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

theorem Th1: :: TH1
  for G being Group
  for H being Subgroup of G
  holds the multMagma of H is strict Subgroup of G
proof
  let G be Group;
  let H be Subgroup of G;
  set H0 = the multMagma of H;
  (the carrier of H0 c= the carrier of G)
  & (the multF of H0 = (the multF of G)||(the carrier of H0))
    by GROUP_2:def 5;
  hence the multMagma of H is strict Subgroup of G by GROUP_2:def 5;
end;
