reserve n,m,i,j,k for Nat,
  x,y,e,X,V,U for set,
  W,f,g for Function;
reserve p,q for FinSequence;
reserve G for Graph,
  pe,qe for FinSequence of the carrier' of G;
reserve v,v1,v2,v3 for Element of G;
reserve p,q for oriented Chain of G;
reserve G for finite Graph,
  ps for Simple oriented Chain of G,
  P,Q for oriented Chain of G,
  v1,v2,v3 for Element of G,
  pe,qe for FinSequence of the carrier' of G;

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;
