This paper provides a refactoring from do notation to >>= operators and proves that this refactoring maintains observational equivalence. As programs grow ever larger and more complex, there is a growing need to automatically apply refactorings to these programs in a dependable manner. Current refactoring engines often contain errors, even if they are widely used and thoroughly tested. The methods used in the proof of contextual equivalence are described in this paper, with the goal of supporting future research into correct-by-construction refactorings.