Formalization of real analysis: a survey of proof assistants and libraries

interfaces are heavily used to ease statements and proofs (Krebbers and Spitters 2013). Thanks to type classes, the algebraic and order hierarchies (setoid, group, ring, and so on) easily benefit from inheritance. Finally, C-CoRN and Coq’s standard library are not entirely unrelated: Kaliszyk and O’Connor (2009) provide an equivalence lemma between both libraries, under the axioms of the standard library. Sylvie Boldo, Catherine Lelay, Guillaume Melquiond 12 3.2.4. NASA PVS Library In addition to its axiomatization of R, PVS also comes with a development of constructive reals by Lester (2008). They are based on a stream of digits that gives Cauchy sequences.