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;
