(15 points) Use Axiomatics semantics to prove the following problems

Find precondition:

j = j + k

fj = 7andk = 4g

Prove Correctness:

{ x > 0 }

while x < 10 {

x=x+1

}

{ x >= 10 }

Prove Correctness:

{ N >= 0 }

k = N;

f = 1;

while k > 0 do

f := f * k;

k := k 1;

end while

{ f = N! }