172.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

1 declarations, 1 contain sorry, 0 declared as axioms

Erdős Problem 172

Reference: erdosproblems.com/172

Imports (1)

FormalConjecturesUtil

theorem Erdos172.erdos_172 Is it true that in any finite colouring of $\mathbb{N}$ there exist arbitrarily large finite $A$ such that all sums and products of distinct elements in $A$ are the same colour? sorry line 35 source
Source documentation
Is it true that in any finite colouring of $\mathbb{N}$ there exist arbitrarily large finite $A$ such that all sums and products of distinct elements in $A$ are the same colour?

depends on sorry what this means
Statement uses: Iff, True, Nat, Fin, Exists, Finset, And, GE.ge, Finset.card, Subtype, Membership.mem, Finset.Nonempty, Eq, Finset.sum, Finset.prod
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous, OfNat.ofNat
13 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_172 : answer(sorry) ↔
    ∀ (n : ℕ) (color : ℕ → Fin n) (m), ∃ (A : Finset ℕ), A.card ≥ m ∧ ∃ c, ∀ (S : Finset A),
    S.Nonempty → color (∑ x ∈ S, x) = c ∧ color (∏ x ∈ S, x) = c := by
…
```
Mentions: c