vcgen and dcexpr correctness fixed (vcg_solver remains)

theories/vcgen/dcexpr.v

@@ -383,11 +383,17 @@ Qed.
 
 Global Instance dcexpr_closed X E de :
   dcexpr_wf X E de →
-  Closed X (cdexpr_interp E de).
-Proof. Admitted.
-(*  induction de; simpl; try solve_closed. rewrite /Closed /=.
-  split_and. change (Closed [] a_ret). solve_closed. apply (dexpr_closed E d).
-Qed. *)
+  Closed X (dcexpr_interp E de).
+Proof.
+  revert X. induction de; intros; unfold Closed in *; simplify_eq /=;
+   try (destruct_and!; split_and; first split_and; [ apply is_closed_of_val | by apply IHde2 | by apply IHde1]);
+   try (destruct_and!; split_and; first split_and; [ apply is_closed_of_val | by apply IHde1 | by apply IHde2]).
+  - split_and; eauto using is_closed_of_val. by apply dexpr_closed.
+  - split_and;  [ apply is_closed_of_val | by apply IHde].
+  - split_and;  [ apply is_closed_of_val | by apply IHde].
+  - split_and; first split_and; [ apply is_closed_of_val | apply is_closed_of_val | by apply  IHde].
+  - by apply W.is_closed_correct.
+Qed.
 
 (** * Reification of C syntax *)
 (** ** LocLookup *)