
theorem
  for a,b be non zero Integer holds Parity (a lcm b) = max (Parity a,Parity b)
  proof
    let a,b be non zero Integer;
    min(Parity a,Parity b)*max(Parity a,Parity b) = (Parity a)*(Parity b)
      by NEWTON04:18
    .= ((Parity a) gcd (Parity b))*((Parity a) lcm (Parity b)) by NAT_D:29
    .= (Parity (a gcd b))*((Parity a) lcm (Parity b)) by PGG
    .= min (Parity a,Parity b)*((Parity a) lcm (Parity b)) by PGC
    .= min (Parity a,Parity b)*(Parity (a lcm b)) by PLG;
    hence thesis by XCMPLX_1:5;
  end;
