Tweak gcd.

theories/tests/gcd.v

@@ -20,60 +20,49 @@ Definition gcd : val := λ: "a" "b",
 Section gcd_spec.
   Context `{locking_heapG Σ, heapG Σ, flockG Σ, spawnG Σ}.
 
-  Lemma gcd_spec (a b : Z) (l r: loc) R:
-    ⌜a >= 0⌝ -∗ ⌜b >= 0⌝ -∗
+  Lemma gcd_spec (a b : Z) (l r: loc) R :
+    0 ≤ a → 0 ≤ b →
     l ↦U #a -∗ r ↦U #b -∗
     awp (gcd #l #r) R (λ v, ⌜v = #(Z.gcd a b)⌝).
   Proof.
-    iIntros "% % Hl Hr".
-    do 2 awp_lam. iApply a_sequence_spec.
-    iApply (a_while_inv_spec
-              (∃ (x y: Z),  l ↦U #x ∗ r ↦U #y ∧
-                            ⌜x >= 0 ∧ y >= 0 ∧ Zgcd x y = Zgcd a b⌝)%I
-              with "[Hl Hr]").
-    - eauto with iFrame.
-    - iModIntro. iIntros "H".  iDestruct "H" as (x y) "(Hl & Hr & % & % & %)".
+    iIntros (??) "Hl Hr". do 2 awp_lam. iApply a_sequence_spec.
+    iApply (a_while_inv_spec (∃ x y : Z,
+      ⌜0 ≤ x ∧ 0 ≤ y ∧ Z.gcd x y = Z.gcd a b⌝ ∧ l ↦U #x ∗ r ↦U #y)%I with "[Hl Hr]").
+    - iExists a, b. eauto with iFrame.
+    - iModIntro. iDestruct 1 as (x y (?&?&Hgcd)) "[Hl Hr]".
       iApply a_un_op_spec.
       iApply (awp_bin_op_load_load with "[$Hl] [$Hr]"). iIntros "Hl Hr".
-      assert (Hxy: x = y ∨ x < y ∨ y < x) by lia.
-      destruct Hxy as [Hxy|[Hxy|Hxy]].
+      assert (x = y ∨ x < y ∨ y < x) as [Hxy|[Hxy|Hxy]] by lia.
       + iExists #true. simplify_eq /=. iSplit.
         { rewrite/ bin_op_eval //=; case_bool_decide; eauto. }
         iExists #false; iSplit; first done. iLeft; iSplit; first done.
         do 2 iModIntro. awp_seq. awp_load_ret l. iIntros.
-        rewrite- H5. iPureIntro. symmetry. rewrite Z.gcd_diag.
-        rewrite Z.abs_eq; eauto with lia.
-      + iExists #false.  simplify_eq /=. iSplit.
-        { rewrite/ bin_op_eval //=.
-          case_bool_decide. inversion H6; subst. lia. eauto. }
-        iExists #true;  iSplit; first done. iRight; iSplit; first done.
+        by rewrite -Hgcd Z.gcd_diag Z.abs_eq.
+      + iExists #false. simplify_eq /=. iSplit.
+        { by rewrite /bin_op_eval //= bool_decide_false; last (intros [= ?]; lia). }
+        iExists #true; iSplit; first done. iRight; iSplit; first done.
         iApply a_if_spec.
         iApply (awp_bin_op_load_load with "[$Hl] [$Hr]"). iIntros "Hl Hr".
         iExists #true; iSplit.
-        { rewrite/ bin_op_eval //=. case_bool_decide; eauto. }
+        { by rewrite /bin_op_eval //= bool_decide_true. }
         iLeft. iSplit; first done. awp_seq.
         iApply a_store_ret.
         iApply (awp_bin_op_load_load with "[$Hr] [$Hl]"). iIntros "Hr Hl".
         iExists #(y - x); iSplit; first by eauto with lia.
-        iExists #y. iFrame. iIntros "Hr". iModIntro.
-        iExists x, (y-x). iFrame. iPureIntro.
-        do 2 (split; first by lia). rewrite -H5; apply Z.gcd_sub_diag_r.
-      + iExists #false.  simplify_eq /=. iSplit.
-        { rewrite/ bin_op_eval //=.
-          case_bool_decide. inversion H6; subst. lia. eauto. }
-        iExists #true;  iSplit; first done. iRight; iSplit; first done.
+        iExists #y. iIntros "{$Hr} Hr !>".
+        iExists x, (y-x). iFrame. rewrite -Hgcd Z.gcd_sub_diag_r. eauto with lia.
+      + iExists #false. simplify_eq /=. iSplit.
+        { by rewrite/ bin_op_eval //= bool_decide_false; last (intros [= ?]; lia). }
+        iExists #true; iSplit; first done. iRight; iSplit; first done.
         iApply a_if_spec.
         iApply (awp_bin_op_load_load with "[$Hl] [$Hr]"). iIntros "Hl Hr".
         iExists #false. iSplit.
-        { rewrite/ bin_op_eval //=.
-          case_bool_decide. inversion H6; subst. lia. eauto. }
+        { by rewrite/ bin_op_eval //= bool_decide_false; last lia. }
         iRight; iSplit; first done. awp_seq.
         iApply a_store_ret.
         iApply (awp_bin_op_load_load with "[$Hl] [$Hr]"). iIntros "Hl Hr".
         iExists #(x - y); iSplit; first by eauto with lia.
-        iExists #x. iFrame. iIntros "Hl". iModIntro.
-        iExists (x-y), y. iFrame. iPureIntro.
-        do 2 (split; first by lia).
-        rewrite -H5 Z.gcd_comm (Z.gcd_comm x); apply Z.gcd_sub_diag_r.
+        iExists #x. iIntros "{$Hl} Hl !>". iExists (x - y), y. iFrame. iPureIntro.
+        rewrite -Hgcd Z.gcd_comm Z.gcd_sub_diag_r Z.gcd_comm. auto with lia.
   Qed.
 End gcd_spec.