
theorem
  for v being Vertex of canCompleteGraph(omega)
  holds v.inDegree() = v & v.outDegree() = omega
proof
  let v be Vertex of canCompleteGraph(omega);
  thus v.inDegree() = card v.inNeighbors() by GLIB_000:109
    .= card v by Th1
    .= v;
  A1: omega \ succ v is infinite by RAMSEY_1:4;
  thus v.outDegree() = card v.outNeighbors() by GLIB_000:110
    .= card(omega\succ v) by Th1
    .= omega by A1, RAMSEY_1:2;
end;
