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 Th9:
  t gcd z is even iff t is even & z is even
  proof
    t gcd z is even implies t is even & z is even
    proof
      assume
      A1: t gcd z is even;
      t gcd z divides t & t gcd z divides z by INT_2:21;
      hence thesis by A1;
    end;
    hence thesis by INT_2:def 2;
  end;
