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

theorem
  for G being simple c-regular _Graph holds c c= G.order()
proof
  let G be simple c-regular _Graph;
  set v = the Vertex of G;
  card v.allNeighbors() c= G.order() by CARD_1:11;
  then v.degree() c= G.order() by GLIB_000:111;
  hence thesis by Def4;
end;
