fix some naming trouble

program_logic/sts.v

@@ -25,14 +25,14 @@ Module Type StsOwnSig.
            (S : sts.states sts) (T : sts.tokens sts), iPropG Λ Σ.
   Parameter sts_own : ∀ `{i : stsG Λ Σ sts} (γ : gname)
            (s : sts.state sts) (T : sts.tokens sts), iPropG Λ Σ.
-  Axiom sts_ownS_def : @sts_ownS = @sts_ownS_def.
-  Axiom sts_own_def : @sts_own = @sts_own_def.
+  Axiom sts_ownS_eq : @sts_ownS = @sts_ownS_def.
+  Axiom sts_own_eq : @sts_own = @sts_own_def.
 End StsOwnSig.
 Module Export StsOwn : StsOwnSig.
   Definition sts_ownS := @sts_ownS_def.
   Definition sts_own := @sts_own_def.
-  Definition sts_ownS_def := Logic.eq_refl (@sts_ownS_def).
-  Definition sts_own_def := Logic.eq_refl (@sts_own_def).
+  Definition sts_ownS_eq := Logic.eq_refl (@sts_ownS_def).
+  Definition sts_own_eq := Logic.eq_refl (@sts_own_def).
 End StsOwn. 
 
 Definition sts_inv `{i : stsG Λ Σ sts} (γ : gname)
@@ -64,10 +64,10 @@ Section sts.
   Proof. by intros φ1 φ2 Hφ; rewrite /sts_inv; setoid_rewrite Hφ. Qed.
   Global Instance sts_ownS_proper γ : Proper ((≡) ==> (≡) ==> (≡)) (sts_ownS γ).
   Proof.
-    intros S1 S2 HS T1 T2 HT. by rewrite !sts_ownS_def /Top.sts_ownS_def HS HT.
+    intros S1 S2 HS T1 T2 HT. by rewrite !sts_ownS_eq /sts_ownS_def HS HT.
   Qed.
   Global Instance sts_own_proper γ s : Proper ((≡) ==> (≡)) (sts_own γ s).
-  Proof. intros T1 T2 HT. by rewrite !sts_own_def /Top.sts_own_def HT. Qed.
+  Proof. intros T1 T2 HT. by rewrite !sts_own_eq /sts_own_def HT. Qed.
   Global Instance sts_ctx_ne n γ N :
     Proper (pointwise_relation _ (dist n) ==> dist n) (sts_ctx γ N).
   Proof. by intros φ1 φ2 Hφ; rewrite /sts_ctx Hφ. Qed.
@@ -81,23 +81,21 @@ Section sts.
     T2 ⊆ T1 → S1 ⊆ S2 → sts.closed S2 T2 →
     sts_ownS γ S1 T1 ⊑ (|={E}=> sts_ownS γ S2 T2).
   Proof.
-    intros ? ? ?. rewrite sts_ownS_def. by apply own_update, sts_update_frag.
+    intros ? ? ?. rewrite sts_ownS_eq. by apply own_update, sts_update_frag.
   Qed.
 
   Lemma sts_own_weaken E γ s S T1 T2 :
     T2 ⊆ T1 → s ∈ S → sts.closed S T2 →
     sts_own γ s T1 ⊑ (|={E}=> sts_ownS γ S T2).
   Proof.
-    intros ???. rewrite sts_ownS_def sts_own_def.
+    intros ???. rewrite sts_ownS_eq sts_own_eq.
     by apply own_update, sts_update_frag_up.
   Qed.
 
   Lemma sts_ownS_op γ S1 S2 T1 T2 :
     T1 ∩ T2 ⊆ ∅ → sts.closed S1 T1 → sts.closed S2 T2 →
     sts_ownS γ (S1 ∩ S2) (T1 ∪ T2) ≡ (sts_ownS γ S1 T1 ★ sts_ownS γ S2 T2)%I.
-  Proof.
-    intros. by rewrite sts_ownS_def /Top.sts_ownS_def -own_op sts_op_frag.
-  Qed.
+  Proof. intros. by rewrite sts_ownS_eq /sts_ownS_def -own_op sts_op_frag. Qed.
 
   Lemma sts_alloc E N s :
     nclose N ⊆ E →
@@ -111,7 +109,7 @@ Section sts.
     rewrite sep_exist_l. apply exist_elim=>γ. rewrite -(exist_intro γ).
     trans (▷ sts_inv γ φ ★ sts_own γ s (⊤ ∖ sts.tok s))%I.
     { rewrite /sts_inv -(exist_intro s) later_sep.
-      ecancel [▷ φ _]%I. rewrite sts_own_def.
+      ecancel [▷ φ _]%I. rewrite sts_own_eq.
       by rewrite -later_intro -own_op sts_op_auth_frag_up; last set_solver. }
     rewrite (inv_alloc N) /sts_ctx pvs_frame_r.
     by rewrite always_and_sep_l.
@@ -121,7 +119,7 @@ Section sts.
     (▷ sts_inv γ φ ★ sts_ownS γ S T)
     ⊑ (|={E}=> ∃ s, ■ (s ∈ S) ★ ▷ φ s ★ own γ (sts_auth s T)).
   Proof.
-    rewrite /sts_inv sts_ownS_def later_exist sep_exist_r. apply exist_elim=>s.
+    rewrite /sts_inv sts_ownS_eq later_exist sep_exist_r. apply exist_elim=>s.
     rewrite later_sep pvs_timeless !pvs_frame_r. apply pvs_mono.
     rewrite -(exist_intro s).
     rewrite [(_ ★ ▷φ _)%I]comm -!assoc -own_op -[(▷φ _ ★ _)%I]comm.
@@ -138,7 +136,7 @@ Section sts.
     sts.steps (s, T) (s', T') →
     (▷ φ s' ★ own γ (sts_auth s T)) ⊑ (|={E}=> ▷ sts_inv γ φ ★ sts_own γ s' T').
   Proof.
-    intros Hstep. rewrite /sts_inv sts_own_def -(exist_intro s') later_sep.
+    intros Hstep. rewrite /sts_inv sts_own_eq -(exist_intro s') later_sep.
     (* TODO it would be really nice to use cancel here *)
     rewrite [(_ ★ ▷ φ _)%I]comm -assoc.
     rewrite -pvs_frame_l. apply sep_mono_r. rewrite -later_intro.
@@ -189,7 +187,7 @@ Section sts.
             (sts_own γ s' T' -★ Ψ x))) →
     P ⊑ fsa E Ψ.
   Proof.
-    rewrite sts_own_def. intros. eapply sts_fsaS; try done; [].
-    by rewrite sts_ownS_def sts_own_def. 
+    rewrite sts_own_eq. intros. eapply sts_fsaS; try done; [].
+    by rewrite sts_ownS_eq sts_own_eq. 
   Qed.
 End sts.