
theorem
  for n being Element of NAT, T being connected admissible TermOrder of
  n, L being add-associative right_complementable right_zeroed commutative
  associative well-unital distributive Abelian almost_left_invertible non
  degenerated non empty doubleLoopStr, f being Polynomial of n,L, P being non
  empty Subset of Polynom-Ring(n,L) st P is_Groebner_basis_wrt T holds f in P
  -Ideal iff PolyRedRel(P,T) reduces f,0_(n,L)
by Th15,POLYRED:60;
