Tweak.

theories/examples/list_sort_instances.v

@@ -4,45 +4,42 @@ From iris.heap_lang Require Import proofmode notation.
 From osiris.utils Require Import list.
 From osiris.examples Require Import list_sort.
 
+Definition cmpZ : val :=
+  λ: "x" "y", "x" ≤ "y".
+
 Section list_sort_instances.
   Context `{!heapG Σ, !proto_chanG Σ} (N : namespace).
 
   (* Example: Sort of integers *)
-  Definition IZ (x : Z) (v : val) : iProp Σ :=
-    ⌜∃ w, v = LitV $ LitInt w ∧ x = w⌝%I.
-
-  Definition compareZ : val :=
-    λ: "x" "y", "x" ≤ "y".
+  Definition IZ (x : Z) (v : val) : iProp Σ := ⌜v = #x⌝%I.
 
-  Lemma compareZ_spec : cmp_spec IZ (≤) compareZ.
+  Lemma cmpZ_spec : cmp_spec IZ (≤) cmpZ.
   Proof.
-    iIntros (x x' v v' Φ) "!>".
-    iIntros ([[w [-> ->]] [w' [-> ->]]]) "HΦ".
-    wp_lam. wp_pures. iApply "HΦ". eauto 10 with iFrame.
+    rewrite /IZ. iIntros (x x' v v' Φ [-> ->]) "!> HΦ".
+    wp_lam. wp_pures. by iApply "HΦ".
   Qed.
-  
+
   Local Arguments val_encode _ _ !_ /.
 
   Lemma list_sort_client_le_spec l (xs : list Z) :
     {{{ l ↦ val_encode xs }}}
-      list_sort_client compareZ #l
+      list_sort_client cmpZ #l
       {{{ ys, RET #(); ⌜Sorted (≤) ys⌝ ∗ ⌜ ys ≡ₚ xs⌝ ∗ l ↦ val_encode ys }}}.
   Proof.
     assert (∀ zs : list Z, val_encode zs = val_encode (LitV ∘ LitInt <$> zs)) as Henc.
     { intros zs. induction zs; f_equal/=; auto with f_equal. }
     iIntros (Φ) "Hl HΦ".
     iApply (list_sort_client_spec N IZ (≤) _ _ (LitV ∘ LitInt <$> xs) xs with "[] [Hl] [HΦ]").
-    { iApply compareZ_spec. }
+    { iApply cmpZ_spec. }
     { rewrite -Henc. iFrame "Hl".
       iInduction xs as [|x xs] "IH"; csimpl; first by iFrame.
-      iFrame "IH". by iExists x. }
+      by iFrame "IH". }
     iIntros "!>" (ys ws) "(?&?&?&HI)".
     iAssert ⌜ ws = (LitV ∘ LitInt) <$> ys ⌝%I with "[HI]" as %->.
     { iInduction ys as [|y ys] "IH" forall (ws);
       destruct ws as [|w ws]; csimpl; try done.
-      iDestruct "HI" as "[HI1 HI2]"; iDestruct "HI1" as %(?&->&->).
+      iDestruct "HI" as "[-> HI2]".
       by iDestruct ("IH" with "HI2") as %->. }
     rewrite -Henc. iApply ("HΦ" $! ys with "[$]").
   Qed.
-
 End list_sort_instances.