Fixpoint make_conj (A : Type) (eval : A -> Prop) (l : list A) {struct l} : Prop :=
  match l with
    | nil => True
    | cons e nil => (eval e)
    | cons e l2 => ((eval e) /\ (make_conj eval l2))
  end.

(* Specifications: *)
Theorem make_conj_cons : forall (A : Type) (eval : A -> Prop) (a : A) (l : list A), make_conj eval (a :: l) <-> eval a /\ make_conj eval l.
Lemma make_conj_impl : forall (A : Type) (eval : A -> Prop) (l : list A) (g : Prop), (make_conj eval l -> g) <-> make_impl eval l g.
Lemma make_conj_in : forall (A : Type) (eval : A -> Prop) (l : list A), make_conj eval l -> (forall p, In p l -> eval p).
Lemma make_conj_app : forall A eval l1 l2, @make_conj A eval (l1 ++ l2) <-> @make_conj A eval l1 /\ @make_conj A eval l2.