FormalConjectures/OEIS/64169.lean

GitHub source file

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

8 declarations, 1 contain sorry, 0 declared as axioms

Numerator - denominator in $n$-th harmonic number

$a(n) = \text{numerator}(H_n) - \text{denominator}(H_n)$, where $H_n = 1 + 1/2 + \dots + 1/n$.

References:

Imports (1)
  1. def OeisA64169.H The $n$-th harmonic number $H_n = \sum_{k=1}^n \frac{1}{k}$ as a rational number line 34 source

    Source documentation

    The $n$-th harmonic number $H_n = \sum_{k=1}^n \frac{1}{k}$ as a rational number.

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

    Statement uses: Nat, Rat

    Proof uses: Finset.sum, Finset.Icc, OfNat.ofNat, HDiv.hDiv

    9 instances, coercions and auxiliary constants left out.

    def H (n : ℕ) : ℚ :=
…
  2. def OeisA64169.a $a(n) = \text{numerator}(H_n) - \text{denominator}(H_n)$ line 38 source

    Source documentation

    $a(n) = \text{numerator}(H_n) - \text{denominator}(H_n)$.

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

    Statement uses: Nat, Int

    Proof uses: HSub.hSub, Rat.num, OeisA64169.H, Rat.den

    4 instances, coercions and auxiliary constants left out.

    def a (n : ℕ) : ℤ :=
…
  3. theorem OeisA64169.a_1 line 42 source

    extra axioms: _private.0.OeisA64169.a_1._native.decide.ax_1 what this means

    Statement uses: Eq, Int, OeisA64169.a, OfNat.ofNat, Nat

    Proof uses: of_decide_eq_true

    6 instances, coercions and auxiliary constants left out.

    Tactic trace: 1 steps

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

  4. theorem OeisA64169.a_2 line 46 source

    extra axioms: _private.0.OeisA64169.a_2._native.decide.ax_1 what this means

    Statement uses: Eq, Int, OeisA64169.a, OfNat.ofNat, Nat

    Proof uses: of_decide_eq_true

    6 instances, coercions and auxiliary constants left out.

    Tactic trace: 1 steps

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

  5. theorem OeisA64169.a_3 line 50 source

    extra axioms: _private.0.OeisA64169.a_3._native.decide.ax_1 what this means

    Statement uses: Eq, Int, OeisA64169.a, OfNat.ofNat, Nat

    Proof uses: of_decide_eq_true

    6 instances, coercions and auxiliary constants left out.

    Tactic trace: 1 steps

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

  6. theorem OeisA64169.a_4 line 54 source

    extra axioms: _private.0.OeisA64169.a_4._native.decide.ax_1 what this means

    Statement uses: Eq, Int, OeisA64169.a, OfNat.ofNat, Nat

    Proof uses: of_decide_eq_true

    6 instances, coercions and auxiliary constants left out.

    Tactic trace: 1 steps

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

  7. theorem OeisA64169.a_5 line 58 source

    extra axioms: _private.0.OeisA64169.a_5._native.decide.ax_1 what this means

    Statement uses: Eq, Int, OeisA64169.a, OfNat.ofNat, Nat

    Proof uses: of_decide_eq_true

    6 instances, coercions and auxiliary constants left out.

    Tactic trace: 1 steps

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

  8. theorem OeisA64169.conjecture sorry line 68 source

    depends on sorry what this means

    Statement uses: Not, Nat, LT.lt, OfNat.ofNat, Iff, Dvd.dvd, Int, OeisA64169.a, HSub.hSub, Nat.Prime

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

    14 instances, coercions and auxiliary constants left out.

    Tactic trace: 1 steps

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