
theorem Th93:
  for G being _Graph, v,w being Vertex of G st v is with_min_out_degree
  holds v.outDegree() c= w.outDegree()
proof
  let G be _Graph, v,w be Vertex of G;
  assume v is with_min_out_degree;
  then v.outDegree() = G.minOutDegree();
  then consider v0 being Vertex of G such that
    A1: v0.outDegree() = v.outDegree() and
    A2: for u being Vertex of G holds v0.outDegree() c= u.outDegree() by Th38;
  thus thesis by A1, A2;
end;
