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Proof step 13 from proof unmodified-clean-eq-keys-subseteq (previous step)

# zbrar0 = BRANCH_SIZE, BRANCH_SIZE = # zbrar1, iast1[adr] = indexnode(save(zbrar1, 0, nused), bv, nused), iast0[adr] = indexnode(save(zbrar1, 0, nused), bv, nused), save(zbrar0, 0, nused) = save(zbrar1, 0, nused), n < nused, n < BRANCH_SIZE, adr ∈ iast1, adr ∈ iast0, nused ≤ BRANCH_SIZE ⊦ zbrar1[n].key = zbrar0[n].key

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ brar = brar0 ↔ # brar = # brar0 ∧ (∀ n. n < # brar → brar[n] = brar0[n])
Proof step 15:
# save(zbrar1, 0, nused) = # save(zbrar0, 0, nused), # zbrar0 = BRANCH_SIZE, BRANCH_SIZE = # zbrar1, iast0[adr] = indexnode(save(zbrar1, 0, nused), bv, nused), iast1[adr] = indexnode(save(zbrar1, 0, nused), bv, nused), n < BRANCH_SIZE, n < nused, adr ∈ iast0, adr ∈ iast1, nused ≤ BRANCH_SIZE, ∀ n. n < # save(zbrar1, 0, nused) → save(zbrar1, 0, nused)[n] = save(zbrar0, 0, nused)[n] ⊦ zbrar1[n].key = zbrar0[n].key

Rule argument

spec: array, inst: branch-array name: Extension seq: ⊦ brar = brar0 ↔ # brar = # brar0 ∧ (∀ n. n < # brar → brar[n] = brar0[n]) subst: [brar0, brar] → [save(zbrar0, 0, nused), save(zbrar1, 0, nused)] flags: <all paths>

Additional information

Used terms: save(zbrar0, 0, nused), save(zbrar1, 0, nused)