
theorem Th96:
  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).inDegree() c= v.inDegree() &
    (F_V/.v).outDegree() c= v.outDegree()
proof
  let G1, G2 be _Graph, F be PGraphMapping of G1, G2, v being Vertex of G1;
  assume F is onto semi-Dcontinuous & v in dom F_V;
  then F_E.:(v.edgesIn()) = (F_V/.v).edgesIn() &
    F_E.:(v.edgesOut()) = (F_V/.v).edgesOut() by Th89;
  hence thesis by CARD_1:67;
end;
