Definition expr_closed_wrt_lvars (S: ident -> Prop) (e: expr) : Prop :=
  forall (cs: compspecs) rho ve',
     (forall i, S i \/ Map.get (ve_of rho) i = Map.get ve' i) ->
     eval_expr e rho = eval_expr e (mkEnviron (ge_of rho) ve' (te_of rho)).Definition lvalue_closed_wrt_lvars (S: ident -> Prop) (e: expr) : Prop :=
  forall (cs: compspecs) rho ve',
     (forall i, S i \/ Map.get (ve_of rho) i = Map.get ve' i) ->
     eval_lvalue e rho = eval_lvalue e (mkEnviron (ge_of rho) ve'  (te_of rho)).

Lemma closed_wrt_tc_test_eq: forall {cs: compspecs} S e e', expr_closed_wrt_vars S e -> expr_closed_wrt_vars S e' -> closed_wrt_vars S (denote_tc_assert (tc_test_eq e e')).