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Proof step 5 from proof payload-keys (previous step)

nused + n ≤ # zbrar, n + nused ≤ # zbrar, ∃ n0. n0 < nused ∧ zbrar[n + n0].entry? ∧ zbrar[n + n0].key = key ⊦ key ∈ keys(zbrar, n, nused)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
zbrar[n + n0].entry?, n0 < nused, nused + n ≤ # zbrar, n + nused ≤ # zbrar ⊦ zbrar[n + n0].key ∈ keys(zbrar, n, nused)

Rule argument

Additional information

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