. rw[hrank_of_cons] at *
  unfold bne at *
  rw[Bool.not_eq_false', beq_iff_eq] at *
  simp at *
  contradiction
case cons
α : Type u_1
le : α → α → Bool
rx : ℕ
xs : List (BinTree α)
ry : ℕ
ys : List (BinTree α)
h₁ h₂ : BinTree α
t₂ : List (BinTree α)
not_le_le : ∀ (x y : α), le x y = false → le y x = true
h✝⁴ : h₂.rank ≤ h₁.rank
h✝³ : h₁.rank ≤ h₂.rank
heq : h₁.rank = h₂.rank
a✝⁶ : IsBinTree h₁
a✝⁵ : rx < h₁.rank
a✝⁴ : IsBinTree h₂
a✝³ : ry < h₂.rank
hf₂ : IsHeapForest' h₂.rank t₂
h✝² : (h₁.rank + 1 != hRank []) = false
t✝ : BinTree α
ts✝ : List (BinTree α)
a✝² : IsBinTree t✝
a✝¹ : IsHeapForest' t✝.rank ts✝
a✝ : h₁.rank < t✝.rank
h✝¹ : (h₁.rank + 1 != hRank (t✝ :: ts✝)) = false
ih : IsHeapForest' (min h₁.rank h₂.rank) (t✝ :: ts✝)
h : ¬(t✝ :: ts✝ = [] ∧ [] = [])
h✝ : ¬hRank (t✝ :: ts✝) ≤ hRank []
hle : hRank [] ≤ hRank (t✝ :: ts✝)
⊢ h₁.rank + 1 < hRank (t✝ :: ts✝)
no goals