reserve G for _Graph;
reserve G2 for _Graph, G1 for Supergraph of G2;

theorem Th68:
  for G2, G1 holds the_Source_of G2 c= the_Source_of G1 &
    the_Target_of G2 c= the_Target_of G1
proof
  let G2, G1;
  A1: dom the_Source_of G2 = the_Edges_of G2 &
    dom the_Target_of G2 = the_Edges_of G2 &
    dom the_Source_of G1 = the_Edges_of G1 &
    dom the_Target_of G1 = the_Edges_of G1 by GLIB_000:4;
  A2: dom the_Source_of G2 c= dom the_Source_of G1 &
    dom the_Target_of G2 c= dom the_Target_of G1 by A1, Def9;
  for e being object holds e in dom the_Source_of G2 implies
    (the_Source_of G2).e = (the_Source_of G1).e by Def9;
  hence the_Source_of G2 c= the_Source_of G1 by A2, GRFUNC_1:2;
  for e being object holds e in dom the_Target_of G2 implies
    (the_Target_of G2).e = (the_Target_of G1).e by Def9;
  hence the_Target_of G2 c= the_Target_of G1 by A2, GRFUNC_1:2;
end;
