reserve a,b,c,d,m,x,n,j,k,l for Nat,
  t,u,v,z for Integer,
  f,F for FinSequence of NAT;
reserve p,q,r,s for real number;

theorem Th5:
  (t+u*z) gcd z = t gcd z & (t-u*z) gcd z = t gcd z
  proof
    (t-u*z) gcd z = t gcd z
    proof
      (t-u*z) gcd z = ((t-u*z) + u*z) gcd z by Lm0d
      .= t gcd z;
      hence thesis;
    end;
    hence thesis by Lm0d;
  end;
