This article precisely defines huge proofs within the system of Natural Deduction for the Minimal implicational propositional logic \mil. This is what we call an unlimited family of super-polynomial proofs. We consider huge families of expanded normal form mapped proofs, a device to explicitly help to count the E-parts of a normal proof in an adequate way. Thus, we show that for almost all members of a super-polynomial family there at least one sub-proof or derivation of each of them that is repeated super-polynomially many times. This last property we call super-polynomial redundancy. Almost all, precisely means that there is a size of the conclusion of proofs that every proof with conclusion bigger than this size and that is huge is highly redundant too. This result points out to a refinement of compression methods previously presented and an alternative and simpler proof that CoNP=NP.

翻译：这篇文章精确地定义了自然降价体系中 极小隐含理论逻辑的巨额证据。 这就是我们所谓的无限制的超球体证据大家庭。 我们考虑的是扩大的正常格式的庞大家庭, 绘制了图表的证明, 明确帮助以适当的方式计算正常证据的E部分的装置。 因此, 我们显示, 对于一个超级多球体家庭的几乎所有成员来说, 其中每个成员至少有一个次校准或衍生的次校准, 重复了多次超球体学。 我们称之为超球体冗余的最后一个属性。 几乎全部, 确切地说, 每一个大于此大小且庞大的证明都是非常多余的。 这个结果显示, 压缩方法已经得到了改进, 而一个替代的、 简单的证据就是CONP=NP。