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This papers extends the Nuprl proof assistant (a system representative of the class of extensional type theoriesà la Martin-Löf) with named exceptions and handlers, as well as a nominal fresh operator. Using these new features, we prove a version of Brouwer's Continuity Principle for numbers. We also provide a simpler proof of a weaker version of this principle that only uses diverging terms. We prove these two principles in Nuprl's meta-theory using our formalization of Nuprl in Coq and showdoi:10.1145/2854065.2854077 dblp:conf/cpp/RahliB16 fatcat:55xfsdlzcrc3zoxyhv64kqrz3a