import Pretty.Claims.MeasRender

/--
Measure computation at higher column position or indentation level 
is worse
-/
lemma 
MeasRender_dom_monotonic: ∀ {α : Type} {d : Doc} {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas} {F : Factory α},
  MeasRender F d c i m₁ → MeasRender F d c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true
MeasRender_dom_monotonic {
F: Factory α
F : 
Factory: Type → Type
Factory 
α: ?m.3
α}
    (
h: MeasRender F d c i m₁
h : 
MeasRender: {α : Type} → Factory α → Doc → ℕ → ℕ → Meas → Prop
MeasRender 
F: Factory α
F 
d: ?m.11
d 
c: ?m.18
c 
i: ?m.25
i 
m₁: ?m.32
m₁) (
h': MeasRender F d c' i' m₂
h' : 
MeasRender: {α : Type} → Factory α → Doc → ℕ → ℕ → Meas → Prop
MeasRender 
F: Factory α
F 
d: ?m.11
d 
c': ?m.43
c' 
i': ?m.53
i' 
m₂: ?m.63
m₂)
    (
h_c: c ≤ c'
h_c : 
c: ?m.18
c ≤ 
c': ?m.43
c') (
h_i: i ≤ i'
h_i : 
i: ?m.25
i ≤ 
i': ?m.53
i') : 
dominates: {α : Type} → Factory α → Meas → Meas → Bool
dominates 
F: Factory α
F 
m₁: ?m.32
m₁ 
m₂: ?m.63
m₂ := by
Goals accomplished! 🐙 
α: Type

d: Doc

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

F: Factory α

h: MeasRender F d c i m₁

h': MeasRender F d c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

dominates F m₁ m₂ = true{
α: Type

d: Doc

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

F: Factory α

h: MeasRender F d c i m₁

h': MeasRender F d c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

dominates F m₁ m₂ = true
  
α: Type

d: Doc

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

F: Factory α

h: MeasRender F d c i m₁

h': MeasRender F d c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

dominates F m₁ m₂ = trueinduction 
d: Doc
d generalizing 
c: ℕ
c 
c': ℕ
c' 
i: ℕ
i 
i': ℕ
i' 
m₁: Meas
m₁ 
m₂: Meas
m₂
α: Type

F: Factory α

s✝: String

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F (Doc.text s✝) c i m₁

h': MeasRender F (Doc.text s✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

text
dominates F m₁ m₂ = true
α: Type

F: Factory α

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F Doc.nl c i m₁

h': MeasRender F Doc.nl c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

nl
dominates F m₁ m₂ = true
α: Type

F: Factory α

d₁✝, d₂✝: Doc

d₁_ih✝: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₁✝ c i m₁ → MeasRender F d₁✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

d₂_ih✝: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ → MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F (Doc.concat d₁✝ d₂✝) c i m₁

h': MeasRender F (Doc.concat d₁✝ d₂✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

concat
dominates F m₁ m₂ = true
α: Type

F: Factory α

n✝: ℕ

d✝: Doc

d_ih✝: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ → MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F (Doc.nest n✝ d✝) c i m₁

h': MeasRender F (Doc.nest n✝ d✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

nest
dominates F m₁ m₂ = true
α: Type

F: Factory α

d✝: Doc

d_ih✝: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ → MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F (Doc.align d✝) c i m₁

h': MeasRender F (Doc.align d✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

align
dominates F m₁ m₂ = true
α: Type

F: Factory α

d₁✝, d₂✝: Doc

d₁_ih✝: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₁✝ c i m₁ → MeasRender F d₁✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

d₂_ih✝: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ → MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F (Doc.choice d₁✝ d₂✝) c i m₁

h': MeasRender F (Doc.choice d₁✝ d₂✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

choice
dominates F m₁ m₂ = true
  
α: Type

d: Doc

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

F: Factory α

h: MeasRender F d c i m₁

h': MeasRender F d c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

dominates F m₁ m₂ = truecase text => 
    
α: Type

F: Factory α

s✝: String

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F (Doc.text s✝) c i m₁

h': MeasRender F (Doc.text s✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

dominates F m₁ m₂ = truecases 
h: MeasRender F (Doc.text s✝) c i m₁
h
α: Type

F: Factory α

s✝: String

c, i, c', i': ℕ

m₂: Meas

h': MeasRender F (Doc.text s✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

text
dominates F
    { last := c + String.length s✝, cost := Factory.text F c (String.length s✝), doc := Doc.text s✝,
      x := c + String.length s✝, y := i }
    m₂ =   true
    
α: Type

F: Factory α

s✝: String

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F (Doc.text s✝) c i m₁

h': MeasRender F (Doc.text s✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

dominates F m₁ m₂ = truecases 
h': MeasRender F (Doc.text s✝) c' i' m₂
h'
α: Type

F: Factory α

s✝: String

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

text.text
dominates F
    { last := c + String.length s✝, cost := Factory.text F c (String.length s✝), doc := Doc.text s✝,
      x := c + String.length s✝, y := i }
    { last := c' + String.length s✝, cost := Factory.text F c' (String.length s✝), doc := Doc.text s✝,
      x := c' + String.length s✝, y := i' } =   true
    
α: Type

F: Factory α

s✝: String

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F (Doc.text s✝) c i m₁

h': MeasRender F (Doc.text s✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

dominates F m₁ m₂ = truesimp only [
      
dominates: {α : Type} → Factory α → Meas → Meas → Bool
dominates, 
add_le_add_iff_right: ∀ {α : Type ?u.815} [inst : Add α] [inst_1 : LE α]
  [inst_2 : CovariantClass α α (Function.swap fun x x_1 => x + x_1) fun x x_1 => x ≤ x_1]
  [inst_3 : ContravariantClass α α (Function.swap fun x x_1 => x + x_1) fun x x_1 => x ≤ x_1] (a : α) {b c : α},
  b + a ≤ c + a ↔ b ≤ c
add_le_add_iff_right, 
Bool.decide_and: ∀ (p q : Prop) [inst : Decidable p] [inst_1 : Decidable q], decide (p ∧ q) = (decide p && decide q)
Bool.decide_and, 
Bool.decide_coe: ∀ (b : Bool) {h : Decidable (b = true)}, decide (b = true) = b
Bool.decide_coe,
      
Bool.and_eq_true: ∀ (a b : Bool), ((a && b) = true) = (a = true ∧ b = true)
Bool.and_eq_true, 
decide_eq_true_eq: ∀ {p : Prop} [inst : Decidable p], (decide p = true) = p
decide_eq_true_eq
    ]
α: Type

F: Factory α

s✝: String

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

text.text
c ≤ c' ∧ Factory.le F (Factory.text F c (String.length s✝)) (Factory.text F c' (String.length s✝)) = true
    
α: Type

F: Factory α

s✝: String

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F (Doc.text s✝) c i m₁

h': MeasRender F (Doc.text s✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

dominates F m₁ m₂ = trueconstructor
α: Type

F: Factory α

s✝: String

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

text.text.left
c ≤ c'
α: Type

F: Factory α

s✝: String

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

text.text.right
Factory.le F (Factory.text F c (String.length s✝)) (Factory.text F c' (String.length s✝)) = true
    
α: Type

F: Factory α

s✝: String

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F (Doc.text s✝) c i m₁

h': MeasRender F (Doc.text s✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

dominates F m₁ m₂ = truecase left => 
α: Type

F: Factory α

s✝: String

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

c ≤ c'linarith
Goals accomplished! 🐙 
    
α: Type

F: Factory α

s✝: String

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F (Doc.text s✝) c i m₁

h': MeasRender F (Doc.text s✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

dominates F m₁ m₂ = truecase right => 
α: Type

F: Factory α

s✝: String

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

Factory.le F (Factory.text F c (String.length s✝)) (Factory.text F c' (String.length s✝)) = truedwi { 
α: Type

F: Factory α

s✝: String

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

Factory.le F (Factory.text F c (String.length s✝)) (Factory.text F c' (String.length s✝)) = trueapply 
F: Factory α
F.
text_monotonic: ∀ {α : Type} (self : Factory α) {c c' l : ℕ},
  c ≤ c' → Factory.le self (Factory.text self c l) (Factory.text self c' l) = true
text_monotonic
α: Type

F: Factory α

s✝: String

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

c ≤ c' }
Goals accomplished! 🐙
  
α: Type

d: Doc

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

F: Factory α

h: MeasRender F d c i m₁

h': MeasRender F d c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

dominates F m₁ m₂ = truecase nl =>
    
α: Type

F: Factory α

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F Doc.nl c i m₁

h': MeasRender F Doc.nl c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

dominates F m₁ m₂ = truecases 
h: MeasRender F Doc.nl c i m₁
h
α: Type

F: Factory α

c, i, c', i': ℕ

m₂: Meas

h': MeasRender F Doc.nl c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

nl
dominates F { last := i, cost := Factory.nl F i, doc := Doc.nl, x := max c i, y := i } m₂ = true
    
α: Type

F: Factory α

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F Doc.nl c i m₁

h': MeasRender F Doc.nl c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

dominates F m₁ m₂ = truecases 
h': MeasRender F Doc.nl c' i' m₂
h'
α: Type

F: Factory α

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

nl.nl
dominates F { last := i, cost := Factory.nl F i, doc := Doc.nl, x := max c i, y := i }
    { last := i', cost := Factory.nl F i', doc := Doc.nl, x := max c' i', y := i' } =   true
    
α: Type

F: Factory α

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F Doc.nl c i m₁

h': MeasRender F Doc.nl c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

dominates F m₁ m₂ = truesimp only [
      
dominates: {α : Type} → Factory α → Meas → Meas → Bool
dominates, 
Bool.decide_and: ∀ (p q : Prop) [inst : Decidable p] [inst_1 : Decidable q], decide (p ∧ q) = (decide p && decide q)
Bool.decide_and, 
Bool.decide_coe: ∀ (b : Bool) {h : Decidable (b = true)}, decide (b = true) = b
Bool.decide_coe, 
Bool.and_eq_true: ∀ (a b : Bool), ((a && b) = true) = (a = true ∧ b = true)
Bool.and_eq_true, 
      
decide_eq_true_eq: ∀ {p : Prop} [inst : Decidable p], (decide p = true) = p
decide_eq_true_eq
    ]
α: Type

F: Factory α

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

nl.nl
i ≤ i' ∧ Factory.le F (Factory.nl F i) (Factory.nl F i') = true
    
α: Type

F: Factory α

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F Doc.nl c i m₁

h': MeasRender F Doc.nl c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

dominates F m₁ m₂ = truedwi { 
α: Type

F: Factory α

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

nl.nl
i ≤ i' ∧ Factory.le F (Factory.nl F i) (Factory.nl F i') = trueconstructor
α: Type

F: Factory α

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

nl.nl.left
i ≤ i'
α: Type

F: Factory α

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

nl.nl.right
Factory.le F (Factory.nl F i) (Factory.nl F i') = true }
α: Type

F: Factory α

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

nl.nl.right
Factory.le F (Factory.nl F i) (Factory.nl F i') = true
    
α: Type

F: Factory α

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F Doc.nl c i m₁

h': MeasRender F Doc.nl c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

dominates F m₁ m₂ = truecase right => 
α: Type

F: Factory α

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

Factory.le F (Factory.nl F i) (Factory.nl F i') = truedwi { 
α: Type

F: Factory α

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

Factory.le F (Factory.nl F i) (Factory.nl F i') = trueapply 
Factory.nl_monotonic: ∀ {α : Type} (self : Factory α) {i i' : ℕ}, i ≤ i' → Factory.le self (Factory.nl self i) (Factory.nl self i') = true
Factory.nl_monotonic
α: Type

F: Factory α

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

a
i ≤ i' }
Goals accomplished! 🐙
      
  
α: Type

d: Doc

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

F: Factory α

h: MeasRender F d c i m₁

h': MeasRender F d c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

dominates F m₁ m₂ = truecase nest 
ih: ?m.151 d✝
ih | align 
ih: ?m.151 d✝
ih =>
    
α: Type

F: Factory α

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ → MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F (Doc.align d✝) c i m₁

h': MeasRender F (Doc.align d✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

dominates F m₁ m₂ = truecases 
h: MeasRender F (Doc.nest n✝ d✝) c i m₁
h
α: Type

F: Factory α

n✝: ℕ

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ → MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

c, i, c', i': ℕ

m₂: Meas

h': MeasRender F (Doc.nest n✝ d✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

last✝: ℕ

cost✝: α

x✝, y✝: ℕ

h✝: MeasRender F d✝ c (i + n✝) { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }

nest
dominates F { last := last✝, cost := cost✝, doc := Doc.nest n✝ d✝, x := x✝, y := y✝ } m₂ = true
    
α: Type

F: Factory α

n✝: ℕ

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ → MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F (Doc.nest n✝ d✝) c i m₁

h': MeasRender F (Doc.nest n✝ d✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

dominates F m₁ m₂ = truerename_i 
h: MeasRender F d✝ c c { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }
h
α: Type

F: Factory α

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ → MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

c, i, c', i': ℕ

m₂: Meas

h': MeasRender F (Doc.align d✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

last✝: ℕ

cost✝: α

x✝, y✝: ℕ

h: MeasRender F d✝ c c { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }

align
dominates F { last := last✝, cost := cost✝, doc := Doc.align d✝, x := x✝, y := max i y✝ } m₂ = true
    
α: Type

F: Factory α

n✝: ℕ

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ → MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F (Doc.nest n✝ d✝) c i m₁

h': MeasRender F (Doc.nest n✝ d✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

dominates F m₁ m₂ = truecases 
h': MeasRender F (Doc.nest n✝ d✝) c' i' m₂
h'
α: Type

F: Factory α

n✝: ℕ

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ → MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

last✝¹: ℕ

cost✝¹: α

x✝¹, y✝¹: ℕ

h: MeasRender F d✝ c (i + n✝) { last := last✝¹, cost := cost✝¹, doc := d✝, x := x✝¹, y := y✝¹ }

last✝: ℕ

cost✝: α

x✝, y✝: ℕ

h✝: MeasRender F d✝ c' (i' + n✝) { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }

nest.nest
dominates F { last := last✝¹, cost := cost✝¹, doc := Doc.nest n✝ d✝, x := x✝¹, y := y✝¹ }
    { last := last✝, cost := cost✝, doc := Doc.nest n✝ d✝, x := x✝, y := y✝ } =   true 
    
α: Type

F: Factory α

n✝: ℕ

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ → MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F (Doc.nest n✝ d✝) c i m₁

h': MeasRender F (Doc.nest n✝ d✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

dominates F m₁ m₂ = truerename_i 
h': MeasRender F d✝ c' (i' + n✝) { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }
h'
α: Type

F: Factory α

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ → MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

last✝¹: ℕ

cost✝¹: α

x✝¹, y✝¹: ℕ

h: MeasRender F d✝ c c { last := last✝¹, cost := cost✝¹, doc := d✝, x := x✝¹, y := y✝¹ }

last✝: ℕ

cost✝: α

x✝, y✝: ℕ

h': MeasRender F d✝ c' c' { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }

align.align
dominates F { last := last✝¹, cost := cost✝¹, doc := Doc.align d✝, x := x✝¹, y := max i y✝¹ }
    { last := last✝, cost := cost✝, doc := Doc.align d✝, x := x✝, y := max i' y✝ } =   true
    
α: Type

F: Factory α

n✝: ℕ

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ → MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F (Doc.nest n✝ d✝) c i m₁

h': MeasRender F (Doc.nest n✝ d✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

dominates F m₁ m₂ = truespecialize 
ih: ?m.151 d✝
ih 
h: MeasRender F d✝ c (i + n✝) { last := last✝¹, cost := cost✝¹, doc := d✝, x := x✝¹, y := y✝¹ }
h 
h': MeasRender F d✝ c' (i' + n✝) { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }
h' 
h_c: c ≤ c'
h_c (
α: Type

F: Factory α

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ → MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

last✝¹: ℕ

cost✝¹: α

x✝¹, y✝¹: ℕ

h: MeasRender F d✝ c c { last := last✝¹, cost := cost✝¹, doc := d✝, x := x✝¹, y := y✝¹ }

last✝: ℕ

cost✝: α

x✝, y✝: ℕ

h': MeasRender F d✝ c' c' { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }

align.align
dominates F { last := last✝¹, cost := cost✝¹, doc := Doc.align d✝, x := x✝¹, y := max i y✝¹ }
    { last := last✝, cost := cost✝, doc := Doc.align d✝, x := x✝, y := max i' y✝ } =   trueby
Goals accomplished! 🐙 
α: Type

F: Factory α

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ → MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

last✝¹: ℕ

cost✝¹: α

x✝¹, y✝¹: ℕ

h: MeasRender F d✝ c c { last := last✝¹, cost := cost✝¹, doc := d✝, x := x✝¹, y := y✝¹ }

last✝: ℕ

cost✝: α

x✝, y✝: ℕ

h': MeasRender F d✝ c' c' { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }

c ≤ c'simpa
Goals accomplished! 🐙)
α: Type

F: Factory α

d✝: Doc

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

last✝¹: ℕ

cost✝¹: α

x✝¹, y✝¹: ℕ

h: MeasRender F d✝ c c { last := last✝¹, cost := cost✝¹, doc := d✝, x := x✝¹, y := y✝¹ }

last✝: ℕ

cost✝: α

x✝, y✝: ℕ

h': MeasRender F d✝ c' c' { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }

ih: dominates F { last := last✝¹, cost := cost✝¹, doc := d✝, x := x✝¹, y := y✝¹ }
    { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ } =   true

align.align
dominates F { last := last✝¹, cost := cost✝¹, doc := Doc.align d✝, x := x✝¹, y := max i y✝¹ }
    { last := last✝, cost := cost✝, doc := Doc.align d✝, x := x✝, y := max i' y✝ } =   true
    
α: Type

F: Factory α

n✝: ℕ

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ → MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F (Doc.nest n✝ d✝) c i m₁

h': MeasRender F (Doc.nest n✝ d✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

dominates F m₁ m₂ = trueassumption
Goals accomplished! 🐙
  
α: Type

d: Doc

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

F: Factory α

h: MeasRender F d c i m₁

h': MeasRender F d c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

dominates F m₁ m₂ = truecase concat 
ih₁: ?m.151 d₁✝
ih₁ 
ih₂: ?m.151 d₂✝
ih₂ => 
    
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₁: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₁✝ c i m₁ → MeasRender F d₁✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ → MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F (Doc.concat d₁✝ d₂✝) c i m₁

h': MeasRender F (Doc.concat d₁✝ d₂✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

dominates F m₁ m₂ = truecases 
h: MeasRender F (Doc.concat d₁✝ d₂✝) c i m₁
h
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₁: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₁✝ c i m₁ → MeasRender F d₁✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ → MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h': MeasRender F (Doc.concat d₁✝ d₂✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝, m₂✝: Meas

h₂✝: MeasRender F d₂✝ m₁✝.last i m₂✝

h₁✝: MeasRender F d₁✝ c i m₁✝

h✝: m₁ = Meas.concat F m₁✝ m₂✝

concat
dominates F m₁ m₂ = true 
    
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₁: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₁✝ c i m₁ → MeasRender F d₁✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ → MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F (Doc.concat d₁✝ d₂✝) c i m₁

h': MeasRender F (Doc.concat d₁✝ d₂✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

dominates F m₁ m₂ = truecase concat 
h₂: MeasRender F d₂✝ m₁✝.last i m₂✝
h₂ 
h₁: MeasRender F d₁✝ c i m₁✝
h₁ 
h_eq: m₁ = Meas.concat F m₁✝ m₂✝
h_eq => 
    
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₁: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₁✝ c i m₁ → MeasRender F d₁✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ → MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h': MeasRender F (Doc.concat d₁✝ d₂✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝, m₂✝: Meas

h₂: MeasRender F d₂✝ m₁✝.last i m₂✝

h₁: MeasRender F d₁✝ c i m₁✝

h_eq: m₁ = Meas.concat F m₁✝ m₂✝

dominates F m₁ m₂ = truecases 
h': MeasRender F (Doc.concat d₁✝ d₂✝) c' i' m₂
h'
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₁: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₁✝ c i m₁ → MeasRender F d₁✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ → MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

h_eq: m₁ = Meas.concat F m₁✝¹ m₂✝¹

m₁✝, m₂✝: Meas

h₂✝: MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁✝: MeasRender F d₁✝ c' i' m₁✝

h✝: m₂ = Meas.concat F m₁✝ m₂✝

concat
dominates F m₁ m₂ = true 
    
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₁: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₁✝ c i m₁ → MeasRender F d₁✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ → MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h': MeasRender F (Doc.concat d₁✝ d₂✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝, m₂✝: Meas

h₂: MeasRender F d₂✝ m₁✝.last i m₂✝

h₁: MeasRender F d₁✝ c i m₁✝

h_eq: m₁ = Meas.concat F m₁✝ m₂✝

dominates F m₁ m₂ = truecase concat 
h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝
h₂' 
h₁': MeasRender F d₁✝ c' i' m₁✝
h₁' 
h_eq': m₂ = Meas.concat F m₁✝ m₂✝
h_eq' => 
    
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₁: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₁✝ c i m₁ → MeasRender F d₁✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ → MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

h_eq: m₁ = Meas.concat F m₁✝¹ m₂✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_eq': m₂ = Meas.concat F m₁✝ m₂✝

dominates F m₁ m₂ = truespecialize 
ih₁: ?m.151 d₁✝
ih₁ 
h₁: MeasRender F d₁✝ c i m₁✝¹
h₁ 
h₁': MeasRender F d₁✝ c' i' m₁✝
h₁' 
h_c: c ≤ c'
h_c (
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₁: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₁✝ c i m₁ → MeasRender F d₁✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ → MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

h_eq: m₁ = Meas.concat F m₁✝¹ m₂✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_eq': m₂ = Meas.concat F m₁✝ m₂✝

dominates F m₁ m₂ = trueby
Goals accomplished! 🐙 
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₁: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₁✝ c i m₁ → MeasRender F d₁✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ → MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

h_eq: m₁ = Meas.concat F m₁✝¹ m₂✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_eq': m₂ = Meas.concat F m₁✝ m₂✝

i ≤ i'assumption
Goals accomplished! 🐙)
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ → MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

h_eq: m₁ = Meas.concat F m₁✝¹ m₂✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_eq': m₂ = Meas.concat F m₁✝ m₂✝

ih₁: dominates F m₁✝¹ m₁✝ = true

dominates F m₁ m₂ = true
    
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₁: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₁✝ c i m₁ → MeasRender F d₁✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ → MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

h_eq: m₁ = Meas.concat F m₁✝¹ m₂✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_eq': m₂ = Meas.concat F m₁✝ m₂✝

dominates F m₁ m₂ = truesimp only [
      
dominates: {α : Type} → Factory α → Meas → Meas → Bool
dominates, 
Bool.decide_and: ∀ (p q : Prop) [inst : Decidable p] [inst_1 : Decidable q], decide (p ∧ q) = (decide p && decide q)
Bool.decide_and, 
Bool.decide_coe: ∀ (b : Bool) {h : Decidable (b = true)}, decide (b = true) = b
Bool.decide_coe,
      
Bool.and_eq_true: ∀ (a b : Bool), ((a && b) = true) = (a = true ∧ b = true)
Bool.and_eq_true, 
decide_eq_true_eq: ∀ {p : Prop} [inst : Decidable p], (decide p = true) = p
decide_eq_true_eq
    ] at 
ih₁: dominates F m₁✝¹ m₁✝ = true
ih₁
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ → MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

h_eq: m₁ = Meas.concat F m₁✝¹ m₂✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_eq': m₂ = Meas.concat F m₁✝ m₂✝

ih₁: m₁✝¹.last ≤ m₁✝.last ∧ Factory.le F m₁✝¹.cost m₁✝.cost = true

dominates F m₁ m₂ = true
    
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₁: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₁✝ c i m₁ → MeasRender F d₁✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ → MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

h_eq: m₁ = Meas.concat F m₁✝¹ m₂✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_eq': m₂ = Meas.concat F m₁✝ m₂✝

dominates F m₁ m₂ = truespecialize 
ih₂: ?m.151 d₂✝
ih₂ 
h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹
h₂ 
h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝
h₂' (
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ → MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

h_eq: m₁ = Meas.concat F m₁✝¹ m₂✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_eq': m₂ = Meas.concat F m₁✝ m₂✝

ih₁: m₁✝¹.last ≤ m₁✝.last ∧ Factory.le F m₁✝¹.cost m₁✝.cost = true

dominates F m₁ m₂ = trueby
Goals accomplished! 🐙 
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ → MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

h_eq: m₁ = Meas.concat F m₁✝¹ m₂✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_eq': m₂ = Meas.concat F m₁✝ m₂✝

ih₁: m₁✝¹.last ≤ m₁✝.last ∧ Factory.le F m₁✝¹.cost m₁✝.cost = true

m₁✝¹.last ≤ m₁✝.lastsimp [
ih₁: m₁✝¹.last ≤ m₁✝.last ∧ Factory.le F m₁✝¹.cost m₁✝.cost = true
ih₁]
Goals accomplished! 🐙) (
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ → MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

h_eq: m₁ = Meas.concat F m₁✝¹ m₂✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_eq': m₂ = Meas.concat F m₁✝ m₂✝

ih₁: m₁✝¹.last ≤ m₁✝.last ∧ Factory.le F m₁✝¹.cost m₁✝.cost = true

dominates F m₁ m₂ = trueby
Goals accomplished! 🐙 
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ → MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

h_eq: m₁ = Meas.concat F m₁✝¹ m₂✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_eq': m₂ = Meas.concat F m₁✝ m₂✝

ih₁: m₁✝¹.last ≤ m₁✝.last ∧ Factory.le F m₁✝¹.cost m₁✝.cost = true

i ≤ i'assumption
Goals accomplished! 🐙)
α: Type

F: Factory α

d₁✝, d₂✝: Doc

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

h_eq: m₁ = Meas.concat F m₁✝¹ m₂✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_eq': m₂ = Meas.concat F m₁✝ m₂✝

ih₁: m₁✝¹.last ≤ m₁✝.last ∧ Factory.le F m₁✝¹.cost m₁✝.cost = true

ih₂: dominates F m₂✝¹ m₂✝ = true

dominates F m₁ m₂ = true
    
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₁: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₁✝ c i m₁ → MeasRender F d₁✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ → MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

h_eq: m₁ = Meas.concat F m₁✝¹ m₂✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_eq': m₂ = Meas.concat F m₁✝ m₂✝

dominates F m₁ m₂ = truesimp [
dominates: {α : Type} → Factory α → Meas → Meas → Bool
dominates] at 
ih₂: dominates F m₂✝¹ m₂✝ = true
ih₂ ⊢
α: Type

F: Factory α

d₁✝, d₂✝: Doc

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

h_eq: m₁ = Meas.concat F m₁✝¹ m₂✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_eq': m₂ = Meas.concat F m₁✝ m₂✝

ih₁: m₁✝¹.last ≤ m₁✝.last ∧ Factory.le F m₁✝¹.cost m₁✝.cost = true

ih₂: m₂✝¹.last ≤ m₂✝.last ∧ Factory.le F m₂✝¹.cost m₂✝.cost = true

m₁.last ≤ m₂.last ∧ Factory.le F m₁.cost m₂.cost = true 
    
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₁: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₁✝ c i m₁ → MeasRender F d₁✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ → MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

h_eq: m₁ = Meas.concat F m₁✝¹ m₂✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_eq': m₂ = Meas.concat F m₁✝ m₂✝

dominates F m₁ m₂ = trueconstructor
α: Type

F: Factory α

d₁✝, d₂✝: Doc

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

h_eq: m₁ = Meas.concat F m₁✝¹ m₂✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_eq': m₂ = Meas.concat F m₁✝ m₂✝

ih₁: m₁✝¹.last ≤ m₁✝.last ∧ Factory.le F m₁✝¹.cost m₁✝.cost = true

ih₂: m₂✝¹.last ≤ m₂✝.last ∧ Factory.le F m₂✝¹.cost m₂✝.cost = true

left
m₁.last ≤ m₂.last
α: Type

F: Factory α

d₁✝, d₂✝: Doc

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

h_eq: m₁ = Meas.concat F m₁✝¹ m₂✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_eq': m₂ = Meas.concat F m₁✝ m₂✝

ih₁: m₁✝¹.last ≤ m₁✝.last ∧ Factory.le F m₁✝¹.cost m₁✝.cost = true

ih₂: m₂✝¹.last ≤ m₂✝.last ∧ Factory.le F m₂✝¹.cost m₂✝.cost = true

right
Factory.le F m₁.cost m₂.cost = true
    
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₁: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₁✝ c i m₁ → MeasRender F d₁✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ → MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

h_eq: m₁ = Meas.concat F m₁✝¹ m₂✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_eq': m₂ = Meas.concat F m₁✝ m₂✝

dominates F m₁ m₂ = truecase left => 
α: Type

F: Factory α

d₁✝, d₂✝: Doc

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

h_eq: m₁ = Meas.concat F m₁✝¹ m₂✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_eq': m₂ = Meas.concat F m₁✝ m₂✝

ih₁: m₁✝¹.last ≤ m₁✝.last ∧ Factory.le F m₁✝¹.cost m₁✝.cost = true

ih₂: m₂✝¹.last ≤ m₂✝.last ∧ Factory.le F m₂✝¹.cost m₂✝.cost = true

m₁.last ≤ m₂.lastsimp [*]
Goals accomplished! 🐙
    
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₁: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₁✝ c i m₁ → MeasRender F d₁✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ → MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

h_eq: m₁ = Meas.concat F m₁✝¹ m₂✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_eq': m₂ = Meas.concat F m₁✝ m₂✝

dominates F m₁ m₂ = truecase right => 
      
α: Type

F: Factory α

d₁✝, d₂✝: Doc

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

h_eq: m₁ = Meas.concat F m₁✝¹ m₂✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_eq': m₂ = Meas.concat F m₁✝ m₂✝

ih₁: m₁✝¹.last ≤ m₁✝.last ∧ Factory.le F m₁✝¹.cost m₁✝.cost = true

ih₂: m₂✝¹.last ≤ m₂✝.last ∧ Factory.le F m₂✝¹.cost m₂✝.cost = true

Factory.le F m₁.cost m₂.cost = truesimp [*]
α: Type

F: Factory α

d₁✝, d₂✝: Doc

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

h_eq: m₁ = Meas.concat F m₁✝¹ m₂✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_eq': m₂ = Meas.concat F m₁✝ m₂✝

ih₁: m₁✝¹.last ≤ m₁✝.last ∧ Factory.le F m₁✝¹.cost m₁✝.cost = true

ih₂: m₂✝¹.last ≤ m₂✝.last ∧ Factory.le F m₂✝¹.cost m₂✝.cost = true

Factory.le F (Factory.concat F m₁✝¹.cost m₂✝¹.cost) (Factory.concat F m₁✝.cost m₂✝.cost) = true
      
α: Type

F: Factory α

d₁✝, d₂✝: Doc

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

h_eq: m₁ = Meas.concat F m₁✝¹ m₂✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_eq': m₂ = Meas.concat F m₁✝ m₂✝

ih₁: m₁✝¹.last ≤ m₁✝.last ∧ Factory.le F m₁✝¹.cost m₁✝.cost = true

ih₂: m₂✝¹.last ≤ m₂✝.last ∧ Factory.le F m₂✝¹.cost m₂✝.cost = true

Factory.le F m₁.cost m₂.cost = trueapply 
Factory.concat_monotonic: ∀ {α : Type} (self : Factory α) {cost₁ cost₂ cost₃ cost₄ : α},
  Factory.le self cost₁ cost₂ = true →
    Factory.le self cost₃ cost₄ = true →
      Factory.le self (Factory.concat self cost₁ cost₃) (Factory.concat self cost₂ cost₄) = true
Factory.concat_monotonic
α: Type

F: Factory α

d₁✝, d₂✝: Doc

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

h_eq: m₁ = Meas.concat F m₁✝¹ m₂✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_eq': m₂ = Meas.concat F m₁✝ m₂✝

ih₁: m₁✝¹.last ≤ m₁✝.last ∧ Factory.le F m₁✝¹.cost m₁✝.cost = true

ih₂: m₂✝¹.last ≤ m₂✝.last ∧ Factory.le F m₂✝¹.cost m₂✝.cost = true

a
Factory.le F m₁✝¹.cost m₁✝.cost = true
α: Type

F: Factory α

d₁✝, d₂✝: Doc

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

h_eq: m₁ = Meas.concat F m₁✝¹ m₂✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_eq': m₂ = Meas.concat F m₁✝ m₂✝

ih₁: m₁✝¹.last ≤ m₁✝.last ∧ Factory.le F m₁✝¹.cost m₁✝.cost = true

ih₂: m₂✝¹.last ≤ m₂✝.last ∧ Factory.le F m₂✝¹.cost m₂✝.cost = true

a
Factory.le F m₂✝¹.cost m₂✝.cost = true
      
α: Type

F: Factory α

d₁✝, d₂✝: Doc

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

h_eq: m₁ = Meas.concat F m₁✝¹ m₂✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_eq': m₂ = Meas.concat F m₁✝ m₂✝

ih₁: m₁✝¹.last ≤ m₁✝.last ∧ Factory.le F m₁✝¹.cost m₁✝.cost = true

ih₂: m₂✝¹.last ≤ m₂✝.last ∧ Factory.le F m₂✝¹.cost m₂✝.cost = true

Factory.le F m₁.cost m₂.cost = true. 
α: Type

F: Factory α

d₁✝, d₂✝: Doc

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

h_eq: m₁ = Meas.concat F m₁✝¹ m₂✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_eq': m₂ = Meas.concat F m₁✝ m₂✝

ih₁: m₁✝¹.last ≤ m₁✝.last ∧ Factory.le F m₁✝¹.cost m₁✝.cost = true

ih₂: m₂✝¹.last ≤ m₂✝.last ∧ Factory.le F m₂✝¹.cost m₂✝.cost = true

a
Factory.le F m₁✝¹.cost m₁✝.cost = true
α: Type

F: Factory α

d₁✝, d₂✝: Doc

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

h_eq: m₁ = Meas.concat F m₁✝¹ m₂✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_eq': m₂ = Meas.concat F m₁✝ m₂✝

ih₁: m₁✝¹.last ≤ m₁✝.last ∧ Factory.le F m₁✝¹.cost m₁✝.cost = true

ih₂: m₂✝¹.last ≤ m₂✝.last ∧ Factory.le F m₂✝¹.cost m₂✝.cost = true

a
Factory.le F m₂✝¹.cost m₂✝.cost = truesimp [
ih₁: m₁✝¹.last ≤ m₁✝.last ∧ Factory.le F m₁✝¹.cost m₁✝.cost = true
ih₁.
right: ∀ {a b : Prop}, a ∧ b → b
right]
Goals accomplished! 🐙
      
α: Type

F: Factory α

d₁✝, d₂✝: Doc

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

h_eq: m₁ = Meas.concat F m₁✝¹ m₂✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_eq': m₂ = Meas.concat F m₁✝ m₂✝

ih₁: m₁✝¹.last ≤ m₁✝.last ∧ Factory.le F m₁✝¹.cost m₁✝.cost = true

ih₂: m₂✝¹.last ≤ m₂✝.last ∧ Factory.le F m₂✝¹.cost m₂✝.cost = true

Factory.le F m₁.cost m₂.cost = true. 
α: Type

F: Factory α

d₁✝, d₂✝: Doc

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

h_eq: m₁ = Meas.concat F m₁✝¹ m₂✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_eq': m₂ = Meas.concat F m₁✝ m₂✝

ih₁: m₁✝¹.last ≤ m₁✝.last ∧ Factory.le F m₁✝¹.cost m₁✝.cost = true

ih₂: m₂✝¹.last ≤ m₂✝.last ∧ Factory.le F m₂✝¹.cost m₂✝.cost = true

a
Factory.le F m₂✝¹.cost m₂✝.cost = truesimp [
ih₂: m₂✝¹.last ≤ m₂✝.last ∧ Factory.le F m₂✝¹.cost m₂✝.cost = true
ih₂]
Goals accomplished! 🐙
  
α: Type

d: Doc

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

F: Factory α

h: MeasRender F d c i m₁

h': MeasRender F d c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

dominates F m₁ m₂ = truecase choice => 
α: Type

F: Factory α

d₁✝, d₂✝: Doc

d₁_ih✝: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₁✝ c i m₁ → MeasRender F d₁✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

d₂_ih✝: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ → MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F (Doc.choice d₁✝ d₂✝) c i m₁

h': MeasRender F (Doc.choice d₁✝ d₂✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

dominates F m₁ m₂ = truecases 
h: MeasRender F (Doc.choice d₁✝ d₂✝) c i m₁
h
Goals accomplished! 🐙
}
Goals accomplished! 🐙

/--
Measure computation on a choiceless document preserves 
the doc component
-/
lemma 
MeasRender_doc: ∀ {α : Type} {F : Factory α} {d : Doc} {c i : ℕ} {m : Meas}, MeasRender F d c i m → Choiceless d → m.doc = d
MeasRender_doc (
h_render: MeasRender F d c i m
h_render : 
MeasRender: {α : Type} → Factory α → Doc → ℕ → ℕ → Meas → Prop
MeasRender 
F: ?m.10215
F 
d: ?m.10222
d 
c: ?m.10228
c 
i: ?m.10234
i 
m: ?m.10240
m) (
h: Choiceless d
h : 
Choiceless: Doc → Prop
Choiceless 
d: ?m.10222
d) : 
m: ?m.10240
m.
doc: {α : Type} → Meas → Doc
doc = 
d: ?m.10222
d := by
Goals accomplished! 🐙 
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

h_render: MeasRender F d c i m

h: Choiceless d

m.doc = d{
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

h_render: MeasRender F d c i m

h: Choiceless d

m.doc = d
  
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

h_render: MeasRender F d c i m

h: Choiceless d

m.doc = dlet ⟨⟨
s: String
s, 
ss: List String
ss⟩, 
h: Render d c i { fst := s, rst := ss }
h⟩ := @
Render_total: ∀ {d : Doc} (c i : ℕ), Choiceless d → ∃ L, Render d c i L
Render_total 
d: Doc
d 
c: ℕ
c 
i: ℕ
i 
h: Choiceless d
h
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

h_render: MeasRender F d c i m

h✝: Choiceless d

s: String

ss: List String

h: Render d c i { fst := s, rst := ss }

m.doc = d
  
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

h_render: MeasRender F d c i m

h: Choiceless d

m.doc = dcases 
ss: List String
ss
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

h_render: MeasRender F d c i m

h✝: Choiceless d

s: String

h: Render d c i { fst := s, rst := [] }

nil
m.doc = d
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

h_render: MeasRender F d c i m

h✝: Choiceless d

s, head✝: String

tail✝: List String

h: Render d c i { fst := s, rst := head✝ :: tail✝ }

cons
m.doc = d 
  
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

h_render: MeasRender F d c i m

h: Choiceless d

m.doc = dcase nil => 
    
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

h_render: MeasRender F d c i m

h✝: Choiceless d

s: String

h: Render d c i { fst := s, rst := [] }

m.doc = dlet ⟨
cost: α✝
cost, ⟨
y: ℕ
y, 
h_render': MeasRender F d c i { last := c + String.length s, cost := cost, doc := d, x := c + String.length s, y := y }
h_render'⟩⟩ := 
MeasRender_single_correct: ∀ {α : Type} {d : Doc} {c i : ℕ} {s : String} (F : Factory α),
  Render d c i { fst := s, rst := [] } →
    ∃ cost y,
      MeasRender F d c i { last := c + String.length s, cost := cost, doc := d, x := c + String.length s, y := y }
MeasRender_single_correct 
F: Factory α✝
F 
h: Render d c i { fst := s, rst := [] }
h
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

h_render: MeasRender F d c i m

h✝: Choiceless d

s: String

h: Render d c i { fst := s, rst := [] }

cost: α✝

y: ℕ

h_render': MeasRender F d c i { last := c + String.length s, cost := cost, doc := d, x := c + String.length s, y := y }

m.doc = d
    
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

h_render: MeasRender F d c i m

h✝: Choiceless d

s: String

h: Render d c i { fst := s, rst := [] }

m.doc = dcases 
MeasRender_deterministic: ∀ {α : Type} {d : Doc} {c i : ℕ} {F : Factory α} {m₁ m₂ : Meas}, MeasRender F d c i m₁ → MeasRender F d c i m₂ → m₁ = m₂
MeasRender_deterministic 
h_render: MeasRender F d c i m
h_render 
h_render': MeasRender F d c i { last := c + String.length s, cost := cost, doc := d, x := c + String.length s, y := y }
h_render'
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

h✝: Choiceless d

s: String

h: Render d c i { fst := s, rst := [] }

cost: α✝

y: ℕ

h_render', h_render: MeasRender F d c i { last := c + String.length s, cost := cost, doc := d, x := c + String.length s, y := y }

refl
{ last := c + String.length s, cost := cost, doc := d, x := c + String.length s, y := y }.doc = d
    
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

h_render: MeasRender F d c i m

h✝: Choiceless d

s: String

h: Render d c i { fst := s, rst := [] }

m.doc = dsimp
Goals accomplished! 🐙
  
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

h_render: MeasRender F d c i m

h: Choiceless d

m.doc = dcase cons 
hd: ?m.10423
hd 
tl: List ?m.10423
tl => 
    
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

h_render: MeasRender F d c i m

h✝: Choiceless d

s, hd: String

tl: List String

h: Render d c i { fst := s, rst := hd :: tl }

m.doc = dlet ⟨
cost: α✝
cost, ⟨
y: ℕ
y, 
h_render': MeasRender F d c i
  { last := String.length (List.getLast (hd :: tl) ?m.10797), cost := cost, doc := d,
    x := Layout.max_with_offset c { fst := s, rst := hd :: tl }, y := y }
h_render'⟩⟩ := 
MeasRender_multi_correct: ∀ {α : Type} {d : Doc} {c i : ℕ} {s : String} {ss : List String} (F : Factory α),
  Render d c i { fst := s, rst := ss } →
    ∀ (h_non_empty : ss ≠ []),
      ∃ cost y,
        MeasRender F d c i
          { last := String.length (List.getLast ss h_non_empty), cost := cost, doc := d,
            x := Layout.max_with_offset c { fst := s, rst := ss }, y := y }
MeasRender_multi_correct 
F: Factory α✝
F 
h: Render d c i { fst := s, rst := hd :: tl }
h (
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

h_render: MeasRender F d c i m

h✝: Choiceless d

s, hd: String

tl: List String

h: Render d c i { fst := s, rst := hd :: tl }

m.doc = dby
Goals accomplished! 🐙 
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

h_render: MeasRender F d c i m

h✝: Choiceless d

s, hd: String

tl: List String

h: Render d c i { fst := s, rst := hd :: tl }

hd :: tl ≠ []simp
Goals accomplished! 🐙)
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

h_render: MeasRender F d c i m

h✝: Choiceless d

s, hd: String

tl: List String

h: Render d c i { fst := s, rst := hd :: tl }

cost: α✝

y: ℕ

h_render': MeasRender F d c i
  { last := String.length (List.getLast (hd :: tl) (_ : ¬hd :: tl = [])), cost := cost, doc := d,
    x := Layout.max_with_offset c { fst := s, rst := hd :: tl }, y := y }

m.doc = d
    
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

h_render: MeasRender F d c i m

h✝: Choiceless d

s, hd: String

tl: List String

h: Render d c i { fst := s, rst := hd :: tl }

m.doc = dcases 
MeasRender_deterministic: ∀ {α : Type} {d : Doc} {c i : ℕ} {F : Factory α} {m₁ m₂ : Meas}, MeasRender F d c i m₁ → MeasRender F d c i m₂ → m₁ = m₂
MeasRender_deterministic 
h_render: MeasRender F d c i m
h_render 
h_render': MeasRender F d c i
  { last := String.length (List.getLast (hd :: tl) ?m.10797), cost := cost, doc := d,
    x := Layout.max_with_offset c { fst := s, rst := hd :: tl }, y := y }
h_render'
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

h✝: Choiceless d

s, hd: String

tl: List String

h: Render d c i { fst := s, rst := hd :: tl }

cost: α✝

y: ℕ

h_render', h_render: MeasRender F d c i
  { last := String.length (List.getLast (hd :: tl) (_ : ¬hd :: tl = [])), cost := cost, doc := d,
    x := Layout.max_with_offset c { fst := s, rst := hd :: tl }, y := y }

refl
{ last := String.length (List.getLast (hd :: tl) (_ : ¬hd :: tl = [])), cost := cost, doc := d,
      x := Layout.max_with_offset c { fst := s, rst := hd :: tl }, y := y }.doc =   d
    
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

h_render: MeasRender F d c i m

h✝: Choiceless d

s, hd: String

tl: List String

h: Render d c i { fst := s, rst := hd :: tl }

m.doc = dsimp
Goals accomplished! 🐙
}
Goals accomplished! 🐙

/--
If measure computation at higher column position or indentation level 
does not exceed the computation width limit, then the current measure computation 
also does not exceed the computation width limit
-/
lemma 
MeasRender_dom_is_good: ∀ {α : Type} {d : Doc} {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas} {F : Factory α},
  MeasRender F d c i m₁ → MeasRender F d c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W
MeasRender_dom_is_good {
F: Factory α
F : 
Factory: Type → Type
Factory 
α: ?m.11376
α}
    (
h: MeasRender F d c i m₁
h : 
MeasRender: {α : Type} → Factory α → Doc → ℕ → ℕ → Meas → Prop
MeasRender 
F: Factory α
F 
d: ?m.11384
d 
c: ?m.11391
c 
i: ?m.11398
i 
m₁: ?m.11405
m₁) (
h': MeasRender F d c' i' m₂
h' : 
MeasRender: {α : Type} → Factory α → Doc → ℕ → ℕ → Meas → Prop
MeasRender 
F: Factory α
F 
d: ?m.11384
d 
c': ?m.11416
c' 
i': ?m.11426
i' 
m₂: ?m.11436
m₂)
    (
h_c: c ≤ c'
h_c : 
c: ?m.11391
c ≤ 
c': ?m.11416
c') (
h_i: i ≤ i'
h_i : 
i: ?m.11398
i ≤ 
i': ?m.11426
i') (
h_x: m₂.x ≤ F.W
h_x : 
m₂: ?m.11436
m₂.
x: {α : Type} → Meas → ℕ
x ≤ 
F: Factory α
F.
W: {α : Type} → Factory α → ℕ
W) (
h_y: m₂.y ≤ F.W
h_y : 
m₂: ?m.11436
m₂.
y: {α : Type} → Meas → ℕ
y ≤ 
F: Factory α
F.
W: {α : Type} → Factory α → ℕ
W) : 
    
m₁: ?m.11405
m₁.
x: {α : Type} → Meas → ℕ
x ≤ 
F: Factory α
F.
W: {α : Type} → Factory α → ℕ
W ∧ 
m₁: ?m.11405
m₁.
y: {α : Type} → Meas → ℕ
y ≤ 
F: Factory α
F.
W: {α : Type} → Factory α → ℕ
W := by
Goals accomplished! 🐙 
α: Type

d: Doc

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

F: Factory α

h: MeasRender F d c i m₁

h': MeasRender F d c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁.x ≤ F.W ∧ m₁.y ≤ F.W{
α: Type

d: Doc

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

F: Factory α

h: MeasRender F d c i m₁

h': MeasRender F d c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁.x ≤ F.W ∧ m₁.y ≤ F.W
  
α: Type

d: Doc

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

F: Factory α

h: MeasRender F d c i m₁

h': MeasRender F d c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁.x ≤ F.W ∧ m₁.y ≤ F.Winduction 
d: Doc
d generalizing 
c: ℕ
c 
c': ℕ
c' 
i: ℕ
i 
i': ℕ
i' 
m₁: Meas
m₁ 
m₂: Meas
m₂
α: Type

F: Factory α

s✝: String

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F (Doc.text s✝) c i m₁

h': MeasRender F (Doc.text s✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

text
m₁.x ≤ F.W ∧ m₁.y ≤ F.W
α: Type

F: Factory α

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F Doc.nl c i m₁

h': MeasRender F Doc.nl c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

nl
m₁.x ≤ F.W ∧ m₁.y ≤ F.W
α: Type

F: Factory α

d₁✝, d₂✝: Doc

d₁_ih✝: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₁✝ c i m₁ →
    MeasRender F d₁✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

d₂_ih✝: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ →
    MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F (Doc.concat d₁✝ d₂✝) c i m₁

h': MeasRender F (Doc.concat d₁✝ d₂✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

concat
m₁.x ≤ F.W ∧ m₁.y ≤ F.W
α: Type

F: Factory α

n✝: ℕ

d✝: Doc

d_ih✝: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F (Doc.nest n✝ d✝) c i m₁

h': MeasRender F (Doc.nest n✝ d✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

nest
m₁.x ≤ F.W ∧ m₁.y ≤ F.W
α: Type

F: Factory α

d✝: Doc

d_ih✝: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F (Doc.align d✝) c i m₁

h': MeasRender F (Doc.align d✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

align
m₁.x ≤ F.W ∧ m₁.y ≤ F.W
α: Type

F: Factory α

d₁✝, d₂✝: Doc

d₁_ih✝: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₁✝ c i m₁ →
    MeasRender F d₁✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

d₂_ih✝: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ →
    MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F (Doc.choice d₁✝ d₂✝) c i m₁

h': MeasRender F (Doc.choice d₁✝ d₂✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

choice
m₁.x ≤ F.W ∧ m₁.y ≤ F.W
  
α: Type

d: Doc

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

F: Factory α

h: MeasRender F d c i m₁

h': MeasRender F d c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁.x ≤ F.W ∧ m₁.y ≤ F.Wcase text => 
    
α: Type

F: Factory α

s✝: String

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F (Doc.text s✝) c i m₁

h': MeasRender F (Doc.text s✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁.x ≤ F.W ∧ m₁.y ≤ F.Wcases 
h: MeasRender F (Doc.text s✝) c i m₁
h
α: Type

F: Factory α

s✝: String

c, i, c', i': ℕ

m₂: Meas

h': MeasRender F (Doc.text s✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

text
{ last := c + String.length s✝, cost := Factory.text F c (String.length s✝), doc := Doc.text s✝,
        x := c + String.length s✝, y := i }.x ≤     F.W ∧   { last := c + String.length s✝, cost := Factory.text F c (String.length s✝), doc := Doc.text s✝,
        x := c + String.length s✝, y := i }.y ≤     F.W
    
α: Type

F: Factory α

s✝: String

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F (Doc.text s✝) c i m₁

h': MeasRender F (Doc.text s✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁.x ≤ F.W ∧ m₁.y ≤ F.Wcases 
h': MeasRender F (Doc.text s✝) c' i' m₂
h'
α: Type

F: Factory α

s✝: String

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

h_x: { last := c' + String.length s✝, cost := Factory.text F c' (String.length s✝), doc := Doc.text s✝,
      x := c' + String.length s✝, y := i' }.x ≤   F.W

h_y: { last := c' + String.length s✝, cost := Factory.text F c' (String.length s✝), doc := Doc.text s✝,
      x := c' + String.length s✝, y := i' }.y ≤   F.W

text.text
{ last := c + String.length s✝, cost := Factory.text F c (String.length s✝), doc := Doc.text s✝,
        x := c + String.length s✝, y := i }.x ≤     F.W ∧   { last := c + String.length s✝, cost := Factory.text F c (String.length s✝), doc := Doc.text s✝,
        x := c + String.length s✝, y := i }.y ≤     F.W
    
α: Type

F: Factory α

s✝: String

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F (Doc.text s✝) c i m₁

h': MeasRender F (Doc.text s✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁.x ≤ F.W ∧ m₁.y ≤ F.Wsimp only [
      
dominates: {α : Type} → Factory α → Meas → Meas → Bool
dominates, 
add_le_add_iff_right: ∀ {α : Type ?u.12217} [inst : Add α] [inst_1 : LE α]
  [inst_2 : CovariantClass α α (Function.swap fun x x_1 => x + x_1) fun x x_1 => x ≤ x_1]
  [inst_3 : ContravariantClass α α (Function.swap fun x x_1 => x + x_1) fun x x_1 => x ≤ x_1] (a : α) {b c : α},
  b + a ≤ c + a ↔ b ≤ c
add_le_add_iff_right, 
Bool.decide_and: ∀ (p q : Prop) [inst : Decidable p] [inst_1 : Decidable q], decide (p ∧ q) = (decide p && decide q)
Bool.decide_and, 
Bool.decide_coe: ∀ (b : Bool) {h : Decidable (b = true)}, decide (b = true) = b
Bool.decide_coe,
      
Bool.and_eq_true: ∀ (a b : Bool), ((a && b) = true) = (a = true ∧ b = true)
Bool.and_eq_true, 
decide_eq_true_eq: ∀ {p : Prop} [inst : Decidable p], (decide p = true) = p
decide_eq_true_eq
    ]
α: Type

F: Factory α

s✝: String

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

h_x: { last := c' + String.length s✝, cost := Factory.text F c' (String.length s✝), doc := Doc.text s✝,
      x := c' + String.length s✝, y := i' }.x ≤   F.W

h_y: { last := c' + String.length s✝, cost := Factory.text F c' (String.length s✝), doc := Doc.text s✝,
      x := c' + String.length s✝, y := i' }.y ≤   F.W

text.text
c + String.length s✝ ≤ F.W ∧ i ≤ F.W
    
α: Type

F: Factory α

s✝: String

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F (Doc.text s✝) c i m₁

h': MeasRender F (Doc.text s✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁.x ≤ F.W ∧ m₁.y ≤ F.Wconstructor
α: Type

F: Factory α

s✝: String

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

h_x: { last := c' + String.length s✝, cost := Factory.text F c' (String.length s✝), doc := Doc.text s✝,
      x := c' + String.length s✝, y := i' }.x ≤   F.W

h_y: { last := c' + String.length s✝, cost := Factory.text F c' (String.length s✝), doc := Doc.text s✝,
      x := c' + String.length s✝, y := i' }.y ≤   F.W

text.text.left
c + String.length s✝ ≤ F.W
α: Type

F: Factory α

s✝: String

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

h_x: { last := c' + String.length s✝, cost := Factory.text F c' (String.length s✝), doc := Doc.text s✝,
      x := c' + String.length s✝, y := i' }.x ≤   F.W

h_y: { last := c' + String.length s✝, cost := Factory.text F c' (String.length s✝), doc := Doc.text s✝,
      x := c' + String.length s✝, y := i' }.y ≤   F.W

text.text.right
i ≤ F.W
    
α: Type

F: Factory α

s✝: String

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F (Doc.text s✝) c i m₁

h': MeasRender F (Doc.text s✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁.x ≤ F.W ∧ m₁.y ≤ F.Wcase left => 
α: Type

F: Factory α

s✝: String

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

h_x: { last := c' + String.length s✝, cost := Factory.text F c' (String.length s✝), doc := Doc.text s✝,
      x := c' + String.length s✝, y := i' }.x ≤   F.W

h_y: { last := c' + String.length s✝, cost := Factory.text F c' (String.length s✝), doc := Doc.text s✝,
      x := c' + String.length s✝, y := i' }.y ≤   F.W

c + String.length s✝ ≤ F.Wlinarith
Goals accomplished! 🐙 
    
α: Type

F: Factory α

s✝: String

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F (Doc.text s✝) c i m₁

h': MeasRender F (Doc.text s✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁.x ≤ F.W ∧ m₁.y ≤ F.Wcase right => 
      
α: Type

F: Factory α

s✝: String

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

h_x: { last := c' + String.length s✝, cost := Factory.text F c' (String.length s✝), doc := Doc.text s✝,
      x := c' + String.length s✝, y := i' }.x ≤   F.W

h_y: { last := c' + String.length s✝, cost := Factory.text F c' (String.length s✝), doc := Doc.text s✝,
      x := c' + String.length s✝, y := i' }.y ≤   F.W

i ≤ F.Wsimp at 
h_y: { last := c' + String.length s✝, cost := Factory.text F c' (String.length s✝), doc := Doc.text s✝,
      x := c' + String.length s✝, y := i' }.y ≤   F.W
h_y
α: Type

F: Factory α

s✝: String

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

h_x: { last := c' + String.length s✝, cost := Factory.text F c' (String.length s✝), doc := Doc.text s✝,
      x := c' + String.length s✝, y := i' }.x ≤   F.W

h_y: i' ≤ F.W

i ≤ F.W 
      
α: Type

F: Factory α

s✝: String

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

h_x: { last := c' + String.length s✝, cost := Factory.text F c' (String.length s✝), doc := Doc.text s✝,
      x := c' + String.length s✝, y := i' }.x ≤   F.W

h_y: { last := c' + String.length s✝, cost := Factory.text F c' (String.length s✝), doc := Doc.text s✝,
      x := c' + String.length s✝, y := i' }.y ≤   F.W

i ≤ F.Wdwi { 
α: Type

F: Factory α

s✝: String

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

h_x: { last := c' + String.length s✝, cost := Factory.text F c' (String.length s✝), doc := Doc.text s✝,
      x := c' + String.length s✝, y := i' }.x ≤   F.W

h_y: i' ≤ F.W

i ≤ F.Wapply 
le_trans: ∀ {α : Type ?u.14663} [inst : Preorder α] {a b c : α}, a ≤ b → b ≤ c → a ≤ c
le_trans
α: Type

F: Factory α

s✝: String

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

h_x: { last := c' + String.length s✝, cost := Factory.text F c' (String.length s✝), doc := Doc.text s✝,
      x := c' + String.length s✝, y := i' }.x ≤   F.W

h_y: i' ≤ F.W

a
i ≤ ?b
α: Type

F: Factory α

s✝: String

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

h_x: { last := c' + String.length s✝, cost := Factory.text F c' (String.length s✝), doc := Doc.text s✝,
      x := c' + String.length s✝, y := i' }.x ≤   F.W

h_y: i' ≤ F.W

a
?b ≤ F.W
α: Type

F: Factory α

s✝: String

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

h_x: { last := c' + String.length s✝, cost := Factory.text F c' (String.length s✝), doc := Doc.text s✝,
      x := c' + String.length s✝, y := i' }.x ≤   F.W

h_y: i' ≤ F.W

b
ℕ }
Goals accomplished! 🐙 

  
α: Type

d: Doc

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

F: Factory α

h: MeasRender F d c i m₁

h': MeasRender F d c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁.x ≤ F.W ∧ m₁.y ≤ F.Wcase nl =>
    
α: Type

F: Factory α

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F Doc.nl c i m₁

h': MeasRender F Doc.nl c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁.x ≤ F.W ∧ m₁.y ≤ F.Wcases 
h: MeasRender F Doc.nl c i m₁
h
α: Type

F: Factory α

c, i, c', i': ℕ

m₂: Meas

h': MeasRender F Doc.nl c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

nl
{ last := i, cost := Factory.nl F i, doc := Doc.nl, x := max c i, y := i }.x ≤ F.W ∧   { last := i, cost := Factory.nl F i, doc := Doc.nl, x := max c i, y := i }.y ≤ F.W
    
α: Type

F: Factory α

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F Doc.nl c i m₁

h': MeasRender F Doc.nl c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁.x ≤ F.W ∧ m₁.y ≤ F.Wcases 
h': MeasRender F Doc.nl c' i' m₂
h'
α: Type

F: Factory α

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

h_x: { last := i', cost := Factory.nl F i', doc := Doc.nl, x := max c' i', y := i' }.x ≤ F.W

h_y: { last := i', cost := Factory.nl F i', doc := Doc.nl, x := max c' i', y := i' }.y ≤ F.W

nl.nl
{ last := i, cost := Factory.nl F i, doc := Doc.nl, x := max c i, y := i }.x ≤ F.W ∧   { last := i, cost := Factory.nl F i, doc := Doc.nl, x := max c i, y := i }.y ≤ F.W
    
α: Type

F: Factory α

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F Doc.nl c i m₁

h': MeasRender F Doc.nl c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁.x ≤ F.W ∧ m₁.y ≤ F.Wsimp only [
      
dominates: {α : Type} → Factory α → Meas → Meas → Bool
dominates, 
Bool.decide_and: ∀ (p q : Prop) [inst : Decidable p] [inst_1 : Decidable q], decide (p ∧ q) = (decide p && decide q)
Bool.decide_and, 
Bool.decide_coe: ∀ (b : Bool) {h : Decidable (b = true)}, decide (b = true) = b
Bool.decide_coe, 
Bool.and_eq_true: ∀ (a b : Bool), ((a && b) = true) = (a = true ∧ b = true)
Bool.and_eq_true, 
      
decide_eq_true_eq: ∀ {p : Prop} [inst : Decidable p], (decide p = true) = p
decide_eq_true_eq
    ]
α: Type

F: Factory α

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

h_x: { last := i', cost := Factory.nl F i', doc := Doc.nl, x := max c' i', y := i' }.x ≤ F.W

h_y: { last := i', cost := Factory.nl F i', doc := Doc.nl, x := max c' i', y := i' }.y ≤ F.W

nl.nl
max c i ≤ F.W ∧ i ≤ F.W
    
α: Type

F: Factory α

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F Doc.nl c i m₁

h': MeasRender F Doc.nl c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁.x ≤ F.W ∧ m₁.y ≤ F.Wconstructor
α: Type

F: Factory α

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

h_x: { last := i', cost := Factory.nl F i', doc := Doc.nl, x := max c' i', y := i' }.x ≤ F.W

h_y: { last := i', cost := Factory.nl F i', doc := Doc.nl, x := max c' i', y := i' }.y ≤ F.W

nl.nl.left
max c i ≤ F.W
α: Type

F: Factory α

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

h_x: { last := i', cost := Factory.nl F i', doc := Doc.nl, x := max c' i', y := i' }.x ≤ F.W

h_y: { last := i', cost := Factory.nl F i', doc := Doc.nl, x := max c' i', y := i' }.y ≤ F.W

nl.nl.right
i ≤ F.W 
    
α: Type

F: Factory α

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F Doc.nl c i m₁

h': MeasRender F Doc.nl c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁.x ≤ F.W ∧ m₁.y ≤ F.Wcase left => 
      
α: Type

F: Factory α

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

h_x: { last := i', cost := Factory.nl F i', doc := Doc.nl, x := max c' i', y := i' }.x ≤ F.W

h_y: { last := i', cost := Factory.nl F i', doc := Doc.nl, x := max c' i', y := i' }.y ≤ F.W

max c i ≤ F.Wsimp at 
h_x: { last := i', cost := Factory.nl F i', doc := Doc.nl, x := max c' i', y := i' }.x ≤ F.W
h_x 
h_y: { last := i', cost := Factory.nl F i', doc := Doc.nl, x := max c' i', y := i' }.y ≤ F.W
h_y ⊢
α: Type

F: Factory α

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

h_y: i' ≤ F.W

h_x: c' ≤ F.W ∧ i' ≤ F.W

c ≤ F.W ∧ i ≤ F.W   
      
α: Type

F: Factory α

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

h_x: { last := i', cost := Factory.nl F i', doc := Doc.nl, x := max c' i', y := i' }.x ≤ F.W

h_y: { last := i', cost := Factory.nl F i', doc := Doc.nl, x := max c' i', y := i' }.y ≤ F.W

max c i ≤ F.Wconstructor
α: Type

F: Factory α

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

h_y: i' ≤ F.W

h_x: c' ≤ F.W ∧ i' ≤ F.W

left
c ≤ F.W
α: Type

F: Factory α

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

h_y: i' ≤ F.W

h_x: c' ≤ F.W ∧ i' ≤ F.W

right
i ≤ F.W 
      
α: Type

F: Factory α

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

h_x: { last := i', cost := Factory.nl F i', doc := Doc.nl, x := max c' i', y := i' }.x ≤ F.W

h_y: { last := i', cost := Factory.nl F i', doc := Doc.nl, x := max c' i', y := i' }.y ≤ F.W

max c i ≤ F.Wcase left => 
        
α: Type

F: Factory α

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

h_y: i' ≤ F.W

h_x: c' ≤ F.W ∧ i' ≤ F.W

c ≤ F.Wapply 
le_trans: ∀ {α : Type ?u.18588} [inst : Preorder α] {a b c : α}, a ≤ b → b ≤ c → a ≤ c
le_trans
α: Type

F: Factory α

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

h_y: i' ≤ F.W

h_x: c' ≤ F.W ∧ i' ≤ F.W

a
c ≤ ?b
α: Type

F: Factory α

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

h_y: i' ≤ F.W

h_x: c' ≤ F.W ∧ i' ≤ F.W

a
?b ≤ F.W
α: Type

F: Factory α

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

h_y: i' ≤ F.W

h_x: c' ≤ F.W ∧ i' ≤ F.W

b
ℕ 
        
α: Type

F: Factory α

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

h_y: i' ≤ F.W

h_x: c' ≤ F.W ∧ i' ≤ F.W

c ≤ F.W. 
α: Type

F: Factory α

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

h_y: i' ≤ F.W

h_x: c' ≤ F.W ∧ i' ≤ F.W

a
c ≤ ?b
α: Type

F: Factory α

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

h_y: i' ≤ F.W

h_x: c' ≤ F.W ∧ i' ≤ F.W

a
?b ≤ F.W
α: Type

F: Factory α

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

h_y: i' ≤ F.W

h_x: c' ≤ F.W ∧ i' ≤ F.W

b
ℕassumption
Goals accomplished! 🐙 
        
α: Type

F: Factory α

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

h_y: i' ≤ F.W

h_x: c' ≤ F.W ∧ i' ≤ F.W

c ≤ F.W. 
α: Type

F: Factory α

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

h_y: i' ≤ F.W

h_x: c' ≤ F.W ∧ i' ≤ F.W

a
c' ≤ F.Wsimp [
h_x: c' ≤ F.W ∧ i' ≤ F.W
h_x]
Goals accomplished! 🐙
      
α: Type

F: Factory α

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

h_x: { last := i', cost := Factory.nl F i', doc := Doc.nl, x := max c' i', y := i' }.x ≤ F.W

h_y: { last := i', cost := Factory.nl F i', doc := Doc.nl, x := max c' i', y := i' }.y ≤ F.W

max c i ≤ F.Wcase right => 
        
α: Type

F: Factory α

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

h_y: i' ≤ F.W

h_x: c' ≤ F.W ∧ i' ≤ F.W

i ≤ F.Wapply 
le_trans: ∀ {α : Type ?u.18721} [inst : Preorder α] {a b c : α}, a ≤ b → b ≤ c → a ≤ c
le_trans
α: Type

F: Factory α

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

h_y: i' ≤ F.W

h_x: c' ≤ F.W ∧ i' ≤ F.W

a
i ≤ ?b
α: Type

F: Factory α

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

h_y: i' ≤ F.W

h_x: c' ≤ F.W ∧ i' ≤ F.W

a
?b ≤ F.W
α: Type

F: Factory α

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

h_y: i' ≤ F.W

h_x: c' ≤ F.W ∧ i' ≤ F.W

b
ℕ 
        
α: Type

F: Factory α

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

h_y: i' ≤ F.W

h_x: c' ≤ F.W ∧ i' ≤ F.W

i ≤ F.W. 
α: Type

F: Factory α

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

h_y: i' ≤ F.W

h_x: c' ≤ F.W ∧ i' ≤ F.W

a
i ≤ ?b
α: Type

F: Factory α

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

h_y: i' ≤ F.W

h_x: c' ≤ F.W ∧ i' ≤ F.W

a
?b ≤ F.W
α: Type

F: Factory α

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

h_y: i' ≤ F.W

h_x: c' ≤ F.W ∧ i' ≤ F.W

b
ℕassumption
Goals accomplished! 🐙
        
α: Type

F: Factory α

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

h_y: i' ≤ F.W

h_x: c' ≤ F.W ∧ i' ≤ F.W

i ≤ F.W. 
α: Type

F: Factory α

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

h_y: i' ≤ F.W

h_x: c' ≤ F.W ∧ i' ≤ F.W

a
i' ≤ F.Wsimp [
h_y: i' ≤ F.W
h_y]
Goals accomplished! 🐙
    
α: Type

F: Factory α

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F Doc.nl c i m₁

h': MeasRender F Doc.nl c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁.x ≤ F.W ∧ m₁.y ≤ F.Wcase right => 
      
α: Type

F: Factory α

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

h_x: { last := i', cost := Factory.nl F i', doc := Doc.nl, x := max c' i', y := i' }.x ≤ F.W

h_y: { last := i', cost := Factory.nl F i', doc := Doc.nl, x := max c' i', y := i' }.y ≤ F.W

i ≤ F.Wsimp at 
h_y: { last := i', cost := Factory.nl F i', doc := Doc.nl, x := max c' i', y := i' }.y ≤ F.W
h_y
α: Type

F: Factory α

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

h_x: { last := i', cost := Factory.nl F i', doc := Doc.nl, x := max c' i', y := i' }.x ≤ F.W

h_y: i' ≤ F.W

i ≤ F.W 
      
α: Type

F: Factory α

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

h_x: { last := i', cost := Factory.nl F i', doc := Doc.nl, x := max c' i', y := i' }.x ≤ F.W

h_y: { last := i', cost := Factory.nl F i', doc := Doc.nl, x := max c' i', y := i' }.y ≤ F.W

i ≤ F.Wdwi { 
α: Type

F: Factory α

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

h_x: { last := i', cost := Factory.nl F i', doc := Doc.nl, x := max c' i', y := i' }.x ≤ F.W

h_y: i' ≤ F.W

i ≤ F.Wapply 
le_trans: ∀ {α : Type ?u.19056} [inst : Preorder α] {a b c : α}, a ≤ b → b ≤ c → a ≤ c
le_trans
α: Type

F: Factory α

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

h_x: { last := i', cost := Factory.nl F i', doc := Doc.nl, x := max c' i', y := i' }.x ≤ F.W

h_y: i' ≤ F.W

a
i ≤ ?b
α: Type

F: Factory α

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

h_x: { last := i', cost := Factory.nl F i', doc := Doc.nl, x := max c' i', y := i' }.x ≤ F.W

h_y: i' ≤ F.W

a
?b ≤ F.W
α: Type

F: Factory α

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

h_x: { last := i', cost := Factory.nl F i', doc := Doc.nl, x := max c' i', y := i' }.x ≤ F.W

h_y: i' ≤ F.W

b
ℕ }
Goals accomplished! 🐙 
  
α: Type

d: Doc

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

F: Factory α

h: MeasRender F d c i m₁

h': MeasRender F d c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁.x ≤ F.W ∧ m₁.y ≤ F.Wcase nest 
ih: ?m.11535 d✝
ih =>
    
α: Type

F: Factory α

n✝: ℕ

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F (Doc.nest n✝ d✝) c i m₁

h': MeasRender F (Doc.nest n✝ d✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁.x ≤ F.W ∧ m₁.y ≤ F.Wcases 
h: MeasRender F (Doc.nest n✝ d✝) c i m₁
h
α: Type

F: Factory α

n✝: ℕ

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

m₂: Meas

h': MeasRender F (Doc.nest n✝ d✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

last✝: ℕ

cost✝: α

x✝, y✝: ℕ

h✝: MeasRender F d✝ c (i + n✝) { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }

nest
{ last := last✝, cost := cost✝, doc := Doc.nest n✝ d✝, x := x✝, y := y✝ }.x ≤ F.W ∧   { last := last✝, cost := cost✝, doc := Doc.nest n✝ d✝, x := x✝, y := y✝ }.y ≤ F.W
    
α: Type

F: Factory α

n✝: ℕ

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F (Doc.nest n✝ d✝) c i m₁

h': MeasRender F (Doc.nest n✝ d✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁.x ≤ F.W ∧ m₁.y ≤ F.Wrename_i 
h: MeasRender F d✝ c (i + n✝) { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }
h
α: Type

F: Factory α

n✝: ℕ

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

m₂: Meas

h': MeasRender F (Doc.nest n✝ d✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

last✝: ℕ

cost✝: α

x✝, y✝: ℕ

h: MeasRender F d✝ c (i + n✝) { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }

nest
{ last := last✝, cost := cost✝, doc := Doc.nest n✝ d✝, x := x✝, y := y✝ }.x ≤ F.W ∧   { last := last✝, cost := cost✝, doc := Doc.nest n✝ d✝, x := x✝, y := y✝ }.y ≤ F.W
    
α: Type

F: Factory α

n✝: ℕ

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F (Doc.nest n✝ d✝) c i m₁

h': MeasRender F (Doc.nest n✝ d✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁.x ≤ F.W ∧ m₁.y ≤ F.Wcases 
h': MeasRender F (Doc.nest n✝ d✝) c' i' m₂
h'
α: Type

F: Factory α

n✝: ℕ

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

last✝¹: ℕ

cost✝¹: α

x✝¹, y✝¹: ℕ

h: MeasRender F d✝ c (i + n✝) { last := last✝¹, cost := cost✝¹, doc := d✝, x := x✝¹, y := y✝¹ }

last✝: ℕ

cost✝: α

x✝, y✝: ℕ

h✝: MeasRender F d✝ c' (i' + n✝) { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }

h_x: { last := last✝, cost := cost✝, doc := Doc.nest n✝ d✝, x := x✝, y := y✝ }.x ≤ F.W

h_y: { last := last✝, cost := cost✝, doc := Doc.nest n✝ d✝, x := x✝, y := y✝ }.y ≤ F.W

nest.nest
{ last := last✝¹, cost := cost✝¹, doc := Doc.nest n✝ d✝, x := x✝¹, y := y✝¹ }.x ≤ F.W ∧   { last := last✝¹, cost := cost✝¹, doc := Doc.nest n✝ d✝, x := x✝¹, y := y✝¹ }.y ≤ F.W 
    
α: Type

F: Factory α

n✝: ℕ

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F (Doc.nest n✝ d✝) c i m₁

h': MeasRender F (Doc.nest n✝ d✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁.x ≤ F.W ∧ m₁.y ≤ F.Wrename_i 
h': MeasRender F d✝ c' (i' + n✝) { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }
h'
α: Type

F: Factory α

n✝: ℕ

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

last✝¹: ℕ

cost✝¹: α

x✝¹, y✝¹: ℕ

h: MeasRender F d✝ c (i + n✝) { last := last✝¹, cost := cost✝¹, doc := d✝, x := x✝¹, y := y✝¹ }

last✝: ℕ

cost✝: α

x✝, y✝: ℕ

h': MeasRender F d✝ c' (i' + n✝) { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }

h_x: { last := last✝, cost := cost✝, doc := Doc.nest n✝ d✝, x := x✝, y := y✝ }.x ≤ F.W

h_y: { last := last✝, cost := cost✝, doc := Doc.nest n✝ d✝, x := x✝, y := y✝ }.y ≤ F.W

nest.nest
{ last := last✝¹, cost := cost✝¹, doc := Doc.nest n✝ d✝, x := x✝¹, y := y✝¹ }.x ≤ F.W ∧   { last := last✝¹, cost := cost✝¹, doc := Doc.nest n✝ d✝, x := x✝¹, y := y✝¹ }.y ≤ F.W
    
α: Type

F: Factory α

n✝: ℕ

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F (Doc.nest n✝ d✝) c i m₁

h': MeasRender F (Doc.nest n✝ d✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁.x ≤ F.W ∧ m₁.y ≤ F.Wsimp at 
ih: ?m.11535 d✝
ih 
h_x: { last := last✝, cost := cost✝, doc := Doc.nest n✝ d✝, x := x✝, y := y✝ }.x ≤ F.W
h_x 
h_y: { last := last✝, cost := cost✝, doc := Doc.nest n✝ d✝, x := x✝, y := y✝ }.y ≤ F.W
h_y ⊢
α: Type

F: Factory α

n✝: ℕ

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

last✝¹: ℕ

cost✝¹: α

x✝¹, y✝¹: ℕ

h: MeasRender F d✝ c (i + n✝) { last := last✝¹, cost := cost✝¹, doc := d✝, x := x✝¹, y := y✝¹ }

last✝: ℕ

cost✝: α

x✝, y✝: ℕ

h': MeasRender F d✝ c' (i' + n✝) { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }

h_x: x✝ ≤ F.W

h_y: y✝ ≤ F.W

nest.nest
x✝¹ ≤ F.W ∧ y✝¹ ≤ F.W
    
α: Type

F: Factory α

n✝: ℕ

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F (Doc.nest n✝ d✝) c i m₁

h': MeasRender F (Doc.nest n✝ d✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁.x ≤ F.W ∧ m₁.y ≤ F.Wexact 
ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W
ih 
h: MeasRender F d✝ c (i + n✝) { last := last✝¹, cost := cost✝¹, doc := d✝, x := x✝¹, y := y✝¹ }
h 
h': MeasRender F d✝ c' (i' + n✝) { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }
h' 
h_c: c ≤ c'
h_c (
α: Type

F: Factory α

n✝: ℕ

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

last✝¹: ℕ

cost✝¹: α

x✝¹, y✝¹: ℕ

h: MeasRender F d✝ c (i + n✝) { last := last✝¹, cost := cost✝¹, doc := d✝, x := x✝¹, y := y✝¹ }

last✝: ℕ

cost✝: α

x✝, y✝: ℕ

h': MeasRender F d✝ c' (i' + n✝) { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }

h_x: x✝ ≤ F.W

h_y: y✝ ≤ F.W

nest.nest
x✝¹ ≤ F.W ∧ y✝¹ ≤ F.Wby
Goals accomplished! 🐙 
α: Type

F: Factory α

n✝: ℕ

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

last✝¹: ℕ

cost✝¹: α

x✝¹, y✝¹: ℕ

h: MeasRender F d✝ c (i + n✝) { last := last✝¹, cost := cost✝¹, doc := d✝, x := x✝¹, y := y✝¹ }

last✝: ℕ

cost✝: α

x✝, y✝: ℕ

h': MeasRender F d✝ c' (i' + n✝) { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }

h_x: x✝ ≤ F.W

h_y: y✝ ≤ F.W

i + n✝ ≤ i' + n✝simpa
Goals accomplished! 🐙) 
h_x: x✝ ≤ F.W
h_x 
h_y: y✝ ≤ F.W
h_y
Goals accomplished! 🐙
  
α: Type

d: Doc

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

F: Factory α

h: MeasRender F d c i m₁

h': MeasRender F d c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁.x ≤ F.W ∧ m₁.y ≤ F.Wcase align 
ih: ?m.11535 d✝
ih =>
    
α: Type

F: Factory α

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F (Doc.align d✝) c i m₁

h': MeasRender F (Doc.align d✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁.x ≤ F.W ∧ m₁.y ≤ F.Wcases 
h: MeasRender F (Doc.align d✝) c i m₁
h
α: Type

F: Factory α

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

m₂: Meas

h': MeasRender F (Doc.align d✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

last✝: ℕ

cost✝: α

x✝, y✝: ℕ

h✝: MeasRender F d✝ c c { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }

align
{ last := last✝, cost := cost✝, doc := Doc.align d✝, x := x✝, y := max i y✝ }.x ≤ F.W ∧   { last := last✝, cost := cost✝, doc := Doc.align d✝, x := x✝, y := max i y✝ }.y ≤ F.W
    
α: Type

F: Factory α

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F (Doc.align d✝) c i m₁

h': MeasRender F (Doc.align d✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁.x ≤ F.W ∧ m₁.y ≤ F.Wrename_i 
h: MeasRender F d✝ c c { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }
h
α: Type

F: Factory α

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

m₂: Meas

h': MeasRender F (Doc.align d✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

last✝: ℕ

cost✝: α

x✝, y✝: ℕ

h: MeasRender F d✝ c c { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }

align
{ last := last✝, cost := cost✝, doc := Doc.align d✝, x := x✝, y := max i y✝ }.x ≤ F.W ∧   { last := last✝, cost := cost✝, doc := Doc.align d✝, x := x✝, y := max i y✝ }.y ≤ F.W
    
α: Type

F: Factory α

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F (Doc.align d✝) c i m₁

h': MeasRender F (Doc.align d✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁.x ≤ F.W ∧ m₁.y ≤ F.Wcases 
h': MeasRender F (Doc.align d✝) c' i' m₂
h'
α: Type

F: Factory α

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

last✝¹: ℕ

cost✝¹: α

x✝¹, y✝¹: ℕ

h: MeasRender F d✝ c c { last := last✝¹, cost := cost✝¹, doc := d✝, x := x✝¹, y := y✝¹ }

last✝: ℕ

cost✝: α

x✝, y✝: ℕ

h✝: MeasRender F d✝ c' c' { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }

h_x: { last := last✝, cost := cost✝, doc := Doc.align d✝, x := x✝, y := max i' y✝ }.x ≤ F.W

h_y: { last := last✝, cost := cost✝, doc := Doc.align d✝, x := x✝, y := max i' y✝ }.y ≤ F.W

align.align
{ last := last✝¹, cost := cost✝¹, doc := Doc.align d✝, x := x✝¹, y := max i y✝¹ }.x ≤ F.W ∧   { last := last✝¹, cost := cost✝¹, doc := Doc.align d✝, x := x✝¹, y := max i y✝¹ }.y ≤ F.W 
    
α: Type

F: Factory α

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F (Doc.align d✝) c i m₁

h': MeasRender F (Doc.align d✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁.x ≤ F.W ∧ m₁.y ≤ F.Wrename_i 
h': MeasRender F d✝ c' c' { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }
h'
α: Type

F: Factory α

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

last✝¹: ℕ

cost✝¹: α

x✝¹, y✝¹: ℕ

h: MeasRender F d✝ c c { last := last✝¹, cost := cost✝¹, doc := d✝, x := x✝¹, y := y✝¹ }

last✝: ℕ

cost✝: α

x✝, y✝: ℕ

h': MeasRender F d✝ c' c' { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }

h_x: { last := last✝, cost := cost✝, doc := Doc.align d✝, x := x✝, y := max i' y✝ }.x ≤ F.W

h_y: { last := last✝, cost := cost✝, doc := Doc.align d✝, x := x✝, y := max i' y✝ }.y ≤ F.W

align.align
{ last := last✝¹, cost := cost✝¹, doc := Doc.align d✝, x := x✝¹, y := max i y✝¹ }.x ≤ F.W ∧   { last := last✝¹, cost := cost✝¹, doc := Doc.align d✝, x := x✝¹, y := max i y✝¹ }.y ≤ F.W
    
α: Type

F: Factory α

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F (Doc.align d✝) c i m₁

h': MeasRender F (Doc.align d✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁.x ≤ F.W ∧ m₁.y ≤ F.Wsimp at 
ih: ?m.11535 d✝
ih 
h_x: { last := last✝, cost := cost✝, doc := Doc.align d✝, x := x✝, y := max i' y✝ }.x ≤ F.W
h_x 
h_y: { last := last✝, cost := cost✝, doc := Doc.align d✝, x := x✝, y := max i' y✝ }.y ≤ F.W
h_y ⊢
α: Type

F: Factory α

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

last✝¹: ℕ

cost✝¹: α

x✝¹, y✝¹: ℕ

h: MeasRender F d✝ c c { last := last✝¹, cost := cost✝¹, doc := d✝, x := x✝¹, y := y✝¹ }

last✝: ℕ

cost✝: α

x✝, y✝: ℕ

h': MeasRender F d✝ c' c' { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }

h_x: x✝ ≤ F.W

h_y: i' ≤ F.W ∧ y✝ ≤ F.W

align.align
x✝¹ ≤ F.W ∧ i ≤ F.W ∧ y✝¹ ≤ F.W
    
α: Type

F: Factory α

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F (Doc.align d✝) c i m₁

h': MeasRender F (Doc.align d✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁.x ≤ F.W ∧ m₁.y ≤ F.Whave := 
ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W
ih 
h: MeasRender F d✝ c c { last := last✝¹, cost := cost✝¹, doc := d✝, x := x✝¹, y := y✝¹ }
h 
h': MeasRender F d✝ c' c' { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }
h' 
h_c: c ≤ c'
h_c (
α: Type

F: Factory α

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

last✝¹: ℕ

cost✝¹: α

x✝¹, y✝¹: ℕ

h: MeasRender F d✝ c c { last := last✝¹, cost := cost✝¹, doc := d✝, x := x✝¹, y := y✝¹ }

last✝: ℕ

cost✝: α

x✝, y✝: ℕ

h': MeasRender F d✝ c' c' { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }

h_x: x✝ ≤ F.W

h_y: i' ≤ F.W ∧ y✝ ≤ F.W

align.align
x✝¹ ≤ F.W ∧ i ≤ F.W ∧ y✝¹ ≤ F.Wby
Goals accomplished! 🐙 
α: Type

F: Factory α

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

last✝¹: ℕ

cost✝¹: α

x✝¹, y✝¹: ℕ

h: MeasRender F d✝ c c { last := last✝¹, cost := cost✝¹, doc := d✝, x := x✝¹, y := y✝¹ }

last✝: ℕ

cost✝: α

x✝, y✝: ℕ

h': MeasRender F d✝ c' c' { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }

h_x: x✝ ≤ F.W

h_y: i' ≤ F.W ∧ y✝ ≤ F.W

c ≤ c'simpa
Goals accomplished! 🐙) 
h_x: x✝ ≤ F.W
h_x (
α: Type

F: Factory α

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

last✝¹: ℕ

cost✝¹: α

x✝¹, y✝¹: ℕ

h: MeasRender F d✝ c c { last := last✝¹, cost := cost✝¹, doc := d✝, x := x✝¹, y := y✝¹ }

last✝: ℕ

cost✝: α

x✝, y✝: ℕ

h': MeasRender F d✝ c' c' { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }

h_x: x✝ ≤ F.W

h_y: i' ≤ F.W ∧ y✝ ≤ F.W

align.align
x✝¹ ≤ F.W ∧ i ≤ F.W ∧ y✝¹ ≤ F.Wby
Goals accomplished! 🐙 
α: Type

F: Factory α

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

last✝¹: ℕ

cost✝¹: α

x✝¹, y✝¹: ℕ

h: MeasRender F d✝ c c { last := last✝¹, cost := cost✝¹, doc := d✝, x := x✝¹, y := y✝¹ }

last✝: ℕ

cost✝: α

x✝, y✝: ℕ

h': MeasRender F d✝ c' c' { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }

h_x: x✝ ≤ F.W

h_y: i' ≤ F.W ∧ y✝ ≤ F.W

{ last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }.y ≤ F.W{
α: Type

F: Factory α

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

last✝¹: ℕ

cost✝¹: α

x✝¹, y✝¹: ℕ

h: MeasRender F d✝ c c { last := last✝¹, cost := cost✝¹, doc := d✝, x := x✝¹, y := y✝¹ }

last✝: ℕ

cost✝: α

x✝, y✝: ℕ

h': MeasRender F d✝ c' c' { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }

h_x: x✝ ≤ F.W

h_y: i' ≤ F.W ∧ y✝ ≤ F.W

{ last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }.y ≤ F.W
      
α: Type

F: Factory α

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

last✝¹: ℕ

cost✝¹: α

x✝¹, y✝¹: ℕ

h: MeasRender F d✝ c c { last := last✝¹, cost := cost✝¹, doc := d✝, x := x✝¹, y := y✝¹ }

last✝: ℕ

cost✝: α

x✝, y✝: ℕ

h': MeasRender F d✝ c' c' { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }

h_x: x✝ ≤ F.W

h_y: i' ≤ F.W ∧ y✝ ≤ F.W

{ last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }.y ≤ F.Wsimp [
h_y: i' ≤ F.W ∧ y✝ ≤ F.W
h_y]
Goals accomplished! 🐙 
    }
Goals accomplished! 🐙)
α: Type

F: Factory α

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

last✝¹: ℕ

cost✝¹: α

x✝¹, y✝¹: ℕ

h: MeasRender F d✝ c c { last := last✝¹, cost := cost✝¹, doc := d✝, x := x✝¹, y := y✝¹ }

last✝: ℕ

cost✝: α

x✝, y✝: ℕ

h': MeasRender F d✝ c' c' { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }

h_x: x✝ ≤ F.W

h_y: i' ≤ F.W ∧ y✝ ≤ F.W

this: { last := last✝¹, cost := cost✝¹, doc := d✝, x := x✝¹, y := y✝¹ }.x ≤ F.W ∧   { last := last✝¹, cost := cost✝¹, doc := d✝, x := x✝¹, y := y✝¹ }.y ≤ F.W

align.align
x✝¹ ≤ F.W ∧ i ≤ F.W ∧ y✝¹ ≤ F.W
    
α: Type

F: Factory α

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F (Doc.align d✝) c i m₁

h': MeasRender F (Doc.align d✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁.x ≤ F.W ∧ m₁.y ≤ F.Wsimp at 
this: ?m.31336
this
α: Type

F: Factory α

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

last✝¹: ℕ

cost✝¹: α

x✝¹, y✝¹: ℕ

h: MeasRender F d✝ c c { last := last✝¹, cost := cost✝¹, doc := d✝, x := x✝¹, y := y✝¹ }

last✝: ℕ

cost✝: α

x✝, y✝: ℕ

h': MeasRender F d✝ c' c' { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }

h_x: x✝ ≤ F.W

h_y: i' ≤ F.W ∧ y✝ ≤ F.W

this: x✝¹ ≤ F.W ∧ y✝¹ ≤ F.W

align.align
x✝¹ ≤ F.W ∧ i ≤ F.W ∧ y✝¹ ≤ F.W 
    
α: Type

F: Factory α

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F (Doc.align d✝) c i m₁

h': MeasRender F (Doc.align d✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁.x ≤ F.W ∧ m₁.y ≤ F.Wconstructor
α: Type

F: Factory α

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

last✝¹: ℕ

cost✝¹: α

x✝¹, y✝¹: ℕ

h: MeasRender F d✝ c c { last := last✝¹, cost := cost✝¹, doc := d✝, x := x✝¹, y := y✝¹ }

last✝: ℕ

cost✝: α

x✝, y✝: ℕ

h': MeasRender F d✝ c' c' { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }

h_x: x✝ ≤ F.W

h_y: i' ≤ F.W ∧ y✝ ≤ F.W

this: x✝¹ ≤ F.W ∧ y✝¹ ≤ F.W

align.align.left
x✝¹ ≤ F.W
α: Type

F: Factory α

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

last✝¹: ℕ

cost✝¹: α

x✝¹, y✝¹: ℕ

h: MeasRender F d✝ c c { last := last✝¹, cost := cost✝¹, doc := d✝, x := x✝¹, y := y✝¹ }

last✝: ℕ

cost✝: α

x✝, y✝: ℕ

h': MeasRender F d✝ c' c' { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }

h_x: x✝ ≤ F.W

h_y: i' ≤ F.W ∧ y✝ ≤ F.W

this: x✝¹ ≤ F.W ∧ y✝¹ ≤ F.W

align.align.right
i ≤ F.W ∧ y✝¹ ≤ F.W 
    
α: Type

F: Factory α

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F (Doc.align d✝) c i m₁

h': MeasRender F (Doc.align d✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁.x ≤ F.W ∧ m₁.y ≤ F.Wcase left => 
α: Type

F: Factory α

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

last✝¹: ℕ

cost✝¹: α

x✝¹, y✝¹: ℕ

h: MeasRender F d✝ c c { last := last✝¹, cost := cost✝¹, doc := d✝, x := x✝¹, y := y✝¹ }

last✝: ℕ

cost✝: α

x✝, y✝: ℕ

h': MeasRender F d✝ c' c' { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }

h_x: x✝ ≤ F.W

h_y: i' ≤ F.W ∧ y✝ ≤ F.W

this: x✝¹ ≤ F.W ∧ y✝¹ ≤ F.W

x✝¹ ≤ F.Wsimp [*]
Goals accomplished! 🐙
    
α: Type

F: Factory α

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F (Doc.align d✝) c i m₁

h': MeasRender F (Doc.align d✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁.x ≤ F.W ∧ m₁.y ≤ F.Wcase right => 
      
α: Type

F: Factory α

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

last✝¹: ℕ

cost✝¹: α

x✝¹, y✝¹: ℕ

h: MeasRender F d✝ c c { last := last✝¹, cost := cost✝¹, doc := d✝, x := x✝¹, y := y✝¹ }

last✝: ℕ

cost✝: α

x✝, y✝: ℕ

h': MeasRender F d✝ c' c' { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }

h_x: x✝ ≤ F.W

h_y: i' ≤ F.W ∧ y✝ ≤ F.W

this: x✝¹ ≤ F.W ∧ y✝¹ ≤ F.W

i ≤ F.W ∧ y✝¹ ≤ F.Wconstructor
α: Type

F: Factory α

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

last✝¹: ℕ

cost✝¹: α

x✝¹, y✝¹: ℕ

h: MeasRender F d✝ c c { last := last✝¹, cost := cost✝¹, doc := d✝, x := x✝¹, y := y✝¹ }

last✝: ℕ

cost✝: α

x✝, y✝: ℕ

h': MeasRender F d✝ c' c' { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }

h_x: x✝ ≤ F.W

h_y: i' ≤ F.W ∧ y✝ ≤ F.W

this: x✝¹ ≤ F.W ∧ y✝¹ ≤ F.W

left
i ≤ F.W
α: Type

F: Factory α

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

last✝¹: ℕ

cost✝¹: α

x✝¹, y✝¹: ℕ

h: MeasRender F d✝ c c { last := last✝¹, cost := cost✝¹, doc := d✝, x := x✝¹, y := y✝¹ }

last✝: ℕ

cost✝: α

x✝, y✝: ℕ

h': MeasRender F d✝ c' c' { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }

h_x: x✝ ≤ F.W

h_y: i' ≤ F.W ∧ y✝ ≤ F.W

this: x✝¹ ≤ F.W ∧ y✝¹ ≤ F.W

right
y✝¹ ≤ F.W 
      
α: Type

F: Factory α

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

last✝¹: ℕ

cost✝¹: α

x✝¹, y✝¹: ℕ

h: MeasRender F d✝ c c { last := last✝¹, cost := cost✝¹, doc := d✝, x := x✝¹, y := y✝¹ }

last✝: ℕ

cost✝: α

x✝, y✝: ℕ

h': MeasRender F d✝ c' c' { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }

h_x: x✝ ≤ F.W

h_y: i' ≤ F.W ∧ y✝ ≤ F.W

this: x✝¹ ≤ F.W ∧ y✝¹ ≤ F.W

i ≤ F.W ∧ y✝¹ ≤ F.Wcase left => 
        
α: Type

F: Factory α

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

last✝¹: ℕ

cost✝¹: α

x✝¹, y✝¹: ℕ

h: MeasRender F d✝ c c { last := last✝¹, cost := cost✝¹, doc := d✝, x := x✝¹, y := y✝¹ }

last✝: ℕ

cost✝: α

x✝, y✝: ℕ

h': MeasRender F d✝ c' c' { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }

h_x: x✝ ≤ F.W

h_y: i' ≤ F.W ∧ y✝ ≤ F.W

this: x✝¹ ≤ F.W ∧ y✝¹ ≤ F.W

i ≤ F.Wapply 
le_trans: ∀ {α : Type ?u.32386} [inst : Preorder α] {a b c : α}, a ≤ b → b ≤ c → a ≤ c
le_trans
α: Type

F: Factory α

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

last✝¹: ℕ

cost✝¹: α

x✝¹, y✝¹: ℕ

h: MeasRender F d✝ c c { last := last✝¹, cost := cost✝¹, doc := d✝, x := x✝¹, y := y✝¹ }

last✝: ℕ

cost✝: α

x✝, y✝: ℕ

h': MeasRender F d✝ c' c' { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }

h_x: x✝ ≤ F.W

h_y: i' ≤ F.W ∧ y✝ ≤ F.W

this: x✝¹ ≤ F.W ∧ y✝¹ ≤ F.W

a
i ≤ ?b
α: Type

F: Factory α

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

last✝¹: ℕ

cost✝¹: α

x✝¹, y✝¹: ℕ

h: MeasRender F d✝ c c { last := last✝¹, cost := cost✝¹, doc := d✝, x := x✝¹, y := y✝¹ }

last✝: ℕ

cost✝: α

x✝, y✝: ℕ

h': MeasRender F d✝ c' c' { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }

h_x: x✝ ≤ F.W

h_y: i' ≤ F.W ∧ y✝ ≤ F.W

this: x✝¹ ≤ F.W ∧ y✝¹ ≤ F.W

a
?b ≤ F.W
α: Type

F: Factory α

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

last✝¹: ℕ

cost✝¹: α

x✝¹, y✝¹: ℕ

h: MeasRender F d✝ c c { last := last✝¹, cost := cost✝¹, doc := d✝, x := x✝¹, y := y✝¹ }

last✝: ℕ

cost✝: α

x✝, y✝: ℕ

h': MeasRender F d✝ c' c' { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }

h_x: x✝ ≤ F.W

h_y: i' ≤ F.W ∧ y✝ ≤ F.W

this: x✝¹ ≤ F.W ∧ y✝¹ ≤ F.W

b
ℕ 
        
α: Type

F: Factory α

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

last✝¹: ℕ

cost✝¹: α

x✝¹, y✝¹: ℕ

h: MeasRender F d✝ c c { last := last✝¹, cost := cost✝¹, doc := d✝, x := x✝¹, y := y✝¹ }

last✝: ℕ

cost✝: α

x✝, y✝: ℕ

h': MeasRender F d✝ c' c' { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }

h_x: x✝ ≤ F.W

h_y: i' ≤ F.W ∧ y✝ ≤ F.W

this: x✝¹ ≤ F.W ∧ y✝¹ ≤ F.W

i ≤ F.W. 
α: Type

F: Factory α

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

last✝¹: ℕ

cost✝¹: α

x✝¹, y✝¹: ℕ

h: MeasRender F d✝ c c { last := last✝¹, cost := cost✝¹, doc := d✝, x := x✝¹, y := y✝¹ }

last✝: ℕ

cost✝: α

x✝, y✝: ℕ

h': MeasRender F d✝ c' c' { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }

h_x: x✝ ≤ F.W

h_y: i' ≤ F.W ∧ y✝ ≤ F.W

this: x✝¹ ≤ F.W ∧ y✝¹ ≤ F.W

a
i ≤ ?b
α: Type

F: Factory α

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

last✝¹: ℕ

cost✝¹: α

x✝¹, y✝¹: ℕ

h: MeasRender F d✝ c c { last := last✝¹, cost := cost✝¹, doc := d✝, x := x✝¹, y := y✝¹ }

last✝: ℕ

cost✝: α

x✝, y✝: ℕ

h': MeasRender F d✝ c' c' { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }

h_x: x✝ ≤ F.W

h_y: i' ≤ F.W ∧ y✝ ≤ F.W

this: x✝¹ ≤ F.W ∧ y✝¹ ≤ F.W

a
?b ≤ F.W
α: Type

F: Factory α

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

last✝¹: ℕ

cost✝¹: α

x✝¹, y✝¹: ℕ

h: MeasRender F d✝ c c { last := last✝¹, cost := cost✝¹, doc := d✝, x := x✝¹, y := y✝¹ }

last✝: ℕ

cost✝: α

x✝, y✝: ℕ

h': MeasRender F d✝ c' c' { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }

h_x: x✝ ≤ F.W

h_y: i' ≤ F.W ∧ y✝ ≤ F.W

this: x✝¹ ≤ F.W ∧ y✝¹ ≤ F.W

b
ℕassumption
Goals accomplished! 🐙
        
α: Type

F: Factory α

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

last✝¹: ℕ

cost✝¹: α

x✝¹, y✝¹: ℕ

h: MeasRender F d✝ c c { last := last✝¹, cost := cost✝¹, doc := d✝, x := x✝¹, y := y✝¹ }

last✝: ℕ

cost✝: α

x✝, y✝: ℕ

h': MeasRender F d✝ c' c' { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }

h_x: x✝ ≤ F.W

h_y: i' ≤ F.W ∧ y✝ ≤ F.W

this: x✝¹ ≤ F.W ∧ y✝¹ ≤ F.W

i ≤ F.W. 
α: Type

F: Factory α

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

last✝¹: ℕ

cost✝¹: α

x✝¹, y✝¹: ℕ

h: MeasRender F d✝ c c { last := last✝¹, cost := cost✝¹, doc := d✝, x := x✝¹, y := y✝¹ }

last✝: ℕ

cost✝: α

x✝, y✝: ℕ

h': MeasRender F d✝ c' c' { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }

h_x: x✝ ≤ F.W

h_y: i' ≤ F.W ∧ y✝ ≤ F.W

this: x✝¹ ≤ F.W ∧ y✝¹ ≤ F.W

a
i' ≤ F.Wsimp [
h_y: i' ≤ F.W ∧ y✝ ≤ F.W
h_y]
Goals accomplished! 🐙
      
α: Type

F: Factory α

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

last✝¹: ℕ

cost✝¹: α

x✝¹, y✝¹: ℕ

h: MeasRender F d✝ c c { last := last✝¹, cost := cost✝¹, doc := d✝, x := x✝¹, y := y✝¹ }

last✝: ℕ

cost✝: α

x✝, y✝: ℕ

h': MeasRender F d✝ c' c' { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }

h_x: x✝ ≤ F.W

h_y: i' ≤ F.W ∧ y✝ ≤ F.W

this: x✝¹ ≤ F.W ∧ y✝¹ ≤ F.W

i ≤ F.W ∧ y✝¹ ≤ F.Wcase right => 
α: Type

F: Factory α

d✝: Doc

ih: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d✝ c i m₁ →
    MeasRender F d✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

last✝¹: ℕ

cost✝¹: α

x✝¹, y✝¹: ℕ

h: MeasRender F d✝ c c { last := last✝¹, cost := cost✝¹, doc := d✝, x := x✝¹, y := y✝¹ }

last✝: ℕ

cost✝: α

x✝, y✝: ℕ

h': MeasRender F d✝ c' c' { last := last✝, cost := cost✝, doc := d✝, x := x✝, y := y✝ }

h_x: x✝ ≤ F.W

h_y: i' ≤ F.W ∧ y✝ ≤ F.W

this: x✝¹ ≤ F.W ∧ y✝¹ ≤ F.W

y✝¹ ≤ F.Wsimp [*]
Goals accomplished! 🐙  
  
α: Type

d: Doc

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

F: Factory α

h: MeasRender F d c i m₁

h': MeasRender F d c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁.x ≤ F.W ∧ m₁.y ≤ F.Wcase concat 
ih₁: ?m.11535 d₁✝
ih₁ 
ih₂: ?m.11535 d₂✝
ih₂ => 
    
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₁: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₁✝ c i m₁ →
    MeasRender F d₁✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ →
    MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F (Doc.concat d₁✝ d₂✝) c i m₁

h': MeasRender F (Doc.concat d₁✝ d₂✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁.x ≤ F.W ∧ m₁.y ≤ F.Wcases 
h: MeasRender F (Doc.concat d₁✝ d₂✝) c i m₁
h
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₁: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₁✝ c i m₁ →
    MeasRender F d₁✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ →
    MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h': MeasRender F (Doc.concat d₁✝ d₂✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁✝, m₂✝: Meas

h₂✝: MeasRender F d₂✝ m₁✝.last i m₂✝

h₁✝: MeasRender F d₁✝ c i m₁✝

h✝: m₁ = Meas.concat F m₁✝ m₂✝

concat
m₁.x ≤ F.W ∧ m₁.y ≤ F.W 
    
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₁: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₁✝ c i m₁ →
    MeasRender F d₁✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ →
    MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F (Doc.concat d₁✝ d₂✝) c i m₁

h': MeasRender F (Doc.concat d₁✝ d₂✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁.x ≤ F.W ∧ m₁.y ≤ F.Wcase concat 
h₂: MeasRender F d₂✝ m₁✝.last i m₂✝
h₂ 
h₁: MeasRender F d₁✝ c i m₁✝
h₁ 
h_eq: m₁ = Meas.concat F m₁✝ m₂✝
h_eq => 
    
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₁: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₁✝ c i m₁ →
    MeasRender F d₁✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ →
    MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h': MeasRender F (Doc.concat d₁✝ d₂✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁✝, m₂✝: Meas

h₂: MeasRender F d₂✝ m₁✝.last i m₂✝

h₁: MeasRender F d₁✝ c i m₁✝

h_eq: m₁ = Meas.concat F m₁✝ m₂✝

m₁.x ≤ F.W ∧ m₁.y ≤ F.Wsubst 
h_eq: m₁ = Meas.concat F m₁✝ m₂✝
h_eq
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₁: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₁✝ c i m₁ →
    MeasRender F d₁✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ →
    MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

m₂: Meas

h': MeasRender F (Doc.concat d₁✝ d₂✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁✝, m₂✝: Meas

h₂: MeasRender F d₂✝ m₁✝.last i m₂✝

h₁: MeasRender F d₁✝ c i m₁✝

(Meas.concat F m₁✝ m₂✝).x ≤ F.W ∧ (Meas.concat F m₁✝ m₂✝).y ≤ F.W
    
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₁: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₁✝ c i m₁ →
    MeasRender F d₁✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ →
    MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h': MeasRender F (Doc.concat d₁✝ d₂✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁✝, m₂✝: Meas

h₂: MeasRender F d₂✝ m₁✝.last i m₂✝

h₁: MeasRender F d₁✝ c i m₁✝

h_eq: m₁ = Meas.concat F m₁✝ m₂✝

m₁.x ≤ F.W ∧ m₁.y ≤ F.Wcases 
h': MeasRender F (Doc.concat d₁✝ d₂✝) c' i' m₂
h'
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₁: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₁✝ c i m₁ →
    MeasRender F d₁✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ →
    MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

m₂: Meas

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

m₁✝, m₂✝: Meas

h₂✝: MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁✝: MeasRender F d₁✝ c' i' m₁✝

h✝: m₂ = Meas.concat F m₁✝ m₂✝

concat
(Meas.concat F m₁✝¹ m₂✝¹).x ≤ F.W ∧ (Meas.concat F m₁✝¹ m₂✝¹).y ≤ F.W 
    
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₁: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₁✝ c i m₁ →
    MeasRender F d₁✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ →
    MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h': MeasRender F (Doc.concat d₁✝ d₂✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁✝, m₂✝: Meas

h₂: MeasRender F d₂✝ m₁✝.last i m₂✝

h₁: MeasRender F d₁✝ c i m₁✝

h_eq: m₁ = Meas.concat F m₁✝ m₂✝

m₁.x ≤ F.W ∧ m₁.y ≤ F.Wcase concat 
h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝
h₂' 
h₁': MeasRender F d₁✝ c' i' m₁✝
h₁' 
h_eq': m₂ = Meas.concat F m₁✝ m₂✝
h_eq' => 
    
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₁: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₁✝ c i m₁ →
    MeasRender F d₁✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ →
    MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

m₂: Meas

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_eq': m₂ = Meas.concat F m₁✝ m₂✝

(Meas.concat F m₁✝¹ m₂✝¹).x ≤ F.W ∧ (Meas.concat F m₁✝¹ m₂✝¹).y ≤ F.Wsubst 
h_eq': m₂ = Meas.concat F m₁✝ m₂✝
h_eq'
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₁: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₁✝ c i m₁ →
    MeasRender F d₁✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ →
    MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_x: (Meas.concat F m₁✝ m₂✝).x ≤ F.W

h_y: (Meas.concat F m₁✝ m₂✝).y ≤ F.W

(Meas.concat F m₁✝¹ m₂✝¹).x ≤ F.W ∧ (Meas.concat F m₁✝¹ m₂✝¹).y ≤ F.W
    
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₁: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₁✝ c i m₁ →
    MeasRender F d₁✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ →
    MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

m₂: Meas

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_eq': m₂ = Meas.concat F m₁✝ m₂✝

(Meas.concat F m₁✝¹ m₂✝¹).x ≤ F.W ∧ (Meas.concat F m₁✝¹ m₂✝¹).y ≤ F.Wsimp at 
h_x: (Meas.concat F m₁✝ m₂✝).x ≤ F.W
h_x 
h_y: (Meas.concat F m₁✝ m₂✝).y ≤ F.W
h_y ⊢
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₁: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₁✝ c i m₁ →
    MeasRender F d₁✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ →
    MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_x: m₁✝.x ≤ F.W ∧ m₂✝.x ≤ F.W

h_y: m₁✝.y ≤ F.W ∧ m₂✝.y ≤ F.W

(m₁✝¹.x ≤ F.W ∧ m₂✝¹.x ≤ F.W) ∧ m₁✝¹.y ≤ F.W ∧ m₂✝¹.y ≤ F.W
    
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₁: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₁✝ c i m₁ →
    MeasRender F d₁✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ →
    MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

m₂: Meas

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_eq': m₂ = Meas.concat F m₁✝ m₂✝

(Meas.concat F m₁✝¹ m₂✝¹).x ≤ F.W ∧ (Meas.concat F m₁✝¹ m₂✝¹).y ≤ F.Whave := 
MeasRender_dom_monotonic: ∀ {α : Type} {d : Doc} {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas} {F : Factory α},
  MeasRender F d c i m₁ → MeasRender F d c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true
MeasRender_dom_monotonic 
h₁: MeasRender F d₁✝ c i m₁✝¹
h₁ 
h₁': MeasRender F d₁✝ c' i' m₁✝
h₁' 
h_c: c ≤ c'
h_c 
h_i: i ≤ i'
h_i
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₁: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₁✝ c i m₁ →
    MeasRender F d₁✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ →
    MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_x: m₁✝.x ≤ F.W ∧ m₂✝.x ≤ F.W

h_y: m₁✝.y ≤ F.W ∧ m₂✝.y ≤ F.W

this: dominates F m₁✝¹ m₁✝ = true

(m₁✝¹.x ≤ F.W ∧ m₂✝¹.x ≤ F.W) ∧ m₁✝¹.y ≤ F.W ∧ m₂✝¹.y ≤ F.W
    
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₁: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₁✝ c i m₁ →
    MeasRender F d₁✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ →
    MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

m₂: Meas

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_eq': m₂ = Meas.concat F m₁✝ m₂✝

(Meas.concat F m₁✝¹ m₂✝¹).x ≤ F.W ∧ (Meas.concat F m₁✝¹ m₂✝¹).y ≤ F.Wspecialize 
ih₁: ?m.11535 d₁✝
ih₁ 
h₁: MeasRender F d₁✝ c i m₁✝¹
h₁ 
h₁': MeasRender F d₁✝ c' i' m₁✝
h₁' 
h_c: c ≤ c'
h_c (
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₁: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₁✝ c i m₁ →
    MeasRender F d₁✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ →
    MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_x: m₁✝.x ≤ F.W ∧ m₂✝.x ≤ F.W

h_y: m₁✝.y ≤ F.W ∧ m₂✝.y ≤ F.W

this: dominates F m₁✝¹ m₁✝ = true

(m₁✝¹.x ≤ F.W ∧ m₂✝¹.x ≤ F.W) ∧ m₁✝¹.y ≤ F.W ∧ m₂✝¹.y ≤ F.Wby
Goals accomplished! 🐙 
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₁: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₁✝ c i m₁ →
    MeasRender F d₁✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ →
    MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_x: m₁✝.x ≤ F.W ∧ m₂✝.x ≤ F.W

h_y: m₁✝.y ≤ F.W ∧ m₂✝.y ≤ F.W

this: dominates F m₁✝¹ m₁✝ = true

i ≤ i'assumption
Goals accomplished! 🐙) (
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₁: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₁✝ c i m₁ →
    MeasRender F d₁✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ →
    MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_x: m₁✝.x ≤ F.W ∧ m₂✝.x ≤ F.W

h_y: m₁✝.y ≤ F.W ∧ m₂✝.y ≤ F.W

this: dominates F m₁✝¹ m₁✝ = true

(m₁✝¹.x ≤ F.W ∧ m₂✝¹.x ≤ F.W) ∧ m₁✝¹.y ≤ F.W ∧ m₂✝¹.y ≤ F.Wby
Goals accomplished! 🐙 
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₁: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₁✝ c i m₁ →
    MeasRender F d₁✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ →
    MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_x: m₁✝.x ≤ F.W ∧ m₂✝.x ≤ F.W

h_y: m₁✝.y ≤ F.W ∧ m₂✝.y ≤ F.W

this: dominates F m₁✝¹ m₁✝ = true

m₁✝.x ≤ F.Wsimp [
h_x: m₁✝.x ≤ F.W ∧ m₂✝.x ≤ F.W
h_x]
Goals accomplished! 🐙) (
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₁: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₁✝ c i m₁ →
    MeasRender F d₁✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ →
    MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_x: m₁✝.x ≤ F.W ∧ m₂✝.x ≤ F.W

h_y: m₁✝.y ≤ F.W ∧ m₂✝.y ≤ F.W

this: dominates F m₁✝¹ m₁✝ = true

(m₁✝¹.x ≤ F.W ∧ m₂✝¹.x ≤ F.W) ∧ m₁✝¹.y ≤ F.W ∧ m₂✝¹.y ≤ F.Wby
Goals accomplished! 🐙 
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₁: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₁✝ c i m₁ →
    MeasRender F d₁✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ →
    MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_x: m₁✝.x ≤ F.W ∧ m₂✝.x ≤ F.W

h_y: m₁✝.y ≤ F.W ∧ m₂✝.y ≤ F.W

this: dominates F m₁✝¹ m₁✝ = true

m₁✝.y ≤ F.Wsimp [
h_y: m₁✝.y ≤ F.W ∧ m₂✝.y ≤ F.W
h_y]
Goals accomplished! 🐙)
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ →
    MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_x: m₁✝.x ≤ F.W ∧ m₂✝.x ≤ F.W

h_y: m₁✝.y ≤ F.W ∧ m₂✝.y ≤ F.W

this: dominates F m₁✝¹ m₁✝ = true

ih₁: m₁✝¹.x ≤ F.W ∧ m₁✝¹.y ≤ F.W

(m₁✝¹.x ≤ F.W ∧ m₂✝¹.x ≤ F.W) ∧ m₁✝¹.y ≤ F.W ∧ m₂✝¹.y ≤ F.W
    
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₁: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₁✝ c i m₁ →
    MeasRender F d₁✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ →
    MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

m₂: Meas

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_eq': m₂ = Meas.concat F m₁✝ m₂✝

(Meas.concat F m₁✝¹ m₂✝¹).x ≤ F.W ∧ (Meas.concat F m₁✝¹ m₂✝¹).y ≤ F.Wsimp only [
      
dominates: {α : Type} → Factory α → Meas → Meas → Bool
dominates, 
Bool.decide_and: ∀ (p q : Prop) [inst : Decidable p] [inst_1 : Decidable q], decide (p ∧ q) = (decide p && decide q)
Bool.decide_and, 
Bool.decide_coe: ∀ (b : Bool) {h : Decidable (b = true)}, decide (b = true) = b
Bool.decide_coe,
      
Bool.and_eq_true: ∀ (a b : Bool), ((a && b) = true) = (a = true ∧ b = true)
Bool.and_eq_true, 
decide_eq_true_eq: ∀ {p : Prop} [inst : Decidable p], (decide p = true) = p
decide_eq_true_eq
    ] at 
ih₁: m₁✝¹.x ≤ F.W ∧ m₁✝¹.y ≤ F.W
ih₁
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ →
    MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_x: m₁✝.x ≤ F.W ∧ m₂✝.x ≤ F.W

h_y: m₁✝.y ≤ F.W ∧ m₂✝.y ≤ F.W

this: dominates F m₁✝¹ m₁✝ = true

ih₁: m₁✝¹.x ≤ F.W ∧ m₁✝¹.y ≤ F.W

(m₁✝¹.x ≤ F.W ∧ m₂✝¹.x ≤ F.W) ∧ m₁✝¹.y ≤ F.W ∧ m₂✝¹.y ≤ F.W
    
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₁: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₁✝ c i m₁ →
    MeasRender F d₁✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ →
    MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

m₂: Meas

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_eq': m₂ = Meas.concat F m₁✝ m₂✝

(Meas.concat F m₁✝¹ m₂✝¹).x ≤ F.W ∧ (Meas.concat F m₁✝¹ m₂✝¹).y ≤ F.Wspecialize 
ih₂: ?m.11535 d₂✝
ih₂ 
h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹
h₂ 
h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝
h₂' (
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ →
    MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_x: m₁✝.x ≤ F.W ∧ m₂✝.x ≤ F.W

h_y: m₁✝.y ≤ F.W ∧ m₂✝.y ≤ F.W

this: dominates F m₁✝¹ m₁✝ = true

ih₁: m₁✝¹.x ≤ F.W ∧ m₁✝¹.y ≤ F.W

(m₁✝¹.x ≤ F.W ∧ m₂✝¹.x ≤ F.W) ∧ m₁✝¹.y ≤ F.W ∧ m₂✝¹.y ≤ F.Wby
Goals accomplished! 🐙 
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ →
    MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_x: m₁✝.x ≤ F.W ∧ m₂✝.x ≤ F.W

h_y: m₁✝.y ≤ F.W ∧ m₂✝.y ≤ F.W

this: dominates F m₁✝¹ m₁✝ = true

ih₁: m₁✝¹.x ≤ F.W ∧ m₁✝¹.y ≤ F.W

m₁✝¹.last ≤ m₁✝.last{
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ →
    MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_x: m₁✝.x ≤ F.W ∧ m₂✝.x ≤ F.W

h_y: m₁✝.y ≤ F.W ∧ m₂✝.y ≤ F.W

this: dominates F m₁✝¹ m₁✝ = true

ih₁: m₁✝¹.x ≤ F.W ∧ m₁✝¹.y ≤ F.W

m₁✝¹.last ≤ m₁✝.last
      
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ →
    MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_x: m₁✝.x ≤ F.W ∧ m₂✝.x ≤ F.W

h_y: m₁✝.y ≤ F.W ∧ m₂✝.y ≤ F.W

this: dominates F m₁✝¹ m₁✝ = true

ih₁: m₁✝¹.x ≤ F.W ∧ m₁✝¹.y ≤ F.W

m₁✝¹.last ≤ m₁✝.lastsimp [
dominates: {α : Type} → Factory α → Meas → Meas → Bool
dominates] at 
this: dominates F m₁✝¹ m₁✝ = true
this
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ →
    MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_x: m₁✝.x ≤ F.W ∧ m₂✝.x ≤ F.W

h_y: m₁✝.y ≤ F.W ∧ m₂✝.y ≤ F.W

ih₁: m₁✝¹.x ≤ F.W ∧ m₁✝¹.y ≤ F.W

this: m₁✝¹.last ≤ m₁✝.last ∧ Factory.le F m₁✝¹.cost m₁✝.cost = true

m₁✝¹.last ≤ m₁✝.last
      
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ →
    MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_x: m₁✝.x ≤ F.W ∧ m₂✝.x ≤ F.W

h_y: m₁✝.y ≤ F.W ∧ m₂✝.y ≤ F.W

this: dominates F m₁✝¹ m₁✝ = true

ih₁: m₁✝¹.x ≤ F.W ∧ m₁✝¹.y ≤ F.W

m₁✝¹.last ≤ m₁✝.lastsimp [
this: m₁✝¹.last ≤ m₁✝.last ∧ Factory.le F m₁✝¹.cost m₁✝.cost = true
this]
Goals accomplished! 🐙
    }
Goals accomplished! 🐙) (
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ →
    MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_x: m₁✝.x ≤ F.W ∧ m₂✝.x ≤ F.W

h_y: m₁✝.y ≤ F.W ∧ m₂✝.y ≤ F.W

this: dominates F m₁✝¹ m₁✝ = true

ih₁: m₁✝¹.x ≤ F.W ∧ m₁✝¹.y ≤ F.W

(m₁✝¹.x ≤ F.W ∧ m₂✝¹.x ≤ F.W) ∧ m₁✝¹.y ≤ F.W ∧ m₂✝¹.y ≤ F.Wby
Goals accomplished! 🐙 
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ →
    MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_x: m₁✝.x ≤ F.W ∧ m₂✝.x ≤ F.W

h_y: m₁✝.y ≤ F.W ∧ m₂✝.y ≤ F.W

this: dominates F m₁✝¹ m₁✝ = true

ih₁: m₁✝¹.x ≤ F.W ∧ m₁✝¹.y ≤ F.W

i ≤ i'assumption
Goals accomplished! 🐙)
α: Type

F: Factory α

d₁✝, d₂✝: Doc

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_x: m₁✝.x ≤ F.W ∧ m₂✝.x ≤ F.W

h_y: m₁✝.y ≤ F.W ∧ m₂✝.y ≤ F.W

this: dominates F m₁✝¹ m₁✝ = true

ih₁: m₁✝¹.x ≤ F.W ∧ m₁✝¹.y ≤ F.W

ih₂: m₂✝.x ≤ F.W → m₂✝.y ≤ F.W → m₂✝¹.x ≤ F.W ∧ m₂✝¹.y ≤ F.W

(m₁✝¹.x ≤ F.W ∧ m₂✝¹.x ≤ F.W) ∧ m₁✝¹.y ≤ F.W ∧ m₂✝¹.y ≤ F.W
    
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₁: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₁✝ c i m₁ →
    MeasRender F d₁✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ →
    MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

m₂: Meas

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_eq': m₂ = Meas.concat F m₁✝ m₂✝

(Meas.concat F m₁✝¹ m₂✝¹).x ≤ F.W ∧ (Meas.concat F m₁✝¹ m₂✝¹).y ≤ F.Wsimp [
dominates: {α : Type} → Factory α → Meas → Meas → Bool
dominates] at 
ih₂: m₂✝.x ≤ F.W → m₂✝.y ≤ F.W → m₂✝¹.x ≤ F.W ∧ m₂✝¹.y ≤ F.W
ih₂ ⊢
α: Type

F: Factory α

d₁✝, d₂✝: Doc

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_x: m₁✝.x ≤ F.W ∧ m₂✝.x ≤ F.W

h_y: m₁✝.y ≤ F.W ∧ m₂✝.y ≤ F.W

this: dominates F m₁✝¹ m₁✝ = true

ih₁: m₁✝¹.x ≤ F.W ∧ m₁✝¹.y ≤ F.W

ih₂: m₂✝.x ≤ F.W → m₂✝.y ≤ F.W → m₂✝¹.x ≤ F.W ∧ m₂✝¹.y ≤ F.W

(m₁✝¹.x ≤ F.W ∧ m₂✝¹.x ≤ F.W) ∧ m₁✝¹.y ≤ F.W ∧ m₂✝¹.y ≤ F.W 
    
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₁: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₁✝ c i m₁ →
    MeasRender F d₁✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ →
    MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

m₂: Meas

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_eq': m₂ = Meas.concat F m₁✝ m₂✝

(Meas.concat F m₁✝¹ m₂✝¹).x ≤ F.W ∧ (Meas.concat F m₁✝¹ m₂✝¹).y ≤ F.Wconstructor
α: Type

F: Factory α

d₁✝, d₂✝: Doc

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_x: m₁✝.x ≤ F.W ∧ m₂✝.x ≤ F.W

h_y: m₁✝.y ≤ F.W ∧ m₂✝.y ≤ F.W

this: dominates F m₁✝¹ m₁✝ = true

ih₁: m₁✝¹.x ≤ F.W ∧ m₁✝¹.y ≤ F.W

ih₂: m₂✝.x ≤ F.W → m₂✝.y ≤ F.W → m₂✝¹.x ≤ F.W ∧ m₂✝¹.y ≤ F.W

left
m₁✝¹.x ≤ F.W ∧ m₂✝¹.x ≤ F.W
α: Type

F: Factory α

d₁✝, d₂✝: Doc

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_x: m₁✝.x ≤ F.W ∧ m₂✝.x ≤ F.W

h_y: m₁✝.y ≤ F.W ∧ m₂✝.y ≤ F.W

this: dominates F m₁✝¹ m₁✝ = true

ih₁: m₁✝¹.x ≤ F.W ∧ m₁✝¹.y ≤ F.W

ih₂: m₂✝.x ≤ F.W → m₂✝.y ≤ F.W → m₂✝¹.x ≤ F.W ∧ m₂✝¹.y ≤ F.W

right
m₁✝¹.y ≤ F.W ∧ m₂✝¹.y ≤ F.W
    
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₁: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₁✝ c i m₁ →
    MeasRender F d₁✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ →
    MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

m₂: Meas

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_eq': m₂ = Meas.concat F m₁✝ m₂✝

(Meas.concat F m₁✝¹ m₂✝¹).x ≤ F.W ∧ (Meas.concat F m₁✝¹ m₂✝¹).y ≤ F.Wcase left => 
α: Type

F: Factory α

d₁✝, d₂✝: Doc

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_x: m₁✝.x ≤ F.W ∧ m₂✝.x ≤ F.W

h_y: m₁✝.y ≤ F.W ∧ m₂✝.y ≤ F.W

this: dominates F m₁✝¹ m₁✝ = true

ih₁: m₁✝¹.x ≤ F.W ∧ m₁✝¹.y ≤ F.W

ih₂: m₂✝.x ≤ F.W → m₂✝.y ≤ F.W → m₂✝¹.x ≤ F.W ∧ m₂✝¹.y ≤ F.W

m₁✝¹.x ≤ F.W ∧ m₂✝¹.x ≤ F.Wsimp [*]
Goals accomplished! 🐙
    
α: Type

F: Factory α

d₁✝, d₂✝: Doc

ih₁: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₁✝ c i m₁ →
    MeasRender F d₁✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

ih₂: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ →
    MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i, c', i': ℕ

m₂: Meas

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_eq': m₂ = Meas.concat F m₁✝ m₂✝

(Meas.concat F m₁✝¹ m₂✝¹).x ≤ F.W ∧ (Meas.concat F m₁✝¹ m₂✝¹).y ≤ F.Wcase right => 
      
α: Type

F: Factory α

d₁✝, d₂✝: Doc

c, i, c', i': ℕ

h_c: c ≤ c'

h_i: i ≤ i'

m₁✝¹, m₂✝¹: Meas

h₂: MeasRender F d₂✝ m₁✝¹.last i m₂✝¹

h₁: MeasRender F d₁✝ c i m₁✝¹

m₁✝, m₂✝: Meas

h₂': MeasRender F d₂✝ m₁✝.last i' m₂✝

h₁': MeasRender F d₁✝ c' i' m₁✝

h_x: m₁✝.x ≤ F.W ∧ m₂✝.x ≤ F.W

h_y: m₁✝.y ≤ F.W ∧ m₂✝.y ≤ F.W

this: dominates F m₁✝¹ m₁✝ = true

ih₁: m₁✝¹.x ≤ F.W ∧ m₁✝¹.y ≤ F.W

ih₂: m₂✝.x ≤ F.W → m₂✝.y ≤ F.W → m₂✝¹.x ≤ F.W ∧ m₂✝¹.y ≤ F.W

m₁✝¹.y ≤ F.W ∧ m₂✝¹.y ≤ F.Wsimp [*]
Goals accomplished! 🐙
  
α: Type

d: Doc

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

F: Factory α

h: MeasRender F d c i m₁

h': MeasRender F d c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁.x ≤ F.W ∧ m₁.y ≤ F.Wcase choice => 
α: Type

F: Factory α

d₁✝, d₂✝: Doc

d₁_ih✝: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₁✝ c i m₁ →
    MeasRender F d₁✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

d₂_ih✝: ∀ {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas},
  MeasRender F d₂✝ c i m₁ →
    MeasRender F d₂✝ c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W

c, i: ℕ

m₁: Meas

c', i': ℕ

m₂: Meas

h: MeasRender F (Doc.choice d₁✝ d₂✝) c i m₁

h': MeasRender F (Doc.choice d₁✝ d₂✝) c' i' m₂

h_c: c ≤ c'

h_i: i ≤ i'

h_x: m₂.x ≤ F.W

h_y: m₂.y ≤ F.W

m₁.x ≤ F.W ∧ m₁.y ≤ F.Wcases 
h: MeasRender F (Doc.choice d₁✝ d₂✝) c i m₁
h
Goals accomplished! 🐙
}
Goals accomplished! 🐙