Faithful\nX : D\n⊢ G.map (t.adj₁.counit.app X) ≫ 𝟙 (G.obj X) = inv (t.adj₁.unit.app (G.obj X))",
"ppTerm": "?e_a✝",
... | [
"case e_a\nC : Type u_1\nD : Type u_2\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : Category.{v_2, u_2} D\nF : C ⥤ D\nG : D ⥤ C\nH : C ⥤ D\nt : Triple F G H\ninst✝¹ : F.Full\ninst✝ : F.Faithful\nX : D\n⊢ G.map (t.adj₁.counit.app X) = inv (t.adj₁.unit.app (G.obj X))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Adjunction.Triple | {
"line": 308,
"column": 2
} | {
"line": 308,
"column": 13
} | {
"line": 308,
"column": 14
} | [
{
"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\nF : C ⥤ D\nG : D ⥤ C\nH : C ⥤ D\nt : Triple F G H\ninst✝¹ : F.Full\ninst✝ : F.Faithful\nh : ∀ (X : D), Mono (t.adj₁.counit.app X ≫ t.adj₂.unit.app X)\nX : C\n⊢ Mono (t.adj₂.unit.app (F.obj X))",
"ppTerm": "?... | [
"C : Type u_1\nD : Type u_2\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : Category.{v_2, u_2} D\nF : C ⥤ D\nG : D ⥤ C\nH : C ⥤ D\nt : Triple F G H\ninst✝¹ : F.Full\ninst✝ : F.Faithful\nh : ∀ (X : D), Mono (t.adj₁.counit.app X ≫ t.adj₂.unit.app X)\nX : C\n⊢ Mono (t.adj₂.unit.app (F.obj X))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Action.Monoidal | {
"line": 357,
"column": 24
} | {
"line": 357,
"column": 32
} | {
"line": 358,
"column": 2
} | [
{
"pp": "V : Type u_1\ninst✝⁵ : Category.{v_1, u_1} V\nG : Type u_2\ninst✝⁴ : Monoid G\nW : Type u_3\ninst✝³ : Category.{v_2, u_3} W\ninst✝² : MonoidalCategory V\ninst✝¹ : MonoidalCategory W\nF : V ⥤ W\ninst✝ : F.Monoidal\n⊢ ε F ≫ η F = 𝟙 (𝟙_ W)",
"ppTerm": "?m.49",
"assigned": true,
"usedConstant... | [] | rw [ε_η] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.CategoryTheory.Adjunction.Quadruple | {
"line": 130,
"column": 2
} | {
"line": 130,
"column": 13
} | {
"line": 130,
"column": 14
} | [
{
"pp": "C : Type u₁\nD : Type u₂\ninst✝⁵ : Category.{v₁, u₁} C\ninst✝⁴ : Category.{v₂, u₂} D\nL : C ⥤ D\nF : D ⥤ C\nG : C ⥤ D\nR : D ⥤ C\nq : Quadruple L F G R\ninst✝³ : L.Full\ninst✝² : L.Faithful\ninst✝¹ : G.Full\ninst✝ : G.Faithful\nh :\n (∀ (a : D), Epi (q.op.leftTriple.rightToLeft.app (Opposite.equivToOp... | [
"C : Type u₁\nD : Type u₂\ninst✝⁵ : Category.{v₁, u₁} C\ninst✝⁴ : Category.{v₂, u₂} D\nL : C ⥤ D\nF : D ⥤ C\nG : C ⥤ D\nR : D ⥤ C\nq : Quadruple L F G R\ninst✝³ : L.Full\ninst✝² : L.Faithful\ninst✝¹ : G.Full\ninst✝ : G.Faithful\nh :\n (∀ (a : D), Epi (q.op.leftTriple.rightToLeft.app (Opposite.equivToOpposite a))) ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 322,
"column": 55
} | {
"line": 322,
"column": 82
} | {
"line": 322,
"column": 82
} | [
{
"pp": "case vcomp_right\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝¹ b✝ : B\nf✝ g✝ h✝ : Hom a✝¹ b✝\nη✝ : Hom₂ f✝ g✝\nθ₁✝ θ₂✝ : Hom₂ g✝ h✝\na✝ : Rel θ₁✝ θ₂✝\na_ih✝ : liftHom₂ F θ₁✝ = liftHom₂ F θ₂✝\n⊢ liftHom₂ F (η✝.vco... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 322,
"column": 55
} | {
"line": 322,
"column": 82
} | {
"line": 322,
"column": 82
} | [
{
"pp": "case vcomp_right\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝¹ b✝ : B\nf✝ g✝ h✝ : Hom a✝¹ b✝\nη✝ : Hom₂ f✝ g✝\nθ₁✝ θ₂✝ : Hom₂ g✝ h✝\na✝ : Rel θ₁✝ θ₂✝\na_ih✝ : liftHom₂ F θ₁✝ = liftHom₂ F θ₂✝\n⊢ liftHom₂ F (η✝.vco... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 322,
"column": 55
} | {
"line": 322,
"column": 82
} | {
"line": 322,
"column": 82
} | [
{
"pp": "case vcomp_left\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝¹ b✝ : B\nf✝ g✝ h✝ : Hom a✝¹ b✝\nη₁✝ η₂✝ : Hom₂ f✝ g✝\nθ✝ : Hom₂ g✝ h✝\na✝ : Rel η₁✝ η₂✝\na_ih✝ : liftHom₂ F η₁✝ = liftHom₂ F η₂✝\n⊢ liftHom₂ F (η₁✝.vco... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 322,
"column": 55
} | {
"line": 322,
"column": 82
} | {
"line": 322,
"column": 82
} | [
{
"pp": "case vcomp_left\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝¹ b✝ : B\nf✝ g✝ h✝ : Hom a✝¹ b✝\nη₁✝ η₂✝ : Hom₂ f✝ g✝\nθ✝ : Hom₂ g✝ h✝\na✝ : Rel η₁✝ η₂✝\na_ih✝ : liftHom₂ F η₁✝ = liftHom₂ F η₂✝\n⊢ liftHom₂ F (η₁✝.vco... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 322,
"column": 55
} | {
"line": 322,
"column": 82
} | {
"line": 322,
"column": 82
} | [
{
"pp": "case id_comp\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝ b✝ : B\nf✝ g✝ : Hom a✝ b✝\nη✝ : Hom₂ f✝ g✝\n⊢ liftHom₂ F ((Hom₂.id f✝).vcomp η✝) = liftHom₂ F η✝",
"ppTerm": "?id_comp",
"assigned": true,
"us... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 322,
"column": 55
} | {
"line": 322,
"column": 82
} | {
"line": 322,
"column": 82
} | [
{
"pp": "case id_comp\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝ b✝ : B\nf✝ g✝ : Hom a✝ b✝\nη✝ : Hom₂ f✝ g✝\n⊢ liftHom₂ F ((Hom₂.id f✝).vcomp η✝) = liftHom₂ F η✝",
"ppTerm": "?id_comp",
"assigned": true,
"us... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 322,
"column": 55
} | {
"line": 322,
"column": 82
} | {
"line": 322,
"column": 82
} | [
{
"pp": "case comp_id\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝ b✝ : B\nf✝ g✝ : Hom a✝ b✝\nη✝ : Hom₂ f✝ g✝\n⊢ liftHom₂ F (η✝.vcomp (Hom₂.id g✝)) = liftHom₂ F η✝",
"ppTerm": "?comp_id",
"assigned": true,
"us... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 322,
"column": 55
} | {
"line": 322,
"column": 82
} | {
"line": 322,
"column": 82
} | [
{
"pp": "case comp_id\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝ b✝ : B\nf✝ g✝ : Hom a✝ b✝\nη✝ : Hom₂ f✝ g✝\n⊢ liftHom₂ F (η✝.vcomp (Hom₂.id g✝)) = liftHom₂ F η✝",
"ppTerm": "?comp_id",
"assigned": true,
"us... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 322,
"column": 55
} | {
"line": 322,
"column": 82
} | {
"line": 322,
"column": 82
} | [
{
"pp": "case assoc\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝ b✝ : B\nf✝ g✝ h✝ i✝ : Hom a✝ b✝\nη✝ : Hom₂ f✝ g✝\nθ✝ : Hom₂ g✝ h✝\nι✝ : Hom₂ h✝ i✝\n⊢ liftHom₂ F ((η✝.vcomp θ✝).vcomp ι✝) = liftHom₂ F (η✝.vcomp (θ✝.vcomp ι... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 322,
"column": 55
} | {
"line": 322,
"column": 82
} | {
"line": 322,
"column": 82
} | [
{
"pp": "case assoc\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝ b✝ : B\nf✝ g✝ h✝ i✝ : Hom a✝ b✝\nη✝ : Hom₂ f✝ g✝\nθ✝ : Hom₂ g✝ h✝\nι✝ : Hom₂ h✝ i✝\n⊢ liftHom₂ F ((η✝.vcomp θ✝).vcomp ι✝) = liftHom₂ F (η✝.vcomp (θ✝.vcomp ι... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 322,
"column": 55
} | {
"line": 322,
"column": 82
} | {
"line": 322,
"column": 82
} | [
{
"pp": "case whisker_left\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝¹ b✝ c✝ : B\nf✝ : Hom a✝¹ b✝\ng✝ h✝ : Hom b✝ c✝\nη✝ η'✝ : Hom₂ g✝ h✝\na✝ : Rel η✝ η'✝\na_ih✝ : liftHom₂ F η✝ = liftHom₂ F η'✝\n⊢ liftHom₂ F (Hom₂.whis... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 322,
"column": 55
} | {
"line": 322,
"column": 82
} | {
"line": 322,
"column": 82
} | [
{
"pp": "case whisker_left\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝¹ b✝ c✝ : B\nf✝ : Hom a✝¹ b✝\ng✝ h✝ : Hom b✝ c✝\nη✝ η'✝ : Hom₂ g✝ h✝\na✝ : Rel η✝ η'✝\na_ih✝ : liftHom₂ F η✝ = liftHom₂ F η'✝\n⊢ liftHom₂ F (Hom₂.whis... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 322,
"column": 55
} | {
"line": 322,
"column": 82
} | {
"line": 322,
"column": 82
} | [
{
"pp": "case whisker_left_id\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝ b✝ c✝ : B\nf✝ : Hom a✝ b✝\ng✝ : Hom b✝ c✝\n⊢ liftHom₂ F (Hom₂.whisker_left f✝ (Hom₂.id g✝)) = liftHom₂ F (Hom₂.id (f✝.comp g✝))",
"ppTerm": "?... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 322,
"column": 55
} | {
"line": 322,
"column": 82
} | {
"line": 322,
"column": 82
} | [
{
"pp": "case whisker_left_id\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝ b✝ c✝ : B\nf✝ : Hom a✝ b✝\ng✝ : Hom b✝ c✝\n⊢ liftHom₂ F (Hom₂.whisker_left f✝ (Hom₂.id g✝)) = liftHom₂ F (Hom₂.id (f✝.comp g✝))",
"ppTerm": "?... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 322,
"column": 55
} | {
"line": 322,
"column": 82
} | {
"line": 322,
"column": 82
} | [
{
"pp": "case whisker_left_comp\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝ b✝ c✝ : B\nf✝ : Hom a✝ b✝\ng✝ h✝ i✝ : Hom b✝ c✝\nη✝ : Hom₂ g✝ h✝\nθ✝ : Hom₂ h✝ i✝\n⊢ liftHom₂ F (Hom₂.whisker_left f✝ (η✝.vcomp θ✝)) =\n lift... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 322,
"column": 55
} | {
"line": 322,
"column": 82
} | {
"line": 322,
"column": 82
} | [
{
"pp": "case whisker_left_comp\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝ b✝ c✝ : B\nf✝ : Hom a✝ b✝\ng✝ h✝ i✝ : Hom b✝ c✝\nη✝ : Hom₂ g✝ h✝\nθ✝ : Hom₂ h✝ i✝\n⊢ liftHom₂ F (Hom₂.whisker_left f✝ (η✝.vcomp θ✝)) =\n lift... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 322,
"column": 55
} | {
"line": 322,
"column": 82
} | {
"line": 322,
"column": 82
} | [
{
"pp": "case id_whisker_left\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝ b✝ : B\nf✝ g✝ : Hom a✝ b✝\nη✝ : Hom₂ f✝ g✝\n⊢ liftHom₂ F (Hom₂.whisker_left (Hom.id a✝) η✝) =\n liftHom₂ F ((Hom₂.left_unitor f✝).vcomp (η✝.vco... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Bicategory.Free | {
"line": 322,
"column": 55
} | {
"line": 322,
"column": 82
} | {
"line": 322,
"column": 82
} | [
{
"pp": "case id_whisker_left\nB : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\na✝ b✝ : B\nf✝ g✝ : Hom a✝ b✝\nη✝ : Hom₂ f✝ g✝\n⊢ liftHom₂ F (Hom₂.whisker_left (Hom.id a✝) η✝) =\n liftHom₂ F ((Hom₂.left_unitor f✝).vcomp (η✝.vco... | [] | dsimp [liftHom₂]; cat_disch | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
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