cases xs with | heap ts =>
cases ts with 
| nil =>
  rfl
| cons _ ts =>
  dsimp at heq
  cases ts <;> contradiction
α : Type u_1
le : α → α → Bool
not_le_le : ∀ (x y : α), ¬le x y = true → le y x = true
le_trans : ∀ (x y z : α), le x y = true → le y z = true → le x z = true
le_rfl : ∀ (z : α), le z z = true
xs : Heap α
heq :
  (match xs with
    | Heap.heap [] => none
    | Heap.heap [h] => some (h.val, h.children)
    | Heap.heap hhs@h_1:(h :: hs) =>
      match findMin le hs 1 (h, 0) with
      | (min, minIdx) =>
        let rest := List.eraseIdx hhs minIdx;
        let tail := merge le (Heap.heap rest) min.children;
        some (min.val, tail)) =
    none
⊢ isEmpty xs = true
no goals