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Theorem lexicographic

⊦ ar0 < ar1 ↔ (∃ n. n ≤ # ar0 ∧ n ≤ # ar1 ∧ subarray(ar0, 0, n) = subarray(ar1, 0, n) ∧ (# ar0 = n → # ar1 > n) ∧ (# ar0 ≠ n → # ar1 ≠ n ∧ ar0[n] < ar1[n]))