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 Th3:
  t divides z iff t gcd z = |.t.|
  proof
    |.t.| in NAT & |.z.| in NAT by INT_1:3; then
    consider k,l such that
    A1: k = |.t.| & l = |.z.|;
    k divides l iff k gcd l = k by NEWTON:49,INT_2:def 2;
    hence thesis by A1,INT_2:34,INT_2:16;
  end;
