Incorrect Answer.
We consider the body of the program's only while-statement
z = z + x;
a = a + 1;
To see whether
y = z * a 
is an invariant for the while-statement,
we place it as a postcondition at the bottom of the loop-body and
push it upwards through that body to determine the weakest
precondition that guarantees
y = z * a
to hold after the execution of the loop's body:
y = (z + x) * (a + 1) Weakest Precondition
z = z + x;
y = z * (a + 1) Assignment
a = a + 1;
y = z * a Assignment
- The weakest precondition we determined is
y = (z + x) * (a + 1) .
- With that at hand, the postcondition y = z * a is an invariant for the
program's only while-statement if, and only if,
the weakest precondition is implied by the invariant candidate
y = z * a
in conjunction with the condition of the while-statement's boolean
guard a != y.
- However, the implication
(a = y) 
(y = z * a)
(y = (z + x) * (a + 1)) is not true in general.
(Please find values for a, x, y, and z for which this implication is false.)
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