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
  t*u divides z*u iff |.u.|*(t gcd z) = |.u.|*|.t.|
  proof
    A1: t*u divides z*u iff t*u gcd z*u = |.t*u.| by Th3;
    t*u gcd z*u = |.u.|*(t gcd z) by INT_6:16;
    hence thesis by A1,COMPLEX1:65;
  end;
