Use nice notation in tutorial examples.

tutorial/ex1_oneshot.v

@@ -248,14 +248,8 @@ Section verification.
   (** Instead of reverting to a manual proof, one can also register a hint for Diaframe.
       In this case, this can be done as follows. *)
   Instance shoot_hint γ z :
-    BiAbd (TTl := [tele]) (TTr := [tele]) (* no goal and sidecondition existentials *)
-      false (* indicates key hypothesis is spatial, not persistent *)
-      (own γ $ Cinl $ Excl ()) (* key hypothesis *)
-      (own γ $ Cinr $ to_agree z) (* atomic goal *)
-      (bupd) (* modality behind which goal can be proven *) 
-      emp%I (* sidecondition / anti-frame *)
-      (own γ $ Cinr $ to_agree z) (* residue / frame *).
-  Proof. rewrite /BiAbd /=. iStepS. iApply shoot_update. iStepsS. Qed.
+    HINT own γ (Cinl $ Excl ()) ✱ [- ; emp] ⊫ [bupd]; own γ (Cinr $ to_agree z) ✱ [own γ (Cinr $ to_agree z)].
+  Proof. iStepS. iApply shoot_update. iStepsS. Qed.
   (** Note that we use [bupd] as the modality, instead of [fupd _ _] as in the paper.
     Diaframe uses the fact that [|==> P ⊢ |={E,E}=> P] for all [P] and [E] to apply such hints. *)
 

tutorial/ex2_bag_stack.v

@@ -100,20 +100,13 @@ Section verification.
 
   (** Exercise: change the hint to have proper side-conditions and frame, then prove the hint. *)
   Global Instance biabd_islist_none xs P :
-    BiAbd (TTl := [tele]) (TTr := [tele])
-    false empty_hyp_first
-    (is_list P xs NONEV)
-    id
-    emp%I (* sidecondition - replace me *)
-    False%I (* residue - replace me *).
+    HINT empty_hyp_first ✱ [- ; (* replace me *) emp] ⊫ [id]; is_list P xs NONEV ✱ [False (* replace me *)].
   Proof.
-    rewrite /BiAbd /=. 
     (** This hint has key hypothesis [empty_hyp_first]. This is another special proposition that is treated 
       differently by the proof search strategy, like [empty_hyp_last] (ε₁ in the paper). The semantics of
       [empty_hyp_first] is just [True], but this hypothesis is always the first hypothesis in every environment Δ.
       It can be used for hints to add simplification rules.
      *)
-    iStepS.
   Admitted.
   (** For this hint, we use [id] as the modality. Diaframe automatically uses the fact that
     [id P ⊢ |={E,E}=> P] for all [E] and [P] when applying such hints. *)