theorem Th61:
  for G being addGroup, H being Subgroup of G st the carrier of G c=
  the carrier of H holds the addMagma of H = the addMagma of G
proof
  let G be addGroup, H be Subgroup of G;
  assume
A1: the carrier of G c= the carrier of H;
A2: G is Subgroup of G by ThA54;
  the carrier of G = the carrier of H by A1,DefA5;
  hence thesis by A2,Th59;
end;
