Merged master back in.

.gitlab-ci.yml

@@ -40,3 +40,8 @@ build-coq.8.14.1:
   variables:
     OPAM_PINS: "coq version 8.14.1"
 
+build-coq.8.14.1:
+  <<: *template
+  variables:
+    OPAM_PINS: "coq version 8.14.1"
+

theories/biabd/biabd_local_updates.v

@@ -327,7 +327,9 @@ Section other.
 
 End other.
 
-Class IsValidOp {A : cmra} (a a1 a2 : A) Σ (P : iPropI Σ) := {
+From iris_automation.biabd Require Export proofmode_classes proofmode_instances.
+
+(*Class IsValidOp {A : cmra} (a a1 a2 : A) Σ (P : iPropI Σ) := {
   is_valid_merge : ✓ (a1 ⋅ a2) ⊢ □ P ;
   is_valid_op : ✓ (a1 ⋅ a2) ⊢@{iPropI Σ} a ≡ a1 ⋅ a2 ;
 }.
@@ -353,7 +355,7 @@ Class NonUnital {A : cmra} (a : A) Σ :=
   non_unital_element b : a ≡ a ⋅ b ⊢@{iPropI Σ} False.
 
 Class HasRightId {A : cmra} (a : A) :=
-  has_right_id : ∃ c, a ≡ a ⋅ c.
+  has_right_id : ∃ c, a ≡ a ⋅ c. *)
 
 Class CmraSubtract {A : cmra} (a b : A) (φ : Prop) (c : option A) :=
   cmra_subtract : φ → default b (c' ← c; Some $ b ⋅ c') ≡ a.
@@ -382,7 +384,7 @@ From iris.proofmode Require Import base classes reduction tactics.
 From iris.algebra Require Import agree frac.
 
 Section validity.
-  Implicit Types Σ : gFunctors.
+  Implicit Types Σ : gFunctors. (*
   Lemma from_isop {A : cmra} (a a1 a2 : A) {Σ} :
     IsOp a a1 a2 → IsValidOp a a1 a2 Σ True%I.
   Proof. 
@@ -406,7 +408,7 @@ Section validity.
 
     Global Instance merge_unital_proper a1 a2 Σ : Proper ((≡@{iPropI Σ}) ==> (iff)) (IsIncludedMergeUnital a1 a2).
     Proof. solve_proper. Qed.
-  End proper.
+  End proper. *)
 
   Section base_instances_cmra.
     Context {A : cmra}.
@@ -427,7 +429,7 @@ Section validity.
       split =>//.
       move => c /cmra_valid_validN Hn.
       by eapply H.
-    Qed.
+    Qed. (*
 
     Lemma is_included_merge' (a1 a2 : A) {Σ} (P : iPropI Σ) :
       IsIncludedMerge a1 a2 P →
@@ -467,26 +469,26 @@ Section validity.
         rewrite H.
         iLeft.
         by iApply "H✓".
-    Qed.
+    Qed. *)
 
   End base_instances_cmra.
 
   Section base_instances_ucmra.
-    Context {A : ucmra}.
+    Context {A : ucmra}. (*
     Global Instance valid_op_unit_left (a : A) Σ :
       IsValidOp a ε a Σ True%I | 5.
     Proof. apply from_isop. rewrite /IsOp left_id //. Qed.
 
     Global Instance valid_op_unit_right (a : A) Σ:
       IsValidOp a a ε Σ True%I | 5.
-    Proof. apply from_isop. rewrite /IsOp right_id //. Qed.
+    Proof. apply from_isop. rewrite /IsOp right_id //. Qed. *)
 
     Global Instance ucmra_subtract_all (a : A) : UcmraSubtract a a True ε | 100. 
       (* this one may glance over pcore like info we can actually keep *)
     Proof. by rewrite /UcmraSubtract /CmraSubtract /= right_id => _. Qed.
 
     Global Instance ucmra_subtract_unit (a : A) : UcmraSubtract a ε True a | 101.
-    Proof. rewrite /UcmraSubtract /CmraSubtract /= left_id //. Qed.
+    Proof. rewrite /UcmraSubtract /CmraSubtract /= left_id //. Qed. (*
 
     Global Instance included_merge_unital_from_reg (a1 a2 : A) {Σ} (P : iProp Σ) :
       IsIncludedMerge a1 a2 P →
@@ -502,7 +504,7 @@ Section validity.
         iLeft. by iApply "H✓".
     Qed.
     Global Instance ucmra_has_right_id (a : A) : HasRightId a.
-    Proof. exists ε. by rewrite right_id. Qed. 
+    Proof. exists ε. by rewrite right_id. Qed.  *)
 
     Global Instance find_local_update_from_subtract (x x' : A) r φ : 
       UcmraSubtract x' x φ r →
@@ -539,14 +541,14 @@ Section validity.
     Qed.
   End base_instances_ucmra.
 
-  Section numbers.
+  Section numbers. (*
     Global Instance nat_valid_op (a a1 a2 : nat) Σ: 
       IsOp a a1 a2 → IsValidOp a a1 a2 Σ True%I | 10.
-    Proof. apply from_isop. Qed.
+    Proof. apply from_isop. Qed. *)
     Global Instance ucmra_subtract_nat (a1 a2 : nat) : 
       TCIf (SolveSepSideCondition (a1 < a2)%nat) False TCTrue → (* guards against obviously impossible things *)
       UcmraSubtract a1 a2 (a2 ≤ a1) (a1 - a2)%nat.
-    Proof. rewrite /UcmraSubtract /CmraSubtract /= nat_op => _ Ha. fold_leibniz. lia. Qed.
+    Proof. rewrite /UcmraSubtract /CmraSubtract /= nat_op => _ Ha. fold_leibniz. lia. Qed. (*
     Global Instance nat_included_merge (a1 a2 : nat) {Σ} : IsIncludedMerge a1 a2 (Σ := Σ) ⌜a1 ≤ a2⌝%I.
     Proof.
       rewrite /IsIncludedMerge.
@@ -557,13 +559,13 @@ Section validity.
 
     Global Instance nat_max_valid_op (a a1 a2 : max_nat) Σ :
       IsOp a a1 a2 → IsValidOp a a1 a2 Σ True%I | 10.
-    Proof. apply from_isop. Qed.
+    Proof. apply from_isop. Qed. *)
     Global Instance ucmra_subtract_max_nat (a1 a2 : nat) : 
       UcmraSubtract (MaxNat a1) (MaxNat a2) (a2 ≤ a1) (MaxNat a1).
     Proof.
       rewrite /UcmraSubtract /CmraSubtract /= max_nat_op => Ha. 
       fold_leibniz. f_equal. lia. 
-    Qed.
+    Qed. (*
     Global Instance nat_max_included_merge (a1 a2 : nat) {Σ} : IsIncludedMerge (MaxNat a1) (MaxNat a2) (Σ := Σ) ⌜a1 ≤ a2⌝%I.
     Proof.
       rewrite /IsIncludedMerge. iIntros "_"; iSplit.
@@ -573,32 +575,32 @@ Section validity.
 
     Global Instance nat_min_valid_op (a a1 a2 : min_nat) Σ :
       IsOp a a1 a2 → IsValidOp a a1 a2 Σ True%I.
-    Proof. apply from_isop. Qed.
+    Proof. apply from_isop. Qed. *)
     Global Instance cmra_subtract_min_nat (a1 a2 : nat) :
       CmraSubtract (MinNat a1) (MinNat a2) (a1 ≤ a2) (Some $ MinNat a1).
     Proof.
       rewrite /UcmraSubtract /CmraSubtract /= min_nat_op_min => Ha. 
       fold_leibniz. f_equal. lia.
-    Qed.
+    Qed. (*
     Global Instance nat_min_included_merge (a1 a2 : nat) {Σ} : IsIncludedMerge (MinNat a1) (MinNat a2) (Σ := Σ) ⌜a2 ≤ a1⌝%I.
     Proof.
       rewrite /IsIncludedMerge. iIntros "_"; iSplit.
       - by iDestruct 1 as %?%min_nat_included.
       - iIntros "%". iExists (MinNat a2). rewrite min_nat_op_min. iPureIntro. fold_leibniz. f_equal. lia.
-    Qed.
+    Qed. *)
     Lemma nat_min_coalloc n : CoAllocate (MinNat n) (Some $ MinNat 0). 
     (* 0 is the maximal element for minnat. This is not an instance - we don't usually want to coallocate 0 with n *)
     Proof.
       split => //.
       move => [c] /min_nat_included /= /le_n_0_eq <- _ m.
       apply min_nat_included => /=. lia.
-    Qed.
+    Qed. (*
     Global Instance min_nat_has_right_id n : HasRightId (MinNat n).
     Proof. exists (MinNat n).  rewrite min_nat_op_min. fold_leibniz. f_equal. lia. Qed.
 
     Global Instance positive_valid_op (a a1 a2 : positive) Σ :
       IsOp a a1 a2 → IsValidOp a a1 a2 Σ True%I.
-    Proof. apply from_isop. Qed.
+    Proof. apply from_isop. Qed. *)
     Global Instance cmra_subtract_positive_lt (a1 a2 : positive) : 
       SolveSepSideCondition (a2 < a1)%positive →
       CmraSubtract a1 a2 True (Some (a1 - a2)%positive).
@@ -609,7 +611,7 @@ Section validity.
     Global Instance cmra_subtract_positive_eq (a1 a2 : positive) : 
       SolveSepSideCondition (a2 = a1) →
       CmraSubtract a1 a2 True None.
-    Proof. by rewrite /CmraSubtract /= => ->. Qed.
+    Proof. by rewrite /CmraSubtract /= => ->. Qed. (*
     Global Instance positive_included_merge (a1 a2 : positive) {Σ} : IsIncludedMerge a1 a2 (Σ := Σ) ⌜(a1 < a2)%positive⌝%I.
     Proof. 
       rewrite /IsIncludedMerge. iIntros "_"; iSplit.
@@ -636,7 +638,7 @@ Section validity.
       rewrite /IsOp; split; last first.
       { rewrite H; eauto. }
       by iDestruct 1 as %?%frac_valid.
-    Qed.
+    Qed. *)
     Global Instance frac_subtract_half (q : Qp) :
       CmraSubtract q (q/2)%Qp True (Some (q/2)%Qp) | 10.
     Proof. rewrite /CmraSubtract /= => _. by rewrite frac_op Qp_div_2. Qed.
@@ -667,7 +669,7 @@ Section validity.
     Proof.
       rewrite /CmraSubtract /= => Hφ1 Hφ2.
       case => /Hφ1 <- /Hφ2 <- //.
-    Qed.
+    Qed. (*
     Global Instance frac_included_merge (q1 q2 : Qp) {Σ} : IsIncludedMerge q1 q2 (Σ := Σ) ⌜(q1 < q2)%Qp⌝%I.
     Proof. 
       rewrite /IsIncludedMerge. iIntros "_" ; iSplit.
@@ -692,7 +694,7 @@ Section validity.
     Proof. 
       rewrite /NonUnital => q. iIntros "%". fold_leibniz. 
       rewrite frac_op in H. apply eq_sym in H. by apply Qp_add_id_free in H. 
-    Qed.
+    Qed. *)
 
     Global Instance frac_coallocate_half :
       CoAllocate (1/2)%Qp (Some $ 1/2)%Qp.
@@ -732,7 +734,7 @@ Section validity.
   End numbers.
 
   Section sets.
-    Context `{Countable K}.
+    Context `{Countable K}. (*
     Global Instance set_is_op_emp_l (X : gset K) :
       IsOp X ∅ X | 10.
     Proof. rewrite /IsOp. set_solver. Qed.
@@ -745,11 +747,11 @@ Section validity.
 
     Global Instance set_is_valid_op (a a1 a2 : gset K) Σ :
       IsOp a a1 a2 → IsValidOp a a1 a2 Σ True%I | 10.
-    Proof. apply from_isop. Qed.
+    Proof. apply from_isop. Qed. *)
     Global Instance ucmra_set_subtract_refl (a : gset K): UcmraSubtract a a True a | 10.
     Proof. rewrite /UcmraSubtract /CmraSubtract /= gset_op. set_solver. Qed.
     Global Instance ucmra_set_subtract (a1 a2 : gset K) : UcmraSubtract a1 a2 (a2 ⊆ a1) a1 | 20.
-    Proof. rewrite /UcmraSubtract /CmraSubtract /= gset_op. set_solver. Qed.
+    Proof. rewrite /UcmraSubtract /CmraSubtract /= gset_op. set_solver. Qed. (*
     Global Instance set_included_merge (a1 a2 : gset K) {Σ} : IsIncludedMerge a1 a2 (Σ := Σ) ⌜a1 ⊆ a2⌝%I.
     Proof. 
       rewrite /IsIncludedMerge. iIntros "_"; iSplit.
@@ -770,7 +772,7 @@ Section validity.
     Proof. apply from_isop. rewrite /IsOp. rewrite gset_disj_union; [f_equal | ]; set_solver. Qed.
     Global Instance set_disj_valid_op_emp_r (X Y : gset K) Σ :
       IsValidOp (GSet X) (GSet ∅) (GSet X) Σ True%I | 10.
-    Proof. apply from_isop. rewrite /IsOp. rewrite gset_disj_union; [f_equal | ]; set_solver. Qed.
+    Proof. apply from_isop. rewrite /IsOp. rewrite gset_disj_union; [f_equal | ]; set_solver. Qed. *)
     Global Instance ucmra_disjoint_set_subtract_refl (a : gset K) :
       UcmraSubtract (GSet a) (GSet a) True ε | 10.
     Proof. eapply ucmra_subtract_all. Qed.
@@ -788,7 +790,7 @@ Section validity.
       rewrite decide_True //.
       intros. f_equal.
       by rewrite -union_difference_L.
-    Qed.
+    Qed. (*
     Global Instance disj_set_included_merge (a1 a2 : gset K) {Σ} : IsIncludedMerge (GSet a1) (GSet a2) (Σ := Σ) ⌜a1 ⊆ a2⌝%I.
     Proof. 
       rewrite /IsIncludedMerge. iIntros "_"; iSplit.
@@ -797,13 +799,13 @@ Section validity.
         iExists (GSet (a2 ∖ a1)).
         iPureIntro. rewrite gset_disj_union; [|set_solver].
         fold_leibniz. f_equal. by apply union_difference_L.
-    Qed.
+    Qed. *)
 
     (* no coallocate for both: gset is all _finite_ sets, these have no maximum element *)
   End sets.
 
   Section multisets.
-    Context `{Countable K}.
+    Context `{Countable K}. (*
     Global Instance multiset_is_op_emp_l (X : gmultiset K) :
       IsOp X ∅ X | 10.
     Proof. rewrite /IsOp. multiset_solver. Qed.
@@ -816,7 +818,7 @@ Section validity.
 
     Global Instance multiset_is_valid_op (a a1 a2 : gmultiset K) Σ :
       IsOp a a1 a2 → IsValidOp a a1 a2 Σ True%I | 10.
-    Proof. apply from_isop. Qed.
+    Proof. apply from_isop. Qed. *)
     Global Instance ucmra_multiset_subtract_refl (a : gmultiset K) :
       UcmraSubtract a a True ε | 10.
     Proof. apply ucmra_subtract_all. Qed.
@@ -828,17 +830,17 @@ Section validity.
     Proof. eapply ucmra_subtract_unit. Qed.
     Global Instance ucmra_multiset_subtract (a1 a2 : gmultiset K) :
       UcmraSubtract a1 a2 (a2 ⊆ a1) (a1 ∖ a2) | 20.
-    Proof. rewrite /UcmraSubtract /CmraSubtract /= gmultiset_op. multiset_solver. Qed.
+    Proof. rewrite /UcmraSubtract /CmraSubtract /= gmultiset_op. multiset_solver. Qed. (*
     Global Instance multiset_included_merge (a1 a2 : gmultiset K) {Σ} : IsIncludedMerge a1 a2 (Σ := Σ) ⌜a1 ⊆ a2⌝%I.
     Proof. 
       rewrite /IsIncludedMerge. iIntros "_"; iSplit.
       - by iDestruct 1 as %?%gmultiset_included. 
       - iIntros "%". iExists (a2 ∖ a1). iPureIntro. fold_leibniz. rewrite gmultiset_op. multiset_solver.
-    Qed.
+    Qed. *)
   End multisets.
 
   Section recursive.
-    Implicit Types A : cmra.
+    Implicit Types A : cmra. (*
 
     Global Instance option_some_valid_op {A} (a a1 a2 : A) Σ P :
       IsValidOp a a1 a2 Σ P → IsValidOp (Some a) (Some a1) (Some a2) Σ P.
@@ -846,14 +848,14 @@ Section validity.
       case => HP Ha.
       split; rewrite -Some_op option_validI //.
       by rewrite Ha option_equivI.
-    Qed.
+    Qed. *)
     Global Instance option_subtract {A} (a b : A) φ c :
       CmraSubtract a b φ c →
       UcmraSubtract (Some a) (Some b) φ c.
     Proof.
       rewrite /UcmraSubtract /CmraSubtract /= => Hφ /Hφ <-.
       by destruct c.
-    Qed.
+    Qed. (*
     Global Instance option_included_merge {A} (a1 a2 : A) {Σ} (P : iProp Σ):
       IsIncludedMergeUnital a1 a2 P →
       IsIncludedMerge (Some a1) (Some a2) P | 100.
@@ -882,7 +884,7 @@ Section validity.
           by rewrite option_equivI -Some_op.
         * iExists None. rewrite option_equivI. rewrite Some_op_opM /=.
           by iRewrite "He".
-    Qed. (* we need below, even though it is trivial, to handle recursive cases *)
+    Qed. (* we need below, even though it is trivial, to handle recursive cases *) 
     Global Instance option_none_excl_included_merge {A} (a : optionUR A) {Σ} :
       IsIncludedMerge None a (Σ := Σ) (True)%I.
     Proof.
@@ -901,7 +903,7 @@ Section validity.
         apply (Some_equiv_eq _ (a ⋅ c)) in H as [x [xH _]] => //.
       - rewrite Some_op_opM /= in H.
         apply (Some_equiv_eq _ a) in H as [x [xH _]] => //.
-    Qed.
+    Qed. *)
     Global Instance option_some_coalloc {A} (a : A) (mb : option A) :
       CoAllocate a mb →
       CoAllocate (Some a) (Some mb).
@@ -928,7 +930,7 @@ Section validity.
         { intros. exists None. by rewrite right_id. }
         rewrite -Some_op Some_valid.
         move => /Hmb //.
-    Qed.
+    Qed. (*
 
     Global Instance sum_inl_valid_op {A1 A2} (a a1 a2 : A1) Σ P :
       IsValidOp a a1 a2 Σ P → IsValidOp (Cinl a) (Cinl (B := A2) a1) (Cinl (B := A2) a2) Σ P.
@@ -961,7 +963,7 @@ Section validity.
       split; rewrite /op /= /cmra_op //=; eauto.
       rewrite uPred_cmra_valid_eq /= /uPred_cmra_valid_def /=.
       rewrite /validN /= /cmra_validN //=.
-    Qed.
+    Qed. *)
     Lemma sum_inl_subtract {A1 A2} (a b : A1) φ c :
       CmraSubtract a b φ c →
       CmraSubtract (Cinl (B := A2) a) (Cinl (B := A2) b) φ (fmap Cinl c).
@@ -1001,7 +1003,7 @@ Section validity.
     Proof.
       move => /sum_inr_subtract /= Hc.
       apply Hc.
-    Qed.
+    Qed. (*
     Global Instance sum_inl_included_merge {A1 A2} (a1 a2 : A1) {Σ} (P : iProp Σ):
       IsIncludedMerge a1 a2 P →
       IsIncludedMerge (Cinl (B := A2) a1) (Cinl (B := A2) a2) (P)%I | 100.
@@ -1126,7 +1128,7 @@ Section validity.
       rewrite /MakeAnd. split; rewrite -pair_op prod_validI /=.
       - rewrite -H bi.intuitionistically_and -HP1 -HP2 //.
       - rewrite prod_equivI /= -Hxs -Hys //.
-    Qed.
+    Qed. *)
     Global Instance prod_subtract_Some {A1 A2} (a1 b1 c1 : A1) (a2 b2 c2 : A2) φ1 φ2 :
       CmraSubtract a1 b1 φ1 (Some c1) → 
       CmraSubtract a2 b2 φ2 (Some c2) → 
@@ -1142,7 +1144,7 @@ Section validity.
       UcmraSubtract a2 b2 φ2 c2 → 
       TCEq p (c1, c2) → (* avoids some unification troubles *)
       UcmraSubtract (a1, a2) (b1, b2) (φ1 ∧ φ2) p.
-    Proof. rewrite /UcmraSubtract /CmraSubtract => Hφ1 Hφ2 -> [/Hφ1 <- /Hφ2 <-] //=. Qed.
+    Proof. rewrite /UcmraSubtract /CmraSubtract => Hφ1 Hφ2 -> [/Hφ1 <- /Hφ2 <-] //=. Qed. (*
     Global Instance prod_included_merge {A1 A2} (x1 x2 : A1) (y1 y2 : A2) {Σ} P1 P2 P :
       IsIncludedMerge x1 x2 (Σ := Σ) P1 →
       IsIncludedMerge y1 y2 (Σ := Σ) P2 →
@@ -1384,7 +1386,7 @@ Section validity.
       eapply prod_included_merge_unital => //.
       - right. split => //.
       - right. split => //.
-    Qed.
+    Qed. *)
     Global Instance prod_coalloc {A1 A2} x1 mx2 y1 my2 :
       CoAllocate (A := A1) x1 mx2 →
       CoAllocate (A := A2) y1 my2 →
@@ -1409,7 +1411,7 @@ Section validity.
         case => a1 a2.
         rewrite -pair_op => /pair_valid.
         case => /Hxmax //.
-    Qed.
+    Qed. (*
     Global Instance prod_left_non_unital {A1 A2} (x1 : A1) (x2 : A2) Σ :
       NonUnital x1 Σ → NonUnital (x1, x2) Σ.
     Proof.
@@ -1434,11 +1436,14 @@ Section validity.
 
     Global Instance excl_valid_op {O : ofe} (a1 a2 : excl O) Σ:
       IsValidOp ExclBot a1 a2 Σ False%I.