diff --git a/theories/typing/function.v b/theories/typing/function.v
index ac9c37cbed279b54c8335cf2de84ca033ce6435b..50ddd4295d4024956e2a4e23a798281b5f52981d 100644
--- a/theories/typing/function.v
+++ b/theories/typing/function.v
@@ -244,11 +244,11 @@ Section typing.
       eapply type_call'; try done. constructor. done.
   Qed.
 
-  Lemma type_fn {A} E L E' fb kb (argsb : list binder) e
+  Lemma type_rec {A} E L E' fb kb (argsb : list binder) e
         (tys : A → vec type (length argsb)) ty
         T `{!CopyC T, !SendC T} :
     Closed (fb :b: kb :b: argsb +b+ []) e →
-    (∀ x (f : val) k (args : vec val _),
+    (∀ x (f : val) k (args : vec val (length argsb)),
         typed_body (E' x) [] [k ◁cont([], λ v : vec _ 1, [v!!!0 ◁ ty x])]
                    ((f ◁ fn E' tys ty) ::
                       zip_with (TCtx_hasty ∘ of_val) args (tys x) ++ T)
@@ -265,6 +265,20 @@ Section typing.
     rewrite tctx_interp_cons tctx_interp_app. iFrame "HT' IH".
     by iApply sendc_change_tid.
   Qed.
+
+  Lemma type_fn {A} E L E' kb (argsb : list binder) e
+        (tys : A → vec type (length argsb)) ty
+        T `{!CopyC T, !SendC T} :
+    Closed (kb :b: argsb +b+ []) e →
+    (∀ x k (args : vec val (length argsb)),
+        typed_body (E' x) [] [k ◁cont([], λ v : vec _ 1, [v!!!0 ◁ ty x])]
+                   (zip_with (TCtx_hasty ∘ of_val) args (tys x) ++ T)
+                   (subst_v (kb :: argsb) (k ::: args) e)) →
+    typed_instruction_ty E L T (funrec: <> argsb → kb := e) (fn E' tys ty).
+  Proof.
+    intros. apply type_rec; try done. intros. rewrite -typed_body_mono //=.
+    eapply contains_tctx_incl. by constructor.
+  Qed.
 End typing.
 
 Hint Resolve fn_subtype_full : lrust_typing.
diff --git a/theories/typing/tests/get_x.v b/theories/typing/tests/get_x.v
index 48290a3fc8d1288b2ab80b9227b6e70ee30fc1ee..b7e263d2614b440b95f8fe782a403c98cb376086 100644
--- a/theories/typing/tests/get_x.v
+++ b/theories/typing/tests/get_x.v
@@ -7,7 +7,7 @@ Section get_x.
   Context `{typeG Σ}.
 
   Definition get_x :=
-    (funrec: "get_x" ["p"] → "ret" :=
+    (funrec: <> ["p"] → "ret" :=
        let: "p'" := !"p" in
        letalloc: "r" := "p'" +â‚— #0 in
        delete [ #1; "p"] ;; "ret" ["r":expr])%E.
@@ -17,7 +17,7 @@ Section get_x.
         (fn (λ α, [☀α])%EL (λ α, [# own 1 (&uniq{α}Π[int; int])])
             (λ α, own 1 (&shr{α} int))).
   Proof.
-    apply type_fn; try apply _. intros α get_x ret args. inv_vec args=>p args.
+    apply type_fn; try apply _. move=> /= α ret args. inv_vec args=>p args.
     inv_vec args. simpl_subst.
 
     eapply type_let'.