theorem Th48:
  v9 = v & v <> v1 & v <> v2 implies Degree(v9, X) = Degree(v, X)
proof
  assume that
A1: v9 = v and
A2: v <> v1 and
A3: v <> v2;
  thus Degree(v9, X) = card Edges_In(v,X) + card Edges_Out(v9,X) by A1,A3,Th43
    .= Degree(v, X) by A1,A2,Th44;
end;
