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 Th1:
  t gcd z = -t gcd z
  proof
    t gcd z = |.t.| gcd |.z.| by INT_2:34
    .= |.-t.| gcd |.z.| by COMPLEX1:52
    .= -t gcd z by INT_2:34;
    hence thesis;
  end;
