 reserve G, A for Group;
 reserve phi for Homomorphism of A,AutGroup(G);

theorem Th48:
  for G being Group
  for A being Subset of G st A = the carrier of G
  holds gr A = the multMagma of G
proof
  let G be Group;
  let A be Subset of G;
  assume A = the carrier of G;
  then the carrier of G c= the carrier of gr A by GROUP_4:def 4;
  hence the multMagma of G = gr A by GROUP_2:61;
end;
