Add some rel_ tactics for the LHS, enough to do the late-early choice refinement

F_mu_ref_conc/examples/counter.v

@@ -280,12 +280,12 @@ Section CG_Counter.
   Proof.
     iIntros "#H".
     Transparent FG_increment. unfold FG_increment. unlock. simpl.
-    iLöb as "IH".   
-    iApply (bin_log_related_rec_l _ E1 K); auto. iNext. simpl.
+    iLöb as "IH".
+    rel_rec_l.
     Opaque FG_increment.
-    rel_bind_l (Load (Loc x)). 
-    iPoseProof "H" as "H2". (* lolwhat *)    
     Opaque bin_log_related.
+    rel_bind_l (Load (Loc x)).
+    iPoseProof "H" as "H2". (* lolwhat *)
     iApply (bin_log_related_load_l).
     iMod "H" as (n) "[Hx [HR Hrev]]".  iModIntro.
     iExists (#nv n). iFrame. iIntros "Hx".
@@ -293,10 +293,8 @@ Section CG_Counter.
     iApply fupd_logrel.
     iMod ("Hrev" with "[HR Hx]").
     { iExists _. iFrame. } iModIntro. simpl.
-    iApply (bin_log_related_rec_l); auto. simpl.
-    iNext.
-    rel_bind_l (BinOp _ _ _).
-    iApply (bin_log_related_binop_l). iNext. simpl.
+    rel_rec_l.
+    rel_op_l. simpl.
     rel_bind_l (CAS _ _ _).
     iApply (bin_log_related_cas_l); auto.
     iMod "H2" as (n') "[Hx [HR HQ]]". iModIntro. simpl.

F_mu_ref_conc/examples/lateearlychoice.v

@@ -139,18 +139,16 @@ Section Refinement.
   Proof.
     iIntros "#Hspec Hx Hx'".
     unfold lateChoice, earlyChoice. unlock.
-    rel_rec_l. rel_rec_r.
+    rel_rec_l.
+    rel_rec_r.
 
-    rel_bind_l (#x <- _)%E.
-    iApply (bin_log_related_store_l' with "Hx"); eauto. iIntros "Hx".
-    simpl.
+    rel_store_l. simpl.
     rel_rec_l.
 
     unfold rand at 1. unlock.
-    iApply (bin_log_related_rec_l _ _ []); eauto. iNext. simpl.
-    rel_bind_l (Alloc _).
-    iApply bin_log_related_alloc_l'; eauto. iIntros (y) "Hy". simpl.
-    iApply (bin_log_related_rec_l _ _ []); eauto. iNext. simpl.
+    rel_rec_l.
+    rel_alloc_l as y "Hy". simpl.
+    rel_rec_l.
 
     unfold rand. unlock.
     rel_rec_r.
@@ -161,11 +159,11 @@ Section Refinement.
     { iExists false. by iFrame. }
     iMod (inv_alloc choiceN with "[Hinv]") as "#Hinv".
     { iNext. iApply "Hinv". }
-    rel_bind_r (Fork _).
-    iApply bin_log_related_fork_r; eauto. iIntros (i) "Hi".
+    
+    rel_fork_r as i "Hi".
+    rel_rec_r.
 
-    rel_bind_l (Fork _).
-    iApply bin_log_related_fork_l;simpl. iModIntro.
+    rel_fork_l. iModIntro.
     iSplitL "Hi".
     - iNext.
       iInv choiceN as (f) "[Hy Hy']" "Hcl".
@@ -175,11 +173,10 @@ Section Refinement.
       { iNext. iExists true. by iFrame. }
       done.
     - rel_rec_l.
-      rel_rec_r.
       
-      iApply (bin_log_related_load_l _ _ _ []).
-      iInv choiceN as (f) "[Hy >Hy']" "Hcl". iModIntro.
-      iExists (#♭v f). iFrame. iIntros "Hy".
+      rel_load_l under choiceN as "Hys" "Hcl".
+        iDestruct "Hys" as (f) "[Hy >Hy']". iModIntro.
+        iExists (#♭v f). iFrame. iIntros "Hy". simpl.
       rel_load_r.
       iMod ("Hcl" with "[Hy Hy']").
       { iNext. iExists f. iFrame. }
@@ -187,8 +184,7 @@ Section Refinement.
       rel_rec_r.
       rel_store_r. simpl.
       rel_seq_r.
-      iApply bin_log_related_val; eauto.
-      { iIntros (Δ). iModIntro. simpl. eauto. }
+      rel_vals. eauto.
   Qed.
 
   Lemma refinement Γ ρ :