
theorem :: lemma 5.24 (iii), p. 200
  for n being Ordinal, T being connected admissible TermOrder of n, L
  being Abelian add-associative right_complementable right_zeroed commutative
  associative well-unital distributive almost_left_invertible non degenerated
  non empty doubleLoopStr, P being Subset of Polynom-Ring(n,L), f being
Polynomial of n,L, m being Monomial of n,L holds PolyRedRel(P,T) reduces f,0_(n
  ,L) implies PolyRedRel(P,T) reduces m*'f,0_(n,L)
proof
  let n be Ordinal, T be connected admissible TermOrder of n, L be Abelian
  add-associative right_complementable right_zeroed commutative associative
  well-unital distributive almost_left_invertible non degenerated non empty
doubleLoopStr, P be Subset of Polynom-Ring(n,L), f be Polynomial of n,L, m be
  Monomial of n,L;
  assume PolyRedRel(P,T) reduces f,0_(n,L);
  then PolyRedRel(P,T) reduces m*'f,m*'0_(n,L) by Th47;
  hence thesis by POLYNOM1:28;
end;
