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Proof step 47 from proof refine-read-data (previous step)

# 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, n < n2 + n1, n < # buf0, n2 < # buf0, 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, n2 ≤ n ⊦ n3 + n1 = 0, buf3[n] = buf1[(n - n2) + m1], n1 = 0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 48:
# buf3 = # buf0, # buf0 = n3 + n2 + n1, apebs[m3] = mkpeb(aehdr, avhdr, buf1, m2, false), pebs[m3] = mkpeb(buf2, m4, false), n = n0 + n2, subarray(buf3, n2, n1) = subarray(buf2, m1 + 2 * EB_PAGE_SIZE, n1), n2 < # buf0, n < # buf0, n < n2 + 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 ≤ n, n2 + n1 ≤ # buf0, (m1 + 2 * EB_PAGE_SIZE) + n1 ≤ PEB_SIZE, m1 + n1 ≤ LEB_SIZE ⊦ n3 + n1 = 0, buf3[n] = buf1[n0 + m1], n1 = 0

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [n, n2, n0]

Additional information

Used simplifier rules: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: n, n2, n0