(** Particular case : dividing by 2 is related with parity *)

(** * Interaction with "historic" Zdiv *)
(** They agree at least on positive numbers: *)
Theorem Zquotrem_Zdiv_eucl_pos : forall a b:Z, 0 <= a -> 0 < b ->
a÷b = a/b /\ Z.rem a b = a mod b.