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Proof step 119 from proof payload-shift-left (previous step)

zbrar[n0 + 1] = mkzentry(key, adr), n0 < # zbrar, nused < # zbrar, n < # zbrar, n0 < nused, n0 + 1 < # zbrar, sorted(zbrar, 0, nused + 1), n ≤ nused ⊦ zbrar[n].entry?, n0 < n, ∃ n1. ¬ nused < n1 ∧ zbrar[n1].entry? ∧ zbrar[n1].key = key

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 120:
zbrar[n0 + 1] = mkzentry(key, adr), n0 + 1 < # zbrar, n0 < nused, n < # zbrar, nused < # zbrar, n0 < # zbrar, n < nused, n + 1 < # zbrar, sorted(zbrar, 0, nused + 1), n ≤ n0 ⊦ zbrar[n].entry?, ∃ n1. ¬ nused < n1 ∧ zbrar[n1].entry? ∧ zbrar[n1].key = key

Rule argument

Additional information

Used simplifier rules: ⊦ m +1 = m + 1; (s)%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic% ⊦ m < n → m ≤ n; (s)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ m < n ↔ ¬ n ≤ m; (ss)