JugglerConjecture.lean`

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

3 declarations, 1 contain sorry, 0 declared as axioms

Juggler conjecture

Reference: Wikipedia

Imports (1)

FormalConjecturesUtil

def JugglerConjecture.jugglerStep Consider the following operation on the natural numbers: If the number is even, take the floor of the square root line 35 source
Source documentation
Consider the following operation on the natural numbers: If the number is even, take the floor of the square root. If the number is odd, take the floor of n raised to the 3/2 power.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat
Proof uses: ite, Even, Nat.floor, Real, HPow.hPow, HDiv.hDiv, OfNat.ofNat
20 instances, coercions and auxiliary constants left out.
```
noncomputable def jugglerStep (n : ℕ) : ℕ :=
…
```
theorem JugglerConjecture.juggler_conjecture Now form a sequence beginning with any positive integer, where each subsequent term is obtained by applying the operation defined above to the previous term sorry line 45 source
Source documentation
Now form a sequence beginning with any positive integer, where each subsequent term is obtained by applying the operation defined above to the previous term. The Juggler Conjecture states that for any positive integer $n$, there exists a natural number $m$ such that the $m$-th term of the sequence is $1$.

depends on sorry what this means
Statement uses: Nat, GT.gt, OfNat.ofNat, Exists, Eq, Nat.iterate, JugglerConjecture.jugglerStep
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
4 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem juggler_conjecture (n : ℕ) (hn : n > 0) : ∃ m, jugglerStep^[m] n = 1 := by
…
```
Mentions: JugglerConjecture.jugglerStep
theorem JugglerConjecture.jugglerStep_36 Example: jugglerStep 36 = ⌊36^(1/2)⌋ = ⌊6⌋ = 6 (since 36 is even) line 50 source
Source documentation
Example: jugglerStep 36 = ⌊36^(1/2)⌋ = ⌊6⌋ = 6 (since 36 is even).

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, JugglerConjecture.jugglerStep, OfNat.ofNat
Proof uses: id, of_eq_true, ite, Even, Nat.floor, Real, HPow.hPow, HDiv.hDiv, Eq.trans, True, congrFun', congrArg, ite_congr, eq_true, Iff.mp, HMod.hMod, Bool.rec, Bool, Not, Bool.true and 27 more
43 instances, coercions and auxiliary constants left out.

Tactic trace: 2 steps
Open to load the checked before-and-after goal states.
```
theorem jugglerStep_36 : jugglerStep 36 = 6 := by
…
```
Mentions: JugglerConjecture.jugglerStep