Fix the last admits in the refinement proof

theories/logrel/F_mu_ref_conc/examples/queue/refinement.v

@@ -27,22 +27,6 @@ Canonical Structure gnameO := leibnizO gname.
 Definition mapUR : ucmraT := gmapUR loc (agreeR (leibnizO (gname * loc))).
 Definition nodeUR : ucmraT := authUR (gmapUR loc (agreeR (leibnizO (gname * loc)))).
 
-Section my_map.
-  Context `{Monoid M o}.
-  Context `{Countable K} {A : Type}.
-  Implicit Types m : gmap K A.
-  Context {PROP : bi}.
-  Implicit Types Φ : K → A → PROP.
-  Infix "`o`" := o (at level 50, left associativity).
-
-  (* This lemma is committed upstream and should be available from Iris at
-     some point (when?) *)
-  Lemma big_sepM_insert_delete Φ m i x :
-    (([∗ map] k↦y ∈ <[i:=x]> m, Φ k y) ⊣⊢ Φ i x ∗ [∗ map] k↦y ∈ (delete i m), Φ k y)%I.
-  Proof. Admitted.
-
-End my_map.
-
 Section Queue_refinement.
   Context `{heapIG Σ, cfgSG Σ, inG Σ fracAgreeR, inG Σ exlTokR, inG Σ nodeUR, inG Σ nodeStateR}.
 
@@ -235,10 +219,10 @@ Section Queue_refinement.
   Lemma map_singleton_included (m : gmap loc (gname * loc)) (l : loc) v :
     ({[l := to_agree v]} : mapUR) ≼ ((to_agree <$> m) : mapUR) → m !! l = Some v.
   Proof.
-    rewrite singleton_included_l=> -[[q' av] []].
-    (* rewrite lookup_fmap fmap_Some_equiv => -[v' [Hl [/= -> ->]]].
-    move=> /Some_pair_included_total_2 [_] /to_agree_included /leibniz_equiv_iff -> //. *)
-  Admitted.
+    move /singleton_included_l=> -[y].
+    rewrite lookup_fmap fmap_Some_equiv => -[[x [-> ->]]].
+    by move /Some_included_total /to_agree_included /leibniz_equiv_iff ->.
+  Qed.
 
   Lemma auth_node_mapsto_Some γ m ℓs ι ℓn :
     own γ (● (to_agree <$> m) : nodeUR) -∗
@@ -256,7 +240,7 @@ Section Queue_refinement.
     iDestruct (own_valid_2 with "a b") as %Hv.
     rewrite -auth_frag_op in Hv.
     apply (auth_frag_valid (_ ⋅ _)) in Hv. (* Why is this necessary? *)
-    rewrite op_singleton in Hv.
+    rewrite singleton_op in Hv.
     apply singleton_valid, agree_op_invL' in Hv.
     inversion Hv.
     done.
@@ -274,8 +258,7 @@ Section Queue_refinement.
     iDestruct (big_sepM_insert_delete with "[new $mon]") as "mon".
     { iExists ι, ℓn. iFrame. done. }
     rewrite insert_id; done.
-    (* FIXME: Coq complains: Some unresolved existential variables remain *)
-  Admitted.
+  Qed.
 
   (* Reinsert a node that has been taken out. *)
   Lemma reinsert_node γ κ ℓq ℓs ι ℓn (m : gmap loc (gname * loc)) :
@@ -381,16 +364,16 @@ Section Queue_refinement.
       iFrame. iExists _, _. iFrame "tailPts". iFrame.
     - iDestruct "nodeList" as (ℓ0 ℓnext q ι) "(FOO & BAR & BAZ & HIHI & nodeListTail)".
       iApply ("IH" with "authM bigSep nilPts tailPts nodePts nodeListTail ℓPts tok").
-      iNext. iIntros "HI".
+      iNext.
+      iDestruct 1 as (ι') "(authM & bigSep & nilPts & tailPts & nodePts & nodeListTail & ℓPts)".
       iApply "Hϕ".
-      iDestruct "HI" as (ι') "(authM & bigSep & nilPts & tailPts & nodePts & nodeListTail & ℓPts)".
       iExistsFrame.
   Qed.
 
+  (* This lemma has been commited upstream to Iris and will be available in the future. *)
   Lemma auth_update_core_id_frac {A : ucmraT} (a b : A) `{!CoreId b} q :
     b ≼ a → ●{q} a ~~> ●{q} a ⋅ ◯ b.
-  Proof.
-  Admitted.
+  Proof. Admitted.
 
   Lemma MS_CG_counter_refinement :
     [] ⊨ MS_queue ≤log≤ CG_queue :
@@ -808,8 +791,8 @@ Section Queue_refinement.
           simpl.
           iApply (enqueue_cas with "[$authM $bigSep $nodesInv $nilPts $tailPts $nodePts $nodeList $ℓPts $tok]").
           { done. }
-          iNext. iIntros "HI". 
-          iDestruct "HI" as (ι3) "(authM & bigSep & nodePts & nodeList & #frag & ℓPts)".
+          iNext.
+          iDestruct 1 as (ι3) "(authM & bigSep & nodePts & nodeList & #frag & ℓPts)".
           iMod (steps_CG_enqueue with "[$Hspec $Hj $lofal $Hsq]") as "(Hj & Hsq & lofal)".
           { solve_ndisj. }
           iDestruct (reinsert_node with "authM fragO bigSep [sentinelPts ℓPts nodePts rest]") as "(authM & bigSep)".