End Bool.
Section cond_Ropp.
Definition cond_Ropp (b : bool) m := if b then Ropp m else m.

Theorem cond_Ropp_odd_function :
forall (f : R -> R),
(forall x, f (Ropp x) = Ropp (f x)) ->
forall b x, f (cond_Ropp b x) = cond_Ropp b (f x).