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Proof step 10 from proof payload-drop-lower (previous step)

zbrar[m + n].entry?, m + n + nused0 < # zbrar, m + n < # zbrar, ∀ m, n, zbrar, zbr. m + n + nused0 ≤ # zbrar → n = 0 ∨ payload(zbrar[m, zbr], m + n, nused0) = payload(zbrar, m + n, nused0) ⊦ payload(zbrar[m, zbr], (m + n) + 1, nused0)[zbrar[m + n].key, zbrar[m + n].adr] = payload(zbrar, (m + n) + 1, nused0)[zbrar[m + n].key, zbrar[m + n].adr], n = 0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 11:
zbrar[m + n] = mkzentry(key, adr), zbrar[m + n].entry?, m + n < # zbrar, m + n + nused0 < # zbrar, ∀ m, n, zbrar, zbr. m + n + nused0 ≤ # zbrar → n = 0 ∨ payload(zbrar[m, zbr], m + n, nused0) = payload(zbrar, m + n, nused0) ⊦ payload(zbrar[m, zbr], (m + n) + 1, nused0)[key, adr] = payload(zbrar, (m + n) + 1, nused0)[key, adr], n = 0

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 + n], key, adr]

Additional information

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