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

theorem Th161:
  SubtreeRel(G) partially_orders G.allTrees()
proof
  SubgraphRel(G) partially_orders G.allTrees() by Th41, ORDERS_1:35;
  then SubtreeRel(G) is being_partial-order by ORDERS_1:36;
  then SubtreeRel(G) partially_orders field SubtreeRel(G) by ORDERS_1:34;
  hence thesis by Th160;
end;
