FormalConjectures/OEIS/7013.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

Catalan-Mersenne numbers

Catalan-Mersenne numbers: $a(0) = 2$; for $n \ge 0$, $a(n+1) = 2^{a(n)} - 1$.

References:

Imports (1)
  1. def OeisA7013.a Catalan-Mersenne numbers: $a(0) = 2$, $a(n+1) = 2^{a(n)} - 1$ line 34 source

    Source documentation

    Catalan-Mersenne numbers: $a(0) = 2$, $a(n+1) = 2^{a(n)} - 1$.

    standard axioms: propext what this means

    Statement uses: Nat

    2 instances, coercions and auxiliary constants left out.

    def a (n : ℕ) : ℕ :=
…
  2. theorem OeisA7013.a_0 line 40 source

    standard axioms: propext what this means

    Statement uses: Eq, Nat, OeisA7013.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. theorem OeisA7013.a_1 line 43 source

    standard axioms: propext what this means

    Statement uses: Eq, Nat, OeisA7013.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. theorem OeisA7013.a_2 line 46 source

    standard axioms: propext what this means

    Statement uses: Eq, Nat, OeisA7013.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. theorem OeisA7013.a_3 line 49 source

    standard axioms: propext what this means

    Statement uses: Eq, Nat, OeisA7013.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. theorem OeisA7013.a_4 line 52 source

    standard axioms: propext what this means

    Statement uses: Eq, Nat, OeisA7013.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 OeisA7013.conjecture Catalan-Mersenne conjecture: All terms of the Catalan-Mersenne sequence are prime sorry line 58 source

    Source documentation

    Catalan-Mersenne conjecture: All terms of the Catalan-Mersenne sequence are prime.

    depends on sorry what this means

    Statement uses: Nat, Nat.Prime, OeisA7013.a

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

    1 instances, coercions and auxiliary constants left out.

    Tactic trace: 1 steps

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

    theorem conjecture (n : ℕ) : (a n).Prime := by
…

    Mentions: OeisA7013.a