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Proof step 29 from proof refine-read-data (previous step)

# buf3 = # buf0, # buf0 = n3 + n2 + n1, apebs[m3] = mkpeb(aehdr, avhdr, buf1, m2, false), pebs[m3] = mkpeb(buf2, m4, false), subarray(buf3, n2, n1) = subarray(buf2, m1 + 2 * EB_PAGE_SIZE, n1), m3 < # pebs, m3 < # apebs, abs(pebs, apebs), abs-peb(mkpeb(buf2, m4, false), mkpeb(aehdr, avhdr, buf1, m2, false)), mtd-cons(pebs), range=(buf3, 0, buf0, 0, n2), range=(buf3, n2 + n1, buf0, n2 + n1, n3), ubi-io-inv(apebs), n2 + n1 ≤ # buf0, (m1 + 2 * EB_PAGE_SIZE) + n1 ≤ PEB_SIZE, m1 + n1 ≤ LEB_SIZE ⊦ buf3 = copy(buf1, m1, buf0, n2, n1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 30:
⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n])
Proof step 31:
# buf0 = n3 + n2 + n1, # buf3 = # buf0, pebs[m3] = mkpeb(buf2, m4, false), apebs[m3] = mkpeb(aehdr, avhdr, buf1, m2, false), subarray(buf3, n2, n1) = subarray(buf2, m1 + 2 * EB_PAGE_SIZE, n1), m3 < # apebs, m3 < # pebs, abs(pebs, apebs), abs-peb(mkpeb(buf2, m4, false), mkpeb(aehdr, avhdr, buf1, m2, false)), mtd-cons(pebs), range=(buf3, n2 + n1, buf0, n2 + n1, n3), range=(buf3, 0, buf0, 0, n2), ubi-io-inv(apebs), m1 + n1 ≤ LEB_SIZE, (m1 + 2 * EB_PAGE_SIZE) + n1 ≤ PEB_SIZE, n2 + n1 ≤ # buf0 ⊦ # buf3 = # copy(buf1, m1, buf0, n2, n1) ∧ (∀ n. n < # buf3 → buf3[n] = copy(buf1, m1, buf0, n2, n1)[n])

Rule argument

spec: array, inst: buffer name: Extension seq: ⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n]) subst: [buf0, buf] → [copy(buf1, m1, buf0, n2, n1), buf3] flags: <all paths>

Additional information

Used terms: copy(buf1, m1, buf0, n2, n1), buf3