Lax Lean Archive

Every number greater than 1 has a prime divisor

Lax242665.PrimeDivisor · concepts/Lax242665/PrimeDivisor.lean · lax-242665

proven

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    Natural Language Statement

    Lemma

    Every natural number greater than 11 has a prime divisor.

    Concept map
    2 concepts
    100%
    Proven claimDefinitionThis conceptRelated conceptA → B: B builds on A
    Evidence

    Each proof establishes this claim relative to its assumptions.

    In the paper

    • page 2 of this submission's paper

    Lean source view on GitHub

    1import Lax242665.Primes
    2
    3/-!
    4---
    5title: Every number greater than 1 has a prime divisor
    6type: lemma
    7---
    8Every natural number greater than 11 has a prime divisor.
    9-/
    10
    11namespace Lax242665.PrimeDivisor
    12
    13/-- Every natural number `n > 1` has a prime divisor. -/
    14axiom exists_prime_dvd : ∀ n : ℕ, 1 < n → ∃ p : ℕ, Primes.Prime p ∧ p ∣ n
    15
    16end Lax242665.PrimeDivisor
    17
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