
theorem
  for G2 being _Graph, V being Subset of the_Vertices_of G2
  for G1 being addLoops of G2, V holds G1.size() = G2.size() +` card V
proof
  let G2 be _Graph, V be Subset of the_Vertices_of G2, G1 be addLoops of G2, V;
  consider E being set, f being one-to-one Function such that
    A1: E misses the_Edges_of G2 & the_Edges_of G1 = the_Edges_of G2 \/ E &
      dom f = E & rng f = V & the_Source_of G1 = the_Source_of G2 +* f &
      the_Target_of G1 = the_Target_of G2 +* f by Def5;
  thus G1.size() = card the_Edges_of G2 +` card E by A1, CARD_2:35
    .= G2.size() +` card V by A1, CARD_1:70;
end;
