fact: Definition extended_composition {T : algebraic_theory_data} {m n : nat} (f : T (S m)) (g : stn m → T n) : T (S n) := f • (extend_tuple (λ i, (g i) • (λ i, pr (dni lastelement i))) (pr lastelement)).
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Fiber UniMath.CategoryTheory.DisplayedCats.Limits UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.Graphs.Limits UniMath.Combinatorics.StandardFiniteSets UniMath.Combinatorics.Vectors UniMath.AlgebraicTheories.AlgebraicTheories UniMath.AlgebraicTheories.AlgebraicTheoryCategoryCore UniMath.AlgebraicTheories.AlgebraicTheoryMorphisms UniMath.Combinatorics.Tuples