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Proof step 25 from proof in-playload-data (previous step)

zbrar[n] = mkzentry(key, adr0), zbrar[m].entry?, m < # zbrar, n + m0 < # zbrar, n < # zbrar, n < m, n + 1 < # zbrar, sorted(zbrar, 0, n + m0 + 1), zbrar[m].adr ∈ payload(zbrar, n + 1, m0), m ≤ n + m0 ⊦ m0 = 0, key ∈ payload(zbrar, n + 1, m0), ∃ m1. n ≤ m1 ∧ ¬ n + m0 < m1 ∧ zbrar[m1].entry? ∧ zbrar[m1].adr = zbrar[m].adr

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 26:
zbrar[n] = mkzentry(key, adr0), zbrar[m] = mkzentry(key0, adr), zbrar[m].entry?, n + 1 < # zbrar, n < m, n < # zbrar, n + m0 < # zbrar, m < # zbrar, sorted(zbrar, 0, n + m0 + 1), adr ∈ payload(zbrar, n + 1, m0), m ≤ n + m0 ⊦ m0 = 0, key ∈ payload(zbrar, n + 1, m0), ∃ m1. n ≤ m1 ∧ ¬ n + m0 < m1 ∧ zbrar[m1].entry? ∧ zbrar[m1].adr = 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], 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