A Lean Paper About Paper: A Formal Framework for Origami

Abstract

The mathematics of Origami have been well studied and shown to develop several interesting results. We use Lean 4 tactics and build on Mathlib to redefine the 7 Huzita operations as theorems instead of axioms and prove their existence. We develop proofs for important origami constructions (such as trisecting an angle), implement origami-constructible numbers and prove the associated Cardano's formula, and formalize Haga's theorem. A Crease Pattern Inspector explores physical folding by providing a full pipeline to create and visualize models constrained by the Huzita formalism. The Lean codebase brings 100+ theorems and lemmas.