Section hlist_rel_map.
Variable A : Type.
Variables F G F' G' : A -> Type.
Variable R : forall x : A, F x -> G x -> Prop.
Variable R' : forall x : A, F' x -> G' x -> Prop.
Variable ff : forall x : A, F x -> F' x.
Variable gg : forall x : A, G x -> G' x.
Hypothesis R_ff_R' :
forall t x y, @R t x y ->
@R' t (ff x) (gg y).

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).