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

theorem Th139:
  G.allTrees() = G.allForests() /\ G.allConnectedSG()
proof
  now
    let x be object;
    hereby
      assume x in G.allTrees();
      then x is plain Tree-like Subgraph of G by Th138;
      hence x in G.allForests() & x in G.allConnectedSG() by Th78, Th124;
    end;
    assume x in G.allForests() & x in G.allConnectedSG();
    hence x in G.allTrees() by Th138;
  end;
  hence thesis by XBOOLE_0:def 4;
end;
