(l l' : list A) : Type := match l, l' with | nil, nil => Unit | cons x xs, cons x' xs' => (x = x') * xs xs' | _, _ => Empty end. Global Instance reflexive_listeq : Reflexive . Proof. intros l. induction l as [| a l IHl]. - exact tt. - exact (idpath, IHl). Defined.
Require Import Basics.Overture Basics.Tactics Basics.PathGroupoids Basics.Trunc. Require Import Basics.Equivalences Types.Empty Types.Unit Types.Prod. Require Import Modalities.ReflectiveSubuniverse Truncations.Core. Require Import Spaces.List.Core.