
theorem for a,b be non zero Integer st
  a+b <> 0 & Parity a = Parity b &
  parity ((Oddity a) div 2) <> parity ((Oddity b) div 2) holds
    Parity (a+b) > (Parity a)+(Parity b)
  proof
    let a,b be non zero Integer such that
    A1: a + b <> 0 & Parity a = Parity b &
      parity ((Oddity a) div 2) <> parity ((Oddity b) div 2);
    A2: Parity (a+b) >= Parity a + Parity b by A1,PEQ;
    Parity (a+b) <> Parity a + Parity b by A1,PSU;
    hence thesis by A2,XXREAL_0:1;
  end;
