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;

theorem Th36:
  AcyclicPaths(p) c= AcyclicPaths(G)
proof
  let e be object;
  assume e in AcyclicPaths(p);
  then ex q being Simple oriented Chain of G st ( e=q)&( q <> {} )&( (the
Source of G).(q.1) = (the Source of G).(p.1))&( (the Target of G).(q.( len q))
  = (the Target of G).(p.(len p)))&( rng q c= rng p);
  hence thesis;
end;
