
theorem ThreeConsecutive: ::: similar to NEWTON02:188
  for n being Nat holds
    3 divides n or 3 divides n+1 or 3 divides n+2
  proof
    let n be Nat;
    3 divides n-1 iff 3 divides n+2
    proof
      hereby assume
C1:     3 divides n-1;
        3 divides n - 1 + 3 by C1,WSIERP_1:4;
        hence 3 divides n+2;
      end;
      assume 3 divides n+2; then
      3 divides n+2-3 by PREPOWER:94;
      hence thesis;
    end;
    hence thesis by NEWTON02:188;
  end;
