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Proof step 176 from proof refine-read-buf (previous step)

# buf2 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, n3 + n5 + n1 = # buf3, min(n1, n2) + n4 = n1 + n5, LEB_SIZE = n0 + # buf0 + # buf, avol1[m2] = mapped(buf0 + buf), avol0[m2] = mapped(buf0 + buf), subarray(buf2, 0, n2) = subarray(buf, n3, n2), n6 + n3 < # buf, n6 < min(n1, n2), n6 < n5 + n1, n3 < n0 + # buf, (n3 + # buf0) + n2 < LEB_SIZE, # buf0 < LEB_SIZE, n2 < EB_PAGE_SIZE, m2 < # avol1, n3 < # buf, n3 + n2 < # buf, n3 < # buf3, n6 < n1 + n5, n6 < EB_PAGE_SIZE, awbuf-inv(avol1, buffered(m2)), ebm-vol-inv(avol0), is-aligned(n3 + # buf0, EB_PAGE_SIZE), n1 + n3 ≤ # buf + n0, min(n1, n2) ≤ n1 + n5, min(n1, n2) ≤ EB_PAGE_SIZE ⊦ buf2[n6] = buf[n6 + n3]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 177:
⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n])
Proof step 178:
# subarray(buf2, 0, n2) = # subarray(buf, n3, n2), # avol0 = # avol1, # lpt0 = # avol1, # buf2 = EB_PAGE_SIZE, min(n1, n2) + n4 = n1 + n5, n3 + n5 + n1 = # buf3, LEB_SIZE = n0 + # buf0 + # buf, avol0[m2] = mapped(buf0 + buf), avol1[m2] = mapped(buf0 + buf), n6 < EB_PAGE_SIZE, n6 < n1 + n5, n3 < # buf3, n3 + n2 < # buf, n3 < # buf, m2 < # avol1, n2 < EB_PAGE_SIZE, # buf0 < LEB_SIZE, (n3 + # buf0) + n2 < LEB_SIZE, n3 < n0 + # buf, n6 < n5 + n1, n6 < min(n1, n2), n6 + n3 < # buf, awbuf-inv(avol1, buffered(m2)), ebm-vol-inv(avol0), is-aligned(n3 + # buf0, EB_PAGE_SIZE), min(n1, n2) ≤ EB_PAGE_SIZE, min(n1, n2) ≤ n1 + n5, n1 + n3 ≤ # buf + n0, ∀ n. n < # subarray(buf2, 0, n2) → subarray(buf2, 0, n2)[n] = subarray(buf, n3, n2)[n] ⊦ buf2[n6] = buf[n6 + n3]

Rule argument

spec: array, inst: buffer name: Extension seq: ⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n]) subst: [buf0, buf] → [subarray(buf, n3, n2), subarray(buf2, 0, n2)] flags: <all paths>

Additional information

Used terms: subarray(buf, n3, n2), subarray(buf2, 0, n2)