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

theorem Th164:
  for H being removeLoops of G holds SubtreeRel(G) = SubtreeRel(H)
proof
  let H be removeLoops of G;
  thus SubtreeRel(G) = (SubtreeRel G) |_2 G.allTrees() by WELLORD1:21
    .= (SubtreeRel G) |_2 H.allTrees() by Th146
    .= SubtreeRel(H) by Th162;
end;
