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

theorem
  for H being spanning acyclic Subgraph of G st H is connected
  holds H | _GraphSelectors in G.allSpanningTrees()
proof
  let H be spanning acyclic Subgraph of G;
  assume A1: H is connected;
  A2: H | _GraphSelectors == H by GLIB_000:128;
  then H | _GraphSelectors is spanning acyclic Subgraph of G
    by GLIB_000:171, GLIB_002:44;
  hence thesis by A1, A2, Th168, GLIB_002:8;
end;
