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

theorem Th123:
  the_Vertices_of G.allSpanningForests() = { the_Vertices_of G }
proof
  G.allSpanningForests() = G.allSpanningSG() /\ G.allForests() by Th103;
  then G.allSpanningForests() c= G.allSpanningSG() by XBOOLE_1:17;
  then the_Vertices_of G.allSpanningForests() c=
    the_Vertices_of G.allSpanningSG() by GLIBPRE1:115;
  then the_Vertices_of G.allSpanningForests() c= {the_Vertices_of G} by Th75;
  hence thesis by ZFMISC_1:33;
end;
