Theorem: Ordnode.Valid'.balanceR_aux
File: Mathlib/Data/Ordmap/Ordset.lean

Proof steps:
state_before: α : Type u_1
inst✝ : Preorder α
l : Ordnode α
x : α
r : Ordnode α
o₁ : WithBot α
o₂ : WithTop α
hl : Valid' o₁ l ↑x
hr : Valid' (↑x) r o₂
H₁ : r.size = 0 → l.size ≤ 1
H₂ : 1 ≤ r.size → 1 ≤ l.size → l.size ≤ delta * r.size
H₃ : 2 * r.size ≤ 9 * l.size + 5 ∨ r.size ≤ 3
⊢ Valid' o₁ (l.balanceR x r) o₂
state_after: α : Type u_1
inst✝ : Preorder α
l : Ordnode α
x : α
r : Ordnode α
o₁ : WithBot α
o₂ : WithTop α
hl : Valid' o₁ l ↑x
hr : Valid' (↑x) r o₂
H₁ : r.size = 0 → l.size ≤ 1
H₂ : 1 ≤ r.size → 1 ≤ l.size → l.size ≤ delta * r.size
H₃ : 2 * r.size ≤ 9 * l.size + 5 ∨ r.size ≤ 3
⊢ Valid' o₂ (r.dual.balanceL x l.dual) o₁
tactic: rw [Valid'.dual_iff, dual_balanceR]
state_before: α : Type u_1
inst✝ : Preorder α
l : Ordnode α
x : α
r : Ordnode α
o₁ : WithBot α
o₂ : WithTop α
hl : Valid' o₁ l ↑x
hr : Valid' (↑x) r o₂
H₁ : r.size = 0 → l.size ≤ 1
H₂ : 1 ≤ r.size → 1 ≤ l.size → l.size ≤ delta * r.size
H₃ : 2 * r.size ≤ 9 * l.size + 5 ∨ r.size ≤ 3
⊢ Valid' o₂ (r.dual.balanceL x l.dual) o₁
state_after: α : Type u_1
inst✝ : Preorder α
l : Ordnode α
x : α
r : Ordnode α
o₁ : WithBot α
o₂ : WithTop α
hl : Valid' o₁ l ↑x
hr : Valid' (↑x) r o₂
H₁ : r.size = 0 → l.size ≤ 1
H₂ : 1 ≤ r.size → 1 ≤ l.size → l.size ≤ delta * r.size
H₃ : 2 * r.size ≤ 9 * l.size + 5 ∨ r.size ≤ 3
this :
  (r.dual.size = 0 → l.dual.size ≤ 1) →
    (1 ≤ r.dual.size → 1 ≤ l.dual.size → l.dual.size ≤ delta * r.dual.size) →
      2 * r.dual.size ≤ 9 * l.dual.size + 5 ∨ r.dual.size ≤ 3 → Valid' o₂ (r.dual.balanceL x l.dual) o₁
⊢ Valid' o₂ (r.dual.balanceL x l.dual) o₁
tactic: have := hr.dual.balanceL_aux hl.dual
state_before: α : Type u_1
inst✝ : Preorder α
l : Ordnode α
x : α
r : Ordnode α
o₁ : WithBot α
o₂ : WithTop α
hl : Valid' o₁ l ↑x
hr : Valid' (↑x) r o₂
H₁ : r.size = 0 → l.size ≤ 1
H₂ : 1 ≤ r.size → 1 ≤ l.size → l.size ≤ delta * r.size
H₃ : 2 * r.size ≤ 9 * l.size + 5 ∨ r.size ≤ 3
this :
  (r.dual.size = 0 → l.dual.size ≤ 1) →
    (1 ≤ r.dual.size → 1 ≤ l.dual.size → l.dual.size ≤ delta * r.dual.size) →
      2 * r.dual.size ≤ 9 * l.dual.size + 5 ∨ r.dual.size ≤ 3 → Valid' o₂ (r.dual.balanceL x l.dual) o₁
⊢ Valid' o₂ (r.dual.balanceL x l.dual) o₁
state_after: α : Type u_1
inst✝ : Preorder α
l : Ordnode α
x : α
r : Ordnode α
o₁ : WithBot α
o₂ : WithTop α
hl : Valid' o₁ l ↑x
hr : Valid' (↑x) r o₂
H₁ : r.size = 0 → l.size ≤ 1
H₂ : 1 ≤ r.size → 1 ≤ l.size → l.size ≤ delta * r.size
H₃ : 2 * r.size ≤ 9 * l.size + 5 ∨ r.size ≤ 3
this :
  (r.size = 0 → l.size ≤ 1) →
    (1 ≤ r.size → 1 ≤ l.size → l.size ≤ delta * r.size) →
      2 * r.size ≤ 9 * l.size + 5 ∨ r.size ≤ 3 → Valid' o₂ (r.dual.balanceL x l.dual) o₁
⊢ Valid' o₂ (r.dual.balanceL x l.dual) o₁
tactic: rw [size_dual, size_dual] at this
state_before: α : Type u_1
inst✝ : Preorder α
l : Ordnode α
x : α
r : Ordnode α
o₁ : WithBot α
o₂ : WithTop α
hl : Valid' o₁ l ↑x
hr : Valid' (↑x) r o₂
H₁ : r.size = 0 → l.size ≤ 1
H₂ : 1 ≤ r.size → 1 ≤ l.size → l.size ≤ delta * r.size
H₃ : 2 * r.size ≤ 9 * l.size + 5 ∨ r.size ≤ 3
this :
  (r.size = 0 → l.size ≤ 1) →
    (1 ≤ r.size → 1 ≤ l.size → l.size ≤ delta * r.size) →
      2 * r.size ≤ 9 * l.size + 5 ∨ r.size ≤ 3 → Valid' o₂ (r.dual.balanceL x l.dual) o₁
⊢ Valid' o₂ (r.dual.balanceL x l.dual) o₁
state_after: no goals
tactic: exact this H₁ H₂ H₃