green_12

Let $G$ be an abelian group of size $N$, and suppose that $A \subset G$ has density $\alpha$. Are there at least $\alpha^{15} N^{10}$ tuples $(x_1, \dots, x_5, y_1, \dots, y_5) \in G^{10}$ such that $x_i + y_j \in A$ whenever $j \in \{i, i+1, i+2\}$? Note: We interpret indices modulo 5.

theorem green_12 : answer(sorry) ↔
    ∀ {G : Type*} [AddCommGroup G] [Fintype G] [DecidableEq G],
    ∀ (A : Finset G),
    let N

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