
theorem Th1:
  for G being Group for H1, H2 being Subgroup of G holds the
  carrier of H1 /\ H2 = (the carrier of H1) /\ the carrier of H2
proof
  let G be Group;
  let H1, H2 be Subgroup of G;
  the carrier of H2 = carr H2 by GROUP_2:def 9;
  then (the carrier of H1) /\ the carrier of H2 = carr H1 /\ carr H2 by
GROUP_2:def 9;
  hence thesis by GROUP_2:def 10;
end;
