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Proof step 7 from proof save-same-payload-same (previous step)

# zbrar1 = BRANCH_SIZE, # zbrar0 = BRANCH_SIZE, save(zbrar0, n, m0)[n + m0, save(zbrar0[n + m0])] = save(zbrar1, n, m0 + 1), n + m0 < BRANCH_SIZE, ∀ zbrar1, zbrar0, n. # zbrar1 = BRANCH_SIZE ∧ # zbrar0 = BRANCH_SIZE ∧ save(zbrar0, n, m0) = save(zbrar1, n, m0) ∧ n + m0 ≤ BRANCH_SIZE → payload(zbrar0, n, m0) = payload(zbrar1, n, m0) ⊦ payload(zbrar0, n, m0 + 1) = payload(zbrar1, n, m0 + 1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ save(zbrar, m, nused + 1) = save(zbrar, m, nused)[m + nused, save(zbrar[m + nused])]
Proof step 9:
# 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])], n + m0 < BRANCH_SIZE, ∀ zbrar1, zbrar0, n. # zbrar1 = BRANCH_SIZE ∧ # zbrar0 = BRANCH_SIZE ∧ save(zbrar0, n, m0) = save(zbrar1, n, m0) ∧ n + m0 ≤ BRANCH_SIZE → payload(zbrar0, n, m0) = payload(zbrar1, n, m0) ⊦ payload(zbrar0, n, m0 + 1) = payload(zbrar1, n, m0 + 1)

Rule argument

spec: znode-ops name: save-branches-last seq: ⊦ save(zbrar, m, nused + 1) = save(zbrar, m, nused)[m + nused, save(zbrar[m + nused])] subst: [nused, m, zbrar] → [m0, n, zbrar1] flags: <all paths>

Additional information

Used terms: m0, n, zbrar1