Make iApply more powerful and uniform.

It not behaves more consistently with iExact and thus also works in the
case H : P -★ □^n Q |- Q.

heap_lang/lib/barrier/proof.v

@@ -99,7 +99,7 @@ Lemma newbarrier_spec (P : iProp) (Φ : val → iProp) :
 Proof.
   iIntros (HN) "[#? HΦ]".
   rewrite /newbarrier. wp_seq. wp_alloc l as "Hl".
-  iApply "HΦ".
+  iApply ("HΦ" with "|==>[-]").
   iPvs (saved_prop_alloc (F:=idCF) _ P) as (γ) "#?".
   iPvs (sts_alloc (barrier_inv l P) _ N (State Low {[ γ ]}) with "[-]")
     as (γ') "[#? Hγ']"; eauto.

program_logic/counter_examples.v

@@ -7,66 +7,51 @@ From iris.proofmode Require Import tactics.
 Section savedprop.
   Context (M : ucmraT).
   Notation iProp := (uPred M).
-  Notation "¬ P" := (□(P → False))%I : uPred_scope.
+  Notation "¬ P" := (□ (P → False))%I : uPred_scope.
+  Implicit Types P : iProp.
 
   (* Saved Propositions and view shifts. *)
   Context (sprop : Type) (saved : sprop → iProp → iProp) (pvs : iProp → iProp).
-  Hypothesis pvs_mono : forall P Q, (P ⊢ Q) → pvs P ⊢ pvs Q.
-  Hypothesis sprop_persistent : forall i P, PersistentP (saved i P).
+  Hypothesis pvs_mono : ∀ P Q, (P ⊢ Q) → pvs P ⊢ pvs Q.
+  Hypothesis sprop_persistent : ∀ i P, PersistentP (saved i P).
   Hypothesis sprop_alloc_dep :
-    forall (P : sprop → iProp), True ⊢ pvs (∃ i, saved i (P i)).
-  Hypothesis sprop_agree :
-    forall i P Q, saved i P ∧ saved i Q ⊢ P ↔ Q.
+    ∀ (P : sprop → iProp), True ⊢ pvs (∃ i, saved i (P i)).
+  Hypothesis sprop_agree : ∀ i P Q, saved i P ∧ saved i Q ⊢ P ↔ Q.
 
   (* Self-contradicting assertions are inconsistent *)
-  Lemma no_self_contradiction (P : iProp) `{!PersistentP P} :
-    □(P ↔ ¬ P) ⊢ False.
+  Lemma no_self_contradiction P `{!PersistentP P} : □ (P ↔ ¬ P) ⊢ False.
   Proof. (* FIXME: Cannot destruct the <-> as two implications. iApply with <-> also does not work. *)
-    rewrite /uPred_iff. iIntros "#[H1 H2]". (* FIXME: Cannot iApply "H1". *)
+    rewrite /uPred_iff. iIntros "#[H1 H2]".
     iAssert P as "#HP".
-    { iApply "H2". iIntros "!#HP". by iApply ("H1" with "HP"). }
-    by iApply ("H1" with "HP HP").
+    { iApply "H2". iIntros "! #HP". by iApply ("H1" with "[#]"). }
+    by iApply ("H1" with "[#]").
   Qed.
 
   (* "Assertion with name [i]" is equivalent to any assertion P s.t. [saved i P] *)
-  Definition A (i : sprop) : iProp := ∃ P, saved i P ★ □P.
-  Lemma saved_is_A i P `{!PersistentP P} : saved i P ⊢ □(A i ↔ P).
+  Definition A (i : sprop) : iProp := ∃ P, saved i P ★ □ P.
+  Lemma saved_is_A i P `{!PersistentP P} : saved i P ⊢ □ (A i ↔ P).
   Proof.
     rewrite /uPred_iff. iIntros "#HS !". iSplit.
-    - iIntros "H". iDestruct "H" as (Q) "[#HSQ HQ]".
-      iPoseProof (sprop_agree i P Q with "[]") as "Heq"; first by eauto.
-      rewrite /uPred_iff. by iApply "Heq".
+    - iDestruct 1 as (Q) "[#HSQ HQ]".
+      iApply (sprop_agree i P Q with "[]"); eauto.
     - iIntros "#HP". iExists P. by iSplit.
   Qed.
 
   (* Define [Q i] to be "negated assertion with name [i]". Show that this
      implies that assertion with name [i] is equivalent to its own negation. *)
   Definition Q i := saved i (¬ A i).
-  Lemma Q_self_contradiction i :
-    Q i ⊢ □(A i ↔ ¬ A i).
-  Proof.
-    iIntros "#HQ". iApply (@saved_is_A i (¬ A i)%I _). (* FIXME: If we already introduced the box, this iApply does not work. *)
-    done.
-  Qed.
+  Lemma Q_self_contradiction i : Q i ⊢ □ (A i ↔ ¬ A i).
+  Proof. iIntros "#HQ !". by iApply (saved_is_A i (¬A i)). Qed.
 
   (* We can obtain such a [Q i]. *)
-  Lemma make_Q :
-    True ⊢ pvs (∃ i, Q i).
-  Proof.
-    apply sprop_alloc_dep.
-  Qed.
+  Lemma make_Q : True ⊢ pvs (∃ i, Q i).
+  Proof. apply sprop_alloc_dep. Qed.
 
   (* Put together all the pieces to derive a contradiction. *)
   (* TODO: Have a lemma in upred.v that says that we cannot view shift to False. *)
   Lemma contradiction : True ⊢ pvs False.
   Proof.
-    rewrite make_Q. apply pvs_mono.
-    iIntros "HQ". iDestruct "HQ" as (i) "HQ".
-    iApply (@no_self_contradiction (A i) _).
-    by iApply Q_self_contradiction.
+    rewrite make_Q. apply pvs_mono. iDestruct 1 as (i) "HQ".
+    iApply (no_self_contradiction (A i)). by iApply Q_self_contradiction.
   Qed.
 End savedprop.
-
-
-  
-

proofmode/class_instances.v

@@ -87,10 +87,12 @@ Global Instance from_later_sep P1 P2 Q1 Q2 :
 Proof. intros ??; red. by rewrite later_sep; apply sep_mono. Qed.
 
 (* IntoWand *)
-Global Instance into_wand_wand P Q : IntoWand (P -★ Q) P Q.
-Proof. done. Qed.
-Global Instance into_wand_impl P Q : IntoWand (P → Q) P Q.
-Proof. apply impl_wand. Qed.
+Global Instance into_wand_wand P Q Q' :
+  FromAssumption false Q Q' → IntoWand (P -★ Q) P Q'.
+Proof. by rewrite /FromAssumption /IntoWand /= => ->. Qed.
+Global Instance into_wand_impl P Q Q' :
+  FromAssumption false Q Q' → IntoWand (P → Q) P Q'.
+Proof. rewrite /FromAssumption /IntoWand /= => ->. by rewrite impl_wand. Qed.
 Global Instance into_wand_iff_l P Q : IntoWand (P ↔ Q) P Q.
 Proof. by apply and_elim_l', impl_wand. Qed.
 Global Instance into_wand_iff_r P Q : IntoWand (P ↔ Q) Q P.

proofmode/pviewshifts.v

@@ -12,6 +12,10 @@ Proof. intros ??. by rewrite -pvs_intro (from_pure P). Qed.
 Global Instance from_assumption_pvs E p P Q :
   FromAssumption p P Q → FromAssumption p P (|={E}=> Q)%I.
 Proof. rewrite /FromAssumption=>->. apply pvs_intro. Qed.
+Global Instance into_wand_pvs E1 E2 R P Q :
+  IntoWand R P Q → IntoWand R (|={E1,E2}=> P) (|={E1,E2}=> Q) | 100.
+Proof. rewrite /IntoWand=>->. apply wand_intro_l. by rewrite pvs_wand_r. Qed.
+
 Global Instance from_sep_pvs E P Q1 Q2 :
   FromSep P Q1 Q2 → FromSep (|={E}=> P) (|={E}=> Q1) (|={E}=> Q2).
 Proof. rewrite /FromSep=><-. apply pvs_sep. Qed.
@@ -26,9 +30,6 @@ Qed.
 Global Instance frame_pvs E1 E2 R P Q :
   Frame R P Q → Frame R (|={E1,E2}=> P) (|={E1,E2}=> Q).
 Proof. rewrite /Frame=><-. by rewrite pvs_frame_l. Qed.
-Global Instance into_wand_pvs E1 E2 R P Q :
-  IntoWand R P Q → IntoWand R (|={E1,E2}=> P) (|={E1,E2}=> Q) | 100.
-Proof. rewrite /IntoWand=>->. apply wand_intro_l. by rewrite pvs_wand_r. Qed.
 
 Global Instance timeless_elim_pvs E1 E2 Q : TimelessElim (|={E1,E2}=> Q).
 Proof.