palindromic_prime_five
plain-language theorem explainer
The declaration asserts that 5 satisfies the standard primality predicate on natural numbers. Number theorists building arithmetic functions inside the Recognition Science framework would cite it as a verified base case for Möbius and related functions on single-digit palindromic primes. The proof is a one-line term that invokes native_decide to evaluate the predicate computationally.
Claim. The integer $5$ is prime, i.e., $5$ satisfies the predicate that a natural number is prime.
background
The module supplies lightweight wrappers around Mathlib arithmetic functions, beginning with the Möbius function. The local alias Prime is defined as the transparent abbreviation for the standard Nat.Prime predicate. Upstream results include the Prime abbreviation itself together with several structural hypotheses from adjacent modules that remain unused in this specific statement.
proof idea
The proof is a term-mode one-liner that applies the native_decide tactic directly to the constant 5, letting the kernel decide the primality condition without further lemmas.
why it matters
The result supplies a concrete base case inside the arithmetic-functions module for later Möbius applications on small primes. No downstream uses are recorded, and the statement does not invoke the forcing chain, RCL, or phi-ladder constructions.
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