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

theorem Th108:
  for H being spanning Subgraph of G
  holds H.allSpanningForests() c= G.allSpanningForests()
proof
  let H be spanning Subgraph of G;
  now
    let x be object;
    assume x in H.allSpanningForests();
    then reconsider H9 = x as plain spanning acyclic Subgraph of H by Th102;
    the_Vertices_of H9 = the_Vertices_of H by GLIB_000:def 33
      .= the_Vertices_of G by GLIB_000:def 33;
    then H9 is plain spanning acyclic Subgraph of G
      by GLIB_000:43, GLIB_000:def 33;
    hence x in G.allSpanningForests() by Th102;
  end;
  hence thesis by TARSKI:def 3;
end;
