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Proof step 55 from proof in-playload-data (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 56:
zbrar[m] = mkzentry(key, adr0), n < # zbrar, n + m0 < # zbrar, m < # zbrar, sorted(zbrar, 0, n + m0 + 1), n ≤ m, m ≤ n + m0 ⊦ zbrar[n].entry?, adr0 ∈ payload(zbrar, n + 1, m0), ∃ m1. n < m1 ∧ ¬ n + m0 < m1 ∧ zbrar[m1].entry? ∧ zbrar[m1].adr = adr0

Rule argument

Additional information

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