Stone locales together with continuous maps form a coreflective subcategory of spectral locales and perfect maps. A proof in the internal language of an elementary topos was previously given by the second-named author. This proof can be easily translated to univalent type theory using resizing axioms. In this work, we show how to achieve such a translation without resizing axioms, by working with large, locally small, and small complete frames with small bases. This turns out to be nontrivial and involves predicative reformulations of several fundamental concepts of locale theory.

翻译：石块位置与连续地图一起形成一个光谱位置和完美地图的核心反光亚类。 由第二名作者先前用一个基本图文的内部语言提供了证据。 这个证据可以很容易地被转换成单体型理论, 使用重塑轴法。 在这项工作中, 我们展示了如何在不重塑轴法的情况下实现这种翻译, 不重塑轴法, 与大体、 局部小体和小型完整框架合作, 使用小基底。 事实证明这是非技术性的, 并包含对几个地方理论基本概念的推测性重塑。