theorem GCDP:
  for p be prime Nat holds
    a gcd p = 1 or a gcd p = p
  proof
    let p be prime Nat;
    per cases by NAT_6:6;
    suppose p divides a;
      hence thesis by NEWTON:49;
    end;
    suppose
      a gcd p = 1;
      hence thesis;
    end;
  end;
