Arguments Zdiv_eucl_extended : default implicits.
Module Z.

(* Specifications: *)
Lemma mod_id_iff a b : a mod b = a <-> 0 <= a < b \/ b = 0 \/ b < a <= 0.
Lemma gcd_mod_r a b : Z.gcd a (b mod a) = Z.gcd a b.
Lemma cong_iff_0 a b m : a mod m = b mod m <-> (a - b) mod m = 0.
Lemma cong_iff_ex a b m : a mod m = b mod m <-> exists n, a - b = n * m.
Lemma mod_mod_divide a b c : (c | b) -> (a mod b) mod c = a mod c.
Lemma mod_opp_mod_opp a b : - (-a mod b) mod b = a mod b.
Lemma mod_mod_opp_r a b : (a mod - b) mod b = a mod b.
Lemma mod_opp_r_mod a b : (a mod b) mod - b = a mod - b.
Lemma mod_abs_r_mod a b : (a mod b) mod Z.abs b = a mod Z.abs b.
End Z.