theorem Th62:
  (for g being Element of G holds g in H) implies the addMagma of
  H = the addMagma of G
proof
  assume for g being Element of G holds g in H;
  then
A1: for g be Element of G holds ( g in H implies g in G) &( g in G implies g
  in H);
  G is Subgroup of G by ThA54;
  hence thesis by A1,Th60;
end;
