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Proof step 33 from proof save-same-payload-same (previous step)

# zbrar0 = BRANCH_SIZE, # zbrar1 = BRANCH_SIZE, save(zbrar0, n, m0)[n + m0, save(zbrar0[n + m0])] = save(zbrar1, n, m0)[n + m0, save(zbrar1[n + m0])], n0 < BRANCH_SIZE, n + m0 < BRANCH_SIZE ⊦ save(zbrar1, n, m0)[n0] = save(zbrar0, n, m0)[n0]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 34:
⊦ brar = brar0 ↔ # brar = # brar0 ∧ (∀ n. n < # brar → brar[n] = brar0[n])
Proof step 35:
# save(zbrar0, n, m0)[n + m0, save(zbrar0[n + m0])] = # save(zbrar1, n, m0)[n + m0, save(zbrar1[n + m0])], # zbrar1 = BRANCH_SIZE, # zbrar0 = BRANCH_SIZE, n + m0 < BRANCH_SIZE, n0 < BRANCH_SIZE, ∀ n0. n0 < # save(zbrar0, n, m0)[n + m0, save(zbrar0[n + m0])] → save(zbrar0, n, m0)[n + m0, save(zbrar0[n + m0])][n0] = save(zbrar1, n, m0)[n + m0, save(zbrar1[n + m0])][n0] ⊦ save(zbrar1, n, m0)[n0] = save(zbrar0, n, m0)[n0]

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(zbrar1, n, m0)[n + m0, save(zbrar1[n + m0])], save(zbrar0, n, m0)[n + m0, save(zbrar0[n + m0])]] flags: <all paths>

Additional information

Used terms: save(zbrar1, n, m0)[n + m0, save(zbrar1[n + m0])], save(zbrar0, n, m0)[n + m0, save(zbrar0[n + m0])]