(** *** Search using Choose *)
Section Fix_f.
Variable u : term.
Hypothesis proc_u : proc u.
Hypothesis total_u : forall n, u (enc n) ≡ none \/ exists s, u (enc n) ≡ oenc (Some s).
Definition Re : term := Eval cbv in
.\ "s"; !C (.\ "n"; !u "n" (.\ "t"; !Eq "s" "t") !F).

Lemma Re_sound s : eva (Re (tenc s)) -> exists n, u (enc n) ≡ oenc (Some s).