reserve c,c1,c2 for Cardinal, G,G1,G2 for _Graph, v for Vertex of G;

theorem
  for G being Dsimple c-Dregular _Graph holds c c= G.order()
proof
  let G be Dsimple c-Dregular _Graph;
  set v = the Vertex of G;
  card v.inNeighbors() c= G.order() by CARD_1:11;
  then v.inDegree() c= G.order() by GLIB_000:109;
  hence thesis by Def8;
end;
