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

theorem
  for a being Element of A
  for g being Element of G
  holds <* g, a *> is Element of semidirect_product (G, A, phi) by Th9;
