
theorem :: lemma 5.26, p. 202
  for n being Ordinal, T being connected TermOrder of n, L being Abelian
  add-associative right_complementable right_zeroed commutative associative
well-unital distributive almost_left_invertible non trivial doubleLoopStr, P
being Subset of Polynom-Ring(n,L), f being Polynomial of n,L holds PolyRedRel(P
  ,T) reduces f,0_(n,L) implies f in P-Ideal
proof
  let n be Ordinal, T be connected TermOrder of n, L be Abelian
  add-associative right_complementable right_zeroed commutative associative
well-unital distributive almost_left_invertible non trivial doubleLoopStr, P
  be Subset of Polynom-Ring(n,L), f be Polynomial of n,L;
  assume PolyRedRel(P,T) reduces f,0_(n,L);
  then f-0_(n,L) in P-Ideal by Th59;
  hence thesis by Th4;
end;
