93456.lean`

Explanation legend Lean4 Domain Explanation Language (L4DEL)

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L4DEL: Lean4 Domain Explanation Language

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

7 declarations, 1 contain sorry, 0 declared as axioms

Product of composite numbers in triangular intervals

Product of all composite numbers between $n(n-1)/2+1$ and $n(n+1)/2$ (including boundaries), where $n(n-1)/2 = \binom{n}{2}$ and $n(n+1)/2 = \binom{n+1}{2}$.

References:

A093456

Imports (1)

FormalConjecturesUtil

def OeisA93456.a Product of all composite numbers in the interval $[\binom{n}{2} + 1, \binom{n+1}{2}]$ line 34 source
Source documentation
Product of all composite numbers in the interval $[\binom{n}{2} + 1, \binom{n+1}{2}]$.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat
Proof uses: HAdd.hAdd, Nat.choose, OfNat.ofNat, Finset.prod, Finset.filter, And, LT.lt, Not, Nat.Prime, Finset.Icc, id
11 instances, coercions and auxiliary constants left out.
```
def a (n : ℕ) : ℕ :=
…
```
theorem OeisA93456.a_0 Value of the sequence a at 0 line 41 source
Source documentation
Value of the sequence a at 0.

extra axioms: _private.0.OeisA93456.a_0._native.decide.ax_1 what this means
Statement uses: Eq, Nat, OeisA93456.a, OfNat.ofNat
Proof uses: of_decide_eq_true
4 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem a_0 : a 0 = 1 := by decide +native
…
```
Mentions: OeisA93456.a
theorem OeisA93456.a_1 Value of the sequence a at 1 line 45 source
Source documentation
Value of the sequence a at 1.

extra axioms: _private.0.OeisA93456.a_1._native.decide.ax_1 what this means
Statement uses: Eq, Nat, OeisA93456.a, OfNat.ofNat
Proof uses: of_decide_eq_true
4 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem a_1 : a 1 = 1 := by decide +native
…
```
Mentions: OeisA93456.a
theorem OeisA93456.a_2 Value of the sequence a at 2 line 49 source
Source documentation
Value of the sequence a at 2.

extra axioms: _private.0.OeisA93456.a_2._native.decide.ax_1 what this means
Statement uses: Eq, Nat, OeisA93456.a, OfNat.ofNat
Proof uses: of_decide_eq_true
4 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem a_2 : a 2 = 1 := by decide +native
…
```
Mentions: OeisA93456.a
theorem OeisA93456.a_3 Value of the sequence a at 3 line 53 source
Source documentation
Value of the sequence a at 3.

extra axioms: _private.0.OeisA93456.a_3._native.decide.ax_1 what this means
Statement uses: Eq, Nat, OeisA93456.a, OfNat.ofNat
Proof uses: of_decide_eq_true
4 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem a_3 : a 3 = 24 := by decide +native
…
```
Mentions: OeisA93456.a
theorem OeisA93456.a_4 Value of the sequence a at 4 line 57 source
Source documentation
Value of the sequence a at 4.

extra axioms: _private.0.OeisA93456.a_4._native.decide.ax_1 what this means
Statement uses: Eq, Nat, OeisA93456.a, OfNat.ofNat
Proof uses: of_decide_eq_true
4 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem a_4 : a 4 = 720 := by decide +native
…
```
Mentions: OeisA93456.a
theorem OeisA93456.conjecture sorry line 64 source
depends on sorry what this means
Statement uses: Not, Set.Finite, Nat, Set.ofPred, And, LT.lt, OfNat.ofNat, Dvd.dvd, OeisA93456.a, HSub.hSub
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
10 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.