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Local Open Scope R_scope.

Theorem MVT_cor2 :
forall (f f':R -> R) (a b:R),
a < b ->
(forall c:R, a <= c <= b -> derivable_pt_lim f c (f' c)) ->
exists c : R, f b - f a = f' c * (b - a) /\ a < c < b.