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Proof step 3 from proof unmodified-payload (previous step)

BRANCH_SIZE = # zbrar, iast[adr] = indexnode(brar, bv1, nused), indexnode(brar, bv1, nused) = save(mkznode(rp, zbrar, bv1, false, nused)), sorted(zbrar, 0, nused), adr ∈ iast, nused ≤ BRANCH_SIZE ⊦ payload(load(brar, 0, nused), 0, nused) = payload(zbrar, 0, nused)

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:
BRANCH_SIZE = # zbrar, iast[adr] = indexnode(brar, bv1, nused), indexnode(brar, bv1, nused) = save(mkznode(rp, zbrar, bv1, false, nused)), sorted(zbrar, 0, nused), adr ∈ iast, nused ≤ BRANCH_SIZE ⊦ ∀ key. (key ∈ payload(load(brar, 0, nused), 0, nused) ↔ key ∈ payload(zbrar, 0, nused)) ∧ (key ∈ payload(load(brar, 0, nused), 0, nused) → payload(load(brar, 0, nused), 0, nused)[key] = payload(zbrar, 0, nused)[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] → [payload(zbrar, 0, nused), payload(load(brar, 0, nused), 0, nused)] flags: <all paths>

Additional information

Used terms: payload(zbrar, 0, nused), payload(load(brar, 0, nused), 0, nused)