Lemma Rolle : forall (f:R -> R) (a b:R) (pr:forall x:R, a < x < b -> derivable_pt f x), (forall x:R, a <= x <= b -> continuity_pt f x) -> a < b -> f a = f b -> exists c : R, (exists P : a < c < b, derive_pt f c (pr c P) = 0).