reserve c,c1,c2 for Cardinal, G,G1,G2 for _Graph, v for Vertex of G;

theorem Th66:
  for G being _finite _Graph, v being Denumeration of the_Vertices_of G
  holds 2*G.size() = Sum(G.degreeMap()*v)
proof
  let G be _finite _Graph, v be Denumeration of the_Vertices_of G;
  thus 2*G.size() = G.size() + G.size()
    .= Sum(G.inDegreeMap()*v) + G.size() by Th65
    .= Sum(G.inDegreeMap()*v) + Sum(G.outDegreeMap()*v) by Th65
    .= Sum(G.inDegreeMap()*v + G.outDegreeMap()*v) by RVSUM_4:49
    .= Sum(G.degreeMap()*v) by Th64;
end;
