
theorem
  for G being _Graph, v,w being Vertex of G st w is with_max_degree
  holds v.degree() c= w.degree()
proof
  let G be _Graph, v,w be Vertex of G;
  assume w is with_max_degree;
  then w.degree() = G.supDegree();
  then consider v0 being Vertex of G such that
    A1: v0.degree() = w.degree() and
    A2: for u being Vertex of G holds u.degree() c= v0.degree()
    by Th79, Lm3;
  thus thesis by A1, A2;
end;
