reserve a,b,c,d,x,j,k,l,m,n,o,xi,xj for Nat,
  p,q,t,z,u,v for Integer,
  a1,b1,c1,d1 for Complex;

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;
