theorem Th9:
  the carrier of semidirect_product (G, A, phi) =
    the carrier of product <*G,A*>
proof
  thus the carrier of semidirect_product (G,A,phi)
   = product Carrier <*G,A*> by Def1
  .= the carrier of product <*G,A*> by GROUP_7:def 2;
end;
