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 Th41:
  m1 = denominator p & m2 = denominator q &
  n1 = numerator p & n2 = numerator q & n2 <> 0 implies
  denominator(p/q) = (m1*n2) div ( (n1*m2) gcd (m1*n2) ) &
  numerator(p/q) = (n1*m2) div ( (n1*m2) gcd (m1*n2) )
  proof
    assume
A1: m1 = denominator p & m2 = denominator q &
    n1 = numerator p & n2 = numerator q & n2 <> 0;
    then p = n1/m1 & q = n2/m2 by RAT_1:15;
    hence thesis by A1,Th27;
  end;
