Lemma mweak_slice_ok (Γ1: HSET_over_sort) {Γ2: HSET_over_sort} (M: wellsorted_in Γ2) : sort_in (mweak_slice Γ1 Γ2 M) = sort_in M. Proof. set (H1 := pr2 (mweak_instantiated(Γ2:=Γ2) Γ1)). apply toforallpaths in H1. apply pathsinv0. now rewrite H1. Qed.
Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Limits.BinCoproducts. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Monads.Monads. Require Import UniMath.CategoryTheory.Categories.HSET.Core. Require Import UniMath.CategoryTheory.Categories.HSET.Colimits. Require Import UniMath.CategoryTheory.Categories.HSET.Limits. Require Import UniMath.CategoryTheory.Categories.HSET.Slice. Require Import UniMath.CategoryTheory.slicecat.