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We present a library to verify rigorous approximations of univariate functions on real numbers, with the Coq proof assistant. Based on interval arithmetic, this library also implements a technique of validation a posteriori based on the Banach fixed-point theorem. We illustrate this technique on the case of operations of division and square root. This library features a collection of abstract structures that organise the specfication of rigorous approximations, and modularise the relateddoi:10.4230/lipics.itp.2019.8 dblp:conf/itp/BrehardMP19 fatcat:b2twcbftqrdihpid6s3fxlw4ha