(** Old-style rich specification by proof of existence *)
Inductive Zdiv_rest_proofs (x:Z) (p:positive) : Set :=
Zdiv_rest_proof :
forall q r:Z,
x = q * two_power_pos p + r ->
0 <= r -> r < two_power_pos p -> Zdiv_rest_proofs x p.

Lemma Zdiv_rest_correct (x:Z) (p:positive) : Zdiv_rest_proofs x p.