Suggest adding another nonstandard IVT reference   In addition to the alternative proof link nonstandard calculus possibly add refference to the Constructivist analysis article  There is a is a long section on IVT in that page  The Constructivist analysis IVT section forward references to this page  A link to that discussion might be usefull in this article  However I believe the that the the discussion of classical analysis IVT on that page is not in close aggrement with this page