
theorem
  for a,b be non zero Integer holds
    b mod a = (-b) mod a implies a is even or a divides b
  proof
    let a,b be non zero Integer;
    assume
    A1: b mod a = -b mod a;
    assume not thesis; then
    b mod a is odd iff -b mod a is even by MOO;
    hence thesis by A1;
  end;
