let G be _Graph; :: thesis: ( G is with_max_degree iff ex v being Vertex of G st v is with_max_degree )

hereby :: thesis: ( ex v being Vertex of G st v is with_max_degree implies G is with_max_degree )

assume G is with_max_degree ; :: thesis: ex v being Vertex of G st v 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 = v; :: thesis: v is with_max_degree
thus v is with_max_degree by A1; :: thesis: verum

end;

thus ( ex v being Vertex of G st v is with_max_degree implies G is with_max_degree ) by Lm3; :: thesis: verum