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Theorem valid-idx-xhg

⊦ valid-idx(kar, ar, n) ∧ m0 < n ∧ m1 < n ∧ kar[m0] = key-index(key1, n1) ∧ kar[m1] = key-index(key0, n0) → valid-idx(kar[m0, key-index(key0, n0)][m1, key-index(key1, n1)], ar[n0, ar[n0].idx:= m0][n1, ar[n0, ar0[n0].idx:= m0][n1].idx:= m1], n)

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