1. Use the proof rules Assignment and Implied to show the validity of:
a) |--_(par )(x>0) y = x + 1 (y > 1)
b) |--_(par )(T) y = x; y = x + x + y (y = 3 * x)
2. Show that |--_(par )(T) P(z = min(x, y)) is valid
where P is:
if (x > y) {
z = y;
} else {
z = x;
}
3. Show that |--_(par )(x >= 0) Copy1 (x = y) is valid,
where Copy1 is:
a = x;
y = 0;
while (a != 0) {
y = y + 1;
a = a - 1;
}
4. Show that |--_(par )(y = y_0 ^ ( ^() ) y >= 0) Multi2 (z = x * y_0) is valid,
where Multi2 is:
z = 0;
while (y != 0) {
z = z + x;
y = y - 1;