28859.lean`

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

7 declarations, 1 contain sorry, 0 declared as axioms

Combinatorial representation of the recurrence $a(n+2) = 2a(n+1) + 2a(n)$

A028859 (OEIS): $a(n+2) = 2 \cdot a(n+1) + 2 \cdot a(n)$; $a(0) = 1$, $a(1) = 3$.

References:

A028859
arxiv/2605.22763 Advancing Mathematics Research with AI-Driven Formal Proof Search by George Tsoukalas et al.

Imports (1)

FormalConjecturesUtil

def OeisA28859.a A028859 (OEIS): $a(n+2) = 2 \cdot a(n+1) + 2 \cdot a(n)$; $a(0) = 1$, $a(1) = 3$ line 38 source
Source documentation
A028859 (OEIS): $a(n+2) = 2 \cdot a(n+1) + 2 \cdot a(n)$; $a(0) = 1$, $a(1) = 3$.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat
Proof uses: WellFounded.Nat.fix, InvImage, LT.lt, OeisA28859.a.match_1, Unit, OfNat.ofNat, Nat.succ, HAdd.hAdd, HMul.hMul
8 instances, coercions and auxiliary constants left out.
```
def a (n : ℕ) : ℕ :=
…
```
lemma OeisA28859.a_0 line 49 source
extra axioms: _private.0.OeisA28859.a_0._native.native_decide.ax_1 what this means
Statement uses: Eq, Nat, OeisA28859.a, OfNat.ofNat
Proof uses: of_decide_eq_true
4 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
lemma OeisA28859.a_1 line 52 source
extra axioms: _private.0.OeisA28859.a_1._native.native_decide.ax_1 what this means
Statement uses: Eq, Nat, OeisA28859.a, OfNat.ofNat
Proof uses: of_decide_eq_true
4 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
lemma OeisA28859.a_2 line 55 source
extra axioms: _private.0.OeisA28859.a_2._native.native_decide.ax_1 what this means
Statement uses: Eq, Nat, OeisA28859.a, OfNat.ofNat
Proof uses: of_decide_eq_true
4 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
lemma OeisA28859.a_3 line 58 source
extra axioms: _private.0.OeisA28859.a_3._native.native_decide.ax_1 what this means
Statement uses: Eq, Nat, OeisA28859.a, OfNat.ofNat
Proof uses: of_decide_eq_true
4 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
lemma OeisA28859.a_4 line 61 source
extra axioms: _private.0.OeisA28859.a_4._native.native_decide.ax_1 what this means
Statement uses: Eq, Nat, OeisA28859.a, OfNat.ofNat
Proof uses: of_decide_eq_true
4 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem OeisA28859.exists_finset_sequence sorry line 73 source
depends on sorry what this means
Statement uses: Nat, HAdd.hAdd, OfNat.ofNat, Fin, Set, Set.ofPred, And, GT.gt, Finset.sup, Finset.univ, LE.le, Exists, Eq, LT.lt, Ne, GE.ge, Finset, Finset.card, OeisA28859.a
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
26 instances, coercions and auxiliary constants left out.

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