type Set a = [a]bool;

function union<a>(x: Set a, y: Set a) : Set a;

axiom (forall<a> x: Set a, y: Set a, z: a :: (x[z] || y[z]) == union(x, y)[z]);

const intSet0: Set int;

axiom (forall x: int :: intSet0[x] == (x == 0 || x == 2 || x == 3));

const intSet1: Set int;

axiom (forall x: int :: intSet1[x] == (x == -5 || x == 3));

procedure P();



implementation P()
{
    assert (forall x: int :: union(intSet0, intSet1)[x] == (x == -5 || x == 0 || x == 2 || x == 3));
}



type Set a = [a]bool;

function union<a>(x: Set a, y: Set a) : Set a;

axiom (forall<a> x: Set a, y: Set a, z: a :: x[z] || y[z] <==> union(x, y)[z]);

const intSet0: Set int;

axiom (forall x: int :: intSet0[x] <==> x == 0 || x == 2 || x == 3);

const intSet1: Set int;

axiom (forall x: int :: intSet1[x] <==> x == -5 || x == 3);

procedure P();



implementation P()
{
    assert (forall x: int :: union(intSet0, intSet1)[x] <==> x == -5 || x == 0 || x == 2 || x == 3);
}



Boogie program verifier finished with 0 verified, 0 errors