1. For the following code fragments provide a loop invariant for the while-loop and prove its correctness (place the appropriate assertions between all body/constituent statements).

Code fragment S: // Pre: integer N is defined and >= 0, and integer n = N. f := 1; while not (n = 0) loop f := f*n; n := n - 1; end loop; // Post: Code fragment S2: // Pre: integers a and b are defined, and a >= 0 and b > 0. X := a; y := 0; b; while b = 0, and integer n = N. f := 1; while not (n = 0) loop f := f*n; n := n - 1; end loop; // Post: Code fragment S2: // Pre: integers a and b are defined, and a >= 0 and b > 0. X := a; y := 0; b; while b