
theorem
  for G being Group for H being strict Subgroup of G for g being Element
  of G holds g in carr G.H implies g" in carr G.H
proof
  let G be Group;
  let H be strict Subgroup of G;
  let g be Element of G;
  assume g in carr G.H;
  then g in H by Th13;
  then g" in H by GROUP_2:51;
  hence thesis by Th13;
end;
