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class Set { var elems: seq[int]
constructor Empty()
ensures elems = []
constructor Singleton(t: int)
ensures elems = [t]
constructor Sum(p: int, q: int)
ensures elems = [p + q]
}
model Set {
var root: SetNode
frame
root
invariant
root = null ==> elems = []
root != null ==> elems = root.elems
}
class SetNode {
var elems: seq[int]
constructor Init(x: int)
ensures elems = [x]
constructor Double(a: int, b: int)
requires a != b
ensures |elems| = 2 && a in elems && b in elems
constructor DoubleBase(x: int, y: int)
requires x < y
ensures elems = [x y]
constructor Triple(x: int, y: int, z: int)
requires x != y && y != z && z != x
ensures |elems| = 3 && x in elems && y in elems && z in elems
constructor TripleBase(x: int, y: int, z: int)
requires x < y && y < z
ensures elems = [x y z]
}
model SetNode {
var data: int
var left: SetNode
var right: SetNode
frame
left * right
invariant
elems = (left != null ? left.elems : []) + [data] + (right != null ? right.elems : [])
left != null ==> forall e :: e in left.elems ==> e < data
right != null ==> forall e :: e in right.elems ==> e > data
}
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