
theorem Th37:
  for n being Ordinal, T being connected TermOrder of n, L being
  add-associative right_complementable right_zeroed commutative associative
well-unital distributive almost_left_invertible non trivial doubleLoopStr, p
  being Polynomial of n,L holds 0_(n,L) is_irreducible_wrt p,T
proof
  let n be Ordinal, T be connected TermOrder of n, L be add-associative
  right_complementable right_zeroed commutative associative well-unital
  distributive almost_left_invertible non trivial doubleLoopStr, p be
  Polynomial of n,L;
  assume 0_(n,L) is_reducible_wrt p,T;
  then consider g being Polynomial of n,L such that
A1: 0_(n,L) reduces_to g,p,T;
  ex b being bag of n st 0_(n,L) reduces_to g,p,b,T by A1;
  hence thesis;
end;
