  Chemical theory can be made more rigorous using the Lean theorem prover, an
interactive theorem prover for complex mathematics. We formalize the Langmuir
and BET theories of adsorption, making each scientific premise clear and every
step of the derivations explicit. Lean's math library, mathlib, provides
formally verified theorems for infinite geometries series, which are central to
BET theory. While writing these proofs, Lean prompts us to include mathematical
constraints that were not originally reported. We also illustrate how Lean
flexibly enables the reuse of proofs that build on more complex theories
through the use of functions, definitions, and structures. Finally, we
construct scientific frameworks for interoperable proofs, by creating
structures for classical thermodynamics and kinematics, using them to formalize
gas law relationships like Boyle's Law and equations of motion underlying
Newtonian mechanics, respectively. This approach can be extended to other
fields, enabling the formalization of rich and complex theories in science and
engineering.
