reserve x,y,X for set,
  i,j,k,m,n for Nat,
  p for FinSequence of X,
  ii for Integer;
reserve G for Graph,
  pe,qe for FinSequence of the carrier' of G,
  p,q for oriented Chain of G,
  W for Function,
  U,V,e,ee for set,
  v1,v2,v3,v4 for Vertex of G;

theorem Th5:
  e in the carrier' of G implies <*e*> is Simple oriented Chain of G
proof
  assume e in the carrier' of G;
  then
A1: <*e*> is FinSequence of the carrier' of G by FINSEQ_1:74;
  len <*e*> = 1 by FINSEQ_1:40;
  hence thesis by A1,GRAPH_5:15;
end;
