1199.lean`

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

2 declarations, 2 contain sorry, 0 declared as axioms

Erdős Problem 1199

References:

erdosproblems.com/1199
[Hi79] Hindman, Neil, Partitions and sums of integers with repetition. J. Combin. Theory Ser. A (1979), 19--32.
[Ow74] J. Owings, E2494. Amer. Math. Monthly (1974), 902.

Imports (1)

FormalConjecturesUtil

theorem Erdos1199.erdos_1199 Is it true that in any 2-colouring of $\mathbb{N}$ there exists an infinite set $A$ such that all elements of $A+A$ are the same colour? sorry line 43 source
Source documentation
Is it true that in any 2-colouring of $\mathbb{N}$ there exists an infinite set $A$ such that all elements of $A+A$ are the same colour?
A conjecture of Owings [Ow74].

depends on sorry what this means
Statement uses: Iff, True, Nat, Fin, OfNat.ofNat, Exists, Set, And, Set.Infinite, Membership.mem, HAdd.hAdd, Eq
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_1199 :
    answer(sorry) ↔
    ∀ (color : ℕ → Fin 2), ∃ (A : Set ℕ),
    A.Infinite ∧ ∀ n ∈ (A+A), ∀ m ∈ (A+A), color n = color m := by
…
```
theorem Erdos1199.erdos_1199.variants.three sorry line 54 source
depends on sorry what this means
Statement uses: Exists, Nat, Fin, OfNat.ofNat, Set, Set.Infinite, And, Membership.mem, HAdd.hAdd, Ne
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.