Fixpoint hlist_Forall ls (hs : hlist P ls) : Forall P ls :=
    match hs with
    | Hnil => Forall_nil _
    | Hcons _ _ H hs' => Forall_cons _ H (hlist_Forall hs')
    end.Inductive hlist_hrel : forall ls, hlist F ls -> hlist G ls -> Prop :=
  | hrel_Hnil : hlist_hrel Hnil Hnil
  | hrel_Hcons : forall t ts x y xs ys, @R t x y -> @hlist_hrel ts xs ys ->
                                        @hlist_hrel (t :: ts) (Hcons x xs) (Hcons y ys).Inductive hlist_hrel : forall ls, hlist F ls -> hlist G ls -> Prop :=
  | hrel_Hnil : hlist_hrel Hnil Hnil
  | hrel_Hcons : forall t ts x y xs ys, @R t x y -> @hlist_hrel ts xs ys ->
                                        @hlist_hrel (t :: ts) (Hcons x xs) (Hcons y ys).Inductive hlist_hrel : forall ls, hlist F ls -> hlist G ls -> Prop :=
  | hrel_Hnil : hlist_hrel Hnil Hnil
  | hrel_Hcons : forall t ts x y xs ys, @R t x y -> @hlist_hrel ts xs ys ->
                                        @hlist_hrel (t :: ts) (Hcons x xs) (Hcons y ys).

Theorem hlist_hrel_map : forall ls xs ys, @hlist_hrel A F G R ls xs ys -> @hlist_hrel A F' G' R' ls (hlist_map ff xs) (hlist_map gg ys).