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Proof step 69 from proof refine-write-data (previous step)

# buf1 = PEB_SIZE, 2 * EB_PAGE_SIZE + m2 = (avhdr = empty ⊃ EB_PAGE_SIZE;m2 + 2 * EB_PAGE_SIZE), n3 + m2 = LEB_SIZE, LEB_SIZE = (n1 + n) + m1, PEB_SIZE = n3 + 2 * EB_PAGE_SIZE + m2, apebs[m3] = mkpeb(aehdr, avhdr, subarray(buf1, 2 * EB_PAGE_SIZE, LEB_SIZE), m2, false), pebs[m3] = mkpeb(buf1, 2 * EB_PAGE_SIZE + m2, false), avhdr.valid?, aehdr.valid?, m3 < # apebs, m3 < # pebs, n0 < n1, abs(pebs, apebs), abs-echdr(subarray(buf1, 0, EB_PAGE_SIZE), aehdr), abs-vidhdr(subarray(buf1, EB_PAGE_SIZE, EB_PAGE_SIZE), avhdr), is-aligned(m1, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), is-aligned(m2, EB_PAGE_SIZE), range=(buf1, 2 * EB_PAGE_SIZE + m2, emptypeb, 2 * EB_PAGE_SIZE + m2, n3), ubi-io-inv(apebs), n + m1 ≤ LEB_SIZE, m1 + n ≤ LEB_SIZE, (m1 + 2 * EB_PAGE_SIZE) + n ≤ PEB_SIZE, m2 ≤ m1, m2 ≤ LEB_SIZE, m1 ≤ LEB_SIZE, n2 + n ≤ # buf, 2 * EB_PAGE_SIZE + m2 ≤ PEB_SIZE ⊦ buf1[(2 * EB_PAGE_SIZE + m1 + n) + n0] = empty, aehdr = empty

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 70:
⊦ range=(buf, n0, buf0, n1, m) ↔ n0 + m ≤ # buf ∧ n1 + m ≤ # buf0 ∧ (∀ n. n < m → buf[n0 + n] = buf0[n1 + n])
Proof step 71:
# buf1 = PEB_SIZE, n3 + m2 = LEB_SIZE, 2 * EB_PAGE_SIZE + m2 = (avhdr = empty ⊃ EB_PAGE_SIZE;m2 + 2 * EB_PAGE_SIZE), LEB_SIZE = (n1 + n) + m1, PEB_SIZE = n3 + 2 * EB_PAGE_SIZE + m2, pebs[m3] = mkpeb(buf1, 2 * EB_PAGE_SIZE + m2, false), apebs[m3] = mkpeb(aehdr, avhdr, subarray(buf1, 2 * EB_PAGE_SIZE, LEB_SIZE), m2, false), aehdr.valid?, avhdr.valid?, n0 < n1, m3 < # pebs, m3 < # apebs, abs(pebs, apebs), abs-echdr(subarray(buf1, 0, EB_PAGE_SIZE), aehdr), abs-vidhdr(subarray(buf1, EB_PAGE_SIZE, EB_PAGE_SIZE), avhdr), is-aligned(m2, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), is-aligned(m1, EB_PAGE_SIZE), ubi-io-inv(apebs), 2 * EB_PAGE_SIZE + m2 ≤ PEB_SIZE, n2 + n ≤ # buf, m1 ≤ LEB_SIZE, m2 ≤ LEB_SIZE, m2 ≤ m1, (m1 + 2 * EB_PAGE_SIZE) + n ≤ PEB_SIZE, m1 + n ≤ LEB_SIZE, n + m1 ≤ LEB_SIZE, (2 * EB_PAGE_SIZE + m2) + n3 ≤ # buf1, (2 * EB_PAGE_SIZE + m2) + n3 ≤ # emptypeb, ∀ n. n < n3 → buf1[(2 * EB_PAGE_SIZE + m2) + n] = (emptypeb)[(2 * EB_PAGE_SIZE + m2) + n] ⊦ buf1[(2 * EB_PAGE_SIZE + m1 + n) + n0] = empty, aehdr = empty

Rule argument

spec: array-splice, inst: buffer name: range-eq-ext seq: ⊦ range=(buf, n0, buf0, n1, m) ↔ n0 + m ≤ # buf ∧ n1 + m ≤ # buf0 ∧ (∀ n. n < m → buf[n0 + n] = buf0[n1 + n]) subst: [m, n1, buf0, n0, buf] → [n3, 2 * EB_PAGE_SIZE + m2, emptypeb, 2 * EB_PAGE_SIZE + m2, buf1] flags: <all paths>

Additional information

Used terms: n3, 2 * EB_PAGE_SIZE + m2, emptypeb, 2 * EB_PAGE_SIZE + m2, buf1