mark a stronger-than-on-paper rule as such

theories/typing/cont_context.v

@@ -82,7 +82,7 @@ Section cont_context.
     iApply ("H" with "[%]"). by apply HC1C2.
   Qed.
 
-  Lemma cctx_incl_cons_match E k L n (T1 T2 : vec val n → tctx) C1 C2 :
+  Lemma cctx_incl_cons E k L n (T1 T2 : vec val n → tctx) C1 C2 :
     cctx_incl E C1 C2 → (∀ args, tctx_incl E L (T2 args) (T1 args)) →
     cctx_incl E (k ◁cont(L, T1) :: C1) (k ◁cont(L, T2) :: C2).
   Proof.
@@ -99,14 +99,15 @@ Section cont_context.
   Lemma cctx_incl_nil E C : cctx_incl E C [].
   Proof. apply incl_cctx_incl. by set_unfold. Qed.
 
-  Lemma cctx_incl_cons E k L n (T1 T2 : vec val n → tctx) C1 C2 :
+  (* Extra strong cctx inclusion rule that we do not have on paper. *)
+  Lemma cctx_incl_cons_dup E k L n (T1 T2 : vec val n → tctx) C1 C2 :
     k ◁cont(L, T1) ∈ C1 →
     (∀ args, tctx_incl E L (T2 args) (T1 args)) →
     cctx_incl E C1 C2 →
     cctx_incl E C1 (k ◁cont(L, T2) :: C2).
   Proof.
-    intros Hin ??. rewrite <-cctx_incl_cons_match; try done.
-    iIntros (?) "_ #HE HC".
+    intros Hin ??. rewrite <-cctx_incl_cons; try done.
+    clear -Hin. iIntros (?) "_ #HE HC".
     rewrite cctx_interp_cons. iSplit; last done. clear -Hin.
     iInduction Hin as [] "IH"; rewrite cctx_interp_cons;
       [iDestruct "HC" as "[$ _]" | iApply "IH"; iDestruct "HC" as "[_ $]"].

theories/typing/function.v

@@ -349,7 +349,7 @@ Section typing.
     intros Hfn HL HE HTT' HC HT'T''.
     rewrite -typed_body_mono /flip; last done; first by eapply type_call'.
     - etrans. eapply (incl_cctx_incl _ [_]); first by intros ? ->%stdpp.list.elem_of_list_singleton.
-      apply cctx_incl_cons_match; first done. intros args. by inv_vec args.
+      apply cctx_incl_cons; first done. intros args. by inv_vec args.
     - etrans; last by apply (tctx_incl_frame_l [_]).
       apply copy_elem_of_tctx_incl; last done. apply _.
   Qed.