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Proof step 16 from proof payload-copy-right-upper (previous step)

zbrar[n0].entry?, n0 + nused0 + 1 < # zbrar, n0 + 1 < # zbrar, n0 < # zbrar, ∀ n, zbrar. n + nused0 < # zbrar → payload(copy(zbrar, n, zbrar, n + 1, nused0), n + 1, nused0) = payload(zbrar, n, nused0) ⊦ payload(copy(zbrar, n0 + 1, zbrar, 2 + n0, nused0)[n0 + 1, zbrar[n0]], 2 + n0, nused0)[zbrar[n0].key, zbrar[n0].adr] = payload(zbrar, n0 + 1, nused0)[zbrar[n0].key, zbrar[n0].adr]

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 17:
zbrar[n0] = mkzentry(key, adr), zbrar[n0].entry?, n0 < # zbrar, n0 + 1 < # zbrar, n0 + nused0 + 1 < # zbrar, ∀ n, zbrar. n + nused0 < # zbrar → payload(copy(zbrar, n, zbrar, n + 1, nused0), n + 1, nused0) = payload(zbrar, n, nused0) ⊦ payload(copy(zbrar, n0 + 1, zbrar, 2 + n0, nused0)[n0 + 1, zbrar[n0]], 2 + n0, nused0)[key, adr] = payload(zbrar, n0 + 1, nused0)[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[n0], key, adr]

Additional information

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