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Proof step 6 from proof payload-keys (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 7:
zbrar[n + n0] = mkzentry(key, adr), zbrar[n + n0].entry?, n0 < nused, n + nused ≤ # zbrar, nused + n ≤ # zbrar ⊦ key ∈ keys(zbrar, n, nused)

Rule argument

spec: zbranch name: elim-03 seq: ⊦ zbr.entry? → (key = zbr.key ∧ adr = zbr.adr ↔ zbr = mkzentry(key, adr)) subst: [zbr, key, adr] → [zbrar[n + n0], key, adr]

Additional information

Used simplifier rules: ⊦ zbr.entry? → (key = zbr.key ∧ adr = zbr.adr ↔ zbr = mkzentry(key, adr)); (elim) Used terms: zbrar[n + n0], key, adr