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.