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

theorem Th64:
  for G being non edgeless _Graph, e being Edge of G
  for H being plain addVertices of createGraph(e), the_Vertices_of G
  holds H in G.allSpanningSG()
proof
  let G be non edgeless _Graph, e be Edge of G;
  let H be plain addVertices of createGraph(e), the_Vertices_of G;
  A1: the_Vertices_of H
     = the_Vertices_of createGraph(e) \/ the_Vertices_of G by GLIB_006:def 10
    .= the_Vertices_of G by XBOOLE_1:12;
  the_Vertices_of G c= the_Vertices_of G;
  then H is spanning Subgraph of G by A1, Th21, GLIB_000:def 33;
  hence thesis by Th60;
end;
