Reasoning about real number expressions in a proof assistant is challenging. Several problems in theorem proving can be solved by using  exact real number computation. I have implemented a library for reasoning and computing with complete metric spaces in the Coq proof assistant and used this library to build a constructive real number implementation including elementary real number functions and proofs of correctness. Using this library, I have created a tactic that automatically proves strict inequalities over closed elementary real number expressions by computation.
["Russell O'Connor"]
Certified Exact Transcendental Real Number Computation in Coq