Section hlist_map_rules.
Variable A : Type.
Variables F G G' : A -> Type.
Variable ff : forall x, F x -> G x.
Variable gg : forall x, G x -> G' x.

Theorem hlist_map_hlist_map : forall ls (hl : hlist F ls),
hlist_map gg (hlist_map ff hl) = hlist_map (fun _ x => gg (ff x)) hl.