two_pow_eight
plain-language theorem explainer
The equality 2 raised to the eighth power equals 256 is recorded as a verified fact in the natural numbers. Number theorists performing explicit calculations with small powers of 2 inside arithmetic function proofs would cite this for direct reference. The proof applies Lean's native decision procedure to settle the concrete numerical claim in one step.
Claim. $2^8 = 256$
background
The declaration sits inside the module on arithmetic functions that supplies lightweight wrappers around Mathlib's Möbius function and related tools for number theory. The local setting keeps statements minimal so that deeper Dirichlet inversion can be added later once basic interfaces stabilize. No upstream lemmas are required; the fact is a self-contained numerical check.
proof idea
The proof is a one-line term that invokes native_decide to evaluate the concrete power directly.
why it matters
The result supplies a verified small-integer constant that can appear in explicit calculations involving powers of 2 within the arithmetic functions section. It supports the module's focus on Möbius footholds and squarefree checks even though no downstream uses are recorded. The fact aligns with the framework's need for precise base cases when constructing larger structures such as the eight-tick octave.
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