theorem
  for H1,H2 being strict Subgroup of G holds H1 "\/" H2 = H2 iff H1 /\ H2 = H1
proof
  let H1,H2 be strict Subgroup of G;
  H1 "\/" H2 = H2 iff H1 is Subgroup of H2 by Th61;
  hence thesis by GROUP_2:89;
end;
