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Proof step 129 from proof refine-write-data-wl (previous step)

2 * EB_PAGE_SIZE = (avhdr = empty ⊃ EB_PAGE_SIZE;2 * EB_PAGE_SIZE), LEB_SIZE = n1 + n2, apebs[m1] = mkpeb(aehdr, avhdr, subarray(buf0, 2 * EB_PAGE_SIZE, LEB_SIZE), 0, false), pebs[m1] = mkpeb(buf0, 2 * EB_PAGE_SIZE, false), n = align↑(datasize(buf, n), EB_PAGE_SIZE), aehdr.valid?, avhdr.valid?, m1 < # pebs, n0 < n1, n2 < datasize(buf, n), n2 < # buf, n2 < LEB_SIZE, n2 < n, m1 < # apebs, abs(pebs, apebs), abs-echdr(subarray(buf0, 0, EB_PAGE_SIZE), aehdr), abs-vidhdr(subarray(buf0, EB_PAGE_SIZE, EB_PAGE_SIZE), avhdr), is-aligned(n, EB_PAGE_SIZE), is-aligned(n2, EB_PAGE_SIZE), mtd-cons(pebs), range=(buf0, 2 * EB_PAGE_SIZE, emptypeb, 2 * EB_PAGE_SIZE, LEB_SIZE), ubi-io-inv(apebs), 2 * EB_PAGE_SIZE ≤ PEB_SIZE, n ≤ # buf, n ≤ LEB_SIZE, 2 * EB_PAGE_SIZE + n2 ≤ PEB_SIZE, ⌊err1⌋ ⊦ buf0[(2 * EB_PAGE_SIZE + n2) + n0] = empty, aehdr = empty, n2 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 130:
⊦ range=(buf, n0, buf0, n1, m) ↔ n0 + m ≤ # buf ∧ n1 + m ≤ # buf0 ∧ (∀ n. n < m → buf[n0 + n] = buf0[n1 + n])
Proof step 131:
2 * EB_PAGE_SIZE = (avhdr = empty ⊃ EB_PAGE_SIZE;2 * EB_PAGE_SIZE), LEB_SIZE = n1 + n2, pebs[m1] = mkpeb(buf0, 2 * EB_PAGE_SIZE, false), apebs[m1] = mkpeb(aehdr, avhdr, subarray(buf0, 2 * EB_PAGE_SIZE, LEB_SIZE), 0, false), n = align↑(datasize(buf, n), EB_PAGE_SIZE), avhdr.valid?, aehdr.valid?, m1 < # apebs, n2 < n, n2 < LEB_SIZE, n2 < # buf, n2 < datasize(buf, n), n0 < n1, m1 < # pebs, abs(pebs, apebs), abs-echdr(subarray(buf0, 0, EB_PAGE_SIZE), aehdr), abs-vidhdr(subarray(buf0, EB_PAGE_SIZE, EB_PAGE_SIZE), avhdr), is-aligned(n2, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), mtd-cons(pebs), ubi-io-inv(apebs), 2 * EB_PAGE_SIZE + n2 ≤ PEB_SIZE, n ≤ LEB_SIZE, n ≤ # buf, 2 * EB_PAGE_SIZE ≤ PEB_SIZE, 2 * EB_PAGE_SIZE + LEB_SIZE ≤ # buf0, 2 * EB_PAGE_SIZE + LEB_SIZE ≤ # emptypeb, ⌊err1⌋ , ∀ n. n < LEB_SIZE → buf0[2 * EB_PAGE_SIZE + n] = (emptypeb)[2 * EB_PAGE_SIZE + n] ⊦ buf0[(2 * EB_PAGE_SIZE + n2) + n0] = empty, aehdr = empty, n2 = 0

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] → [LEB_SIZE, 2 * EB_PAGE_SIZE, emptypeb, 2 * EB_PAGE_SIZE, buf0] flags: <all paths>

Additional information

Used terms: LEB_SIZE, 2 * EB_PAGE_SIZE, emptypeb, 2 * EB_PAGE_SIZE, buf0