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Proof step 25 from proof ri-range-ext (previous step)

scan(key, zbrar, 1, m) = m + 1, scan(key, zbrar, 1, m) < # zbrar, zbrar[0].key < key, sorted(zbrar, 0, scan(key, zbrar, 1, m)), ∀ n. ¬ m < n → zbrar[n].key < key, ∀ n. n ≤ scan(key, zbrar, 1, m) → key-range(zbrar, n, 2 + m, ri0) = key-range(zbrar, n, 2 + m, ri1) ⊦ (key ∈ ri0 ↔ key ∈ ri1) ∧ (key ∈ ri0 → ri0[key] = ri1[key]), key ∈ ri1 ∧ zbrar[m].key < key, key ∈ ri0 ∧ zbrar[m].key < key

User applied rule all left

And closed the goal!

Rule argument

pos: left 5 terms: m abort: F discard: F computed: T

Additional information

Used simplifier rules: ⊦ ¬ n < n; (s) Used terms: m