reserve X for set;
reserve G for Group;
reserve H for Subgroup of G;
reserve h,x,y for object;
reserve f for Endomorphism of G;
reserve phi for Automorphism of G;

theorem Th19:
  H,phi .: H are_isomorphic
proof
  H,Image(phi|H) are_isomorphic by Lm3,GROUP_6:68;
  hence H,phi .: H are_isomorphic by GRSOLV_1:def 3;
end;
