194806.lean`

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

8 declarations, 1 contain sorry, 0 declared as axioms

Size of smallest subset of $\{1, 2, \dots, n\}$ with distinct subset sums

Size of the smallest subset $S$ of $T = \{1,2,3,\dots,n\}$ such that $S \cdot S$ contains $T$, where $S \cdot S$ is the set of all products of elements of $S$.

References:

A194806
arxiv/2605.22763 Advancing Mathematics Research with AI-Driven Formal Proof Search by George Tsoukalas et al.

Imports (1)

FormalConjecturesUtil

def OeisA194806.setProd The set of all products of elements from a Finset S line 40 source
Source documentation
The set of all products of elements from a Finset S.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Finset, Nat
Proof uses: Finset.image, Prod, HMul.hMul, Prod.fst, Prod.snd, Finset.product
3 instances, coercions and auxiliary constants left out.
```
def setProd (S : Finset ℕ) : Finset ℕ :=
…
```
def OeisA194806.a Size of the smallest subset $S$ of $T = \{1,2,3,\dots,n\}$ such that $S \cdot S$ contains $T$, where $S \cdot S$ is the set of all products of elements of $S$ line 48 source
Source documentation
Size of the smallest subset $S$ of $T = \{1,2,3,\dots,n\}$ such that $S \cdot S$ contains $T$, where $S \cdot S$ is the set of all products of elements of $S$.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat
Proof uses: dite, Eq, OfNat.ofNat, Not, Finset, Finset.Icc, Finset.filter, LE.le, OeisA194806.setProd, Finset.powerset, Membership.mem, Finset.Nonempty, Finset.image, Finset.card, Finset.min'
14 instances, coercions and auxiliary constants left out.

Tactic trace: 14 steps
Open to load the checked before-and-after goal states.
```
def a (n : ℕ) : ℕ :=
…
```
lemma OeisA194806.a_1 line 91 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA194806.a, OfNat.ofNat
Proof uses: Eq.refl
2 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
lemma OeisA194806.a_2 line 94 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA194806.a, OfNat.ofNat
Proof uses: Eq.refl
2 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
lemma OeisA194806.a_3 line 97 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA194806.a, OfNat.ofNat
Proof uses: Eq.refl
2 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
lemma OeisA194806.a_4 line 100 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA194806.a, OfNat.ofNat
Proof uses: Eq.refl
2 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
lemma OeisA194806.a_5 line 103 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA194806.a, OfNat.ofNat
Proof uses: Eq.refl
2 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem OeisA194806.a_div_prime_counting_bounded sorry line 114 source
depends on sorry what this means
Statement uses: Exists, Real, Nat, LE.le, OfNat.ofNat, HDiv.hDiv, OeisA194806.a, Nat.primeCounting
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
16 instances, coercions and auxiliary constants left out.

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