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Proof step 3 from proof range-put (previous step)

n < nused, n < # zbrar, nused ≤ # zbrar, n ≠ 0 → zbrar[n - 1].key < key ⊦ key-range(zbrar, n, nused, ri[key, adr]) = key-range(zbrar, n, nused, ri)[key, adr], zbrar[n].key < key

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ ri = ri0 ↔ (∀ key. (key ∈ ri ↔ key ∈ ri0) ∧ (key ∈ ri → ri[key] = ri0[key]))
Proof step 5:
n < # zbrar, n < nused, nused ≤ # zbrar, n ≠ 0 → zbrar[n - 1].key < key ⊦ zbrar[n].key < key, ∀ key0. (key0 ∈ key-range(zbrar, n, nused, ri[key, adr]) ↔ key0 ∈ key-range(zbrar, n, nused, ri)[key, adr]) ∧ ( key0 ∈ key-range(zbrar, n, nused, ri[key, adr]) → key-range(zbrar, n, nused, ri[key, adr])[key0] = key-range(zbrar, n, nused, ri)[key, adr][key0])

Rule argument

spec: store, inst: node-index name: k-Extension seq: ⊦ ri = ri0 ↔ (∀ key. (key ∈ ri ↔ key ∈ ri0) ∧ (key ∈ ri → ri[key] = ri0[key])) subst: [ri0, ri] → [key-range(zbrar, n, nused, ri)[key, adr], key-range(zbrar, n, nused, ri[key, adr])] flags: <all paths>

Additional information

Used terms: key-range(zbrar, n, nused, ri)[key, adr], key-range(zbrar, n, nused, ri[key, adr])