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Erdős problem 476

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Let A⊆FpA\subseteq \mathbb{F}_p. Let A+^A={a+b:a≠b∈A}. A\hat{+}A = \{ a+b : a\neq b \in A\}. Is it true that ∣A+^A∣≥min⁡(2∣A∣−3,p)? \lvert A\hat{+}A\rvert \geq \min(2\lvert A\rvert-3,p)?

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FormalConjectures/ErdosProblems/

476.lean

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Let A⊆FpA\subseteq \mathbb{F}_p. Let A+^A={a+b:a≠b∈A}. A\hat{+}A = \{ a+b : a\neq b \in A\}. Is it true that ∣A+^A∣≥min⁡(2∣A∣−3,p)? \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.

FormalConjectures/ErdosProblems/476.leanErdos476.erdos_4761 lineExact file
True ↔ ∀ (p : ℕ), Fact (Nat.Prime p) → ∀ (A : Finset (ZMod p)), A.restrictedSumset.card ≥ min (2 * A.card - 3) p
SolvedProof has a holelean4external proof

The proof uses `sorry`: part of the argument is written but not proved. Lean accepts the file; it does not accept the theorem.