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

theorem Th72:
  G is GraphUnion of G.allSpanningSG()
proof
  set G9 = the GraphUnion of G.allSpanningSG();
  set G8 = the GraphUnion of {G};
  G | _GraphSelectors in G.allSpanningSG() by Th62;
  then A1: G | _GraphSelectors is Subgraph of G9 by GLIB_014:21;
  G == G | _GraphSelectors by GLIB_000:128;
  then A2: G is Subgraph of G9 by A1, GLIB_000:92;
  now
    let H2 be Element of G.allSpanningSG();
    reconsider H1 = G as Element of {G} by TARSKI:def 1;
    take H1;
    thus H2 is Subgraph of H1;
  end;
  then G9 is Subgraph of G8 by GLIBPRE1:118;
  then G9 is Subgraph of G by GLIB_000:91, GLIB_014:24;
  hence thesis by A2, GLIB_000:87, GLIB_014:22;
end;
