split at heq
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 : List (HeapNodeAux α (Heap α))
y : α
ys : Heap α
heq :
  (match Heap.heap 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)) =
    some (y, ys)
t : HeapNodeAux α (Heap α)
hel : t ∈ xs
⊢ le y t.val = true
case h_1
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 : List (HeapNodeAux α (Heap α))
y : α
ys : Heap α
t : HeapNodeAux α (Heap α)
hel : t ∈ xs
x✝ : Heap α
heq✝ : Heap.heap xs = Heap.heap []
heq : none = some (y, ys)
⊢ le y t.val = true

case h_2
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 : List (HeapNodeAux α (Heap α))
y : α
ys : Heap α
t : HeapNodeAux α (Heap α)
hel : t ∈ xs
x✝ : Heap α
h✝ : HeapNodeAux α (Heap α)
heq✝ : Heap.heap xs = Heap.heap [h✝]
heq : some (h✝.val, h✝.children) = some (y, ys)
⊢ le y t.val = true

case h_3
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 : List (HeapNodeAux α (Heap α))
y : α
ys : Heap α
t : HeapNodeAux α (Heap α)
hel : t ∈ xs
x✝¹ : Heap α
h✝ : HeapNodeAux α (Heap α)
hs✝ : List (HeapNodeAux α (Heap α))
x✝ : hs✝ = [] → False
heq✝ : Heap.heap xs = Heap.heap (h✝ :: hs✝)
heq :
  (match findMin le hs✝ 1 (h✝, 0) with
    | (min, minIdx) =>
      let rest := List.eraseIdx (h✝ :: hs✝) minIdx;
      let tail := merge le (Heap.heap rest) min.children;
      some (min.val, tail)) =
    some (y, ys)
⊢ le y t.val = true