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type Pair a b;
function MP<a,b>(x:a, y:b) returns (Pair a b);
function Left<a,b>(Pair a b) returns (a);
function Right<a,b>(Pair a b) returns (b);
axiom (forall<a,b> x:a, y:b :: Left(MP(x,y)) == x);
axiom (forall<a,b> x:a, y:b :: Right(MP(x,y)) == y);
type A, B;
procedure P() returns () {
var x:A, y:B, z:A, p : Pair A B;
assert Left(MP(x,y)) == x;
assert Right(MP(x,y)) == y;
assert Right(MP(x,MP(x,y))) == MP(x,y);
assert Left(MP(x,MP(x,y))) == x;
assert Right(Right(MP(x,MP(x,y)))) == y;
p := MP(x, y);
p := MP(Left(p), y);
assert Left(p) == x && Right(p) == y;
assert Left(p) == z; // should not be provable
}
procedure Q() returns () {
assert Left(MP(1,3)) == 1;
assert Right(MP(1,3)) == 3;
assert Right(MP(1,true)) == true;
}
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