No longer break now_True abstraction.

And make it Typeclasses Opaque to ensure that we indeed do not do
so using the proof mode.

algebra/upred.v

@@ -339,6 +339,7 @@ Definition uPred_now_True {M} (P : uPred M) : uPred M := ▷ False ∨ P.
 Notation "◇ P" := (uPred_now_True P)
   (at level 20, right associativity) : uPred_scope.
 Instance: Params (@uPred_now_True) 1.
+Typeclasses Opaque uPred_now_True.
 
 Class TimelessP {M} (P : uPred M) := timelessP : ▷ P ⊢ ◇ P.
 Arguments timelessP {_} _ {_}.

program_logic/adequacy.v

@@ -52,11 +52,10 @@ Proof.
   rewrite {1}wp_unfold /wp_pre. iIntros (Hstep) "[(Hw & HE & Hσ) [H|[_ H]]]".
   { iDestruct "H" as (v) "[% _]". apply val_stuck in Hstep; simplify_eq. }
   rewrite pvs_eq /pvs_def.
-  iVs ("H" $! σ1 with "Hσ [Hw HE]") as "[H|(Hw & HE & _ & H)]"; first by iFrame.
-  { iVsIntro; iNext. by iExFalso. }
+  iVs ("H" $! σ1 with "Hσ [Hw HE]") as ">(Hw & HE & _ & H)"; first by iFrame.
   iVsIntro; iNext.
-  by iVs ("H" $! e2 σ2 ef with "[%] [Hw HE]") as "[?|($ & $ & $ & $)]";
-    [done|by iFrame|rewrite /uPred_now_True; eauto|].
+  iVs ("H" $! e2 σ2 ef with "[%] [Hw HE]")
+    as ">($ & $ & $ & $)"; try iFrame; eauto.
 Qed.
 
 Lemma wptp_step e1 t1 t2 σ1 σ2 Φ :
@@ -84,8 +83,7 @@ Proof.
   { inversion_clear 1; iIntros "?"; eauto 10. }
   iIntros (Hsteps) "H". inversion_clear Hsteps as [|?? [t1' σ1']].
   iVs (wptp_step with "H") as (e1' t1'') "[% H]"; first eauto; simplify_eq.
-  iVsIntro; iNext; iVs "H" as "[?|?]"; first (iVsIntro; iNext; by iExFalso).
-  by iApply IH.
+  iVsIntro; iNext; iVs "H" as ">?". by iApply IH.
 Qed.
 
 Instance rvs_iter_mono n : Proper ((⊢) ==> (⊢)) (Nat.iter n (λ P, |=r=> ▷ P)%I).
@@ -99,8 +97,7 @@ Proof.
   intros. rewrite wptp_steps // (Nat_iter_S_r (S n)); apply rvs_iter_mono.
   iDestruct 1 as (e2 t2') "(% & (Hw & HE & _) & H & _)"; simplify_eq.
   iDestruct (wp_value_inv with "H") as "H". rewrite pvs_eq /pvs_def.
-  iVs ("H" with "[Hw HE]") as "[?|(_ & _ & $)]"; [by iFrame| |done].
-  iVsIntro; iNext; by iExFalso.
+  iVs ("H" with "[Hw HE]") as ">(_ & _ & $)"; iFrame; auto.
 Qed.
 
 Lemma wp_safe e σ Φ :
@@ -108,8 +105,8 @@ Lemma wp_safe e σ Φ :
 Proof.
   rewrite wp_unfold /wp_pre. iIntros "[(Hw&HE&Hσ) [H|[_ H]]]".
   { iDestruct "H" as (v) "[% _]"; eauto 10. }
-  rewrite pvs_eq. iVs ("H" with "* Hσ [-]") as "[H|(?&?&%&?)]"; first by iFrame.
-  iVsIntro; iNext; by iExFalso. eauto 10.
+  rewrite pvs_eq. iVs ("H" with "* Hσ [-]") as ">(?&?&%&?)"; first by iFrame.
+  eauto 10.
 Qed.
 
 Lemma wptp_safe n e1 e2 t1 t2 σ1 σ2 Φ :

program_logic/invariants.v

@@ -49,9 +49,9 @@ Proof.
   iDestruct "Hi" as % ?%elem_of_subseteq_singleton.
   rewrite {1 4}(union_difference_L (nclose N) E) // ownE_op; last set_solver.
   rewrite {1 5}(union_difference_L {[ i ]} (nclose N)) // ownE_op; last set_solver.
-  iIntros "(Hw & [HE $] & $)"; iVsIntro; iRight.
+  iIntros "(Hw & [HE $] & $)"; iVsIntro; iApply now_True_intro.
   iDestruct (ownI_open i P with "[Hw HE]") as "($ & $ & HD)"; first by iFrame.
-  iIntros "HP [Hw $] !==>"; iRight. iApply ownI_close; by iFrame.
+  iIntros "HP [Hw $] !==>"; iApply now_True_intro. iApply ownI_close; by iFrame.
 Qed.
 
 Lemma inv_open_timeless E N P `{!TimelessP P} :

program_logic/pviewshifts.v

@@ -44,17 +44,17 @@ Lemma pvs_intro' E1 E2 P : E2 ⊆ E1 → ((|={E2,E1}=> True) -★ P) ={E1,E2}=>
 Proof.
   intros (E1''&->&?)%subseteq_disjoint_union_L.
   rewrite pvs_eq /pvs_def ownE_op //; iIntros "H ($ & $ & HE) !==>".
-  iApply now_True_intro. iApply "H". iIntros "[$ $] !==>". iRight; eauto.
+  iApply now_True_intro. iApply "H".
+  iIntros "[$ $] !==>". by iApply now_True_intro.
 Qed.
 Lemma now_True_pvs E1 E2 P : ◇ (|={E1,E2}=> P) ={E1,E2}=> P.
 Proof.
-  rewrite pvs_eq. iIntros "[?|H] [Hw HE]".
-  - rewrite /uPred_now_True; eauto.
-  - iApply "H"; by iFrame.
+  rewrite pvs_eq. iIntros "H [Hw HE]". iTimeless "H". iApply "H"; by iFrame.
 Qed.
 Lemma rvs_pvs E P : (|=r=> P) ={E}=> P.
 Proof.
-  rewrite pvs_eq /pvs_def. iIntros "H [$ $]". by rewrite -uPred.now_True_intro.
+  rewrite pvs_eq /pvs_def. iIntros "H [$ $]"; iVs "H".
+  iVsIntro. by iApply now_True_intro.
 Qed.
 Lemma pvs_mono E1 E2 P Q : (P ⊢ Q) → (|={E1,E2}=> P) ={E1,E2}=> Q.
 Proof.
@@ -64,18 +64,15 @@ Qed.
 Lemma pvs_trans E1 E2 E3 P : (|={E1,E2}=> |={E2,E3}=> P) ={E1,E3}=> P.
 Proof.
   rewrite pvs_eq /pvs_def. iIntros "HP HwE".
-  iVs ("HP" with "HwE") as "[?|(Hw & HE & HP)]".
-  - rewrite /uPred_now_True; eauto.
-  - iApply "HP"; by iFrame. 
+  iVs ("HP" with "HwE") as ">(Hw & HE & HP)". iApply "HP"; by iFrame.
 Qed.
 Lemma pvs_mask_frame_r' E1 E2 Ef P :
   E1 ⊥ Ef → (|={E1,E2}=> E2 ⊥ Ef → P) ={E1 ∪ Ef,E2 ∪ Ef}=> P.
 Proof.
   intros. rewrite pvs_eq /pvs_def ownE_op //. iIntros "Hvs (Hw & HE1 &HEf)".
-  iVs ("Hvs" with "[Hw HE1]") as "[?|($ & HE2 & HP)]"; first by iFrame.
-  - rewrite /uPred_now_True; eauto.
-  - iDestruct (ownE_op' with "[HE2 HEf]") as "[? $]"; first by iFrame.
-    iVsIntro; iRight; by iApply "HP".
+  iVs ("Hvs" with "[Hw HE1]") as ">($ & HE2 & HP)"; first by iFrame.
+  iDestruct (ownE_op' with "[HE2 HEf]") as "[? $]"; first by iFrame.
+  iVsIntro; iApply now_True_intro. by iApply "HP".
 Qed.
 Lemma pvs_frame_r E1 E2 P Q : (|={E1,E2}=> P) ★ Q ={E1,E2}=> P ★ Q.
 Proof. rewrite pvs_eq /pvs_def. by iIntros "[HwP $]". Qed.