mod4_eleven_prime
plain-language theorem explainer
Eleven is a prime congruent to three modulo four. Number theorists applying the Möbius function to primes in this residue class would cite the fact when checking squarefreeness or inversion formulas. The proof is a one-line native decision procedure that directly verifies both primality and the modular arithmetic.
Claim. $11$ is prime and $11 ≡ 3 mod 4$.
background
The theorem appears in the module supplying lightweight wrappers around Mathlib arithmetic functions, beginning with the Möbius function μ. Prime is the transparent alias for the standard predicate Nat.Prime on natural numbers. The local setting is the preparation of basic number-theoretic facts that support later Dirichlet inversion and squarefree checks.
proof idea
One-line wrapper that applies the native_decide tactic to the conjunction of primality and the residue condition.
why it matters
Supplies a concrete verified instance of a prime ≡ 3 (mod 4) for use in sibling arithmetic-function statements such as mobius_prime. It fills a basic number-theoretic foothold required before deeper applications of the Recognition Composition Law or phi-ladder mass formulas can invoke specific small primes.
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