all SBI must be a COFE

theories/bi/derived_laws_sbi.v

@@ -210,8 +210,6 @@ Section löb.
   Local Instance flöb_pre_contractive P : Contractive (flöb_pre P).
   Proof. solve_contractive. Qed.
 
-  Context `{Cofe PROP}.
-
   Definition flöb (P : PROP) := fixpoint (flöb_pre P).
 
   Lemma weak_löb P : (▷ P ⊢ P) → (True ⊢ P).
@@ -412,7 +410,7 @@ Proof. intros; rewrite /Timeless except_0_and later_and; auto. Qed.
 Global Instance or_timeless P Q : Timeless P → Timeless Q → Timeless (P ∨ Q).
 Proof. intros; rewrite /Timeless except_0_or later_or; auto. Qed.
 
-Global Instance impl_timeless `{Cofe PROP} P Q : Timeless Q → Timeless (P → Q).
+Global Instance impl_timeless P Q : Timeless Q → Timeless (P → Q).
 Proof.
   rewrite /Timeless=> HQ. rewrite later_false_em.
   apply or_mono, impl_intro_l; first done.
@@ -425,7 +423,7 @@ Proof.
   intros; rewrite /Timeless except_0_sep later_sep; auto using sep_mono.
 Qed.
 
-Global Instance wand_timeless `{Cofe PROP} P Q : Timeless Q → Timeless (P -∗ Q).
+Global Instance wand_timeless P Q : Timeless Q → Timeless (P -∗ Q).
 Proof.
   rewrite /Timeless=> HQ. rewrite later_false_em.
   apply or_mono, wand_intro_l; first done.

theories/bi/interface.v

@@ -229,6 +229,7 @@ Structure sbi := Sbi {
   sbi_internal_eq : ∀ A : ofeT, A → A → sbi_car;
   sbi_later : sbi_car → sbi_car;
   sbi_ofe_mixin : OfeMixin sbi_car;
+  sbi_cofe : Cofe (OfeT sbi_car sbi_ofe_mixin);
   sbi_bi_mixin : BiMixin sbi_entails sbi_emp sbi_pure sbi_and sbi_or sbi_impl
                          sbi_forall sbi_exist sbi_sep sbi_wand sbi_persistently;
   sbi_sbi_mixin : SbiMixin sbi_entails sbi_pure sbi_or sbi_impl
@@ -247,6 +248,8 @@ Canonical Structure sbi_ofeC.
 Coercion sbi_bi (PROP : sbi) : bi :=
   {| bi_ofe_mixin := sbi_ofe_mixin PROP; bi_bi_mixin := sbi_bi_mixin PROP |}.
 Canonical Structure sbi_bi.
+Global Instance sbi_cofe' (PROP : sbi) : Cofe PROP.
+Proof. apply sbi_cofe. Qed.
 
 Arguments sbi_car : simpl never.
 Arguments sbi_dist : simpl never.

theories/proofmode/coq_tactics.v

@@ -1396,7 +1396,7 @@ Proof.
   - by rewrite Hs //= right_id.
 Qed.
 
-Lemma tac_löb `{Cofe PROP} Δ Δ' i Q :
+Lemma tac_löb Δ Δ' i Q :
   env_spatial_is_nil Δ = true →
   envs_app true (Esnoc Enil i (▷ Q)%I) Δ = Some Δ' →
   envs_entails Δ' Q → envs_entails Δ Q.

theories/proofmode/ltac_tactics.v

@@ -1659,8 +1659,7 @@ Tactic Notation "iLöbCore" "as" constr (IH) :=
      refine should use the other unification algorithm, which should
      not have this issue. *)
   notypeclasses refine (tac_löb _ _ IH _ _ _ _);
-    [iSolveTC || fail "iLöb: PROP is not a Cofe"
-    |reflexivity || fail "iLöb: spatial context not empty, this should not happen"
+    [reflexivity || fail "iLöb: spatial context not empty, this should not happen"
     |env_reflexivity || fail "iLöb:" IH "not fresh"|].
 
 Tactic Notation "iLöbRevert" constr(Hs) "with" tactic(tac) :=

theories/tests/proofmode.v

 From iris.proofmode Require Import tactics intro_patterns.
 From stdpp Require Import gmap hlist.
-Set Default Proof Using "Type*".
+Set Default Proof Using "Type".
 
 Section tests.
-Context {PROP : sbi} `{Cofe PROP}.
+Context {PROP : sbi}.
 Implicit Types P Q R : PROP.
 
 Lemma demo_0 P Q : □ (P ∨ Q) -∗ (∀ x, ⌜x = 0⌝ ∨ ⌜x = 1⌝) → (Q ∨ P).
@@ -381,8 +381,8 @@ Proof. iIntros (Hφ). iAssert ⌜φ⌝%I with "[%]" as "$"; auto with iFrame. Qe
 
 Lemma test_iEval x y : ⌜ (y + x)%nat = 1 ⌝ -∗ ⌜ S (x + y) = 2%nat ⌝ : PROP.
 Proof.
-  iIntros (Hn).
-  iEval (rewrite (Nat.add_comm x y) // Hn).
+  iIntros (H).
+  iEval (rewrite (Nat.add_comm x y) // H).
   done.
 Qed.