reserve x,y,X,Y for set,
  k,l,n for Nat,
  i,i1,i2,i3,j for Integer,
  G for Group,
  a,b,c,d for Element of G,
  A,B,C for Subset of G,
  H,H1,H2, H3 for Subgroup of G,
  h for Element of H,
  F,F1,F2 for FinSequence of the carrier of G,
  I,I1,I2 for FinSequence of INT;

theorem
  G is commutative Group implies the carrier of H1 "\/" H2 = H1 * H2
proof
  assume G is commutative Group;
  then H1 * H2 = H2 * H1 by GROUP_2:25;
  hence thesis by Th51;
end;
