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Proof step 13 from proof in-keys (previous step)

m + nused0 < # zbrar, m < # zbrar, ∃ n. ¬ nused0 < n ∧ zbrar[m + n].key = key ⊦ key = zbrar[m].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 14:
m < # zbrar, m + nused0 < # zbrar, n ≤ nused0 ⊦ zbrar[m + n].key = zbrar[m].key, zbrar[m + n].key ∈ keys(zbrar, m + 1, nused0), ∃ n0. n0 < nused0 ∧ zbrar[(m + 1) + n0].key = zbrar[m + n].key

Rule argument

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)