
theorem Th9:
  for G1, G2 being _Graph, F being PGraphMapping of G1,G2
  st F is Dcontinuous strong_SG-embedding
  holds G2 is Dcomplete implies G1 is Dcomplete
proof
  let G1, G2 be _Graph, F be PGraphMapping of G1,G2;
  assume A1: F is Dcontinuous strong_SG-embedding & G2 is Dcomplete;
  let v,w be Vertex of G1;
  assume A2: v <> w;
  dom F_V = the_Vertices_of G1 by A1, GLIB_010:def 11;
  then A3: v in dom F_V & w in dom F_V;
  then A4: F_V.v = F_V/.v & F_V.w = F_V/.w by PARTFUN1:def 6;
  then F_V/.v <> F_V/.w by A1, A2, A3, FUNCT_1:def 4;
  then consider e9 being object such that
    A5: e9 DJoins F_V/.v,F_V/.w,G2 by A1;
  e9 DJoins F_V.v,F_V.w,G2 by A4, A5;
  then consider e being object such that
    A6: e DJoins v,w,G1 & e in dom F_E & F_E.e = e9 by A1, A3, GLIB_010:def 18;
  take e;
  thus thesis by A6;
end;
