Definition cast_pointer_to_bool t1 t2 :=
 match t1 with (Tpointer _ _ | Tarray _ _ _ | Tfunction _ _ _) => 
           match t2 with Tint IBool _ _ => true | _ => false end
 | _ => false
end.

(* Specifications: *)
Lemma sem_cast_e1: forall t t1 v1 v m, sem_cast t t1 v = Some v1 -> cast_pointer_to_bool t t1 = false -> tc_val t v -> Cop.sem_cast v t t1 m = Some v1.
Lemma cop2_sem_cast' : forall {CS: compspecs} t2 e rho m, (denote_tc_assert (isCastResultType (typeof e) t2 e) rho) (m_phi m) -> tc_val (typeof e) (eval_expr e rho) -> Cop.sem_cast (eval_expr e rho) (typeof e) t2 (m_dry m) = sem_cast (typeof e) t2 (eval_expr e rho).
Lemma isBinOpResultType_binop_stable: forall {CS: compspecs} b e1 e2 t rho phi, denote_tc_assert (isBinOpResultType b e1 e2 t) rho phi -> binop_stable cenv_cs b e1 e2 = true.
Lemma eval_unop_relate: forall {CS: compspecs} Delta (ge: genv) te ve rho u e t m (Hcenv : genv_cenv ge = @cenv_cs CS) (H : rho = construct_rho (filter_genv ge) ve te) (H0 : typecheck_environ Delta rho) (H1 : (denote_tc_assert (typecheck_expr Delta e) rho) (m_phi m) -> Clight.eval_expr ge ve te (m_dry m) e (eval_expr e rho)) (H2 : (denote_tc_assert (typecheck_lvalue Delta e) rho) (m_phi m) -> exists (b : block) (ofs : ptrofs), Clight.eval_lvalue ge ve te (m_dry m) e b ofs /\ eval_lvalue e rho = Vptr b ofs) (H3 : (denote_tc_assert (typecheck_expr Delta (Eunop u e t)) rho) (m_phi m)), Clight.eval_expr ge ve te (m_dry m) (Eunop u e t) (eval_expr (Eunop u e t) rho).
Lemma eqb_type_sym: forall a b, eqb_type a b = eqb_type b a.
Lemma Ptrofs_to_int_repr: Archi.ptr64=false -> forall i, Ptrofs.to_int (Ptrofs.repr i) = Int.repr i.
Lemma eval_both_relate: forall {CS: compspecs} Delta ge te ve rho e m, genv_cenv ge = cenv_cs -> rho = construct_rho (filter_genv ge) ve te -> typecheck_environ Delta rho -> (denote_tc_assert (typecheck_expr Delta e) rho (m_phi m) -> Clight.eval_expr ge ve te (m_dry m) e (eval_expr e rho)) /\ (denote_tc_assert (typecheck_lvalue Delta e) rho (m_phi m) -> exists b, exists ofs, Clight.eval_lvalue ge ve te (m_dry m) e b ofs /\ eval_lvalue e rho = Vptr b ofs).
Lemma eval_expr_relate: forall {CS: compspecs} Delta ge te ve rho e m, genv_cenv ge = cenv_cs -> rho = construct_rho (filter_genv ge) ve te -> typecheck_environ Delta rho -> (denote_tc_assert (typecheck_expr Delta e) rho (m_phi m) -> Clight.eval_expr ge ve te (m_dry m) e (eval_expr e rho)).
Lemma eval_lvalue_relate: forall {CS: compspecs} Delta ge te ve rho e m, genv_cenv ge = cenv_cs -> rho = construct_rho (filter_genv ge) ve te-> typecheck_environ Delta rho -> (denote_tc_assert (typecheck_lvalue Delta e) rho (m_phi m) -> exists b, exists ofs, Clight.eval_lvalue ge ve te (m_dry m) e b ofs /\ eval_lvalue e rho = Vptr b ofs).