
theorem Th12:
  for n being Ordinal, L being Abelian add-associative
  right_zeroed right_complementable commutative well-unital distributive non
  trivial doubleLoopStr, p,q being Polynomial of n,L holds p - q = 0_(n,L)
  implies p = q
proof
  let n be Ordinal, L be Abelian add-associative right_zeroed
  right_complementable commutative well-unital distributive non trivial
  doubleLoopStr, p,q be Polynomial of n,L;
  assume p - q = 0_(n,L);
  hence q = q + (p - q) by POLYNOM1:23
    .= q + (p + -q) by POLYNOM1:def 7
    .= (q + -q) + p by POLYNOM1:21
    .= 0_(n,L) + p by POLYRED:3
    .= p by POLYRED:2;
end;
