 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 :: TH37
  for a being Element of A
  for g being Element of G
  holds ((incl1(G,A,phi)).g) |^ ((incl2(G,A,phi)).(a "))
  = <* (phi.a).g, 1_A *>
proof
  let a be Element of A;
  let g be Element of G;
  thus ((incl1(G,A,phi)).g) |^ ((incl2(G,A,phi)).(a "))
   = <* (phi.((a ")")).g, 1_A *> by Th36
  .= <* (phi.a).g, 1_A *>;
end;
