Section Int31_Specs.
Local Open Scope Z_scope.
Notation "[| x |]" := (phi x)  (at level 0, x at level 99).
Local Notation wB := (2 ^ (Z.of_nat size)).
Notation "[+| c |]" :=
(interp_carry 1 wB phi c)  (at level 0, c at level 99).
Notation "[-| c |]" :=
(interp_carry (-1) wB phi c)  (at level 0, c at level 99).
Notation "[|| x ||]" :=
(zn2z_to_Z wB phi x)  (at level 0, x at level 99).
(** Subtraction *)
(** Multiplication *)
(** Division *)

Lemma iter_int31_iter_nat : forall A f i a,
iter_int31 i A f a = iter_nat (Z.abs_nat [|i|]) A f a.