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.

中文翻译：

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论巨大自然演绎证明中的内在冗余 II：分析 $M_{\imply}$ 超多项式证明

本文在自然演绎系统内精确定义了极小蕴涵命题逻辑\mil的巨量证明。这就是我们所说的超多项式证明的无限族。我们考虑了庞大的扩展标准形式映射证明系列，这是一种明确帮助以适当方式计算标准证明的 E 部分的设备。因此，我们表明，对于超多项式族的几乎所有成员，它们中的每一个都至少有一个子证明或推导，这些子证明或推导在超多项式中重复多次。我们称之为超多项式冗余的最后一个属性。几乎所有，精确地意味着有一个证明的结论的大小，每个证明的结论大于这个大小并且是巨大的也是高度冗余的。