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Proof step 5 from proof key-index-in-keyset-array-extract (previous step)

ar[m] = elemindex(a, m0), n ≤ # kar, ∀ m. m < n → kar[m].idx < # ar ∧ ar[kar[m].idx].idx = m, ∃ m0. m0 < n ∧ key-index(key, m) = kar[m0] ⊦ # keyset(kar, n) = 0, kar[m0] = key-index(key, m), keyset(kar, n) = ∅

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
ar[m] = elemindex(a, m0), key-index(key, m) = kar[m1], m1 < n, m1 < # kar, n ≤ # kar, ∀ m. m < n → kar[m].idx < # ar ∧ ar[kar[m].idx].idx = m ⊦ # keyset(kar, n) = 0, kar[m0] = key-index(key, m), keyset(kar, n) = ∅

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic