
theorem LemmaCong:
  for n,k,l being Nat holds
    3 divides n + l iff 3 divides n + l + 3 * k
  proof
    let n,k,l be Nat;
    hereby assume
A1:   3 divides n + l;
      3 divides 3 * k;
      hence 3 divides n + l + 3 * k by A1,WSIERP_1:4;
    end;
    assume
A1: 3 divides n + l + 3 * k;
    3 divides 3 * k; then
    3 divides n + l + 3 * k - 3 * k by A1,PREPOWER:94;
    hence 3 divides n + l;
  end;
