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Theorem next-permutation

⊦ nextperm(ar1, ar2) ↔ perm(ar1, ar2) ∧ ar1 ≠ ar2 ∧ ar1 ≤ ar2 ∧ (∀ ar3. perm(ar1, ar3) ∧ ar3 ≠ ar1 ∧ ar3 ≠ ar2 → ¬(ar1 ≤ ar3 ∧ ar3 ≤ ar2))