let G1, G2 be _Graph; :: thesis: for F being PGraphMapping of G1,G2 st F is onto & F is semi-Dcontinuous & G1 is locally-finite holds
G2 is locally-finite
let F be PGraphMapping of G1,G2; :: thesis: ( F is onto & F is semi-Dcontinuous & G1 is locally-finite implies G2 is locally-finite )
assume A1: ( F is onto & F is semi-Dcontinuous & G1 is locally-finite ) ; :: thesis: G2 is locally-finite

now :: thesis: for v being Vertex of G2 holds v .degree() is finite

let v be Vertex of G2; :: thesis: v .degree() is finite
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 = 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; :: thesis: verum

end;

hence G2 is locally-finite by Th23; :: thesis: verum