Local Open Scope Z_scope.
Module Z.

(* Specifications: *)
Lemma diveq_iff c a b :
(b = 0 /\ c = 0 \/ c*b <= a < c*b + b \/ c*b + b < a <= c*b) <-> a/b = c.
Lemma mod_diveq_iff c a b :
(b = 0 \/ c*b <= a < c*b + b \/ c*b + b < a <= c*b) <-> a mod b = a-b*c.