
theorem Th11:
  for n being Ordinal, T being connected TermOrder of n, L being
  add-associative right_complementable right_zeroed non trivial addLoopStr
  holds Red(0_(n,L),T) = 0_(n,L)
proof
  let n be Ordinal, T be connected TermOrder of n, L be add-associative
  right_complementable right_zeroed non trivial addLoopStr;
  set e = 0_(n,L), h = HM(e,T);
  HC(h,T) = HC(e,T) by TERMORD:27
    .= e.(HT(e,T)) by TERMORD:def 7
    .= 0.L by POLYNOM1:22;
  then h = 0_(n,L) by TERMORD:17;
  hence Red(e,T) = e - 0_(n,L) by TERMORD:def 9
    .= 0_(n,L) by POLYRED:4;
end;
