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Proof step 22 from proof key-set-write-nodups (previous step)

kar[m] = key-index(key, m2), kar[m1] = key-index(key0, m3), n < m0, m0 < # kar, n < # kar, n + 1 < # kar, (m < # kar ∧ m < m0 ∧ m1 < # kar ∧ m1 < m0 ∧ m ≠ m1 → m2 ≠ m3) → keyset(kar[n, ki], m0) = (keyset(kar, m0) -- kar[n]) ++ ki, ∀ m, m1. m < # kar ∧ ¬ m0 < m ∧ m1 < # kar ∧ ¬ m0 < m1 ∧ m ≠ m1 → kar[m].idx ≠ kar[m1].idx ⊦ keyset(kar[n, ki], m0) ++ kar[m0] = ((keyset(kar, m0) ++ kar[m0]) -- kar[n]) ++ ki, m0 = n

User applied rule case distinction

And obtained the following new goals

Rule argument

pos: left 7

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