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Proof step 18 from proof at-payload (previous step)

zbrar[m + n1 + 1] = mkzentry(key, payload(zbrar, m + 1, nused0)[key]), zbrar[m].entry?, m + nused0 < # zbrar, m < # zbrar, n1 < nused0, ∀ n. ¬ n1 < n ∧ zbrar[m + n].entry? → zbrar[m + n].key ≠ key ⊦ payload(zbrar, m + 1, nused0)[zbrar[m].key, zbrar[m].adr][key] = payload(zbrar, m + 1, nused0)[key]

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 19:
zbrar[m + n1 + 1] = mkzentry(key, payload(zbrar, m + 1, nused0)[key]), zbrar[m] = mkzentry(key0, adr), zbrar[m].entry?, n1 < nused0, m < # zbrar, m + nused0 < # zbrar, ∀ n. ¬ n1 < n ∧ zbrar[m + n].entry? → zbrar[m + n].key ≠ key ⊦ payload(zbrar, m + 1, nused0)[key0, adr][key] = payload(zbrar, m + 1, nused0)[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[m], key0, adr]

Additional information

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