BusyBeaver.lean`

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13 declarations, 7 contain sorry, 0 declared as axioms

Busy Beaver

The Busy Beaver problem asks for the maximum number of steps that an n-state, 2-symbol Turing machine can take before halting, when started on an empty tape.

References:

The Busy Beaver Challenge

Imports (1)

FormalConjecturesUtil

Imported by 1 file

FormalConjectures/Subsets/FC100SolvedSet1.lean

structure BusyBeaver.Candidate line 39 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat
instance BusyBeaver.(instance at line 51) line 51 source
instance BusyBeaver.(instance at line 52) line 52 source
instance BusyBeaver.(instance at line 53) line 53 source
instance BusyBeaver.(instance at line 54) line 54 source
def BusyBeaver.BB BB(n) is the n-th Busy Beaver number line 60 source
Source documentation
BB(n) is the n-th Busy Beaver number. This is the maximum shifts function, not the "number of ones function"

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat
Proof uses: SupSet.sSup, Set.ofPred, Exists, BusyBeaver.Candidate, Eq, ENat, Turing.BusyBeaver.Machine.haltingNumber, BusyBeaver.Candidate.Γ, BusyBeaver.Candidate.Λ, BusyBeaver.Candidate.Λ_inhabited, BusyBeaver.Candidate.M
4 instances, coercions and auxiliary constants left out.
```
noncomputable def BB (n : ℕ) : ℕ :=
…
```
theorem BusyBeaver.sanity_check To compute BB n, we need only consider machines with states and symbols indexed in Fin sorry line 67 source
Source documentation
To compute BB n, we need only consider machines with states and symbols indexed in Fin.

depends on sorry what this means
Statement uses: Nat, NeZero, Eq, ENat, BusyBeaver.BB, SupSet.sSup, Set.ofPred, Exists, Turing.BusyBeaver.Machine, Fin, OfNat.ofNat, Turing.BusyBeaver.Machine.IsHalting, Turing.BusyBeaver.Machine.haltingNumber
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
24 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem sanity_check (n : ℕ) [NeZero n] :
    BB n = sSup {N | ∃ (M : Machine (Fin 2) (Fin n)) (_ : M.IsHalting),
      M.haltingNumber = N} := by
…
```
Mentions: BusyBeaver.BB
theorem BusyBeaver.BB_1 The value of the Busy Beaver function for 1 state is 1 sorry line 74 source
Source documentation
The value of the Busy Beaver function for 1 state is 1.

depends on sorry what this means
Statement uses: Eq, Nat, BusyBeaver.BB, OfNat.ofNat
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
2 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem BB_1 : BB 1 = 1 := by
…
```
Mentions: BusyBeaver.BB
theorem BusyBeaver.BB_2 The value of the Busy Beaver function for 2 states is 6 sorry line 79 source
Source documentation
The value of the Busy Beaver function for 2 states is 6.

depends on sorry what this means
Statement uses: Eq, Nat, BusyBeaver.BB, OfNat.ofNat
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
2 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem BB_2 : BB 2 = 6 := by
…
```
Mentions: BusyBeaver.BB
theorem BusyBeaver.BB_3 The value of the Busy Beaver function for 3 states is 21 sorry line 84 source
Source documentation
The value of the Busy Beaver function for 3 states is 21.

depends on sorry what this means
Statement uses: Eq, Nat, BusyBeaver.BB, OfNat.ofNat
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
2 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem BB_3 : BB 3 = 21 := by
…
```
Mentions: BusyBeaver.BB
theorem BusyBeaver.BB_4 The value of the Busy Beaver function for 4 states is 107 sorry line 89 source
Source documentation
The value of the Busy Beaver function for 4 states is 107.

depends on sorry what this means
Statement uses: Eq, Nat, BusyBeaver.BB, OfNat.ofNat
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
2 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem BB_4 : BB 4 = 107 := by
…
```
Mentions: BusyBeaver.BB
theorem BusyBeaver.BB_5 The value of the Busy Beaver function for 5 states is 47176870 sorry line 94 source
Source documentation
The value of the Busy Beaver function for 5 states is 47176870.

depends on sorry what this means
Statement uses: Eq, Nat, BusyBeaver.BB, OfNat.ofNat
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
2 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem BB_5 : BB 5 = 47176870 := by
…
```
Mentions: BusyBeaver.BB
theorem BusyBeaver.BB_6 Determine the value of the Busy Beaver function at n = 6 sorry line 101 source
Source documentation
Determine the value of the Busy Beaver function at n = 6.

depends on sorry what this means
Statement uses: Eq, Nat, BusyBeaver.BB, OfNat.ofNat, sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
2 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem BB_6 : BB 6 = answer(sorry) := by
…
```
Mentions: BusyBeaver.BB