theorem :: GROEB_1:38

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 I being non empty add-closed left-ideal Subset of (Polynom-Ring (n,L))
for G being Subset of (Polynom-Ring (n,L))
for p being Polynomial of n,L
for q being non-zero Polynomial of n,L st p in G & q in G & p <> q & HT (q,T) divides HT (p,T) & G is_Groebner_basis_of I,T holds
G \ {p} is_Groebner_basis_of I,T