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
  p={} implies not p is_acyclicpath_of v1,v2
proof
  assume p={};
  then not p is_orientedpath_of v1,v2;
  hence thesis;
end;
