interface BHeap {
  var elems: set[int]

  constructor Singleton(x: int)
    ensures elems = {x}

  constructor Dupleton(a: int, b: int)
    requires a != b
    ensures elems = {a b}

  constructor Tripleton(x: int, y: int, z: int)
    requires x != y && y != z && z != x
    ensures elems = {x y z}

  method Find(n: int) returns (ret: bool)
    ensures ret = (n in elems)
}

datamodel BHeap {
  var data: int
  var left: BHeap
  var right: BHeap

  frame
    left * right

  invariant
    elems = {data} + (left != null ? left.elems : {}) + (right != null ? right.elems : {})
    left != null  ==> forall e :: e in left.elems ==> e < data
    right != null ==> forall e :: e in right.elems ==> e < data
	left = null ==> right = null
	(left != null && right = null) ==> left.elems = {left.data}
}
