. cases ht₁ with | cons _ _ hf =>
    cases ht₂ with | cons =>
      match hf with
      | .nil =>
        constructor
      | .cons (t := t) (ts := ts) lt _ _ =>
        rename_i neq
        rw[rank_combine heq, hrank_of_cons] at *
        unfold bne at neq
        rw[Nat.not_beq_eq_true_eq] at neq
        have : u.rank + 1 ≤ t.rank := by
          apply Nat.succ_le_of_lt lt
        constructor
        . apply lt_of_le_of_ne <;> assumption
        . assumption
        . assumption
case a
α : Type u_1
le : α → α → Bool
not_le_le : ∀ (x y : α), ¬le x y = true → le y x = true
r : ℕ
u : BinTree α
y : List (BinTree α)
c : BinTree α
z : List (BinTree α)
ht₁ : IsHeapForest' r (u :: y)
ht₂ : IsHeapForest' r (c :: z)
heq : u.rank = c.rank
h✝³ : ¬u.rank < c.rank
h✝² : ¬c.rank < u.rank
h✝¹ : ((combine le u c).rank != hRank y) = true
h✝ : ¬((combine le u c).rank != hRank z) = true
⊢ IsHeapForest' (combine le u c).rank y
no goals