
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
  trivial doubleLoopStr, p being Polynomial of n,L holds {p}
  is_Groebner_basis_of {p}-Ideal,T
proof
  let n be Element of NAT, T be connected admissible TermOrder of n, L be
  add-associative right_complementable right_zeroed commutative associative
  well-unital distributive Abelian almost_left_invertible non trivial
  doubleLoopStr, p be Polynomial of n,L;
  per cases;
  suppose
A1: p = 0_(n,L);
    0_(n,L) = 0.(Polynom-Ring(n,L)) by POLYNOM1:def 11;
    then {p}-Ideal = {0_(n,L)} by A1,IDEAL_1:44;
    hence thesis by A1,Th30;
  end;
  suppose
    p <> 0_(n,L);
    then reconsider p as non-zero Polynomial of n,L by POLYNOM7:def 1;
    PolyRedRel({p},T) is locally-confluent by Th10;
    hence thesis;
  end;
end;
