(** Typical boolean formulae *)
Definition eKind (k: kind) := if k then Prop else bool.Definition BFormula (A : Type) := @GFormula A eKind unit unit.Fixpoint map_bformula (k: kind)(fct : TA -> TA') (f : @GFormula TA TX AA AF k) : @GFormula TA' TX AA AF k:=
    match f with
    | TT k => TT k
    | FF k => FF k
    | X k p => X k p
    | A k a t => A k (fct a) t
    | AND f1 f2 => AND (map_bformula fct f1) (map_bformula fct f2)
    | OR f1 f2 => OR (map_bformula fct f1) (map_bformula fct f2)
    | NOT f     => NOT (map_bformula fct f)
    | IMPL f1 a f2 => IMPL (map_bformula fct f1) a (map_bformula fct f2)
    | IFF f1 f2 => IFF (map_bformula fct f1) (map_bformula fct f2)
    | EQ f1 f2  => EQ (map_bformula fct f1) (map_bformula fct f2)
    end.

(* Specifications: *)
Lemma map_simpl : forall A B f l, @map A B f l = match l with | nil => nil | a :: l=> (f a) :: (@map A B f l) end.