
theorem
  for G being _Graph, v,w being Vertex of G st v is with_min_degree
  holds v.degree() c= w.degree()
proof
  let G be _Graph, v,w be Vertex of G;
  assume v is with_min_degree;
  then v.degree() = G.minDegree();
  then consider v0 being Vertex of G such that
    A1: v0.degree() = v.degree() and
    A2: for u being Vertex of G holds v0.degree() c= u.degree() by Th36;
  thus thesis by A1, A2;
end;
