Global Instance Injection_equiv_hlist_cons ls i a b (c : hlist ls) d
: Injective (equiv_hlist (Hcons a c) (@Hcons i ls b d)) :=
{ result := @eqv i a b /\ equiv_hlist c d
; injection := @equiv_hlist_Hcons _ _ _ _ _ _ }.
Global Instance Injection_equiv_hlist_app a b (c c' : hlist a) (d d' : hlist b)
: Injective (equiv_hlist (hlist_app c d) (hlist_app c' d')) :=
{ result := equiv_hlist c c' /\ equiv_hlist d d'
; injection := fun x => proj2 (@equiv_hlist_app _ _ _ _ _ _) x }.
End equiv.

Lemma hlist_nil_eta : forall (h : hlist nil), h = Hnil.