reserve G, G1, G2 for _Graph, H for Subgraph of G;

theorem Th134:
  for F being PGraphMapping of G1, G2 st F is isomorphism
  holds G2.allConnectedSG() = rng(SG2SGFunc(F) | G1.allConnectedSG())
proof
  let F be PGraphMapping of G1, G2;
  assume F is isomorphism;
  then rng(SG2SGFunc(F) | G1.allConnectedSG()) c= G2.allConnectedSG() &
    G2.allConnectedSG() c= rng(SG2SGFunc(F) | G1.allConnectedSG())
    by Th132, Th133;
  hence thesis by XBOOLE_0:def 10;
end;
