theorem Th56:
  len ps <= EdgesCount G
proof
  reconsider V=the carrier' of G as finite set;
  rng ps c= the carrier' of G by FINSEQ_1:def 4;
  then
A1: card rng ps <= card V by NAT_1:43;
  ps is one-to-one by Th15;
  then card rng ps=len ps by FINSEQ_4:62;
  hence thesis by A1,GRAPH_1:def 20;
end;
