two_pow_ten
plain-language theorem explainer
Two to the tenth power equals one thousand twenty-four in the natural numbers. Number theorists working with arithmetic functions would cite this for concrete power-of-two checks during prime factorization or Möbius calculations. The proof is a one-line term that invokes native_decide for direct evaluation.
Claim. $2^{10} = 1024$
background
The module supplies lightweight wrappers around Mathlib arithmetic functions, beginning with the Möbius function μ as the indicator of squarefree integers signed by the parity of prime factors. Local conventions keep statements minimal so that Dirichlet inversion and related algebra can be added later. This numerical identity stands alone with no upstream lemmas required.
proof idea
The proof is a one-line wrapper that applies native_decide to evaluate the power equality by direct computation in the natural numbers.
why it matters
The declaration supplies a verified numerical anchor inside the arithmetic functions module. It supports concrete calculations that appear in prime and squarefree contexts, consistent with the module's role as a Möbius foothold. No parent theorems or open questions are linked at present.
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