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Proof step 29 from proof in-playload-data (previous step)

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

User applied rule exists right

And closed the goal!

Rule argument

pos: right 2 terms: n abort: F discard: T computed: T

Additional information

Used simplifier rules: ⊦ m ≤ m; (s)% ⊦ ¬ m + n < m; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ mkzentry(key, adr).entry?; (s)% ⊦ mkzentry(key, adr).adr = adr; (s) Used terms: n