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Proof step 16 from proof keys-mod (previous step)

n0 < nused0, m + nused0 < # zbrar, m < # zbrar, sorted(zbrar, m, nused0 + 1), ∀ n, zbrar, m, adr. n < nused0 ∧ sorted(zbrar, m, nused0) ∧ m + nused0 ≤ # zbrar → keys(zbrar[m + n, mkzentry(zbrar[m + n].key, adr)], m, nused0) = keys(zbrar, m, nused0) ++ zbrar[m + n].key ⊦ keys(zbrar[m + n0 + 1, mkzentry(zbrar[m + n0 + 1].key, adr)], m + 1, nused0) ++ zbrar[m].key = keys(zbrar, m + 1, nused0) ++ zbrar[m].key ++ zbrar[m + n0 + 1].key

User applied rule all left

And closed the goal!

Rule argument

pos: left 5 terms: n0, zbrar, m + 1, adr abort: F discard: T computed: F

Additional information

Used simplifier rules: a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ sorted(zbrar, n, m + 1) → (sorted(zbrar, n + 1, m) ↔ true); (ss)% ⊦ m + 1 ≤ n ↔ m < n; (s)% ⊦ ks ++ key ++ key0 = ks ++ key0 ++ key ↔ true; (s) Used terms: n0, zbrar, m + 1, adr