476.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 476

References:

erdosproblems.com/476
[Er65b] Erdős, Paul, Some recent advances and current problems in number theory. Lectures on Modern Mathematics, Vol. III (1965), 196-244.
[ErGr80] Erdős, P. and Graham, R., Old and new problems and results in combinatorial number theory. Monographies de L'Enseignement Mathematique (1980).
[Gu04] Guy, Richard K., Unsolved problems in number theory. (2004), xviii+437.
[dSHa94] Dias da Silva, J. A. and Hamidoune, Y. O., Cyclic spaces for Grassmann derivatives and additive theory. Bull. London Math. Soc. (1994), 140-146.

Imports (1)

FormalConjecturesUtil

theorem Erdos476.erdos_476 Let $A\subseteq \mathbb{F}_p$ sorry line 51 source
Source documentation
Let $A\subseteq \mathbb{F}_p$. Let $$ A\hat{+}A = \{ a+b : a\neq b \in A\}. $$ Is it true that $$ \lvert A\hat{+}A\rvert \geq \min(2\lvert A\rvert-3,p)? $$
This is the Erdős-Heilbronn inequality, proved by Dias da Silva and Hamidoune.

depends on sorry what this means
Statement uses: Iff, True, Nat, Fact, Nat.Prime, Finset, ZMod, GE.ge, Finset.card, Finset.restrictedSumset, Min.min, HSub.hSub, HMul.hMul, OfNat.ofNat
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
26 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_476 : answer(True) ↔
    ∀ p : ℕ, Fact p.Prime → ∀ A : Finset (ZMod p),
      A.restrictedSumset.card ≥ min (2 * A.card - 3) p := by
…
```