theorem Th70:
  ((nf s).len nf s)`1 <> ((nf t).1)`1 implies
    factorization(s * t) = factorization(s) ^ factorization(t)
proof
  reconsider f = uncurry injection H as ManySortedSet of FreeAtoms(H) by Lm5;
  assume ((nf s).len nf s)`1 <> ((nf t).1)`1;
  hence factorization(s * t) = f*((nf s) ^ nf t) by Th66
    .= factorization(s) ^ factorization(t) by FINSEQOP:9;
end;
