reserve p,q for Rational;
reserve g,m,m1,m2,n,n1,n2 for Nat;
reserve i,i1,i2,j,j1,j2 for Integer;

theorem Th25:
  m <> 0 & n <> 0 implies
  denominator((i/m)*(j/n)) = (m*n) div ( (i*j) gcd (m*n) ) &
  numerator((i/m)*(j/n)) = (i*j) div ( (i*j) gcd (m*n) )
  proof
    (i/m)*(j/n) = (i*j)/(m*n) by XCMPLX_1:76;
    hence thesis by Th15;
  end;
