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

theorem Th141:
  G is Tree-like iff G | _GraphSelectors in G.allTrees()
proof
  hereby
    assume A1: G is Tree-like;
    G is Subgraph of G by GLIB_000:40;
    hence G | _GraphSelectors in G.allTrees() by A1, Th140;
  end;
  assume G | _GraphSelectors in G.allTrees();
  then A2: G | _GraphSelectors is Tree-like by Th138;
  G | _GraphSelectors == G by GLIB_000:128;
  hence thesis by A2, GLIB_002:48;
end;
