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Proof step 9 from proof in-keys (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
m < # zbrar, m + nused0 < # zbrar ⊦ key = zbrar[m].key ↔ (∃ n. ¬ nused0 < n ∧ zbrar[m + n].key = key), key ∈ keys(zbrar, m + 1, nused0), ∃ n. n < nused0 ∧ zbrar[(m + 1) + n].key = key

Proof step 9 from proof in-keys (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information