
theorem
  for G being Group for H being strict Subgroup of G for g1, g2 being
Element of G holds g1 in carr G.H & g2 in carr G.H implies g1 * g2 in carr G.H
proof
  let G be Group;
  let H be strict Subgroup of G;
  let g1, g2 be Element of G;
  assume g1 in carr G.H & g2 in carr G.H;
  then g1 in H & g2 in H by Th13;
  then g1 * g2 in H by GROUP_2:50;
  hence thesis by Th13;
end;
