
theorem
  for G1, G2 being non-Dmulti _Graph, f being directed PVertexMapping of G1, G2
  for v being Vertex of G1 st f is Disomorphism holds
    v.inDegree() = (f/.v).inDegree() & v.outDegree() = (f/.v).outDegree()
proof
  let G1, G2 be non-Dmulti _Graph, f be directed PVertexMapping of G1, G2;
  let v be Vertex of G1;
  assume f is Disomorphism;
  then A1: DPVM2PGM(f) is Disomorphism by GLIB_011:48;
  thus v.inDegree() = ((DPVM2PGM f)_V/.v).inDegree() by A1, Th98
    .= (f/.v).inDegree();
  thus v.outDegree() = ((DPVM2PGM f)_V/.v).outDegree() by A1, Th98
    .= (f/.v).outDegree();
end;
