theorem :: GROEB_1:22

for n being Element of NAT
for T being connected admissible TermOrder of n
for L being non empty non degenerated right_complementable almost_left_invertible well-unital distributive Abelian add-associative right_zeroed associative commutative doubleLoopStr
for p, q being Element of (Polynom-Ring (n,L))
for G being non empty Subset of (Polynom-Ring (n,L)) st G is_Groebner_basis_wrt T holds
( p,q are_congruent_mod G -Ideal iff nf (p,(PolyRedRel (G,T))) = nf (q,(PolyRedRel (G,T))) )