
theorem for a,b be non zero Integer, n be Nat holds
  min (Parity (a|^n),Parity (b|^n)) = (min (Parity a,Parity b))|^n
  proof
    let a,b be non zero Integer, n be Nat;
    min (Parity (a|^n),Parity (b|^n)) = Parity ((a|^n) gcd (b|^n)) by PGC
    .= Parity ((a gcd b)|^n) by NEWTON03:4
    .= (Parity (a gcd b))|^n by PAN;
    hence thesis by PGC;
  end;
