superprime_sixtyseven
plain-language theorem explainer
The declaration establishes that both 67 and 19 are prime numbers. Developers maintaining arithmetic functions and Möbius footholds in the Recognition Science framework would cite it when initializing small-prime checks for squarefree predicates or inversion formulas. The proof is a one-line term that invokes native_decide to evaluate the primality predicates by direct computation.
Claim. The natural numbers 67 and 19 are both prime.
background
The ArithmeticFunctions module supplies lightweight wrappers around Mathlib's arithmetic-function library, beginning with the Möbius function μ. The local setting keeps statements minimal so that Dirichlet algebra and inversion can be added once basic interfaces stabilize. The Prime predicate is the transparent repository alias for Nat.Prime. Upstream results supply the supporting “is” structures that certify collision-free or clean constructions in the Foundation and GameTheory layers.
proof idea
The proof is a term-mode one-liner that applies native_decide directly to the conjunction of the two primality statements, reducing them to decidable Boolean evaluation with no intermediate lemmas.
why it matters
The result supplies concrete small-prime facts required by the sibling arithmetic-function definitions in the same module. It supports the NumberTheory.Primes section but carries no downstream uses. It aligns with the framework's need for verified base cases in Möbius computations without touching the T0-T8 forcing chain, the Recognition Composition Law, or the phi-ladder.
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