
theorem
  for G1, G2 being _Graph, F being PGraphMapping of G1, G2
  for v being Vertex of G1 st F is onto semi-Dcontinuous & v in dom F_V
  holds (F_V/.v).degree() c= v.degree()
proof
  let G1, G2 be _Graph, F be PGraphMapping of G1, G2, v be Vertex of G1;
  assume F is onto semi-Dcontinuous & v in dom F_V;
  then (F_V/.v).inDegree() c= v.inDegree() &
    (F_V/.v).outDegree() c= v.outDegree() by Th96;
  hence thesis by CARD_2:83;
end;
