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Proof step 14 from proof payload-shift-left (previous step)

zbrar[n] = mkzentry(key, adr), zbrar[n0].entry?, n < # zbrar, nused < # zbrar, n0 < # zbrar, sorted(zbrar, 0, nused + 1), zbrar[n0].key ∈ payload(shl(zbrar, n, nused + 1), 0, nused), n ≤ nused, n0 ≤ nused ⊦ zbrar[n0].key = key, payload(shl(zbrar, n, nused + 1), 0, nused)[zbrar[n0].key] = payload(zbrar, 0, nused + 1)[zbrar[n0].key]

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 15:
zbrar[n] = mkzentry(key, adr), zbrar[n0] = mkzentry(key0, adr0), zbrar[n0].entry?, n0 < # zbrar, nused < # zbrar, n < # zbrar, sorted(zbrar, 0, nused + 1), key0 ∈ payload(shl(zbrar, n, nused + 1), 0, nused), n0 ≤ nused, n ≤ nused ⊦ payload(shl(zbrar, n, nused + 1), 0, nused)[key0] = payload(zbrar, 0, nused + 1)[key0], key0 = 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[n0], key0, adr0]

Additional information

Used simplifier rules: ⊦ zbr.entry? → (key = zbr.key ∧ adr = zbr.adr ↔ zbr = mkzentry(key, adr)); (elim) Used terms: zbrar[n0], key0, adr0