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Proof step 160 from proof refine-write-buf (previous step)

# buf1 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, avol1[m4] = mapped(buf2 + subarray(buf1, 0, m2)), avol0[m4] = mapped(buf2), align↓(m2 + n3, EB_PAGE_SIZE) = n0 + m2, n1 < # buf3, n1 < n0, m2 < EB_PAGE_SIZE, m4 < # avol1, awbuf-inv(avol1, buffered(m4)), ebm-vol-inv(avol0), is-aligned(# buf2, EB_PAGE_SIZE), is-aligned(n0 + m2, EB_PAGE_SIZE), is-aligned(n1 + m2, EB_PAGE_SIZE), (# buf2 + m2) + n3 ≤ LEB_SIZE, # buf2 + n0 + m2 ≤ LEB_SIZE, # buf2 + m2 + n3 ≤ LEB_SIZE, EB_PAGE_SIZE ≤ m2 + n3, n3 ≤ # buf3, n0 ≤ # buf3, ⌊err1⌋ ⊦ n1 + m2 = 0, subarray(buf1, 0, m2) + subarray(buf3, 0, n1) = subarray(subarray(buf1, 0, m2) + subarray(buf3, 0, n0), 0, n1 + m2), n1 = 0, n3 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 161:
⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n])
Proof step 162:
# avol0 = # avol1, # lpt0 = # avol1, # buf1 = EB_PAGE_SIZE, avol0[m4] = mapped(buf2), avol1[m4] = mapped(buf2 + subarray(buf1, 0, m2)), align↓(m2 + n3, EB_PAGE_SIZE) = n0 + m2, m4 < # avol1, m2 < EB_PAGE_SIZE, n1 < n0, n1 < # buf3, awbuf-inv(avol1, buffered(m4)), ebm-vol-inv(avol0), is-aligned(n1 + m2, EB_PAGE_SIZE), is-aligned(n0 + m2, EB_PAGE_SIZE), is-aligned(# buf2, EB_PAGE_SIZE), n0 ≤ # buf3, n3 ≤ # buf3, EB_PAGE_SIZE ≤ m2 + n3, # buf2 + m2 + n3 ≤ LEB_SIZE, # buf2 + n0 + m2 ≤ LEB_SIZE, (# buf2 + m2) + n3 ≤ LEB_SIZE, ⌊err1⌋ ⊦ n1 + m2 = 0, n1 = 0, n3 = 0, #(subarray(buf1, 0, m2) + subarray(buf3, 0, n1)) = # subarray(subarray(buf1, 0, m2) + subarray(buf3, 0, n0), 0, n1 + m2) ∧ (∀ n. n < #(subarray(buf1, 0, m2) + subarray(buf3, 0, n1)) → (subarray(buf1, 0, m2) + subarray(buf3, 0, n1))[n] = subarray(subarray(buf1, 0, m2) + subarray(buf3, 0, n0), 0, n1 + m2)[n])

Rule argument

spec: array, inst: buffer name: Extension seq: ⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n]) subst: [buf0, buf] → [subarray (subarray(buf1, 0, m2) + subarray(buf3, 0, n0), 0, n1 + m2), subarray(buf1, 0, m2) + subarray(buf3, 0, n1)] flags: <all paths>

Additional information

Used terms: subarray(subarray(buf1, 0, m2) + subarray(buf3, 0, n0), 0, n1 + m2), subarray(buf1, 0, m2) + subarray(buf3, 0, n1)