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Proof step 22 from proof payload-mod (previous step)

payload(zbrar[(m + 1) + n0, mkzentry(zbrar[(m + 1) + n0].key, adr)], m + 1, nused0) = payload(zbrar, m + 1, nused0)[zbrar[(m + 1) + n0].key, adr], zbrar[m].entry?, n0 < nused0, m + nused0 < # zbrar, m < # zbrar, sorted(zbrar, m, nused0 + 1) ⊦ payload(zbrar, m + 1, nused0)[zbrar[(m + 1) + n0].key, adr][zbrar[m].key, zbrar[m].adr] = payload(zbrar, m + 1, nused0)[zbrar[m].key, zbrar[m].adr][zbrar[m + n0 + 1].key, adr]

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 23:
zbrar[m] = mkzentry(key, adr0), payload(zbrar[(m + 1) + n0, mkzentry(zbrar[(m + 1) + n0].key, adr)], m + 1, nused0) = payload(zbrar, m + 1, nused0)[zbrar[(m + 1) + n0].key, adr], zbrar[m].entry?, m < # zbrar, m + nused0 < # zbrar, n0 < nused0, sorted(zbrar, m, nused0 + 1) ⊦ payload(zbrar, m + 1, nused0)[zbrar[(m + 1) + n0].key, adr][key, adr0] = payload(zbrar, m + 1, nused0)[key, adr0][zbrar[m + n0 + 1].key, adr]

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[m], key, adr0]

Additional information

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