Definition tc_expr {CS: compspecs} (Delta: tycontext) (e: expr) : environ -> mpred:=
  fun rho => denote_tc_assert (typecheck_expr Delta e) rho.Definition tc_exprlist {CS: compspecs} (Delta: tycontext) (t : list type) (e: list expr) : environ -> mpred :=
      fun rho => denote_tc_assert (typecheck_exprlist Delta t e) rho.Definition tc_lvalue {CS: compspecs} (Delta: tycontext) (e: expr) : environ -> mpred :=
     fun rho => denote_tc_assert (typecheck_lvalue Delta e) rho.Definition tc_temp_id {CS: compspecs} (id : positive) (ty : type)
  (Delta : tycontext) (e : expr) : environ -> mpred  :=
     fun rho => denote_tc_assert (typecheck_temp_id id ty Delta e) rho.

Lemma extend_tc_int_or_ptr_type: forall {CS: compspecs} A rho, boxy extendM (denote_tc_assert (tc_int_or_ptr_type A) rho).