
theorem Th97:
  for G being _Graph holds G is with_max_degree iff
    ex v being Vertex of G st v is with_max_degree
proof
  let G be _Graph;
  hereby
    assume G is with_max_degree;
    then consider v being Vertex of G such that
      A1: v.degree() = G.supDegree() and
      for w being Vertex of G holds w.degree() c= v.degree() by Th79;
    take v;
    thus v is with_max_degree by A1;
  end;
  thus thesis by Lm3;
end;
