
theorem
  for G2 being _Graph, V being set, G1 being addVertices of G2, V
  st V \ the_Vertices_of G2 <> {}
  holds G1.minDegree() = 0 & G1.minInDegree() = 0 & G1.minOutDegree() = 0
proof
  let G2 be _Graph, V be set, G1 be addVertices of G2, V;
  assume V \ the_Vertices_of G2 <> {};
  then consider v being object such that
    A1: v in V \ the_Vertices_of G2 by XBOOLE_0:def 1;
  reconsider v as Vertex of G1 by A1, GLIB_006:86;
  v is isolated by A1, GLIB_006:88;
  hence thesis by Th46;
end;
