
theorem Th8:
  for a,b be Integer st b <> 0 holds (a mod b),a are_congruent_mod b
  proof
    let a,b be Integer;
    assume b <>0;then
    A1:a mod b = a - (a div b) * b by INT_1:def 10;
    reconsider c = -(a div b) as Element of INT by INT_1:def 2;
    take c;
    thus thesis by A1;
  end;
