Simplifying Casts and Coercions

This paper introduces norm_cast, a toolbox of tactics for the Lean proof assistant designed to manipulate expressions containing coercions and casts. These expressions can be frustrating for beginning and expert users alike; the presence of coercions can cause seemingly identical expressions to fail to unify and rewrites to fail. The norm_cast tactics aim to make reasoning with such expressions as transparent as possible. They are used extensively to eliminate boilerplate arguments in the Lean mathematical library and in external developments.