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

theorem Th84:
  for G being non edgeless _Graph, e being Edge of G
  for V being Subset of the_Vertices_of G
  for H being plain addVertices of createGraph(e), V
  st not e in G.loops() holds H in G.allForests()
proof
  let G be non edgeless _Graph, e be Edge of G;
  let V be Subset of the_Vertices_of G;
  let H be plain addVertices of createGraph(e), V;
  assume not e in G.loops();
  then A1: createGraph(e) is acyclic by Th18;
  H is Subgraph of G by Th21;
  hence thesis by A1, Th78;
end;
