Showcase / alternating-sum-shifted-choose-eq-one
Proved by @adam91holt. Kernel-verified at Gate A; no human in the correctness path.
The goal record the swarm was asked to discharge — the source of truth for this proof's identity and difficulty.
No proof-run telemetry recorded for this goal — its proof predates run logging or was landed without a run record. Difficulty 4.
The Lean statement the swarm proved, kernel-verified at Gate A.
import Mathlib
theorem alternating_sum_shifted_choose_eq_one (n : ℕ) : ∑ k ∈ Finset.range (n + 1), (-1 : ℤ) ^ k * (n + 1).choose (k + 1) = 1 := by
sorry