936.lean`

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

5 declarations, 4 contain sorry, 0 declared as axioms

Erdős Problem 936

Reference: erdosproblems.com/936

Imports (1)

FormalConjecturesUtil

def Erdos936.EventuallyNotPowerful The predicate that a n is only powerful for finitely many n line 35 source
Source documentation
The predicate that a n is only powerful for finitely many n.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat
Proof uses: Filter.Eventually, Not, Nat.Powerful, Filter.atTop
1 instances, coercions and auxiliary constants left out.
```
def EventuallyNotPowerful (a : ℕ → ℕ) : Prop := atTop.Eventually (fun n => ¬ (a n).Powerful)
…
```
theorem Erdos936.erdos_936.variants.two_pow_add_one Is $2^n + 1$ powerful for finitely many $n$? sorry line 39 source
Source documentation
Is $2^n + 1$ powerful for finitely many $n$?

depends on sorry what this means
Statement uses: Iff, True, Erdos936.EventuallyNotPowerful, Nat, HAdd.hAdd, HPow.hPow, OfNat.ofNat
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.
```
theorem erdos_936.variants.two_pow_add_one :
   answer(sorry) ↔ EventuallyNotPowerful (2 ^ · + 1) := by
…
```
Mentions: Erdos936.EventuallyNotPowerful
theorem Erdos936.erdos_936.variants.two_pow_sub_one Is $2^n - 1$ powerful for finitely many $n$? sorry line 45 source
Source documentation
Is $2^n - 1$ powerful for finitely many $n$?

depends on sorry what this means
Statement uses: Iff, True, Erdos936.EventuallyNotPowerful, Nat, HSub.hSub, HPow.hPow, OfNat.ofNat
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.
```
theorem erdos_936.variants.two_pow_sub_one :
   answer(sorry) ↔ EventuallyNotPowerful (2 ^ · - 1) := by
…
```
Mentions: Erdos936.EventuallyNotPowerful
theorem Erdos936.erdos_936.variants.factorial_add_one Is $n! + 1$ powerful for finitely many $n$? sorry line 51 source
Source documentation
Is $n! + 1$ powerful for finitely many $n$?

depends on sorry what this means
Statement uses: Iff, True, Erdos936.EventuallyNotPowerful, Nat, HAdd.hAdd, Nat.factorial, OfNat.ofNat
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
6 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_936.variants.factorial_add_one :
   answer(sorry) ↔ EventuallyNotPowerful (·! + 1) := by
…
```
Mentions: Erdos936.EventuallyNotPowerful
theorem Erdos936.erdos_936.variants.factorial_sub_one Is $n! - 1$ powerful for finitely many $n$? sorry line 57 source
Source documentation
Is $n! - 1$ powerful for finitely many $n$?

depends on sorry what this means
Statement uses: Iff, True, Erdos936.EventuallyNotPowerful, Nat, HSub.hSub, Nat.factorial, OfNat.ofNat
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
6 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_936.variants.factorial_sub_one :
   answer(sorry) ↔ EventuallyNotPowerful (·! - 1) := by
…
```
Mentions: Erdos936.EventuallyNotPowerful