
theorem
  for G1, G2 being _Graph, F being PGraphMapping of G1, G2
  st F is onto semi-Dcontinuous & G1 is locally-finite
  holds G2 is locally-finite
proof
  let G1, G2 be _Graph, F be PGraphMapping of G1, G2;
  assume A1: F is onto semi-Dcontinuous & G1 is locally-finite;
  now
    let v be Vertex of G2;
    rng F_V = the_Vertices_of G2 by A1, GLIB_010:def 12;
    then consider v0 being object such that
      A2: v0 in dom F_V & F_V.v0 = v by FUNCT_1:def 3;
    reconsider v0 as Vertex of G1 by A2;
    (F_V/.v0).degree() c= v0.degree() by A1, A2, GLIBPRE0:91;
    hence v.degree() is finite by A1, A2, PARTFUN1:def 6;
  end;
  hence thesis by Th23;
end;
