(* This is a rather vacuous lemma, since the premise is simply True *)
(* Lemma Int64_eq_repr_signed32_nonzero: forall i, Int.eq i Int.zero = false -> Int64.eq (Int64.repr (Int.signed i)) Int64.zero = false. *)
(*  Lemma Int64_eq_repr_unsigned32_nonzero: forall i, Int.eq i Int.zero = false -> Int64.eq (Int64.repr (Int.unsigned i)) Int64.zero = false. *)
(* Lemma Int64_eq_repr_int_nonzero: forall s i, Int.eq i Int.zero = false -> Int64.eq (cast_int_long s i) Int64.zero = false. *)
Inductive tc_val_PM: type -> val -> Prop :=
| tc_val_PM_Tint: forall sz sg a v, is_int sz sg v -> tc_val_PM (Tint sz sg a) v
| tc_val_PM_Tlong: forall s a v, is_long v -> tc_val_PM (Tlong s a) v
| tc_val_PM_Tfloat_single: forall a v, is_single v -> tc_val_PM (Tfloat F32 a) v
| tc_val_PM_Tfloat_double: forall a v, is_float v -> tc_val_PM (Tfloat F64 a) v
| tc_val_PM_Tpointer: forall t a v,
(if eqb_type (Tpointer t a) int_or_ptr_type
then is_pointer_or_integer
else is_pointer_or_null) v ->
tc_val_PM (Tpointer t a) v
| tc_val_PM_Tarray: forall t n a v, is_pointer_or_null v -> tc_val_PM (Tarray t n a) v
| tc_val_PM_Tfunction: forall ts t a v, is_pointer_or_null v -> tc_val_PM (Tfunction ts t a) v
| tc_val_PM_Tstruct: forall i a v, isptr v -> tc_val_PM (Tstruct i a) v
| tc_val_PM_Tunion: forall i a v, isptr v -> tc_val_PM (Tunion i a) v.

Lemma tc_val_tc_val_PM: forall t v, tc_val t v <-> tc_val_PM t v.