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function f(bool) returns (int);
axiom f(true) == 17;
axiom f(false) == 19;
procedure P() returns () {
assert (forall x:bool :: f(x) >= 0);
}
procedure Q() returns () {
assert (forall x:int :: (x==7 || x==9) ==> x >= 0);
}
procedure R() returns () {
assert f((forall x:bool :: f(x) >= 10)) < 19;
assert (exists x:bool :: f(x) > 20); // should not be provable
}
function g<a>(a) returns (int);
axiom g(true) == 17;
axiom g(false) == 21;
procedure S() returns () {
assert (forall x:bool :: g(x) >= 0);
assert g((forall x:bool :: g(x) >= 0)) >= 17;
assert (forall x:bool :: f(x) == g(x)); // should not be provable
}
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