FormalConjectures/OEIS/91669.lean

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Explanation legend Lean4 Domain Explanation Language (L4DEL)

L4DEL explanations are a separate layer. They do not change the Lean source. Intuition is explanatory prose; numbered items are a reading path; sources link the wording back to evidence.

L4DEL
Lean4 Domain Explanation Language

Credit: The upstream authors and contributors retain credit for the project and mathematics. lean4-explainer only renders their pinned source and adds the separately disclosed explanation layer.

Project sources: Pinned project documentation, Formal Conjectures paper, arXiv v1

7 declarations, 1 contain sorry, 0 declared as axioms

Primality and primitive root property from divisibility $n \mid (a(n-1) + 2^{n-2})$

$a(n) = \frac{2^{n-1}}{n!} \prod_{k=1}^{n-1} (2^k-1)$. The sequence $a(n)$ is composed of natural numbers, thus we define it as a function $\mathbb{N} \to \mathbb{N}$.

References:

Imports (1)
  1. def OeisA91669.a $a(n) = \frac{2^{n-1}}{n!} \prod_{k=1}^{n-1} (2^k-1)$ line 44 source

    Source documentation

    $a(n) = \frac{2^{n-1}}{n!} \prod_{k=1}^{n-1} (2^k-1)$. The sequence $a(n)$ is composed of natural numbers, thus we define it as a function $\mathbb{N} \to \mathbb{N}$.

    standard axioms: Classical.choice, Quot.sound, propext what this means

    Statement uses: Nat

    Proof uses: ite, Eq, OfNat.ofNat, Nat.pred, HMul.hMul, HPow.hPow, Finset.prod, Finset.Ico, HSub.hSub, Nat.factorial, HDiv.hDiv

    15 instances, coercions and auxiliary constants left out.

    def a (n : ℕ) : ℕ :=
…
  2. lemma OeisA91669.a_1 line 60 source

    standard axioms: Classical.choice, Quot.sound, propext what this means

    Statement uses: Eq, Nat, OeisA91669.a, OfNat.ofNat

    Proof uses: Eq.refl

    2 instances, coercions and auxiliary constants left out.

    Tactic trace: 1 steps

    Open to load the checked before-and-after goal states.

  3. lemma OeisA91669.a_2 line 63 source

    standard axioms: Classical.choice, Quot.sound, propext what this means

    Statement uses: Eq, Nat, OeisA91669.a, OfNat.ofNat

    Proof uses: Eq.refl

    2 instances, coercions and auxiliary constants left out.

    Tactic trace: 1 steps

    Open to load the checked before-and-after goal states.

  4. lemma OeisA91669.a_3 line 66 source

    standard axioms: Classical.choice, Quot.sound, propext what this means

    Statement uses: Eq, Nat, OeisA91669.a, OfNat.ofNat

    Proof uses: Eq.refl

    2 instances, coercions and auxiliary constants left out.

    Tactic trace: 1 steps

    Open to load the checked before-and-after goal states.

  5. lemma OeisA91669.a_4 line 69 source

    standard axioms: Classical.choice, Quot.sound, propext what this means

    Statement uses: Eq, Nat, OeisA91669.a, OfNat.ofNat

    Proof uses: Eq.refl

    2 instances, coercions and auxiliary constants left out.

    Tactic trace: 1 steps

    Open to load the checked before-and-after goal states.

  6. lemma OeisA91669.a_5 line 72 source

    standard axioms: Classical.choice, Quot.sound, propext what this means

    Statement uses: Eq, Nat, OeisA91669.a, OfNat.ofNat

    Proof uses: Eq.refl

    2 instances, coercions and auxiliary constants left out.

    Tactic trace: 1 steps

    Open to load the checked before-and-after goal states.

  7. theorem OeisA91669.prime_and_primitive_root_of_dvd sorry line 83 source

    depends on sorry what this means

    Statement uses: Nat, GT.gt, OfNat.ofNat, Dvd.dvd, HAdd.hAdd, OeisA91669.a, HSub.hSub, HPow.hPow, And, Nat.Prime, IsPrimitiveRoot, ZMod, Nat.totient

    Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous

    40 instances, coercions and auxiliary constants left out.

    Tactic trace: 1 steps

    Open to load the checked before-and-after goal states.