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

theorem Th107:
  for G being non edgeless _Graph, e being Edge of G
  for H being plain addVertices of createGraph(e), the_Vertices_of G
  st not e in G.loops() holds H in G.allSpanningForests()
proof
  let G be non edgeless _Graph, e be Edge of G;
  let H be plain addVertices of createGraph(e), the_Vertices_of G;
  assume A1: not e in G.loops();
  the_Vertices_of G c= the_Vertices_of G;
  then H in G.allForests() & H in G.allSpanningSG() by A1, Th64, Th84;
  then H in G.allForests() /\ G.allSpanningSG() by XBOOLE_0:def 4;
  hence thesis by Th103;
end;
