Definition vec_h1const_vec {A: UU} {n: nat} {B: A} {P: A → UU} (v: vec (P B) n) : h1const_to_vec ( vec_to_h1const v ) = v. Proof. induction n. - induction v. apply idpath. - simpl in v. simpl. change v with (pr1 v ::: pr2 v). apply maponpaths. apply (IHn (pr2 v)). Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.Combinatorics.StandardFiniteSets. Require Import UniMath.Induction.PolynomialFunctors. Require Import UniMath.Induction.W.Core. Require Import UniMath.Induction.W.Wtypes. Require Import UniMath.Induction.FunctorAlgebras_legacy. Require Import UniMath.Algebra.Universal.Signatures. Require Import UniMath.Algebra.Universal.Algebras. Require Import UniMath.Algebra.Universal.HVectors. Require Import UniMath.Algebra.Universal.Terms.