Notation for = in uPred_scope.

algebra/upred.v

@@ -209,6 +209,7 @@ Arguments uPred_entails _ _%I _%I.
 Notation "P ⊑ Q" := (uPred_entails P%I Q%I) (at level 70) : C_scope.
 Notation "(⊑)" := uPred_entails (only parsing) : C_scope.
 Notation "■ φ" := (uPred_const φ%type) (at level 20) : uPred_scope.
+Notation "x = y" := (uPred_const (x%type = y%type)) : uPred_scope.
 Notation "'False'" := (uPred_const False) : uPred_scope.
 Notation "'True'" := (uPred_const True) : uPred_scope.
 Infix "∧" := uPred_and : uPred_scope.

heap_lang/lifting.v

@@ -22,7 +22,7 @@ Proof. apply weakestpre.wp_bind. Qed.
 (** Base axioms for core primitives of the language: Stateful reductions. *)
 Lemma wp_alloc_pst E σ e v Q :
   to_val e = Some v →
-  (ownP σ ★ ▷ (∀ l, ■(σ !! l = None) ∧ ownP (<[l:=v]>σ) -★ Q (LocV l)))
+  (ownP σ ★ ▷ (∀ l, σ !! l = None ∧ ownP (<[l:=v]>σ) -★ Q (LocV l)))
        ⊑ wp E (Alloc e) Q.
 Proof.
   (* TODO RJ: This works around ssreflect bug #22. *)
@@ -48,7 +48,7 @@ Qed.
 
 Lemma wp_store_pst E σ l e v v' Q :
   to_val e = Some v → σ !! l = Some v' →
-  (ownP σ ★ ▷ (ownP (<[l:=v]>σ) -★ Q $ LitV LitUnit)) ⊑ wp E (Store (Loc l) e) Q.
+  (ownP σ ★ ▷ (ownP (<[l:=v]>σ) -★ Q (LitV LitUnit))) ⊑ wp E (Store (Loc l) e) Q.
 Proof.
   intros. rewrite -(wp_lift_atomic_det_step σ (LitV LitUnit) (<[l:=v]>σ) None)
     ?right_id //; last by intros; inv_step; eauto.
@@ -73,7 +73,7 @@ Qed.
 
 (** Base axioms for core primitives of the language: Stateless reductions *)
 Lemma wp_fork E e :
-  ▷ wp (Σ:=Σ) coPset_all e (λ _, True) ⊑ wp E (Fork e) (λ v, ■(v = LitV LitUnit)).
+  ▷ wp (Σ:=Σ) coPset_all e (λ _, True) ⊑ wp E (Fork e) (λ v, v = LitV LitUnit).
 Proof.
   rewrite -(wp_lift_pure_det_step (Fork e) (Lit LitUnit) (Some e)) //=;
     last by intros; inv_step; eauto.

heap_lang/tests.v

@@ -28,7 +28,7 @@ Module LiftingTests.
 
   Definition e  : expr :=
     let: "x" := ref (Lit 1) in "x" <- !"x" + Lit 1; !"x".
-  Goal ∀ σ E, (ownP σ : iProp heap_lang Σ) ⊑ (wp E e (λ v, ■ (v = LitV 2))).
+  Goal ∀ σ E, ownP (Σ:=Σ) σ ⊑ wp E e (λ v, v = LitV 2).
   Proof.
     move=> σ E. rewrite /e.
     rewrite -wp_let /= -wp_alloc_pst //=.
@@ -97,7 +97,7 @@ Module LiftingTests.
 
   Goal ∀ E,
     True ⊑ wp (Σ:=Σ) E (let: "x" := Pred (Lit 42) in Pred "x")
-                       (λ v, ■ (v = LitV 40)).
+                       (λ v, v = LitV 40).
   Proof.
     intros E. rewrite -wp_let. rewrite -Pred_spec -!later_intro /=.
     rewrite -Pred_spec -later_intro. by apply const_intro.