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Proof step 6 from proof payload-shift-left (previous step)

zbrar[n] = mkzentry(key, adr), n < # zbrar, nused < # zbrar, sorted(zbrar, 0, nused + 1), n ≤ nused ⊦ payload(shl(zbrar, n, nused + 1), 0, nused) = payload(zbrar, 0, nused + 1) -- key

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ ri = ri0 ↔ (∀ key. (key ∈ ri ↔ key ∈ ri0) ∧ (key ∈ ri → ri[key] = ri0[key]))
Proof step 8:
zbrar[n] = mkzentry(key, adr), nused < # zbrar, n < # zbrar, sorted(zbrar, 0, nused + 1), n ≤ nused ⊦ ∀ key0. (key0 ∈ payload(shl(zbrar, n, nused + 1), 0, nused) ↔ key0 ∈ payload(zbrar, 0, nused + 1) -- key) ∧ ( key0 ∈ payload(shl(zbrar, n, nused + 1), 0, nused) → payload(shl(zbrar, n, nused + 1), 0, nused)[key0] = (payload(zbrar, 0, nused + 1) -- key)[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] → [payload(zbrar, 0, nused + 1) -- key, payload(shl(zbrar, n, nused + 1), 0, nused)] flags: <all paths>

Additional information

Used terms: payload(zbrar, 0, nused + 1) -- key, payload(shl(zbrar, n, nused + 1), 0, nused)