rename valid -> emp_valid

theories/base_logic/lib/own.v

@@ -118,7 +118,7 @@ Lemma own_alloc_strong a (G : gset gname) :
 Proof.
   intros Ha.
   rewrite -(bupd_mono (∃ m, ⌜∃ γ, γ ∉ G ∧ m = iRes_singleton γ a⌝ ∧ uPred_ownM m)%I).
-  - rewrite /uPred_valid /bi_valid ownM_unit.
+  - rewrite /uPred_valid /bi_emp_valid ownM_unit.
     eapply bupd_ownM_updateP, (ofe_fun_singleton_updateP_empty (inG_id _));
       first (eapply alloc_updateP_strong', cmra_transport_valid, Ha);
       naive_solver.
@@ -127,7 +127,7 @@ Proof.
 Qed.
 Lemma own_alloc a : ✓ a → (|==> ∃ γ, own γ a)%I.
 Proof.
-  intros Ha. rewrite /uPred_valid /bi_valid (own_alloc_strong a ∅) //; [].
+  intros Ha. rewrite /uPred_valid /bi_emp_valid (own_alloc_strong a ∅) //; [].
   apply bupd_mono, exist_mono=>?. eauto with I.
 Qed.
 
@@ -168,7 +168,7 @@ Arguments own_update_3 {_ _} [_] _ _ _ _ _ _.
 
 Lemma own_unit A `{inG Σ (A:ucmraT)} γ : (|==> own γ ε)%I.
 Proof.
-  rewrite /uPred_valid /bi_valid ownM_unit !own_eq /own_def.
+  rewrite /uPred_valid /bi_emp_valid ownM_unit !own_eq /own_def.
   apply bupd_ownM_update, ofe_fun_singleton_update_empty.
   apply (alloc_unit_singleton_update (cmra_transport inG_prf ε)); last done.
   - apply cmra_transport_valid, ucmra_unit_valid.

theories/base_logic/lib/wsat.v

@@ -54,7 +54,7 @@ Proof. rewrite /ownI. apply _. Qed.
 
 Lemma ownE_empty : (|==> ownE ∅)%I.
 Proof.
-  rewrite /uPred_valid /bi_valid.
+  rewrite /uPred_valid /bi_emp_valid.
   by rewrite (own_unit (coPset_disjUR) enabled_name).
 Qed.
 Lemma ownE_op E1 E2 : E1 ## E2 → ownE (E1 ∪ E2) ⊣⊢ ownE E1 ∗ ownE E2.
@@ -72,7 +72,7 @@ Proof. rewrite ownE_disjoint. iIntros (?); set_solver. Qed.
 
 Lemma ownD_empty : (|==> ownD ∅)%I.
 Proof.
-  rewrite /uPred_valid /bi_valid.
+  rewrite /uPred_valid /bi_emp_valid.
   by rewrite (own_unit (gset_disjUR positive) disabled_name).
 Qed.
 Lemma ownD_op E1 E2 : E1 ## E2 → ownD (E1 ∪ E2) ⊣⊢ ownD E1 ∗ ownD E2.

theories/base_logic/upred.v

@@ -540,7 +540,7 @@ Canonical Structure uPredSI (M : ucmraT) : sbi :=
   {| sbi_ofe_mixin := ofe_mixin_of (uPred M);
      sbi_bi_mixin := uPred_bi_mixin M; sbi_sbi_mixin := uPred_sbi_mixin M |}.
 
-Coercion uPred_valid {M} : uPred M → Prop := bi_valid.
+Coercion uPred_valid {M} : uPred M → Prop := bi_emp_valid.
 
 (* Latest notation *)
 Notation "✓ x" := (uPred_cmra_valid x) (at level 20) : bi_scope.
@@ -671,7 +671,7 @@ Proof.
   rewrite /bi_persistently /=. unseal.
   split=> n x Hx /=. by apply cmra_core_monoN.
 Qed.
-Lemma ownM_unit : bi_valid (uPred_ownM (ε:M)).
+Lemma ownM_unit : bi_emp_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.
@@ -691,7 +691,7 @@ Proof.
   unseal; split=> n x Hv [a' ?]; ofe_subst; eauto using cmra_validN_op_l.
 Qed.
 Lemma cmra_valid_intro {A : cmraT} (a : A) :
-  ✓ a → bi_valid (PROP:=uPredI M) (✓ a).
+  ✓ a → bi_emp_valid (PROP:=uPredI M) (✓ a).
 Proof. unseal=> ?; split=> n x ? _ /=; by apply cmra_valid_validN. Qed.
 Lemma cmra_valid_elim {A : cmraT} (a : A) : ¬ ✓{0} a → ✓ a ⊢ (False : uPred M).
 Proof.

theories/bi/derived_laws.v

@@ -35,12 +35,12 @@ Lemma entails_equiv_l P Q R : (P ⊣⊢ Q) → (Q ⊢ R) → (P ⊢ R).
 Proof. by intros ->. Qed.
 Lemma entails_equiv_r P Q R : (P ⊢ Q) → (Q ⊣⊢ R) → (P ⊢ R).
 Proof. by intros ? <-. Qed.
-Global Instance bi_valid_proper : Proper ((⊣⊢) ==> iff) (@bi_valid PROP).
+Global Instance bi_emp_valid_proper : Proper ((⊣⊢) ==> iff) (@bi_emp_valid PROP).
 Proof. solve_proper. Qed.
-Global Instance bi_valid_mono : Proper ((⊢) ==> impl) (@bi_valid PROP).
+Global Instance bi_emp_valid_mono : Proper ((⊢) ==> impl) (@bi_emp_valid PROP).
 Proof. solve_proper. Qed.
-Global Instance bi_valid_flip_mono :
-  Proper (flip (⊢) ==> flip impl) (@bi_valid PROP).
+Global Instance bi_emp_valid_flip_mono :
+  Proper (flip (⊢) ==> flip impl) (@bi_emp_valid PROP).
 Proof. solve_proper. Qed.
 
 (* Propers *)
@@ -313,13 +313,13 @@ Proof. rewrite -{1}[P](left_id emp%I bi_sep). auto using sep_mono. Qed.
 Lemma sep_True_2 P : P ⊢ P ∗ True.
 Proof. by rewrite comm -True_sep_2. Qed.
 
-Lemma sep_intro_valid_l P Q R : P → (R ⊢ Q) → R ⊢ P ∗ Q.
+Lemma sep_intro_emp_valid_l P Q R : P → (R ⊢ Q) → R ⊢ P ∗ Q.
 Proof. intros ? ->. rewrite -{1}(left_id emp%I _ Q). by apply sep_mono. Qed.
-Lemma sep_intro_valid_r P Q R : (R ⊢ P) → Q → R ⊢ P ∗ Q.
-Proof. intros -> ?. rewrite comm. by apply sep_intro_valid_l. Qed.
-Lemma sep_elim_valid_l P Q R : P → (P ∗ R ⊢ Q) → R ⊢ Q.
+Lemma sep_intro_emp_valid_r P Q R : (R ⊢ P) → Q → R ⊢ P ∗ Q.
+Proof. intros -> ?. rewrite comm. by apply sep_intro_emp_valid_l. Qed.
+Lemma sep_elim_emp_valid_l P Q R : P → (P ∗ R ⊢ Q) → R ⊢ Q.
 Proof. intros <- <-. by rewrite left_id. Qed.
-Lemma sep_elim_valid_r P Q R : P → (R ∗ P ⊢ Q) → R ⊢ Q.
+Lemma sep_elim_emp_valid_r P Q R : P → (R ∗ P ⊢ Q) → R ⊢ Q.
 Proof. intros <- <-. by rewrite right_id. Qed.
 
 Lemma wand_intro_l P Q R : (Q ∗ P ⊢ R) → P ⊢ Q -∗ R.
@@ -402,7 +402,7 @@ Proof. intros ->; apply wand_iff_refl. Qed.
 Lemma wand_iff_equiv P Q : (P ∗-∗ Q)%I → (P ⊣⊢ Q).
 Proof.
   intros HPQ; apply (anti_symm (⊢));
-    apply wand_entails; rewrite /bi_valid HPQ /bi_wand_iff; auto.
+    apply wand_entails; rewrite /bi_emp_valid HPQ /bi_wand_iff; auto.
 Qed.
 
 Lemma entails_impl P Q : (P ⊢ Q) → (P → Q)%I.
@@ -415,7 +415,7 @@ Proof. intros ->; apply iff_refl. Qed.
 Lemma iff_equiv P Q `{!Affine P, !Affine Q} : (P ↔ Q)%I → (P ⊣⊢ Q).
 Proof.
   intros HPQ; apply (anti_symm (⊢));
-    apply: impl_entails; rewrite /bi_valid HPQ /bi_iff; auto.
+    apply: impl_entails; rewrite /bi_emp_valid HPQ /bi_iff; auto.
 Qed.
 
 (* Pure stuff *)

theories/bi/embedding.v

@@ -99,9 +99,9 @@ Section embed.
     rewrite EQ //.
   Qed.
 
-  Lemma embed_valid (P : PROP1) : ⎡P⎤%I ↔ P.
+  Lemma embed_emp_valid (P : PROP1) : ⎡P⎤%I ↔ P.
   Proof.
-    by rewrite /bi_valid -embed_emp; split=>?; [apply (inj embed)|f_equiv].
+    by rewrite /bi_emp_valid -embed_emp; split=>?; [apply (inj embed)|f_equiv].
   Qed.
 
   Lemma embed_forall A (Φ : A → PROP1) : ⎡∀ x, Φ x⎤ ⊣⊢ ∀ x, ⎡Φ x⎤.

theories/bi/interface.v

@@ -294,11 +294,11 @@ Notation "'<pers>' P" := (bi_persistently P) : bi_scope.
 Infix "≡" := sbi_internal_eq : 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.
+Coercion bi_emp_valid {PROP : bi} (P : PROP) : Prop := emp ⊢ P.
+Coercion sbi_emp_valid {PROP : sbi} : PROP → Prop := bi_emp_valid.
 
-Arguments bi_valid {_} _%I : simpl never.
-Typeclasses Opaque bi_valid.
+Arguments bi_emp_valid {_} _%I : simpl never.
+Typeclasses Opaque bi_emp_valid.
 
 Module bi.
 Section bi_laws.

theories/proofmode/class_instances.v

@@ -992,18 +992,18 @@ Global Instance into_embed_embed {PROP' : bi} `{BiEmbed PROP PROP'} P :
   IntoEmbed ⎡P⎤ P.
 Proof. by rewrite /IntoEmbed. Qed.
 
-(* AsValid *)
-Global Instance as_valid_valid {PROP : bi} (P : PROP) : AsValid0 (bi_valid P) P | 0.
-Proof. by rewrite /AsValid. Qed.
-Global Instance as_valid_entails {PROP : bi} (P Q : PROP) : AsValid0 (P ⊢ Q) (P -∗ Q).
+(* AsEmpValid *)
+Global Instance as_emp_valid_emp_valid {PROP : bi} (P : PROP) : AsEmpValid0 (bi_emp_valid P) P | 0.
+Proof. by rewrite /AsEmpValid. Qed.
+Global Instance as_emp_valid_entails {PROP : bi} (P Q : PROP) : AsEmpValid0 (P ⊢ Q) (P -∗ Q).
 Proof. split. apply bi.entails_wand. apply bi.wand_entails. Qed.
-Global Instance as_valid_equiv {PROP : bi} (P Q : PROP) : AsValid0 (P ≡ Q) (P ∗-∗ Q).
+Global Instance as_emp_valid_equiv {PROP : bi} (P Q : PROP) : AsEmpValid0 (P ≡ Q) (P ∗-∗ Q).
 Proof. split. apply bi.equiv_wand_iff. apply bi.wand_iff_equiv. Qed.
 
-Global Instance as_valid_forall {A : Type} (φ : A → Prop) (P : A → PROP) :
-  (∀ x, AsValid (φ x) (P x)) → AsValid (∀ x, φ x) (∀ x, P x).
+Global Instance as_emp_valid_forall {A : Type} (φ : A → Prop) (P : A → PROP) :
+  (∀ x, AsEmpValid (φ x) (P x)) → AsEmpValid (∀ x, φ x) (∀ x, P x).
 Proof.
-  rewrite /AsValid=>H1. split=>H2.
+  rewrite /AsEmpValid=>H1. split=>H2.
   - apply bi.forall_intro=>?. apply H1, H2.
   - intros x. apply H1. revert H2. by rewrite (bi.forall_elim x).
 Qed.
@@ -1014,10 +1014,10 @@ Qed.
    The first [`{BiEmbed PROP PROP'}] is not considered as a premise by
    Coq TC search mechanism because the rest of the hypothesis is dependent
    on it. *)
-Global Instance as_valid_embed `{BiEmbed PROP PROP'} (φ : Prop) (P : PROP) :
+Global Instance as_emp_valid_embed `{BiEmbed PROP PROP'} (φ : Prop) (P : PROP) :
   BiEmbed PROP PROP' →
-  AsValid0 φ P → AsValid φ ⎡P⎤.
-Proof. rewrite /AsValid0 /AsValid=> _ ->. rewrite embed_valid //. Qed.
+  AsEmpValid0 φ P → AsEmpValid φ ⎡P⎤.
+Proof. rewrite /AsEmpValid0 /AsEmpValid=> _ ->. rewrite embed_emp_valid //. Qed.
 End bi_instances.
 
 Section sbi_instances.

theories/proofmode/classes.v

@@ -455,29 +455,29 @@ Arguments IntoEmbed {_ _ _} _%I _%I.
 Arguments into_embed {_ _ _} _%I _%I {_}.
 Hint Mode IntoEmbed + + + ! -  : typeclass_instances.
 
-(* We use two type classes for [AsValid], in order to avoid loops in
-   typeclass search. Indeed, the [as_valid_embed] instance would try
+(* We use two type classes for [AsEmpValid], in order to avoid loops in
+   typeclass search. Indeed, the [as_emp_valid_embed] instance would try
    to add an arbitrary number of embeddings. To avoid this, the
-   [AsValid0] type class cannot handle embeddings, and therefore
-   [as_valid_embed] only tries to add one embedding, and we never try
+   [AsEmpValid0] type class cannot handle embeddings, and therefore
+   [as_emp_valid_embed] only tries to add one embedding, and we never try
    to insert nested embeddings. This has the additional advantage of
-   always trying [as_valid_embed] as a second option, so that this
+   always trying [as_emp_valid_embed] as a second option, so that this
    instance is never used when the BI is unknown.
 
    No Hint Modes are declared here. The appropriate one would be
    [Hint Mode - ! -], but the fact that Coq ignores primitive
    projections for hints modes would make this fail.*)
-Class AsValid {PROP : bi} (φ : Prop) (P : PROP) := as_valid : φ ↔ P.
-Arguments AsValid {_} _%type _%I.
-Class AsValid0 {PROP : bi} (φ : Prop) (P : PROP) :=
-  as_valid_here : AsValid φ P.
-Arguments AsValid0 {_} _%type _%I.
-Existing Instance as_valid_here | 0.
-
-Lemma as_valid_1 (φ : Prop) {PROP : bi} (P : PROP) `{!AsValid φ P} : φ → P.
-Proof. by apply as_valid. Qed.
-Lemma as_valid_2 (φ : Prop) {PROP : bi} (P : PROP) `{!AsValid φ P} : P → φ.
-Proof. by apply as_valid. Qed.
+Class AsEmpValid {PROP : bi} (φ : Prop) (P : PROP) := as_emp_valid : φ ↔ P.
+Arguments AsEmpValid {_} _%type _%I.
+Class AsEmpValid0 {PROP : bi} (φ : Prop) (P : PROP) :=
+  as_emp_valid_here : AsEmpValid φ P.
+Arguments AsEmpValid0 {_} _%type _%I.
+Existing Instance as_emp_valid_here | 0.
+
+Lemma as_emp_valid_1 (φ : Prop) {PROP : bi} (P : PROP) `{!AsEmpValid φ P} : φ → P.
+Proof. by apply as_emp_valid. Qed.
+Lemma as_emp_valid_2 (φ : Prop) {PROP : bi} (P : PROP) `{!AsEmpValid φ P} : P → φ.
+Proof. by apply as_emp_valid. Qed.
 
 (* Input: [P]; Outputs: [N],
    Extracts the namespace associated with an invariant assertion. Used for [iInv]. *)

theories/proofmode/monpred.v

@@ -148,30 +148,30 @@ Proof.
   by rewrite /KnownRFromAssumption /FromAssumption -monPred_subjectively_intro.
 Qed.
 
-Global Instance as_valid_monPred_at φ P (Φ : I → PROP) :
-  AsValid0 φ P → (∀ i, MakeMonPredAt i P (Φ i)) → AsValid φ (∀ i, Φ i) | 100.
+Global Instance as_emp_valid_monPred_at φ P (Φ : I → PROP) :
+  AsEmpValid0 φ P → (∀ i, MakeMonPredAt i P (Φ i)) → AsEmpValid φ (∀ i, Φ i) | 100.
 Proof.
-  rewrite /MakeMonPredAt /AsValid0 /AsValid /bi_valid=> -> EQ.
+  rewrite /MakeMonPredAt /AsEmpValid0 /AsEmpValid /bi_emp_valid=> -> EQ.
   setoid_rewrite <-EQ. split.
   - move=>[H]. apply bi.forall_intro=>i. rewrite -H. by rewrite monPred_at_emp.
   - move=>HP. split=>i. rewrite monPred_at_emp HP bi.forall_elim //.
 Qed.
-Global Instance as_valid_monPred_at_wand φ P Q (Φ Ψ : I → PROP) :
-  AsValid0 φ (P -∗ Q) →
+Global Instance as_emp_valid_monPred_at_wand φ P Q (Φ Ψ : I → PROP) :
+  AsEmpValid0 φ (P -∗ Q) →
   (∀ i, MakeMonPredAt i P (Φ i)) → (∀ i, MakeMonPredAt i Q (Ψ i)) →
-  AsValid φ (∀ i, Φ i -∗ Ψ i).
+  AsEmpValid φ (∀ i, Φ i -∗ Ψ i).
 Proof.
-  rewrite /AsValid0 /AsValid /MakeMonPredAt. intros -> EQ1 EQ2.
+  rewrite /AsEmpValid0 /AsEmpValid /MakeMonPredAt. intros -> EQ1 EQ2.
   setoid_rewrite <-EQ1. setoid_rewrite <-EQ2. split.
   - move=>/bi.wand_entails HP. setoid_rewrite HP. by iIntros (i) "$".
   - move=>HP. apply bi.entails_wand. split=>i. iIntros "H". by iApply HP.
 Qed.
-Global Instance as_valid_monPred_at_equiv φ P Q (Φ Ψ : I → PROP) :
-  AsValid0 φ (P ∗-∗ Q) →
+Global Instance as_emp_valid_monPred_at_equiv φ P Q (Φ Ψ : I → PROP) :
+  AsEmpValid0 φ (P ∗-∗ Q) →
   (∀ i, MakeMonPredAt i P (Φ i)) → (∀ i, MakeMonPredAt i Q (Ψ i)) →
-  AsValid φ (∀ i, Φ i ∗-∗ Ψ i).
+  AsEmpValid φ (∀ i, Φ i ∗-∗ Ψ i).
 Proof.
-  rewrite /AsValid0 /AsValid /MakeMonPredAt. intros -> EQ1 EQ2.
+  rewrite /AsEmpValid0 /AsEmpValid /MakeMonPredAt. intros -> EQ1 EQ2.
   setoid_rewrite <-EQ1. setoid_rewrite <-EQ2. split.
   - move=>/bi.wand_iff_equiv HP. setoid_rewrite HP. iIntros. iSplit; iIntros "$".
   - move=>HP. apply bi.equiv_wand_iff. split=>i. by iSplit; iIntros; iApply HP.

theories/proofmode/tactics.v

@@ -63,7 +63,7 @@ Tactic Notation "iMatchHyp" tactic1(tac) :=
 Tactic Notation "iStartProof" :=
   lazymatch goal with
   | |- envs_entails _ _ => idtac
-  | |- ?φ => notypeclasses refine (as_valid_2 φ _ _);
+  | |- ?φ => notypeclasses refine (as_emp_valid_2 φ _ _);
                [apply _ || fail "iStartProof: not a Bi entailment"
                |apply tac_adequate]
   end.
@@ -79,12 +79,12 @@ Tactic Notation "iStartProof" uconstr(PROP) :=
     type_term has a non-negligeable performance impact. *)
     let x := type_term (eq_refl : @eq Type PROP PROP') in idtac
 
-  (* We eta-expand [as_valid_2], in order to make sure that
+  (* We eta-expand [as_emp_valid_2], in order to make sure that
      [iStartProof PROP] works even if [PROP] is the carrier type. In
      this case, typing this expression will end up unifying PROP with
      [bi_car _], and hence trigger the canonical structures mechanism
      to find the corresponding bi. *)
-  | |- ?φ => notypeclasses refine ((λ P : PROP, @as_valid_2 φ _ P) _ _ _);
+  | |- ?φ => notypeclasses refine ((λ P : PROP, @as_emp_valid_2 φ _ P) _ _ _);
                [apply _ || fail "iStartProof: not a Bi entailment"
                |apply tac_adequate]
   end.
@@ -684,13 +684,13 @@ Tactic Notation "iIntoValid" open_constr(t) :=
        not necessarilly opaque, and could be unfolded by [hnf].
 
        However, for calling type class search, we only use [cbv zeta]
-       in order to make sure we do not unfold [bi_valid]. *)
+       in order to make sure we do not unfold [bi_emp_valid]. *)
     let tT := type of t in
     first
       [ let tT' := eval hnf in tT in go_specialize t tT'
       | let tT' := eval cbv zeta in tT in go_specialize t tT'
       | let tT' := eval cbv zeta in tT in
-        notypeclasses refine (as_valid_1 tT _ _);
+        notypeclasses refine (as_emp_valid_1 tT _ _);
           [iSolveTC || fail "iPoseProof: not a BI assertion"
           |exact t]]
   with go_specialize t tT :=