532.lean`

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

1 declarations, 1 contain sorry, 0 declared as axioms

Erdős Problem 532

References:

erdosproblems.com/532
[Er73] Erdős, P., Problems and results on combinatorial number theory. A survey of combinatorial theory (1973), 117-138.
[Er75b] Erdős, Paul, Problems and results in combinatorial number theory. Journées Arithmétiques de Bordeaux (1975), 295-310.
[Er77c] Erdős, Paul, Problems and results on combinatorial number theory. III. Number theory day (1977), 43-72.
[Hi74] Hindman, Neil, Finite sums from sequences within cells of a partition of $\mathbb{N}$. J. Combinatorial Theory Ser. A (1974), 1-11.

Imports (1)

FormalConjecturesUtil

theorem Erdos532.erdos_532 Documented declaration: erdos_532 sorry line 43 source
Source documentation
If $\mathbb{N}$ is 2-coloured then is there some infinite set $A\subseteq \mathbb{N}$ such that all finite subset sums$$ \sum_{n\in S}n$$(as $S$ ranges over all non-empty finite subsets of $A$) are monochromatic?
Asked by Graham and Rothschild. Proved by Hindman [Hi74] (for any number of colours).

depends on sorry what this means
Statement uses: Iff, True, Nat, Fin, OfNat.ofNat, Exists, Set, And, Set.Infinite, Finset, Finset.Nonempty, LE.le, Eq, Finset.sum
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
10 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_532 :
    answer(True) ↔ ∀ (c : ℕ → Fin 2),
      ∃ A : Set ℕ, A.Infinite ∧
        ∃ color : Fin 2,
          ∀ S : Finset ℕ, S.Nonempty → ↑S ⊆ A →
            c (∑ n ∈ S, n) = color := by
…
```
Mentions: c