Definition L_term := rho (.\ "L", "n";
"n" !Nil (.\ "n"; !Append ("L" "n") (!Cons (!Var "n") (!Append (!Map_pro !App ("L" "n") ("L" "n")) (!Map !Lam ("L" "n")))))).

Lemma recognisable_range_total f u : proc u -> (forall n, u (enc n) ▷ tenc (f n)) -> recognisable (fun t => exists n, f n = t).