bi_later->sbi_later.

theories/base_logic/derived.v

@@ -77,7 +77,7 @@ Proof.
 Qed.
 Lemma except_0_bupd P : ◇ (|==> P) ⊢ (|==> ◇ P).
 Proof.
-  rewrite /bi_except_0. apply or_elim; auto using bupd_mono, or_intro_r.
+  rewrite /sbi_except_0. apply or_elim; auto using bupd_mono, or_intro_r.
   by rewrite -bupd_intro -or_intro_l.
 Qed.
 

theories/base_logic/soundness.v

@@ -10,7 +10,7 @@ Lemma soundness φ n : (▷^n ⌜ φ ⌝ : uPred M)%I → φ.
 Proof.
   cut ((▷^n ⌜ φ ⌝ : uPred M)%I n ε → φ).
   { intros help H. eapply help, H; eauto using ucmra_unit_validN. by unseal. }
-  rewrite /bi_laterN; unseal. induction n as [|n IH]=> H; auto.
+  rewrite /sbi_laterN; unseal. induction n as [|n IH]=> H; auto.
 Qed.
 
 Corollary consistency_modal n : ¬ (▷^n False : uPred M)%I.

theories/base_logic/upred.v

@@ -341,7 +341,7 @@ Definition unseal_eqs :=
 Ltac unseal := (* Coq unfold is used to circumvent bug #5699 in rewrite /foo *)
   unfold bi_emp; simpl;
   unfold uPred_emp, bi_pure, bi_and, bi_or, bi_impl, bi_forall, bi_exist,
-  bi_internal_eq, bi_sep, bi_wand, bi_plainly, bi_persistently, bi_later; simpl;
+  bi_internal_eq, bi_sep, bi_wand, bi_plainly, bi_persistently, sbi_later; simpl;
   unfold sbi_emp, sbi_pure, sbi_and, sbi_or, sbi_impl, sbi_forall, sbi_exist,
   sbi_internal_eq, sbi_sep, sbi_wand, sbi_plainly, sbi_persistently; simpl;
   rewrite !unseal_eqs /=.
@@ -516,7 +516,7 @@ Lemma uPred_sbi_mixin (M : ucmraT) : SBIMixin
   uPred_sep uPred_plainly uPred_persistently uPred_later.
 Proof.
   split.
-  - (* Contractive bi_later *)
+  - (* Contractive sbi_later *)
     unseal; intros [|n] P Q HPQ; split=> -[|n'] x ?? //=; try omega.
     apply HPQ; eauto using cmra_validN_S.
   - (* Next x ≡ Next y ⊢ ▷ (x ≡ y) *)
@@ -645,7 +645,7 @@ Lemma ownM_unit : bi_valid (uPred_ownM (ε:M)).
 Proof. unseal; split=> n x ??; by  exists x; rewrite left_id. Qed.
 Lemma later_ownM (a : M) : ▷ uPred_ownM a ⊢ ∃ b, uPred_ownM b ∧ ▷ (a ≡ b).
 Proof.
-  rewrite /bi_and /bi_later /bi_exist /bi_internal_eq /=; unseal.
+  rewrite /bi_and /sbi_later /bi_exist /bi_internal_eq /=; unseal.
   split=> -[|n] x /= ? Hax; first by eauto using ucmra_unit_leastN.
   destruct Hax as [y ?].
   destruct (cmra_extend n x a y) as (a'&y'&Hx&?&?); auto using cmra_validN_S.

theories/bi/derived_connectives.v

@@ -94,20 +94,20 @@ Fixpoint bi_hforall {PROP : bi} {As} : himpl As PROP → PROP :=
   | tcons A As => λ Φ, ∀ x, bi_hforall (Φ x)
   end%I.
 
-Definition bi_laterN {PROP : sbi} (n : nat) (P : PROP) : PROP :=
-  Nat.iter n bi_later P.
-Arguments bi_laterN {_} !_%nat_scope _%I.
-Instance: Params (@bi_laterN) 2.
-Notation "▷^ n P" := (bi_laterN n P)
+Definition sbi_laterN {PROP : sbi} (n : nat) (P : PROP) : PROP :=
+  Nat.iter n sbi_later P.
+Arguments sbi_laterN {_} !_%nat_scope _%I.
+Instance: Params (@sbi_laterN) 2.
+Notation "▷^ n P" := (sbi_laterN n P)
   (at level 20, n at level 9, P at level 20, format "▷^ n  P") : bi_scope.
-Notation "▷? p P" := (bi_laterN (Nat.b2n p) P)
+Notation "▷? p P" := (sbi_laterN (Nat.b2n p) P)
   (at level 20, p at level 9, P at level 20, format "▷? p  P") : bi_scope.
 
-Definition bi_except_0 {PROP : sbi} (P : PROP) : PROP := (▷ False ∨ P)%I.
-Arguments bi_except_0 {_} _%I : simpl never.
-Notation "◇ P" := (bi_except_0 P) (at level 20, right associativity) : bi_scope.
-Instance: Params (@bi_except_0) 1.
-Typeclasses Opaque bi_except_0.
+Definition sbi_except_0 {PROP : sbi} (P : PROP) : PROP := (▷ False ∨ P)%I.
+Arguments sbi_except_0 {_} _%I : simpl never.
+Notation "◇ P" := (sbi_except_0 P) (at level 20, right associativity) : bi_scope.
+Instance: Params (@sbi_except_0) 1.
+Typeclasses Opaque sbi_except_0.
 
 Class Timeless {PROP : sbi} (P : PROP) := timeless : ▷ P ⊢ ◇ P.
 Arguments Timeless {_} _%I : simpl never.

theories/bi/derived_laws.v

@@ -1857,7 +1857,7 @@ Hint Resolve or_elim or_intro_l' or_intro_r' True_intro False_elim.
 Hint Resolve and_elim_l' and_elim_r' and_intro forall_intro.
 
 Global Instance later_proper :
-  Proper ((⊣⊢) ==> (⊣⊢)) (@bi_later PROP) := ne_proper _.
+  Proper ((⊣⊢) ==> (⊣⊢)) (@sbi_later PROP) := ne_proper _.
 
 (* Equality *)
 Lemma internal_eq_rewrite_contractive {A : ofeT} a b (Ψ : A → PROP)
@@ -1878,10 +1878,10 @@ Proof. apply (anti_symm _); auto using later_eq_1, later_eq_2. Qed.
 
 (* Later derived *)
 Hint Resolve later_mono.
-Global Instance later_mono' : Proper ((⊢) ==> (⊢)) (@bi_later PROP).
+Global Instance later_mono' : Proper ((⊢) ==> (⊢)) (@sbi_later PROP).
 Proof. intros P Q; apply later_mono. Qed.
 Global Instance later_flip_mono' :
-  Proper (flip (⊢) ==> flip (⊢)) (@bi_later PROP).
+  Proper (flip (⊢) ==> flip (⊢)) (@sbi_later PROP).
 Proof. intros P Q; apply later_mono. Qed.
 
 Lemma later_intro P : P ⊢ ▷ P.
@@ -1944,10 +1944,10 @@ Global Instance later_absorbing P : Absorbing P → Absorbing (▷ P).
 Proof. intros ?. by rewrite /Absorbing -later_absorbingly absorbing. Qed.
 
 (* Iterated later modality *)
-Global Instance laterN_ne m : NonExpansive (@bi_laterN PROP m).
+Global Instance laterN_ne m : NonExpansive (@sbi_laterN PROP m).
 Proof. induction m; simpl. by intros ???. solve_proper. Qed.
 Global Instance laterN_proper m :
-  Proper ((⊣⊢) ==> (⊣⊢)) (@bi_laterN PROP m) := ne_proper _.
+  Proper ((⊣⊢) ==> (⊣⊢)) (@sbi_laterN PROP m) := ne_proper _.
 
 Lemma laterN_0 P : ▷^0 P ⊣⊢ P.
 Proof. done. Qed.
@@ -1962,10 +1962,10 @@ Proof. induction 1; simpl; by rewrite -?later_intro. Qed.
 
 Lemma laterN_mono n P Q : (P ⊢ Q) → ▷^n P ⊢ ▷^n Q.
 Proof. induction n; simpl; auto. Qed.
-Global Instance laterN_mono' n : Proper ((⊢) ==> (⊢)) (@bi_laterN PROP n).
+Global Instance laterN_mono' n : Proper ((⊢) ==> (⊢)) (@sbi_laterN PROP n).
 Proof. intros P Q; apply laterN_mono. Qed.
 Global Instance laterN_flip_mono' n :
-  Proper (flip (⊢) ==> flip (⊢)) (@bi_laterN PROP n).
+  Proper (flip (⊢) ==> flip (⊢)) (@sbi_laterN PROP n).
 Proof. intros P Q; apply laterN_mono. Qed.
 
 Lemma laterN_intro n P : P ⊢ ▷^n P.
@@ -2019,34 +2019,34 @@ Global Instance laterN_absorbing n P : Absorbing P → Absorbing (▷^n P).
 Proof. induction n; apply _. Qed.
 
 (* Except-0 *)
-Global Instance except_0_ne : NonExpansive (@bi_except_0 PROP).
+Global Instance except_0_ne : NonExpansive (@sbi_except_0 PROP).
 Proof. solve_proper. Qed.
-Global Instance except_0_proper : Proper ((⊣⊢) ==> (⊣⊢)) (@bi_except_0 PROP).
+Global Instance except_0_proper : Proper ((⊣⊢) ==> (⊣⊢)) (@sbi_except_0 PROP).
 Proof. solve_proper. Qed.
-Global Instance except_0_mono' : Proper ((⊢) ==> (⊢)) (@bi_except_0 PROP).
+Global Instance except_0_mono' : Proper ((⊢) ==> (⊢)) (@sbi_except_0 PROP).
 Proof. solve_proper. Qed.
 Global Instance except_0_flip_mono' :
-  Proper (flip (⊢) ==> flip (⊢)) (@bi_except_0 PROP).
+  Proper (flip (⊢) ==> flip (⊢)) (@sbi_except_0 PROP).
 Proof. solve_proper. Qed.
 
 Lemma except_0_intro P : P ⊢ ◇ P.
-Proof. rewrite /bi_except_0; auto. Qed.
+Proof. rewrite /sbi_except_0; auto. Qed.
 Lemma except_0_mono P Q : (P ⊢ Q) → ◇ P ⊢ ◇ Q.
 Proof. by intros ->. Qed.
 Lemma except_0_idemp P : ◇ ◇ P ⊣⊢ ◇ P.
-Proof. apply (anti_symm _); rewrite /bi_except_0; auto. Qed.
+Proof. apply (anti_symm _); rewrite /sbi_except_0; auto. Qed.
 
 Lemma except_0_True : ◇ True ⊣⊢ True.
-Proof. rewrite /bi_except_0. apply (anti_symm _); auto. Qed.
+Proof. rewrite /sbi_except_0. apply (anti_symm _); auto. Qed.
 Lemma except_0_emp `{!BiAffine PROP} : ◇ emp ⊣⊢ emp.
 Proof. by rewrite -True_emp except_0_True. Qed.
 Lemma except_0_or P Q : ◇ (P ∨ Q) ⊣⊢ ◇ P ∨ ◇ Q.
-Proof. rewrite /bi_except_0. apply (anti_symm _); auto. Qed.
+Proof. rewrite /sbi_except_0. apply (anti_symm _); auto. Qed.
 Lemma except_0_and P Q : ◇ (P ∧ Q) ⊣⊢ ◇ P ∧ ◇ Q.
-Proof. by rewrite /bi_except_0 or_and_l. Qed.
+Proof. by rewrite /sbi_except_0 or_and_l. Qed.
 Lemma except_0_sep P Q : ◇ (P ∗ Q) ⊣⊢ ◇ P ∗ ◇ Q.
 Proof.
-  rewrite /bi_except_0. apply (anti_symm _).
+  rewrite /sbi_except_0. apply (anti_symm _).
   - apply or_elim; last by auto using sep_mono.
     by rewrite -!or_intro_l -persistently_pure -later_sep -persistently_sep_dup.
   - rewrite sep_or_r !sep_or_l {1}(later_intro P) {1}(later_intro Q).
@@ -2074,15 +2074,15 @@ Proof.
   - apply exist_mono=> a. apply except_0_intro.
 Qed.
 Lemma except_0_later P : ◇ ▷ P ⊢ ▷ P.
-Proof. by rewrite /bi_except_0 -later_or False_or. Qed.
+Proof. by rewrite /sbi_except_0 -later_or False_or. Qed.
 Lemma except_0_plainly_1 P : ◇ bi_plainly P ⊢ bi_plainly (◇ P).
-Proof. by rewrite /bi_except_0 -plainly_or_2 -later_plainly plainly_pure. Qed.
+Proof. by rewrite /sbi_except_0 -plainly_or_2 -later_plainly plainly_pure. Qed.
 Lemma except_0_plainly `{BiPlainlyExist PROP} P :
   ◇ bi_plainly P ⊣⊢ bi_plainly (◇ P).
-Proof. by rewrite /bi_except_0 plainly_or -later_plainly plainly_pure. Qed.
+Proof. by rewrite /sbi_except_0 plainly_or -later_plainly plainly_pure. Qed.
 Lemma except_0_persistently P : ◇ bi_persistently P ⊣⊢ bi_persistently (◇ P).
 Proof.
-  by rewrite /bi_except_0 persistently_or -later_persistently persistently_pure.
+  by rewrite /sbi_except_0 persistently_or -later_persistently persistently_pure.
 Qed.
 Lemma except_0_affinely_2 P : bi_affinely (◇ P) ⊢ ◇ bi_affinely P.
 Proof. rewrite /bi_affinely except_0_and. auto using except_0_intro. Qed.
@@ -2111,11 +2111,11 @@ Proof.
 Qed.
 
 Global Instance except_0_plain P : Plain P → Plain (◇ P).
-Proof. rewrite /bi_except_0; apply _. Qed.
+Proof. rewrite /sbi_except_0; apply _. Qed.
 Global Instance except_0_persistent P : Persistent P → Persistent (◇ P).
-Proof. rewrite /bi_except_0; apply _. Qed.
+Proof. rewrite /sbi_except_0; apply _. Qed.
 Global Instance except_0_absorbing P : Absorbing P → Absorbing (◇ P).
-Proof. rewrite /bi_except_0; apply _. Qed.
+Proof. rewrite /sbi_except_0; apply _. Qed.
 
 (* Timeless instances *)
 Global Instance Timeless_proper : Proper ((≡) ==> iff) (@Timeless PROP).
@@ -2123,7 +2123,7 @@ Proof. solve_proper. Qed.
 
 Global Instance pure_timeless φ : Timeless (⌜φ⌝ : PROP)%I.
 Proof.
-  rewrite /Timeless /bi_except_0 pure_alt later_exist_false.
+  rewrite /Timeless /sbi_except_0 pure_alt later_exist_false.
   apply or_elim, exist_elim; [auto|]=> Hφ. rewrite -(exist_intro Hφ). auto.
 Qed.
 Global Instance emp_timeless `{BiAffine PROP} : Timeless (emp : PROP)%I.
@@ -2139,7 +2139,7 @@ Proof.
   rewrite /Timeless=> HQ. rewrite later_false_em.
   apply or_mono, impl_intro_l; first done.
   rewrite -{2}(löb Q); apply impl_intro_l.
-  rewrite HQ /bi_except_0 !and_or_r. apply or_elim; last auto.
+  rewrite HQ /sbi_except_0 !and_or_r. apply or_elim; last auto.
   by rewrite assoc (comm _ _ P) -assoc !impl_elim_r.
 Qed.
 Global Instance sep_timeless P Q: Timeless P → Timeless Q → Timeless (P ∗ Q).
@@ -2152,7 +2152,7 @@ Proof.
   rewrite /Timeless=> HQ. rewrite later_false_em.
   apply or_mono, wand_intro_l; first done.
   rewrite -{2}(löb Q); apply impl_intro_l.
-  rewrite HQ /bi_except_0 !and_or_r. apply or_elim; last auto.
+  rewrite HQ /sbi_except_0 !and_or_r. apply or_elim; last auto.
   by rewrite (comm _ P) persistent_and_sep_assoc impl_elim_r wand_elim_l.
 Qed.
 Global Instance forall_timeless {A} (Ψ : A → PROP) :
@@ -2165,19 +2165,19 @@ Global Instance exist_timeless {A} (Ψ : A → PROP) :
   (∀ x, Timeless (Ψ x)) → Timeless (∃ x, Ψ x).
 Proof.
   rewrite /Timeless=> ?. rewrite later_exist_false. apply or_elim.
-  - rewrite /bi_except_0; auto.
+  - rewrite /sbi_except_0; auto.
   - apply exist_elim=> x. rewrite -(exist_intro x); auto.
 Qed.
 Global Instance plainly_timeless P  `{BiPlainlyExist PROP} :
   Timeless P → Timeless (bi_plainly P).
 Proof.
-  intros. rewrite /Timeless /bi_except_0 later_plainly_1.
-  by rewrite (timeless P) /bi_except_0 plainly_or {1}plainly_elim.
+  intros. rewrite /Timeless /sbi_except_0 later_plainly_1.
+  by rewrite (timeless P) /sbi_except_0 plainly_or {1}plainly_elim.
 Qed.
 Global Instance persistently_timeless P : Timeless P → Timeless (bi_persistently P).
 Proof.
-  intros. rewrite /Timeless /bi_except_0 later_persistently_1.
-  by rewrite (timeless P) /bi_except_0 persistently_or {1}persistently_elim.
+  intros. rewrite /Timeless /sbi_except_0 later_persistently_1.
+  by rewrite (timeless P) /sbi_except_0 persistently_or {1}persistently_elim.
 Qed.
 
 Global Instance affinely_timeless P :
@@ -2194,64 +2194,64 @@ Global Instance from_option_timeless {A} P (Ψ : A → PROP) (mx : option A) :
 Proof. destruct mx; apply _. Qed.
 
 (* Big op stuff *)
-Global Instance bi_later_monoid_and_homomorphism :
-  MonoidHomomorphism bi_and bi_and (≡) (@bi_later PROP).
+Global Instance sbi_later_monoid_and_homomorphism :
+  MonoidHomomorphism bi_and bi_and (≡) (@sbi_later PROP).
 Proof. split; [split|]; try apply _. apply later_and. apply later_True. Qed.
-Global Instance bi_laterN_and_homomorphism n :
-  MonoidHomomorphism bi_and bi_and (≡) (@bi_laterN PROP n).
+Global Instance sbi_laterN_and_homomorphism n :
+  MonoidHomomorphism bi_and bi_and (≡) (@sbi_laterN PROP n).
 Proof. split; [split|]; try apply _. apply laterN_and. apply laterN_True. Qed.
-Global Instance bi_except_0_and_homomorphism :
-  MonoidHomomorphism bi_and bi_and (≡) (@bi_except_0 PROP).
+Global Instance sbi_except_0_and_homomorphism :
+  MonoidHomomorphism bi_and bi_and (≡) (@sbi_except_0 PROP).
 Proof. split; [split|]; try apply _. apply except_0_and. apply except_0_True. Qed.
 
-Global Instance bi_later_monoid_or_homomorphism :
-  WeakMonoidHomomorphism bi_or bi_or (≡) (@bi_later PROP).
+Global Instance sbi_later_monoid_or_homomorphism :
+  WeakMonoidHomomorphism bi_or bi_or (≡) (@sbi_later PROP).
 Proof. split; try apply _. apply later_or. Qed.
-Global Instance bi_laterN_or_homomorphism n :
-  WeakMonoidHomomorphism bi_or bi_or (≡) (@bi_laterN PROP n).
+Global Instance sbi_laterN_or_homomorphism n :
+  WeakMonoidHomomorphism bi_or bi_or (≡) (@sbi_laterN PROP n).
 Proof. split; try apply _. apply laterN_or. Qed.
-Global Instance bi_except_0_or_homomorphism :
-  WeakMonoidHomomorphism bi_or bi_or (≡) (@bi_except_0 PROP).
+Global Instance sbi_except_0_or_homomorphism :
+  WeakMonoidHomomorphism bi_or bi_or (≡) (@sbi_except_0 PROP).
 Proof. split; try apply _. apply except_0_or. Qed.
 
-Global Instance bi_later_monoid_sep_weak_homomorphism :
-  WeakMonoidHomomorphism bi_sep bi_sep (≡) (@bi_later PROP).
+Global Instance sbi_later_monoid_sep_weak_homomorphism :
+  WeakMonoidHomomorphism bi_sep bi_sep (≡) (@sbi_later PROP).
 Proof. split; try apply _. apply later_sep. Qed.
-Global Instance bi_laterN_sep_weak_homomorphism n :
-  WeakMonoidHomomorphism bi_sep bi_sep (≡) (@bi_laterN PROP n).
+Global Instance sbi_laterN_sep_weak_homomorphism n :
+  WeakMonoidHomomorphism bi_sep bi_sep (≡) (@sbi_laterN PROP n).
 Proof. split; try apply _. apply laterN_sep. Qed.
-Global Instance bi_except_0_sep_weak_homomorphism :
-  WeakMonoidHomomorphism bi_sep bi_sep (≡) (@bi_except_0 PROP).
+Global Instance sbi_except_0_sep_weak_homomorphism :
+  WeakMonoidHomomorphism bi_sep bi_sep (≡) (@sbi_except_0 PROP).
 Proof. split; try apply _. apply except_0_sep. Qed.
 
-Global Instance bi_later_monoid_sep_homomorphism `{!BiAffine PROP} :
-  MonoidHomomorphism bi_sep bi_sep (≡) (@bi_later PROP).
+Global Instance sbi_later_monoid_sep_homomorphism `{!BiAffine PROP} :
+  MonoidHomomorphism bi_sep bi_sep (≡) (@sbi_later PROP).
 Proof. split; try apply _. apply later_emp. Qed.
-Global Instance bi_laterN_sep_homomorphism `{!BiAffine PROP} n :
-  MonoidHomomorphism bi_sep bi_sep (≡) (@bi_laterN PROP n).
+Global Instance sbi_laterN_sep_homomorphism `{!BiAffine PROP} n :
+  MonoidHomomorphism bi_sep bi_sep (≡) (@sbi_laterN PROP n).
 Proof. split; try apply _. apply laterN_emp. Qed.
-Global Instance bi_except_0_sep_homomorphism `{!BiAffine PROP} :
-  MonoidHomomorphism bi_sep bi_sep (≡) (@bi_except_0 PROP).
+Global Instance sbi_except_0_sep_homomorphism `{!BiAffine PROP} :
+  MonoidHomomorphism bi_sep bi_sep (≡) (@sbi_except_0 PROP).
 Proof. split; try apply _. apply except_0_emp. Qed.
 
-Global Instance bi_later_monoid_sep_entails_weak_homomorphism :
-  WeakMonoidHomomorphism bi_sep bi_sep (flip (⊢)) (@bi_later PROP).
+Global Instance sbi_later_monoid_sep_entails_weak_homomorphism :
+  WeakMonoidHomomorphism bi_sep bi_sep (flip (⊢)) (@sbi_later PROP).
 Proof. split; try apply _. intros P Q. by rewrite later_sep. Qed.
-Global Instance bi_laterN_sep_entails_weak_homomorphism n :
-  WeakMonoidHomomorphism bi_sep bi_sep (flip (⊢)) (@bi_laterN PROP n).
+Global Instance sbi_laterN_sep_entails_weak_homomorphism n :
+  WeakMonoidHomomorphism bi_sep bi_sep (flip (⊢)) (@sbi_laterN PROP n).
 Proof. split; try apply _. intros P Q. by rewrite laterN_sep. Qed.
-Global Instance bi_except_0_sep_entails_weak_homomorphism :
-  WeakMonoidHomomorphism bi_sep bi_sep (flip (⊢)) (@bi_except_0 PROP).
+Global Instance sbi_except_0_sep_entails_weak_homomorphism :
+  WeakMonoidHomomorphism bi_sep bi_sep (flip (⊢)) (@sbi_except_0 PROP).
 Proof. split; try apply _. intros P Q. by rewrite except_0_sep. Qed.
 
-Global Instance bi_later_monoid_sep_entails_homomorphism :
-  MonoidHomomorphism bi_sep bi_sep (flip (⊢)) (@bi_later PROP).
+Global Instance sbi_later_monoid_sep_entails_homomorphism :
+  MonoidHomomorphism bi_sep bi_sep (flip (⊢)) (@sbi_later PROP).
 Proof. split; try apply _. apply later_intro. Qed.
-Global Instance bi_laterN_sep_entails_homomorphism n :
-  MonoidHomomorphism bi_sep bi_sep (flip (⊢)) (@bi_laterN PROP n).
+Global Instance sbi_laterN_sep_entails_homomorphism n :
+  MonoidHomomorphism bi_sep bi_sep (flip (⊢)) (@sbi_laterN PROP n).
 Proof. split; try apply _. apply laterN_intro. Qed.
-Global Instance bi_except_0_sep_entails_homomorphism :
-  MonoidHomomorphism bi_sep bi_sep (flip (⊢)) (@bi_except_0 PROP).
+Global Instance sbi_except_0_sep_entails_homomorphism :
+  MonoidHomomorphism bi_sep bi_sep (flip (⊢)) (@sbi_except_0 PROP).
 Proof. split; try apply _. apply except_0_intro. Qed.
 End sbi_derived.
 End bi.

theories/bi/interface.v

@@ -23,7 +23,7 @@ Section bi_mixin.
   Context (bi_wand : PROP → PROP → PROP).
   Context (bi_plainly : PROP → PROP).
   Context (bi_persistently : PROP → PROP).
-  Context (bi_later : PROP → PROP).
+  Context (sbi_later : PROP → PROP).
 
   Local Infix "⊢" := bi_entails.
   Local Notation "'emp'" := bi_emp.
@@ -40,7 +40,7 @@ Section bi_mixin.
   Local Notation "x ≡ y" := (bi_internal_eq _ x y).
   Local Infix "∗" := bi_sep.
   Local Infix "-∗" := bi_wand.
-  Local Notation "▷ P" := (bi_later P).
+  Local Notation "▷ P" := (sbi_later P).
 
   Record BIMixin := {
     bi_mixin_entails_po : PreOrder bi_entails;
@@ -142,7 +142,7 @@ Section bi_mixin.
   }.
 
   Record SBIMixin := {
-    sbi_mixin_later_contractive : Contractive bi_later;
+    sbi_mixin_later_contractive : Contractive sbi_later;
 
     sbi_mixin_later_eq_1 {A : ofeT} (x y : A) : Next x ≡ Next y ⊢ ▷ (x ≡ y);
     sbi_mixin_later_eq_2 {A : ofeT} (x y : A) : ▷ (x ≡ y) ⊢ Next x ≡ Next y;
@@ -241,14 +241,14 @@ Structure sbi := SBI {
   sbi_wand : sbi_car → sbi_car → sbi_car;
   sbi_plainly : sbi_car → sbi_car;
   sbi_persistently : sbi_car → sbi_car;
-  bi_later : sbi_car → sbi_car;
+  sbi_later : sbi_car → sbi_car;
   sbi_ofe_mixin : OfeMixin sbi_car;
   sbi_bi_mixin : BIMixin sbi_ofe_mixin sbi_entails sbi_emp sbi_pure sbi_and
                          sbi_or sbi_impl sbi_forall sbi_exist sbi_internal_eq
                          sbi_sep sbi_wand sbi_plainly sbi_persistently;
   sbi_sbi_mixin : SBIMixin sbi_entails sbi_pure sbi_or sbi_impl
                            sbi_forall sbi_exist sbi_internal_eq
-                           sbi_sep sbi_plainly sbi_persistently bi_later;
+                           sbi_sep sbi_plainly sbi_persistently sbi_later;
 }.
 
 Arguments sbi_car : simpl never.
@@ -288,7 +288,7 @@ Arguments sbi_sep {PROP} _%I _%I : simpl never, rename.
 Arguments sbi_wand {PROP} _%I _%I : simpl never, rename.
 Arguments sbi_plainly {PROP} _%I : simpl never, rename.
 Arguments sbi_persistently {PROP} _%I : simpl never, rename.
-Arguments bi_later {PROP} _%I : simpl never, rename.
+Arguments sbi_later {PROP} _%I : simpl never, rename.
 
 Hint Extern 0 (bi_entails _ _) => reflexivity.
 Instance bi_rewrite_relation (PROP : bi) : RewriteRelation (@bi_entails PROP).
@@ -321,7 +321,7 @@ Notation "∃ x .. y , P" :=
   (bi_exist (λ x, .. (bi_exist (λ y, P)) ..)%I) : bi_scope.
 
 Infix "≡" := bi_internal_eq : bi_scope.
-Notation "▷ P" := (bi_later P) : bi_scope.
+Notation "▷ P" := (sbi_later P) : bi_scope.
 
 Coercion bi_valid {PROP : bi} (P : PROP) : Prop := emp ⊢ P.
 Coercion sbi_valid {PROP : sbi} : PROP → Prop := bi_valid.
@@ -488,7 +488,7 @@ Context {PROP : sbi}.
 Implicit Types φ : Prop.
 Implicit Types P Q R : PROP.
 
-Global Instance later_contractive : Contractive (@bi_later PROP).
+Global Instance later_contractive : Contractive (@sbi_later PROP).
 Proof. eapply sbi_mixin_later_contractive, sbi_sbi_mixin. Qed.
 
 Lemma later_eq_1 {A : ofeT} (x y : A) : Next x ≡ Next y ⊢ ▷ (x ≡ y : PROP).

theories/proofmode/class_instances.v

@@ -956,7 +956,7 @@ Global Instance into_sep_affinely_later `{!Timeless (emp%I : PROP)} P Q1 Q2 :
 Proof.
   rewrite /IntoSep /= => ?? ->.
   rewrite -{1}(affine_affinely Q1) -{1}(affine_affinely Q2) later_sep !later_affinely_1.
-  rewrite -except_0_sep /bi_except_0 affinely_or. apply or_elim, affinely_elim.
+  rewrite -except_0_sep /sbi_except_0 affinely_or. apply or_elim, affinely_elim.
   rewrite -(idemp bi_and (bi_affinely (▷ False))%I) persistent_and_sep_1.
   by rewrite -(False_elim Q1) -(False_elim Q2).
 Qed.