theorem Th61:
  for G being Group, H being Subgroup of G st
  the carrier of G c= the carrier of H holds
    the multMagma of H = the multMagma of G
proof
  let G be Group, H be Subgroup of G;
  assume
A1: the carrier of G c= the carrier of H;
A2: G is Subgroup of G by Th54;
  the carrier of H c= the carrier of G by Def5;
  then the carrier of G = the carrier of H by A1;
  hence thesis by A2,Th59;
end;
