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 Th37:
  AcyclicPaths(v1,v2) c= AcyclicPaths(G)
proof
  let e be object;
  assume e in AcyclicPaths(v1,v2);
  then ex q being Simple oriented Chain of G st ( e=q)&( q is_acyclicpath_of
  v1,v2);
  hence thesis;
end;
