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Proof step 52 from proof in-playload-data (previous step)

zbrar[m] = mkzentry(key, adr0), zbrar[n] = mkzentry(key0, adr1), n < # zbrar, n + m0 < # zbrar, m < # zbrar, sorted(zbrar, 0, n + m0 + 1), n ≤ m, m ≤ n + m0 ⊦ adr0 = adr1, key0 ∈ payload(zbrar, n + 1, m0), adr0 ∈ payload(zbrar, n + 1, m0), ∃ m1. n < m1 ∧ ¬ n + m0 < m1 ∧ zbrar[m1].entry? ∧ zbrar[m1].adr = adr0

User applied rule exists right

And closed the goal!

Rule argument

pos: right 4 terms: m abort: F discard: F computed: T

Additional information

Used simplifier rules: ⊦ m ≤ n → (n < m ↔ false); (s)% ⊦ mkzentry(key, adr).entry?; (s)% ⊦ mkzentry(key, adr).adr = adr; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m ≤ n → (n ≤ m ↔ m = n); (s)% ⊦ m ≤ m; (s)% ⊦ m ≤ m + n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ mkzentry(key, adr) = mkzentry(key0, adr0) ↔ key = key0 ∧ adr = adr0; (ws) Used terms: m