
theorem LEQ:
  for a,b be non zero Integer holds
    Parity (a+b) >= (Parity a)+(Parity b) implies
    Parity a = Parity b
  proof
    let a,b be non zero Integer;
    assume
    A1: Parity (a+b) >= (Parity a)+(Parity b);
    (Parity a) + (Parity b) > (Parity b) + 0 &
    (Parity a) + (Parity b) > (Parity a) + 0 by XREAL_1:6; then
    Parity a <= Parity b & Parity b <= Parity a by A1,PAP;
    hence thesis by XXREAL_0:1;
  end;
