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Proof step 2 from proof valid-idx-update-key (previous step)

kar[m] = key-index(key0, m0), valid-idx(kar, ar, n) ⊦ valid-idx(kar[m, key-index(key, m0)], ar, n)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
kar[m] = key-index(key0, m0), n ≤ # kar, ∀ m. m < n → kar[m].idx < # ar ∧ ar[kar[m].idx].idx = m ⊦ valid-idx(kar[m, key-index(key, m0)], ar, n)

Rule argument

Additional information

Used simplifier rules: valid-idx: ⊦ valid-idx(kar, ar, n) ↔ n ≤ # kar ∧ (∀ m. m < n → kar[m].idx < # ar ∧ ar[kar[m].idx].idx = m);