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

theorem Th26:
  for G being non edgeless _Graph, E being set, e being Edge of G
  for H being removeEdges of G, E st not e in E
  holds createGraph(e) is Subgraph of H
proof
  let G be non edgeless _Graph, E being set, e being Edge of G;
  let H be removeEdges of G, E;
  assume A1: not e in E;
  the_Vertices_of G = the_Vertices_of H by GLIB_000:def 33;
  then A2: the_Vertices_of createGraph(e) c= the_Vertices_of H;
  the_Edges_of H = the_Edges_of G \ E by GLIB_000:53;
  then e in the_Edges_of H by A1, XBOOLE_0:def 5;
  then {e} c= the_Edges_of H by ZFMISC_1:31;
  then the_Edges_of createGraph(e) c= the_Edges_of H by Th13;
  hence thesis by A2, GLIB_000:44;
end;
