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

theorem Th52:
  for F being PGraphMapping of G1, G2 st F is isomorphism
  holds rng(SG2SGFunc(F) | G1.allInducedSG())  = G2.allInducedSG()
proof
  let F be PGraphMapping of G1, G2;
  assume F is isomorphism;
  then rng(SG2SGFunc(F) | G1.allInducedSG())
    c= G2.allInducedSG() & G2.allInducedSG()
    c= rng(SG2SGFunc(F) | G1.allInducedSG())
    by Th50, Th51;
  hence thesis by XBOOLE_0:def 10;
end;
