
theorem Th98:
  for G1, G2 being _Graph, F being PGraphMapping of G1, G2
  for v being Vertex of G1 st F is Disomorphism holds
    v.inDegree() = (F_V/.v).inDegree() & v.outDegree() = (F_V/.v).outDegree()
proof
  let G1, G2 be _Graph, F be PGraphMapping of G1, G2;
  let v be Vertex of G1;
  assume A1: F is Disomorphism;
  then dom F_V = the_Vertices_of G1 by GLIB_010:def 11;
  then A2: (F_V/.v).inDegree() c= v.inDegree() &
    (F_V/.v).outDegree() c= v.outDegree() by A1, Th96;
  v.inDegree() c= (F_V/.v).inDegree() & v.outDegree() c= (F_V/.v).outDegree()
    by A1, Th94;
  hence thesis by A2, XBOOLE_0:def 10;
end;
