let G be _Graph; :: thesis: ( ex v being Vertex of G st v .outDegree() = G .supOutDegree() implies G is with_max_out_degree )
given v being Vertex of G such that A1: v .outDegree() = G .supOutDegree() ; :: thesis: G is with_max_out_degree
for w being Vertex of G holds w .outDegree() c= v .outDegree() by A1, Th35;
hence G is with_max_out_degree ; :: thesis: verum