
theorem
  for a,b be Integer, c be odd Integer holds
    (a + b) mod c = (a - b) mod c implies c divides b
  proof
    let a,b be Integer, c be odd Integer;
    A1: 2|^1,c are_coprime by NEWTON03:def 5;
    assume (a + b) mod c = (a - b) mod c; then
    0 mod c = (((a + b) mod c) - ((a - b) mod c)) mod c
    .= ((a + b) - (a - b)) mod c by INT_6:7
    .= (2*b) mod c;
    hence thesis by A1,INT_2:25,INT162;
  end;
