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Proof step 4 from proof payload-shift-left (previous step)

zbrar[n].entry?, nused < # zbrar, n < # zbrar, sorted(zbrar, 0, nused + 1), n ≤ nused ⊦ payload(shl(zbrar, n, nused + 1), 0, nused) = payload(zbrar, 0, nused + 1) -- zbrar[n].key

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 5:
zbrar[n] = mkzentry(key, adr), zbrar[n].entry?, n < # zbrar, nused < # zbrar, sorted(zbrar, 0, nused + 1), n ≤ nused ⊦ payload(shl(zbrar, n, nused + 1), 0, nused) = payload(zbrar, 0, nused + 1) -- key

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], key, adr]

Additional information

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