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Proof step 13 from proof in-playload-data (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
zbrar[n] = mkzentry(key, adr0), n < # zbrar, n + m0 < # zbrar, sorted(zbrar, 0, n + m0 + 1), adr ∈ payload(zbrar, n + 1, m0)[key, adr0], ∀ zbrar, n, adr. sorted(zbrar, 0, n + m0) ∧ n + m0 ≤ # zbrar → (adr ∈ payload(zbrar, n, m0) ↔ (∃ m1. n ≤ m1 ∧ m1 < n + m0 ∧ zbrar[m1].entry? ∧ zbrar[m1].adr = adr)) ⊦ ∃ m. n ≤ m ∧ ¬ n + m0 < m ∧ zbrar[m].entry? ∧ zbrar[m].adr = adr

Rule argument

Additional information

Used simplifier rules: ⊦ mkzentry(key, adr).entry?; (s)