During their tenure, Deep0Thinking developed foundational mathematical tooling for the leanprover-community/mathlib4 repository, focusing on interval integrals within measure theory. They implemented the first Mean Value Theorem for interval integrals, enabling formal proofs about average values of continuous functions over intervals. Their work included specialized versions for both almost everywhere nonnegative and pointwise nonnegative functions, broadening the applicability of integral calculus in real analysis. Utilizing Lean and functional programming techniques, Deep0Thinking’s contributions strengthened the library’s measure-theoretic framework, allowing for more robust formalization of mathematical properties and supporting future extensions in mathematical analysis and theorem proving within the Lean ecosystem.