Given the recent interest in the fragment of system |$\mathbf{F}$| where universal instantiation is restricted to atomic formulas, a fragment nowadays named system |${\mathbf{F}}_{\textbf{at}}$|⁠, we study directly in system |$\mathbf{F}$| new conversions whose purpose is to enforce that restriction. We show some benefits of these new atomization conversions: (i) they help achieving strict simulation of proof reduction by means of the Russell–Prawitz embedding of |$\textbf{IPC}$| into system |$\mathbf{F}$|⁠, (ii) they are not stronger than a certain ‘dinaturality’ conversion known to generate a consistent equality of proofs, (iii) they provide the bridge between the Russell–Prawitz embedding and another translation, due to the authors, of |$\textbf{IPC}$| directly into system |${\mathbf{F}}_{\textbf{at}}$| and (iv) they give means for explaining why the Russell–Prawitz translation achieves strict simulation whereas the translation into |${\mathbf{F}}_{\textbf{at}}$| does not.

中文翻译：

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Russell-Prawitz嵌入和通用实例化的原子化

鉴于最近对系统片段| $ \ mathbf {F} $ |的关注 在通用实例化仅限于原子公式的情况下，现今一个名为system | $ {\ mathbf {F}} __ {\ textbf {at}} $ |⁠的片段，我们直接在system | $ \ mathbf {F} $ |中进行研究。旨在实施该限制的新转化。我们展示了这些新的雾化转换的一些好处：（i）通过| $ \ textbf {IPC} $ |的Russell-Prawitz嵌入，它们有助于实现严格的减样模拟。进入系统| $ \ mathbf {F} $ |⁠，（ii）它们不强于某种已知的“双自然性”转换，该转换会产生一致的证明相等性；（iii）它们提供了Russell-Prawitz嵌入和作者提出的另一种翻译之间的桥梁| $ \ textbf {IPC} $ | 直接进入系统| $ {\ mathbf {F}} _ {\ textbf {at}} $ | （iv）它们提供了解释为什么Russell-Prawitz翻译达到严格模拟而将翻译成| $ {\ mathbf {F}} _ {\ textbf {at}} $ |的手段。才不是。