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Proof step 1 from proof cyclic-floyd-def (previous step)

⊦ cyclic(r, H) ↔ (∃ m, r0. reachable-n(H, m, r, r0) ∧ (∃ n. n ≠ 0 ∧ (∀ n0. reachable-n(H, m + n0 * n, r, r0))))

Lemma cyclic-alt-def