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Proof step 54 from proof in-playload-data (previous step)

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, 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)) ⊦ zbrar[n].entry?, adr0 ∈ payload(zbrar, n + 1, m0)

User applied rule all left

And obtained the following new goals

Proof step 55:
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)

Rule argument

pos: left 8 terms: zbrar, n + 1, adr0 abort: F discard: T computed: T

Additional information

Used terms: zbrar, n + 1, adr0