
theorem
  for G1, G2 being _Graph, G being GraphUnion of G1, G2
  st G1 tolerates G2 & the_Vertices_of G1 misses the_Vertices_of G2
  holds G.order() = G1.order() +` G2.order()
proof
  let G1, G2 be _Graph, G be GraphUnion of G1, G2;
  assume A1: G1 tolerates G2 & the_Vertices_of G1 misses the_Vertices_of G2;
  then A2: the_Vertices_of G = the_Vertices_of G1 \/ the_Vertices_of G2
    by GLIB_014:25;
  thus G.order() = G1.order() +` G2.order() by A1, A2, CARD_2:35;
end;
