
theorem Th4:
  for G being Group for H1, H2 being Subgroup of G for A being
Subset of G st A = (the carrier of H1) \/ the carrier of H2 holds H1 "\/" H2 =
  gr A
proof
  let G be Group;
  let H1, H2 be Subgroup of G;
A1: the carrier of H2 = carr H2 by GROUP_2:def 9;
  let A be Subset of G;
  assume A = (the carrier of H1) \/ the carrier of H2;
  hence thesis by A1,GROUP_2:def 9;
end;
