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### Abstract

This article contains a formalisation of the Akra-Bazzi method
based on a proof by Leighton. It is a generalisation of the well-known
Master Theorem for analysing the complexity of Divide & Conquer algorithms.
We also include a generalised version of the Master theorem based on the
Akra-Bazzi theorem, which is easier to apply than the Akra-Bazzi theorem
itself.

Some proof methods that facilitate applying the Master theorem are also included. For a more detailed explanation of the formalisation and the proof methods, see the accompanying paper (publication forthcoming).