Consider the following loop:

$//$Precondition: $($index$=$x$)\backslash$wedge$($x$\backslash$geq$1)\backslash$wedge$($y$=0)$

while $($index$>1)$

$\{$

index $=$ index$/2$;

$++$y;

$\}$

$//$Postcondition: $($index $=1)^(2$y$\}\backslash$leqx$)\backslash$wedge$($x$<mi>\backslash </mi>$mp@subsup$\{2\}\{\}\{$y$+1\}$

Suppose we have already proved the first two parts of the postcondition, that is$,($index $=1)$ and $(($:$2^{y}x\}.$ Now we are

trying to prove the last part

If index