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

theorem
  for G2 being _Graph, v being object, G1 being addVertex of G2,v
  st not v in the_Vertices_of G2 holds G1.order() = G2.order() +` 1
proof
  let G2 be _Graph, v be object, G1 be addVertex of G2,v;
  assume not v in the_Vertices_of G2;
  then card ({v} \ the_Vertices_of G2) = 1 by ZFMISC_1:59, CARD_2:42;
  hence thesis by Th99;
end;
