End Zcompare.
Section cond_Zopp.
Definition cond_Zopp (b : bool) m := if b then Zopp m else m.

(* Specifications: *)
Theorem abs_cond_Zopp :
forall b m,
Zabs (cond_Zopp b m) = Zabs m.
Theorem cond_Zopp_Zlt_bool :
forall m,
cond_Zopp (Zlt_bool m 0) m = Zabs m.
Theorem abs_cond_Zopp :
forall b m,
Zabs (cond_Zopp b m) = Zabs m.
Theorem cond_Zopp_Zlt_bool :
forall m,
cond_Zopp (Zlt_bool m 0) m = Zabs m.