 reserve n,s for Nat;

theorem Th4: ::: NTALGO_1:8, 9 should be improved
  for k be Nat st k <> 0 holds n, n mod k are_congruent_mod k
  proof
    let k be Nat;
    assume k <> 0; then
    (n mod k) - 0 = n - (n div k) * k by INT_1:def 10; then
    k divides n - (n mod k) by INT_1:def 3;
    hence thesis by INT_1:def 4;
  end;
