Section L_enum_rec.
Variable X : Type.
Context `{registered X}.
Variable (p : X -> Prop).
Hypotheses (f : nat -> option X) (c_f : computable f) (H_f : enumerates f p).
Hypotheses (d : X -> X -> bool) (c_d : computable d) (H_d : forall x y, reflect (x = y) (d x y)).
Definition test := (fun x n => match f n with Some y => d x y | None => false end).
Instance term_test : computable test.

Lemma proc_test (x : X) :
proc (λ y, !!(ext test) !!(enc x) y).