theorem Th31:
  Degree(v, X) = Degree(v, X/\the carrier' of G)
proof
  set E = the carrier' of G;
  thus Degree(v, X) = card Edges_In(v, X/\E) + card Edges_Out(v, X) by Th30
    .= Degree(v, X/\the carrier' of G) by Th30;
end;
