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Proof step 11 from proof in-keys (previous step)

key = zbrar[m].key, m + nused0 < # zbrar, m < # zbrar ⊦ key ∈ keys(zbrar, m + 1, nused0), ∃ n. n < nused0 ∧ zbrar[(m + 1) + n].key = key, ∃ n. ¬ nused0 < n ∧ zbrar[m + n].key = key

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
m < # zbrar, m + nused0 < # zbrar ⊦ zbrar[m].key ∈ keys(zbrar, m + 1, nused0), ∃ n. ¬ nused0 < n ∧ zbrar[m + n].key = zbrar[m].key, ∃ n. n < nused0 ∧ zbrar[(m + 1) + n].key = zbrar[m].key

Proof step 11 from proof in-keys (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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