844.lean`

Explanation legend Lean4 Domain Explanation Language (L4DEL)

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L4DEL: Lean4 Domain Explanation Language

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Credit: The upstream authors and contributors retain credit for the project and mathematics. lean4-explainer only renders their pinned source and adds the separately disclosed explanation layer.

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

2 declarations, 1 contain sorry, 0 declared as axioms

Erdős Problem 844

References:

erdosproblems.com/844
[AMS25] Alexeev, B., Mixon, D. and Sawin, W., The independence and clique cover numbers of the squarefree graph. arXiv:2507.01928 (2025).
[Ch74] Chvátal, V., Intersecting families of edges in hypergraphs having the hereditary property. (1974), 61-66.

Imports (1)

FormalConjecturesUtil

def Erdos844.evenOrOddNonSquarefree Those $n \in \{1,\ldots,N\}$ which are even or not squarefree, that is, the set of even numbers together with the odd non-squarefree numbers line 37 source
Source documentation
Those $n \in \{1,\ldots,N\}$ which are even or not squarefree, that is, the set of even numbers together with the odd non-squarefree numbers.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat, Finset
Proof uses: Finset.filter, Or, Dvd.dvd, OfNat.ofNat, Not, Squarefree, Finset.Icc
9 instances, coercions and auxiliary constants left out.
```
def evenOrOddNonSquarefree (N : ℕ) : Finset ℕ :=
…
```
theorem Erdos844.erdos_844 sorry line 61 source
depends on sorry what this means
Statement uses: Iff, True, Nat, IsGreatest, Set.ofPred, Exists, Finset, And, LE.le, Finset.Icc, OfNat.ofNat, Membership.mem, Not, Squarefree, HMul.hMul, Eq, Finset.card, Erdos844.evenOrOddNonSquarefree
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
24 instances, coercions and auxiliary constants left out.

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