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Proof step 6 from proof range-put (previous step)

n < nused, n < # zbrar, nused ≤ # zbrar, n ≠ 0 → zbrar[n - 1].key < key ⊦ zbrar[n].key < key, (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]) → ri[key, adr][key0] = key-range(zbrar, n, nused, ri)[key, adr][key0])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ key ∈ ri[key0, adr] ↔ key = key0 ∨ key ∈ ri
Proof step 8:
n < # zbrar, n < nused, nused ≤ # zbrar, n ≠ 0 → zbrar[n - 1].key < key ⊦ zbrar[n].key < key, (key0 ∈ key-range(zbrar, n, nused, ri[key, adr]) ↔ key0 = key ∨ key0 ∈ key-range(zbrar, n, nused, ri)) ∧ (key0 ∈ key-range(zbrar, n, nused, ri[key, adr]) → ri[key, adr][key0] = key-range(zbrar, n, nused, ri)[key, adr][key0])

Rule argument

spec: store, inst: node-index name: In-insert seq: ⊦ key ∈ ri[key0, adr] ↔ key = key0 ∨ key ∈ ri subst: [adr, key0, ri, key] → [adr, key, key-range(zbrar, n, nused, ri), key0] flags: <all paths>

Additional information

Used terms: adr, key, key-range(zbrar, n, nused, ri), key0