Improve True stripping of iPoseProof.

It is no longer triggered when posing [P ⊢ Q] with [P] an evar. This, for
example, makes sure that iApply pvs_intro works, which failed before.

proofmode/coq_tactics.v

@@ -560,12 +560,23 @@ Proof.
   by rewrite right_id {1}(persistentP P) always_and_sep_l wand_elim_r.
 Qed.
 
-Lemma tac_pose_proof Δ Δ' j P Q :
-  True ⊢ P → envs_app true (Esnoc Enil j P) Δ = Some Δ' →
+(** Whenever posing [lem : True ⊢ Q] as [H} we want it to appear as [H : Q] and
+not as [H : True -★ Q]. The class [ToPosedProof] is used to strip off the
+[True]. Note that [to_posed_proof_True] is declared using a [Hint Extern] to
+make sure it is not used while posing [lem : ?P ⊢ Q] with [?P] an evar. *)
+Class ToPosedProof (P1 P2 R : uPred M) := to_pose_proof : P1 ⊢ P2 → True ⊢ R.
+Arguments to_pose_proof : clear implicits.
+Instance to_posed_proof_True P : ToPosedProof True P P.
+Proof. by rewrite /ToPosedProof. Qed.
+Global Instance to_posed_proof_wand P Q : ToPosedProof P Q (P -★ Q).
+Proof. rewrite /ToPosedProof. apply entails_wand. Qed.
+
+Lemma tac_pose_proof Δ Δ' j P1 P2 R Q :
+  P1 ⊢ P2 → ToPosedProof P1 P2 R → envs_app true (Esnoc Enil j R) Δ = Some Δ' →
   Δ' ⊢ Q → Δ ⊢ Q.
 Proof.
-  intros HP ? <-. rewrite envs_app_sound //; simpl.
-  by rewrite -HP left_id always_const wand_True.
+  intros HP ?? <-. rewrite envs_app_sound //; simpl.
+  by rewrite right_id -(to_pose_proof P1 P2 R) // always_const wand_True.
 Qed.
 
 Lemma tac_apply Δ Δ' i p R P1 P2 :
@@ -867,6 +878,8 @@ Proof.
 Qed.
 End tactics.
 
+Hint Extern 0 (ToPosedProof True _ _) =>
+  class_apply @to_posed_proof_True : typeclass_instances.
 (** Make sure we can frame in the presence of evars without making Coq loop due
 to it applying these rules too eager.
 

proofmode/tactics.v

@@ -282,11 +282,11 @@ Tactic Notation "iSpecialize" constr (H) "{" open_constr(x1) open_constr(x2)
 
 (** * Pose proof *)
 Tactic Notation "iPoseProof" open_constr(lem) "as" constr(H) :=
-  eapply tac_pose_proof with _ H _; (* (j:=H) *)
+  eapply tac_pose_proof with _ H _ _ _; (* (j:=H) *)
     [first
        [eapply lem
-       |apply uPred.entails_impl; eapply lem
        |apply uPred.equiv_iff; eapply lem]
+    |apply _
     |env_cbv; reflexivity || fail "iPoseProof:" H "not fresh"|].
 
 Tactic Notation "iPoseProof" open_constr(lem) constr(Hs) "as" constr(H) :=

tests/heap_lang.v

@@ -45,7 +45,7 @@ Section LiftingTests.
     iIntros {Hn} "HΦ". iLöb {n1 Hn} as "IH".
     wp_rec. wp_let. wp_op. wp_let. wp_op=> ?; wp_if.
     - iApply "IH" "% HΦ". omega.
-    - iPvsIntro. by assert (n1 = n2 - 1) as -> by omega.
+    - iApply pvs_intro. by assert (n1 = n2 - 1) as -> by omega.
   Qed.
 
   Lemma Pred_spec n E Φ : ▷ Φ #(n - 1) ⊢ WP Pred #n @ E {{ Φ }}.