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Proof step 47 from proof in-playload-data (previous step)

zbrar[n] = mkzentry(key0, adr1), zbrar[m] = mkzentry(key, adr0), m < # zbrar, n + m0 < # zbrar, n < # zbrar, sorted(zbrar, 0, n + m0 + 1), m ≤ n + m0, n ≤ m, (n + 1) + m0 ≤ # zbrar, ∀ 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)), ∃ n0. n0 < m0 ∧ zbrar[(n + 1) + n0].entry? ∧ zbrar[(n + 1) + n0].key = key0 ⊦ adr0 ∈ payload(zbrar, n + 1, m0)[key0, adr1]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 48:
zbrar[n] = mkzentry(zbrar[(n + 1) + n0].key, adr1), zbrar[m] = mkzentry(key, adr0), zbrar[(n + 1) + n0].entry?, n0 < m0, m < # zbrar, n + m0 < # zbrar, n < # zbrar, sorted(zbrar, 0, n + m0 + 1), m ≤ n + m0, n ≤ m, ∀ 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)) ⊦ adr0 ∈ payload(zbrar, n + 1, m0)[zbrar[(n + 1) + n0].key, adr1]

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + 1 ≤ n ↔ m < n; (s)