Formalization of the variable-length source coding theorem: Direct part

Modern mathematical proofs are becoming so big that they cause a problem of trust. Formal verification using proof-assistants has recently emerged as a solution to ensure the correctness of big proofs. Before being able to verify formally big proofs one must build substantial libraries of formal definitions and formal theorems. In this paper, we explain how we contribute to an existing formalization of information theory by extending it with a foundational theorem; namely, the variable-length source coding theorem.