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Theorem valid-idx-rec

⊦ n < # kar ∧ m < # ar ∧ valid-idx(kar, ar, n) ∧ no-dups-idx(kar[n, key-index(key, m)], n + 1) → (¬ valid-idx(kar[n, key-index(key, m)], ar[m, ar[m].idx:= n], n + 1) ↔ false)

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