
theorem Th95:
  for G being _Graph, v,w being Vertex of G st w is with_max_in_degree
  holds v.inDegree() c= w.inDegree()
proof
  let G be _Graph, v,w be Vertex of G;
  assume w is with_max_in_degree;
  then w.inDegree() = G.supInDegree();
  then consider v0 being Vertex of G such that
    A1: v0.inDegree() = w.inDegree() and
    A2: for u being Vertex of G holds u.inDegree() c= v0.inDegree()
    by Th80, Lm4;
  thus thesis by A1, A2;
end;
