Definition h1map {A: UU} {n: nat} {v: vec A n} {P: A → UU} {Q: A → UU} (f: ∏ (a: A), P a → Q a) (h1v: hvec (vec_map P v)) : hvec (vec_map Q v). Proof. revert n v f h1v. refine (vec_ind _ _ _ ). - intros. exact [()]. - intros x n xs IHxs. simpl. intros f h1v. exact (f x (pr1 h1v) ::: IHxs f (pr2 h1v)). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.Combinatorics.StandardFiniteSets.