Consistently name `wp_value_inv`.

We already used the following naming convention: `wp_value'` is stated in
terms of `of_val` and `wp_value` is stated in terms of `IntoVal`. This
commit applies this convention to `wp_value_inv` as well.

theories/program_logic/adequacy.v

@@ -128,7 +128,7 @@ Lemma wptp_result s n e1 t1 v2 t2 σ1 σ2 φ :
 Proof.
   intros. rewrite wptp_steps // laterN_later. apply: bupd_iter_laterN_mono.
   iDestruct 1 as (e2 t2' ?) "((Hw & HE & _) & H & _)"; simplify_eq.
-  iDestruct (wp_value_inv with "H") as "H". rewrite fupd_eq /fupd_def.
+  iDestruct (wp_value_inv' with "H") as "H". rewrite fupd_eq /fupd_def.
   iMod ("H" with "[Hw HE]") as ">(_ & _ & $)"; iFrame; auto.
 Qed.
 

theories/program_logic/total_weakestpre.v

@@ -222,7 +222,7 @@ Qed.
 
 Lemma twp_value' s E Φ v : Φ v -∗ WP of_val v @ s; E [{ Φ }].
 Proof. iIntros "HΦ". rewrite twp_unfold /twp_pre to_of_val. auto. Qed.
-Lemma twp_value_inv s E Φ v : WP of_val v @ s; E [{ Φ }] ={E}=∗ Φ v.
+Lemma twp_value_inv' s E Φ v : WP of_val v @ s; E [{ Φ }] ={E}=∗ Φ v.
 Proof. by rewrite twp_unfold /twp_pre to_of_val. Qed.
 
 Lemma twp_strong_mono s1 s2 E1 E2 e Φ Ψ :
@@ -267,7 +267,7 @@ Proof.
     + iMod ("H" with "[$]") as "[H _]". iDestruct "H" as %(? & ? & ? & ?).
       by edestruct (atomic _ _ _ _ Hstep).
   - destruct (atomic _ _ _ _ Hstep) as [v <-%of_to_val].
-    iMod (twp_value_inv with "H") as ">H". iFrame "Hphy". by iApply twp_value'.
+    iMod (twp_value_inv' with "H") as ">H". iFrame "Hphy". by iApply twp_value'.
 Qed.
 
 Lemma twp_bind K `{!LanguageCtx K} s E e Φ :
@@ -348,6 +348,8 @@ Lemma twp_value_fupd' s E Φ v : (|={E}=> Φ v) -∗ WP of_val v @ s; E [{ Φ }]
 Proof. intros. by rewrite -twp_fupd -twp_value'. Qed.
 Lemma twp_value_fupd s E Φ e v `{!IntoVal e v} : (|={E}=> Φ v) -∗ WP e @ s; E [{ Φ }].
 Proof. intros. rewrite -twp_fupd -twp_value //. Qed.
+Lemma twp_value_inv s E Φ e v `{!IntoVal e v} : WP e @ s; E [{ Φ }] ={E}=∗ Φ v.
+Proof. intros; rewrite -(of_to_val e v) //; by apply twp_value_inv'. Qed.
 
 Lemma twp_frame_l s E e Φ R : R ∗ WP e @ s; E [{ Φ }] -∗ WP e @ s; E [{ v, R ∗ Φ v }].
 Proof. iIntros "[? H]". iApply (twp_strong_mono with "H"); auto with iFrame. Qed.

theories/program_logic/weakestpre.v

@@ -208,7 +208,7 @@ Qed.
 
 Lemma wp_value' s E Φ v : Φ v ⊢ WP of_val v @ s; E {{ Φ }}.
 Proof. iIntros "HΦ". rewrite wp_unfold /wp_pre to_of_val. auto. Qed.
-Lemma wp_value_inv s E Φ v : WP of_val v @ s; E {{ Φ }} ={E}=∗ Φ v.
+Lemma wp_value_inv' s E Φ v : WP of_val v @ s; E {{ Φ }} ={E}=∗ Φ v.
 Proof. by rewrite wp_unfold /wp_pre to_of_val. Qed.
 
 Lemma wp_strong_mono s1 s2 E1 E2 e Φ Ψ :
@@ -252,7 +252,7 @@ Proof.
     + iMod ("H" with "[$]") as "[H _]". iDestruct "H" as %(? & ? & ? & ?).
       by edestruct (atomic _ _ _ _ Hstep).
   - destruct (atomic _ _ _ _ Hstep) as [v <-%of_to_val].
-    iMod (wp_value_inv with "H") as ">H". iFrame "Hphy". by iApply wp_value'.
+    iMod (wp_value_inv' with "H") as ">H". iFrame "Hphy". by iApply wp_value'.
 Qed.
 
 Lemma wp_step_fupd s E1 E2 e P Φ :
@@ -322,6 +322,8 @@ Proof. intros. by rewrite -wp_fupd -wp_value'. Qed.
 Lemma wp_value_fupd s E Φ e v `{!IntoVal e v} :
   (|={E}=> Φ v) ⊢ WP e @ s; E {{ Φ }}.
 Proof. intros. rewrite -wp_fupd -wp_value //. Qed.
+Lemma wp_value_inv s E Φ e v `{!IntoVal e v} : WP e @ s; E {{ Φ }} ={E}=∗ Φ v.
+Proof. intros; rewrite -(of_to_val e v) //; by apply wp_value_inv'. Qed.
 
 Lemma wp_frame_l s E e Φ R : R ∗ WP e @ s; E {{ Φ }} ⊢ WP e @ s; E {{ v, R ∗ Φ v }}.
 Proof. iIntros "[? H]". iApply (wp_strong_mono with "H"); auto with iFrame. Qed.