Theorem MVT : forall (f g:R -> R) (a b:R) (pr1:forall c:R, a < c < b -> derivable_pt f c) (pr2:forall c:R, a < c < b -> derivable_pt g c), a < b -> (forall c:R, a <= c <= b -> continuity_pt f c) -> (forall c:R, a <= c <= b -> continuity_pt g c) -> exists c : R, (exists P : a < c < b, (g b - g a) * derive_pt f c (pr1 c P) = (f b - f a) * derive_pt g c (pr2 c P)).