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Proof step 3 from proof unmodified-key-range-node (previous step)

# zbrar = BRANCH_SIZE, iast[adr] = indexnode(brar, bv1, nused + 1), indexnode(brar, bv1, nused + 1) = save(mkznode(rp, zbrar, bv1, false, nused + 1)), nused < BRANCH_SIZE, n < BRANCH_SIZE, adr ∈ iast, n ≤ nused ⊦ key-range(load(brar, 0, nused + 1), n, nused + 1, ri) = key-range(zbrar, n, nused + 1, ri)

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:
# zbrar = BRANCH_SIZE, iast[adr] = indexnode(brar, bv1, nused + 1), indexnode(brar, bv1, nused + 1) = save(mkznode(rp, zbrar, bv1, false, nused + 1)), n < BRANCH_SIZE, nused < BRANCH_SIZE, adr ∈ iast, n ≤ nused ⊦ ∀ key. (key ∈ key-range(load(brar, 0, nused + 1), n, nused + 1, ri) ↔ key ∈ key-range(zbrar, n, nused + 1, ri)) ∧ ( key ∈ key-range(load(brar, 0, nused + 1), n, nused + 1, ri) → key-range(load(brar, 0, nused + 1), n, nused + 1, ri)[key] = key-range(zbrar, n, nused + 1, ri)[key])

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 + 1, ri), key-range(load(brar, 0, nused + 1), n, nused + 1, ri)] flags: <all paths>

Additional information

Used terms: key-range(zbrar, n, nused + 1, ri), key-range(load(brar, 0, nused + 1), n, nused + 1, ri)