This exercise contains a while loop and a predicate. Prove that if the values of the variables in the predicate make the predicate true before entry to the loop, then after execution of the loop the new values of the variables also make the predicate true.

loop: while $($m $>=0$ and m $<=100)$

m :$=$ m $+1$

end while

predicate:

$2$m $<($m $+2)!$

Proof: Let mo denote the old value of m before each entry into the loop, and let mn denote the new value of m after each exit from the loop.

Suppose the predicate is true before entry to the loop.

Then