300997.lean`

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

7 declarations, 1 contain sorry, 0 declared as axioms

Step difference bound $a(n+1) - a(n) \in \{1, 2\}$ in mass-redistribution cellular automata

$a(n)$ is the number of steps needed to reach a stable configuration in the 1D cellular automaton initialized with one cell with mass $n$ and based on the rule "each cell gives half of its mass, rounded down, to its right neighbor". The stable configuration is $n$ cells with mass 1.

References:

A300997
arxiv/2605.22763 Advancing Mathematics Research with AI-Driven Formal Proof Search by George Tsoukalas et al.

Imports (1)

FormalConjecturesUtil

def OeisA300997.a Documented declaration: a line 46 source
Source documentation
$a(n)$ is the number of steps needed to reach a stable configuration in the 1D cellular automaton initialized with one cell with mass $n$ and based on the rule "each cell gives half of its mass, rounded down, to its right neighbor". The stable configuration is $n$ cells with mass 1.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat
Proof uses: HDiv.hDiv, HAdd.hAdd, OfNat.ofNat, List, List.reverse, List.dropWhile, Decidable.decide, Eq, HAppend.hAppend, List.map, List.cons, List.nil, List.zipWith, Nat.add, ite, List.replicate, List.foldl, List.range, Set, Set.ofPred and 1 more
9 instances, coercions and auxiliary constants left out.
```
noncomputable def a (n : ℕ) : ℕ :=
…
```
lemma OeisA300997.a_1 line 78 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA300997.a, OfNat.ofNat
Proof uses: of_eq_true, Eq.trans, Or, Membership.mem, Set, Set.ofPred, List, List.foldl, List.reverse, List.dropWhile, Decidable.decide, List.zipWith, Nat.add, HAppend.hAppend, List.map, HDiv.hDiv, HAdd.hAdd, List.cons, List.nil, List.range and 9 more
18 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
lemma OeisA300997.a_2 line 81 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA300997.a, OfNat.ofNat
Proof uses: id, Eq.mpr, HDiv.hDiv, HAdd.hAdd, List, List.reverse, List.dropWhile, Decidable.decide, HAppend.hAppend, List.map, List.cons, List.nil, List.zipWith, Nat.add, ite, List.replicate, List.foldl, List.range, Set, Set.ofPred and 29 more
20 instances, coercions and auxiliary constants left out.

Tactic trace: 17 steps
Open to load the checked before-and-after goal states.
lemma OeisA300997.a_3 line 94 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA300997.a, OfNat.ofNat
Proof uses: Eq.mpr, InfSet.sInf, Set.ofPred, List, List.foldl, List.reverse, List.dropWhile, Decidable.decide, List.zipWith, Nat.add, HAppend.hAppend, List.map, HDiv.hDiv, HAdd.hAdd, List.cons, List.nil, List.range, List.replicate, id, congrFun' and 30 more
32 instances, coercions and auxiliary constants left out.

Tactic trace: 13 steps
Open to load the checked before-and-after goal states.
lemma OeisA300997.a_4 line 106 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA300997.a, OfNat.ofNat
Proof uses: Eq.mpr, InfSet.sInf, Set.ofPred, List, List.foldl, List.reverse, List.dropWhile, Decidable.decide, List.zipWith, Nat.add, HAppend.hAppend, List.map, HDiv.hDiv, HAdd.hAdd, List.cons, List.nil, List.range, List.replicate, id, congrFun' and 30 more
32 instances, coercions and auxiliary constants left out.

Tactic trace: 20 steps
Open to load the checked before-and-after goal states.
lemma OeisA300997.a_5 line 123 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA300997.a, OfNat.ofNat
Proof uses: Set, Membership.mem, LT.lt, Not, InfSet.sInf, le_antisymm, Nat.sInf_le, Decidable.byContradiction, LE.le, Eq.mp, Nat.sInf_mem, Exists.intro, id, Eq.mpr, HDiv.hDiv, HAdd.hAdd, List, List.reverse, List.dropWhile, Decidable.decide and 30 more
27 instances, coercions and auxiliary constants left out.

Tactic trace: 17 steps
Open to load the checked before-and-after goal states.
theorem OeisA300997.a_succ_eq sorry line 148 source
depends on sorry what this means
Statement uses: Nat, LE.le, OfNat.ofNat, Or, Eq, OeisA300997.a, HAdd.hAdd
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
8 instances, coercions and auxiliary constants left out.

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