reserve x,y for set,
  G for Group,
  A,B,H,H1,H2 for Subgroup of G,
  a,b,c for Element of G,
  F,F1 for FinSequence of the carrier of G,
  I,I1 for FinSequence of INT,
  i,j for Element of NAT;

theorem
  [.H1,H2.] is Subgroup of [.H1,(Omega).G.]
proof
A1: H2 is Subgroup of (Omega).G by Lm2;
  H1 is Subgroup of H1 by GROUP_2:54;
  hence thesis by A1,GROUP_5:66;
end;
