
theorem Th20:
  for G1, G2 being _Graph, F being semi-Dcontinuous PGraphMapping of G1, G2
  st rng F_E = the_Edges_of G2 holds F is Dcontinuous
proof
  let G1, G2 be _Graph;
  let F be semi-Dcontinuous PGraphMapping of G1, G2;
  assume A1: rng F_E = the_Edges_of G2;
  let e9,v,w be object;
  assume A2: v in dom F_V & w in dom F_V & e9 DJoins F_V.v,F_V.w,G2;
  then e9 in the_Edges_of G2 by GLIB_000:def 14;
  then consider e being object such that
    A3: e in dom F_E & F_E.e = e9 by A1, FUNCT_1:def 3;
  take e;
  thus thesis by A2, A3, Def17;
end;
