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

theorem Th138:
  G2 in G1.allTrees() iff G2 is plain Tree-like Subgraph of G1
proof
  hereby
    assume G2 in G1.allTrees();
    then consider H being Element of [#]G1.allSG() such that
      A1: G2 = H & H is Tree-like;
    thus G2 is plain Tree-like Subgraph of G1 by A1;
  end;
  assume A2: G2 is plain Tree-like Subgraph of G1;
  then G2 in [#]G1.allSG() by Th1;
  hence thesis by A2;
end;
