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

Theorem cond_Ropp_even_function :
forall {A : Type} (f : R -> A),
(forall x, f (Ropp x) = f x) ->
forall b x, f (cond_Ropp b x) = f x.