1359.lean`

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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

Lesser of twin primes

Primes $p$ such that $p+2$ is also prime.

References:

A001359

Imports (1)

FormalConjecturesUtil

def OeisA1359.a The $n$-th lesser twin prime, with $a(0) = 0$ line 34 source
Source documentation
The $n$-th lesser twin prime, with $a(0) = 0$.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat
Proof uses: ite, GT.gt, OfNat.ofNat, Nat.nth, And, Nat.Prime, HAdd.hAdd, HSub.hSub
7 instances, coercions and auxiliary constants left out.
```
noncomputable def a (n : ℕ) : ℕ :=
…
```
theorem OeisA1359.a_0 Value of the sequence a at 0 line 42 source
Source documentation
Value of the sequence a at 0.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA1359.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.
```
theorem a_0 : a 0 = 0 := by rfl
…
```
Mentions: OeisA1359.a
theorem OeisA1359.a_1 Value of the sequence a at 1 line 46 source
Source documentation
Value of the sequence a at 1.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA1359.a, OfNat.ofNat
Proof uses: Eq.mpr, Nat.nth, And, Nat.Prime, HAdd.hAdd, id, congrFun', congrArg, ite_congr, GT.gt, True, HSub.hSub, eq_true, Mathlib.Meta.NormNum.isNat_lt_true, Mathlib.Meta.NormNum.isNat_ofNat, Eq.refl, Bool, Bool.false, Mathlib.Meta.NormNum.IsNat.to_eq, Mathlib.Meta.NormNum.isNat_natSub and 9 more
19 instances, coercions and auxiliary constants left out.

Tactic trace: 4 steps
Open to load the checked before-and-after goal states.
```
theorem a_1 : a 1 = 3 := by
…
```
Mentions: OeisA1359.a
theorem OeisA1359.a_2 Value of the sequence a at 2 line 52 source
Source documentation
Value of the sequence a at 2.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA1359.a, OfNat.ofNat
Proof uses: id, Eq.trans, Nat.nth, And, Nat.Prime, HAdd.hAdd, HSub.hSub, Nat.count, congr_arg, Eq.refl, Nat.nth_count, of_decide_eq_true, Bool, Decidable.decide, Bool.true
8 instances, coercions and auxiliary constants left out.

Tactic trace: 4 steps
Open to load the checked before-and-after goal states.
```
theorem a_2 : a 2 = 5 := by
…
```
Mentions: OeisA1359.a
theorem OeisA1359.a_3 Value of the sequence a at 3 line 58 source
Source documentation
Value of the sequence a at 3.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA1359.a, OfNat.ofNat
Proof uses: Eq.mpr, Nat.nth, And, Nat.Prime, HAdd.hAdd, id, congrFun', congrArg, ite_congr, GT.gt, True, HSub.hSub, eq_true, Mathlib.Meta.NormNum.isNat_lt_true, Mathlib.Meta.NormNum.isNat_ofNat, Eq.refl, Bool, Bool.false, Mathlib.Meta.NormNum.IsNat.to_eq, Mathlib.Meta.NormNum.isNat_natSub and 8 more
20 instances, coercions and auxiliary constants left out.

Tactic trace: 6 steps
Open to load the checked before-and-after goal states.
```
theorem a_3 : a 3 = 11 := by
…
```
Mentions: OeisA1359.a
theorem OeisA1359.a_4 Value of the sequence a at 4 line 65 source
Source documentation
Value of the sequence a at 4.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA1359.a, OfNat.ofNat
Proof uses: Eq.mpr, Nat.nth, And, Nat.Prime, HAdd.hAdd, id, congrFun', congrArg, ite_cond_eq_true, GT.gt, HSub.hSub, Eq.trans, LT.lt, True, Nat.count, congr_arg, Eq.refl, Nat.nth_count, of_decide_eq_true, Bool and 2 more
21 instances, coercions and auxiliary constants left out.

Tactic trace: 4 steps
Open to load the checked before-and-after goal states.
```
theorem a_4 : a 4 = 17 := by
…
```
Mentions: OeisA1359.a
theorem OeisA1359.conjecture sorry line 79 source
depends on sorry what this means
Statement uses: Nat, GT.gt, OfNat.ofNat, Nat.nth, Nat.Prime, HSub.hSub, Nat.ModEq, Nat.factorial, HAdd.hAdd, Finset.prod, Finset.Icc, Iff, Or, Eq, And
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
18 instances, coercions and auxiliary constants left out.

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