Fixed a quick inconsistency in the RestrictedSemantics result.

RestrictedSemantics.v

@@ -47,7 +47,7 @@ Module RestrictedSemantics (Import E : Expression) (Import TE : TypedExpression
       RChorStep (RIfFF l1) B (If l1 ff C1 C2) C2
   | DefLocalIStep : forall R l C1 C1' C2,
       RChorStep R [] C1 C1' ->
-      RChorStep R [] (DefLocal l C1 C2) (DefLocal l C1' C2)
+      RChorStep (RArg R) [] (DefLocal l C1 C2) (DefLocal l C1' C2)
   | DefLocalStep : forall (l : Loc) (v : Expr) (C2 : Chor),
       ExprVal v ->
       RChorStep (RDefLocal l v) nil (DefLocal l (Done l v) C2) (C2 [ce| ValueSubst l v])
@@ -440,7 +440,7 @@ Module RestrictedSemantics (Import E : Expression) (Import TE : TypedExpression
     intros C1 C2 stdstep; induction stdstep.
     all:try ( eexists; eexists; split; [reflexivity | constructor; auto]; fail).
     - destruct IHstdstep as [R [C2' [equiv step]]].
-      exists R; exists (LetLocal l ⟪new⟫ ← C2' fby C2); split; auto with Chor.
+      exists (RArg R); exists (LetLocal l ⟪new⟫ ← C2' fby C2); split; auto with Chor.
     - destruct IHstdstep as [R [C2' [equiv step]]].
       exists (RFun R); exists (AppLocal l C2' e); split; auto with Chor.
     (* - exists (RAppLocalE l e1 e2); exists (AppLocal l C e2); split; auto with Chor. *)
@@ -462,7 +462,7 @@ Module RestrictedSemantics (Import E : Expression) (Import TE : TypedExpression
   | IfTTOnTop : forall p C1 C2, RedexOnTop (RIfTT p) (If p tt C1 C2)
   | IfFFOnTop : forall p C1 C2, RedexOnTop (RIfFF p) (If p ff C1 C2)
   | SyncOnTop : forall p d q C, RedexOnTop (RSync p d q) (Sync p d q C)
-  | IDefLocalOntop : forall l C1 C2 R, RedexOnTop R C1 -> RedexOnTop R (DefLocal l C1 C2)
+  | IDefLocalOntop : forall l C1 C2 R, RedexOnTop R C1 -> RedexOnTop (RArg R) (DefLocal l C1 C2)
   | DefLocalOnTop : forall l e C, RedexOnTop (RDefLocal l e) (DefLocal l (Done l e) C)
   | AppLocalEOnTop : forall l e1 e2 C, RedexOnTop (RAppLocalE l e1 e2) (AppLocal l C e1)
   | AppLocalOnTop : forall l C e, RedexOnTop (RAppLocal l e) (AppLocal l (RecLocal l C) e)
@@ -482,7 +482,6 @@ Module RestrictedSemantics (Import E : Expression) (Import TE : TypedExpression
              assert (~ In a c) by (let i := fresh in intro i; apply H; right; exact i);
              clear H
            end.
-
   
   Lemma RStepOnTop : forall (R : Redex) (B : list Loc) (C1 C2 : Chor),
       RChorStep R B C1 C2 ->
@@ -601,6 +600,7 @@ Module RestrictedSemantics (Import E : Expression) (Import TE : TypedExpression
     Theorem LiftRestrictedChorStepToUnrestricted : forall C1 C2 B R, RChorStep B R C1 C2 -> ChorStep B R C1 C2.
   Proof using.
     intros C1 C2 B R step; induction step; auto with Chor.
+    
   Qed.
 
   Corollary RestrictedRelativePreservation :