Secured lower bound, composition up, and minimal rights first for bankruptcy problems

We study the implications of secured lower bound when imposed together with minimal rights first or composition up for the resolution of conflicting claims. We show that the Talmud rule is the only rule satisfying secured lower bound, minimal rights first, and consistency. In addition, we show that if minimal rights first and consistency in the above characterization were replaced with composition up and null claims consistency, respectively, the constrained equal awards rule stands out as the only acceptable rule.