
theorem MOO:
  for a be Integer, b be odd Integer st
    not b divides a holds a mod b is odd iff (-a) mod b is even
  proof
    let a be Integer, b be odd Integer such that
    A1: not b divides a;
    (a mod b) + ((-a) mod b) is odd by A1,MOD;
    hence thesis;
  end;
