three_almost_prime_twenty
plain-language theorem explainer
The declaration verifies that 20 has exactly three prime factors counted with multiplicity. Number theorists using the arithmetic functions library would cite this concrete case. The proof is a direct computational check via native_decide.
Claim. The integer 20 satisfies $20=2^2×5$, hence it is a 3-almost prime, i.e., the total number of its prime factors counted with multiplicity equals three.
background
The module supplies lightweight wrappers around Mathlib arithmetic functions, beginning with the Möbius function. The definition states that a number is 3-almost prime precisely when the total number of prime factors counted with multiplicity equals three. The upstream definition encodes this as a Boolean predicate on natural numbers. The local setting keeps statements lightweight pending deeper Dirichlet algebra.
proof idea
The proof is a term-mode one-line wrapper that applies native_decide to evaluate the Boolean equality directly.
why it matters
The result supplies a verified instance inside the arithmetic functions module of the NumberTheory.Primes section. It illustrates the 3-almost prime definition but lists no downstream applications. It aligns with the module's emphasis on lightweight statements and contributes concrete checks that could support prime-factorization work in the Recognition framework.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.