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Proof step 164 from proof refine-write-data-wl (previous step)

apebs[m1] = mkpeb(aehdr, avhdr, buf2, 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, m1 < # apebs, abs(pebs, apebs), abs-peb(mkpeb(buf0, 2 * EB_PAGE_SIZE, false), mkpeb(aehdr, avhdr, buf2, 0, false)), is-aligned(n, 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 ≤ LEB_SIZE, n ≤ # buf, ⌊err1⌋ ⊦ datasize(buf, n) = 0, abs-peb(mkpeb(buf0, 2 * EB_PAGE_SIZE, false), mkpeb(aehdr, avhdr, mkempbuf(LEB_SIZE), 0, false))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 165:
⊦ range=(buf, n0, buf0, n1, m) ↔ n0 + m ≤ # buf ∧ n1 + m ≤ # buf0 ∧ subarray(buf, n0, m) = subarray(buf0, n1, m)
Proof step 166:
pebs[m1] = mkpeb(buf0, 2 * EB_PAGE_SIZE, false), apebs[m1] = mkpeb(aehdr, avhdr, buf2, 0, false), n = align↑(datasize(buf, n), EB_PAGE_SIZE), subarray(buf0, 2 * EB_PAGE_SIZE, LEB_SIZE) = subarray(emptypeb, 2 * EB_PAGE_SIZE, LEB_SIZE), avhdr.valid?, aehdr.valid?, m1 < # apebs, m1 < # pebs, abs(pebs, apebs), abs-peb(mkpeb(buf0, 2 * EB_PAGE_SIZE, false), mkpeb(aehdr, avhdr, buf2, 0, false)), is-aligned(n, EB_PAGE_SIZE), mtd-cons(pebs), ubi-io-inv(apebs), n ≤ # buf, n ≤ LEB_SIZE, 2 * EB_PAGE_SIZE ≤ PEB_SIZE, 2 * EB_PAGE_SIZE + LEB_SIZE ≤ # buf0, 2 * EB_PAGE_SIZE + LEB_SIZE ≤ # emptypeb, ⌊err1⌋ ⊦ datasize(buf, n) = 0, abs-peb(mkpeb(buf0, 2 * EB_PAGE_SIZE, false), mkpeb(aehdr, avhdr, mkempbuf(LEB_SIZE), 0, false))

Rule argument

spec: array-splice, inst: buffer name: range-eq-subarrays seq: ⊦ range=(buf, n0, buf0, n1, m) ↔ n0 + m ≤ # buf ∧ n1 + m ≤ # buf0 ∧ subarray(buf, n0, m) = subarray(buf0, n1, m) 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