Singmaster.lean`

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

2 declarations, 1 contain sorry, 0 declared as axioms

Singmaster's conjecture

Singmaster's conjecture says that for any integer $t>1$, the number of solutions to the equation:

$\binom{n}{k} = t,\quad 1 \le k < n,$

with $\binom{n}{k}$ being the numbers that appear in Pascal's triangle, is bounded by a global constant $O(1)$.

Reference: Wikipedia

Imports (1)

FormalConjecturesUtil

def Singmaster.solutions The set of pairs (n, k) representing the solutions to the equation Nat.choose n k = t for a given t, under the constraint 1 ≤ k < n line 41 source
Source documentation
The set of pairs (n, k) representing the solutions to the equation Nat.choose n k = t for a given t, under the constraint 1 ≤ k < n.

no axioms what this means
Statement uses: Nat, Set, Prod
Proof uses: Set.ofPred, Singmaster.solutions.match_1, And, LE.le, OfNat.ofNat, LT.lt, Eq, Nat.choose
3 instances, coercions and auxiliary constants left out.
```
def solutions (t : ℕ) : Set (ℕ × ℕ) :=
…
```
theorem Singmaster.singmaster Singmaster's conjecture: the number of times any number $t > 1$ appears in Pascal's triangle is bounded sorry line 49 source
Source documentation
Singmaster's conjecture: the number of times any number $t > 1$ appears in Pascal's triangle is bounded.

depends on sorry what this means
Statement uses: Exists, Nat, GT.gt, OfNat.ofNat, And, Set.Finite, Prod, Singmaster.solutions, LE.le, Set.ncard
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
6 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem singmaster: ∃ (C : ℕ), ∀ (t : ℕ), t > 1 →
    (Singmaster.solutions t).Finite ∧ (Singmaster.solutions t).ncard ≤ C := by
…
```
Mentions: Singmaster.solutions