theorem Th43:
  AcyclicPaths(v1,v2,V) c= AcyclicPaths(G)
proof
  let e be object;
  assume e in AcyclicPaths(v1,v2,V);
  then ex q being Simple oriented Chain of G st ( e=q)&( q is_acyclicpath_of
  v1,v2,V);
  hence thesis;
end;
