make sealing naming consistent

heap_lang/heap.v

@@ -27,11 +27,11 @@ Definition heap_mapsto_def `{heapG Σ} (l : loc) (v: val) : iPropG heap_lang Σ
 (* Perform sealing *)
 Module Type HeapMapstoSig.
   Parameter heap_mapsto : ∀ `{heapG Σ} (l : loc) (v: val), iPropG heap_lang Σ.
-  Axiom heap_mapsto_def : @heap_mapsto = @heap_mapsto_def.
+  Axiom heap_mapsto_eq : @heap_mapsto = @heap_mapsto_def.
 End HeapMapstoSig.
 Module Export HeapMapsto : HeapMapstoSig.
   Definition heap_mapsto := @heap_mapsto_def.
-  Definition heap_mapsto_def := Logic.eq_refl (@heap_mapsto).
+  Definition heap_mapsto_eq := Logic.eq_refl (@heap_mapsto).
 End HeapMapsto. 
 
 Definition heap_inv `{i : heapG Σ} (h : heapRA) : iPropG heap_lang Σ :=
@@ -80,8 +80,7 @@ Section heap.
     authG heap_lang Σ heapRA → nclose N ⊆ E →
     ownP σ ⊑ (|={E}=> ∃ _ : heapG Σ, heap_ctx N ∧ Π★{map σ} heap_mapsto).
   Proof.
-    rewrite heap_mapsto_def.
-    intros. rewrite -{1}(from_to_heap σ). etrans.
+    intros. rewrite heap_mapsto_eq -{1}(from_to_heap σ). etrans.
     { rewrite [ownP _]later_intro.
       apply (auth_alloc (ownP ∘ of_heap) E N (to_heap σ)); last done.
       apply to_heap_valid. }
@@ -104,8 +103,7 @@ Section heap.
   (** General properties of mapsto *)
   Lemma heap_mapsto_disjoint l v1 v2 : (l ↦ v1 ★ l ↦ v2)%I ⊑ False.
   Proof.
-    rewrite heap_mapsto_def.
-    rewrite -auto_own_op auto_own_valid map_op_singleton.
+    rewrite heap_mapsto_eq -auto_own_op auto_own_valid map_op_singleton.
     rewrite map_validI (forall_elim l) lookup_singleton.
     by rewrite option_validI excl_validI.
   Qed.
@@ -117,7 +115,7 @@ Section heap.
     P ⊑ (▷ ∀ l, l ↦ v -★ Φ (LocV l)) →
     P ⊑ || Alloc e @ E {{ Φ }}.
   Proof.
-    rewrite /heap_ctx /heap_inv heap_mapsto_def=> ?? Hctx HP.
+    rewrite /heap_ctx /heap_inv heap_mapsto_eq=> ?? Hctx HP.
     trans (|={E}=> auth_own heap_name ∅ ★ P)%I.
     { by rewrite -pvs_frame_r -(auth_empty _ E) left_id. }
     apply wp_strip_pvs, (auth_fsa heap_inv (wp_fsa (Alloc e)))
@@ -143,7 +141,7 @@ Section heap.
     P ⊑ (▷ l ↦ v ★ ▷ (l ↦ v -★ Φ v)) →
     P ⊑ || Load (Loc l) @ E {{ Φ }}.
   Proof.
-    rewrite /heap_ctx /heap_inv heap_mapsto_def=>HN ? HPΦ.
+    rewrite /heap_ctx /heap_inv heap_mapsto_eq=>HN ? HPΦ.
     apply (auth_fsa' heap_inv (wp_fsa _) id)
       with N heap_name {[ l := Excl v ]}; simpl; eauto with I.
     rewrite HPΦ{HPΦ}; apply sep_mono_r, forall_intro=> h; apply wand_intro_l.
@@ -161,7 +159,7 @@ Section heap.
     P ⊑ (▷ l ↦ v' ★ ▷ (l ↦ v -★ Φ (LitV LitUnit))) →
     P ⊑ || Store (Loc l) e @ E {{ Φ }}.
   Proof.
-    rewrite /heap_ctx /heap_inv heap_mapsto_def=>? HN ? HPΦ.
+    rewrite /heap_ctx /heap_inv heap_mapsto_eq=>? HN ? HPΦ.
     apply (auth_fsa' heap_inv (wp_fsa _) (alter (λ _, Excl v) l))
       with N heap_name {[ l := Excl v' ]}; simpl; eauto with I.
     rewrite HPΦ{HPΦ}; apply sep_mono_r, forall_intro=> h; apply wand_intro_l.
@@ -181,7 +179,7 @@ Section heap.
     P ⊑ (▷ l ↦ v' ★ ▷ (l ↦ v' -★ Φ (LitV (LitBool false)))) →
     P ⊑ || Cas (Loc l) e1 e2 @ E {{ Φ }}.
   Proof.
-    rewrite /heap_ctx /heap_inv heap_mapsto_def=>??? HN ? HPΦ.
+    rewrite /heap_ctx /heap_inv heap_mapsto_eq=>??? HN ? HPΦ.
     apply (auth_fsa' heap_inv (wp_fsa _) id)
       with N heap_name {[ l := Excl v' ]}; simpl; eauto 10 with I.
     rewrite HPΦ{HPΦ}; apply sep_mono_r, forall_intro=> h; apply wand_intro_l.
@@ -200,7 +198,7 @@ Section heap.
     P ⊑ (▷ l ↦ v1 ★ ▷ (l ↦ v2 -★ Φ (LitV (LitBool true)))) →
     P ⊑ || Cas (Loc l) e1 e2 @ E {{ Φ }}.
   Proof.
-    rewrite /heap_ctx /heap_inv heap_mapsto_def=> ?? HN ? HPΦ.
+    rewrite /heap_ctx /heap_inv heap_mapsto_eq=> ?? HN ? HPΦ.
     apply (auth_fsa' heap_inv (wp_fsa _) (alter (λ _, Excl v2) l))
       with N heap_name {[ l := Excl v1 ]}; simpl; eauto 10 with I.
     rewrite HPΦ{HPΦ}; apply sep_mono_r, forall_intro=> h; apply wand_intro_l.

program_logic/saved_prop.v

@@ -15,11 +15,11 @@ Definition saved_prop_own_def `{savedPropG Λ Σ}
 Module Type SavedPropOwnSig.
   Parameter saved_prop_own : ∀ `{savedPropG Λ Σ} (γ : gname) (P : iPropG Λ Σ),
     iPropG Λ Σ.
-  Axiom saved_prop_own_def : @saved_prop_own = @saved_prop_own_def.
+  Axiom saved_prop_own_eq : @saved_prop_own = @saved_prop_own_def.
 End SavedPropOwnSig.
 Module Export SavedPropOwn : SavedPropOwnSig.
   Definition saved_prop_own := @saved_prop_own_def.
-  Definition saved_prop_own_def := Logic.eq_refl (@saved_prop_own).
+  Definition saved_prop_own_eq := Logic.eq_refl (@saved_prop_own).
 End SavedPropOwn. 
 Instance: Params (@saved_prop_own) 4.
 
@@ -30,20 +30,20 @@ Section saved_prop.
 
   Global Instance saved_prop_always_stable γ P :
     AlwaysStable (saved_prop_own γ P).
-  Proof. by rewrite /AlwaysStable saved_prop_own_def always_own. Qed.
+  Proof. by rewrite /AlwaysStable saved_prop_own_eq always_own. Qed.
 
   Lemma saved_prop_alloc_strong N P (G : gset gname) :
     True ⊑ pvs N N (∃ γ, ■ (γ ∉ G) ∧ saved_prop_own γ P).
-  Proof. by rewrite saved_prop_own_def; apply own_alloc_strong. Qed.
+  Proof. by rewrite saved_prop_own_eq; apply own_alloc_strong. Qed.
 
   Lemma saved_prop_alloc N P :
     True ⊑ pvs N N (∃ γ, saved_prop_own γ P).
-  Proof. by rewrite saved_prop_own_def; apply own_alloc. Qed.
+  Proof. by rewrite saved_prop_own_eq; apply own_alloc. Qed.
 
   Lemma saved_prop_agree γ P Q :
     (saved_prop_own γ P ★ saved_prop_own γ Q) ⊑ ▷ (P ≡ Q).
   Proof.
-    rewrite saved_prop_own_def -own_op own_valid agree_validI.
+    rewrite saved_prop_own_eq -own_op own_valid agree_validI.
     rewrite agree_equivI later_equivI /=; apply later_mono.
     rewrite -{2}(iProp_fold_unfold P) -{2}(iProp_fold_unfold Q).
     apply (eq_rewrite (iProp_unfold P) (iProp_unfold Q) (λ Q' : iPreProp Λ _,