reserve x,O for set,
  o for Element of O,
  G,H,I for GroupWithOperators of O,
  A, B for Subset of G,
  N for normal StableSubgroup of G,
  H1,H2,H3 for StableSubgroup of G,
  g1,g2 for Element of G,
  h1,h2 for Element of H1,
  h for Homomorphism of G,H;

theorem Th43:
  1_(G./.N) = carr N
proof
  reconsider N9 = the multMagma of N as normal Subgroup of G by Lm6;
  1_(G./.N9) = carr N9 by GROUP_6:24;
  hence thesis by Lm34;
end;
