reserve i,j,k,n,m for Nat,
        X for set,
        b,s for bag of X,
        x for object;

theorem Th3:
  for a,b be Integer st a^2 divides b^2 holds
    a divides b
proof
  let a,b be Integer such that
A1:a^2 divides b^2;
A2: |.a.| = a or |.a.| = -a by COMPLEX1:71;
A3: |.b.| = b or |.b.| = -b by COMPLEX1:71;
  a^2 = |.a.|^2 & b^2 = |.b.|^2 by COMPLEX1:75;
  then |.a.| divides |.b.| by A1,PYTHTRIP:6;
  hence thesis by A2,A3,INT_2:10;
end;
