
theorem Th99:
  for G being _Graph holds G is with_max_out_degree iff
    ex v being Vertex of G st v is with_max_out_degree
proof
  let G be _Graph;
  hereby
    assume G is with_max_out_degree;
    then consider v being Vertex of G such that
      A1: v.outDegree() = G.supOutDegree() and
      for w being Vertex of G holds w.outDegree() c= v.outDegree() by Th81;
    take v;
    thus v is with_max_out_degree by A1;
  end;
  thus thesis by Lm5;
end;
