fact: Definition pr_comp_ax (T : algebraic_theory_data_cat) (m n : nat) (i : stn m) (f : stn m → data_set T n) : UU := data_comp (data_pr i) f = f i.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Total UniMath.Combinatorics.StandardFiniteSets UniMath.AlgebraicTheories.IndexedSetCategory