reserve G for _Graph;
reserve G2 for _Graph, G1 for Supergraph of G2;
reserve V for set;
reserve v for object;

theorem Th100:
  for G2 being _finite _Graph, V being finite set, G1 being addVertices of G2,V
  holds G1.order() = G2.order() + card (V \ the_Vertices_of G2)
proof
  let G2 be _finite _Graph, V be finite set, G1 be addVertices of G2,V;
  thus G1.order() = card the_Vertices_of G1 by GLIB_000:def 24
    .= card (the_Vertices_of G2 \/ V) by Def10
    .= card (the_Vertices_of G2 \/ (V \ the_Vertices_of G2)) by XBOOLE_1:39
    .= card the_Vertices_of G2 + card (V \ the_Vertices_of G2)
      by XBOOLE_1:79, CARD_2:40
    .= G2.order() + card (V \ the_Vertices_of G2) by GLIB_000:def 24;
end;
