reserve G for _Graph;

theorem Th12:
  for G being non-Dmulti _Graph holds G.size() = card VertexDomRel(G)
proof
  let G be non-Dmulti _Graph;
  DEdgeAdjEqRel(G) = id the_Edges_of G by GLIB_009:71;
  then Class DEdgeAdjEqRel(G) = SmallestPartition the_Edges_of G
    by EQREL_1:def 5;
  then card Class DEdgeAdjEqRel(G) = card the_Edges_of G by TOPGEN_2:12;
  then card VertexDomRel(G) = card the_Edges_of G by Th10;
  hence thesis by GLIB_000:def 25;
end;
