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

theorem Th40:
  field SubgraphRel(G) = G.allSG()
proof
  field SubgraphRel(G) c= G.allSG() \/ G.allSG() by RELSET_1:8;
  then A1: field SubgraphRel(G) c= G.allSG();
  G.allSG() c= field SubgraphRel(G)
  proof
    let x be object;
    assume x in G.allSG();
    then reconsider H = x as plain Subgraph of G by Th1;
    H = H | _GraphSelectors by GLIB_000:128, GLIB_009:44;
    then [H, G | _GraphSelectors] in SubgraphRel(G) by Th39;
    hence x in field SubgraphRel(G) by RELAT_1:15;
  end;
  hence thesis by A1, XBOOLE_0:def 10;
end;
