conjecture_1_3_to_2_3.lean`

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

1 declarations, 1 contain sorry, 0 declared as axioms

The $\frac 1 3$–$\frac 2 3$ conjecture

Reference: Wikipedia

Imports (1)

FormalConjecturesUtil

theorem Conjecture_1_3_to_2_3.conjecture_1_3_to_2_3 Does every finite partially ordered set that is not totally ordered contain two elements sorry line 39 source
Source documentation
Does every finite partially ordered set that is not totally ordered contain two elements $x$ and $y$ such that the probability that $x$ appears before $y$ in a random linear extension is between $\frac 1 3$ and $\frac 2 3$?
The set of all total order extensions is represented as order preserving bijections $P$ of $1, ..., n$.

depends on sorry what this means
Statement uses: Iff, True, Finite, PartialOrder, Not, Std.Total, LE.le, Set, OrderHom, Nat, Membership.mem, Eq, Set.range, Set.Icc, OfNat.ofNat, Nat.card, Exists, Rat, HDiv.hDiv, Set.ncard and 3 more
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
28 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem conjecture_1_3_to_2_3 : answer(sorry) ↔ ∀ (P : Type) [Finite P] [PartialOrder P]
    (not_total : ¬ Std.Total (α := P) (· ≤ ·)) (total_ext : Set <| OrderHom P ℕ)
…
```