Proof (eqmod_same_bits wordsize).

(* Specifications: *)
Lemma same_bits_eqmod:
forall n x y i,
eqmod (two_power_nat n) x y -> 0 <= i < Z.of_nat n ->
Z.testbit x i = Z.testbit y i.
Lemma same_bits_eqm:
forall x y i,
eqm x y ->
0 <= i < zwordsize ->
Z.testbit x i = Z.testbit y i.
Lemma same_bits_eqmod:
forall n x y i,
eqmod (two_power_nat n) x y -> 0 <= i < Z.of_nat n ->
Z.testbit x i = Z.testbit y i.
Lemma same_bits_eqm:
forall x y i,
eqm x y ->
0 <= i < zwordsize ->
Z.testbit x i = Z.testbit y i.