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Proof step 51 from proof refine-write-echdr (previous step)

# buf2 = EB_PAGE_SIZE, apebs[m2] = mkpeb(empty, avhdr, subarray(buf1, 2 * EB_PAGE_SIZE, LEB_SIZE), m1, false), pebs[m2] = mkpeb(buf1, 0, false), m2 < # apebs, m2 < # pebs, abs(pebs, apebs), abs-echdr(subarray(buf1, 0, EB_PAGE_SIZE), empty), abs-vidhdr(subarray(buf1, EB_PAGE_SIZE, EB_PAGE_SIZE), avhdr), is-encoded(echdr(m3), buf2), mtd-cons(pebs), range=(buf1, 0, emptypeb, 0, PEB_SIZE), ubi-io-inv(apebs), EB_PAGE_SIZE ≤ PEB_SIZE ⊦ avhdr = empty ∧ abs-echdr(buf2, aechdr(m3))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 52:
⊦ range=(buf, n0, buf0, n1, m) ↔ n0 + m ≤ # buf ∧ n1 + m ≤ # buf0 ∧ subarray(buf, n0, m) = subarray(buf0, n1, m)
Proof step 53:
# buf2 = EB_PAGE_SIZE, pebs[m2] = mkpeb(buf1, 0, false), apebs[m2] = mkpeb(empty, avhdr, subarray(buf1, 2 * EB_PAGE_SIZE, LEB_SIZE), m1, false), subarray(buf1, 0, PEB_SIZE) = subarray(emptypeb, 0, PEB_SIZE), m2 < # pebs, m2 < # apebs, abs(pebs, apebs), abs-echdr(subarray(buf1, 0, EB_PAGE_SIZE), empty), abs-vidhdr(subarray(buf1, EB_PAGE_SIZE, EB_PAGE_SIZE), avhdr), is-encoded(echdr(m3), buf2), mtd-cons(pebs), ubi-io-inv(apebs), EB_PAGE_SIZE ≤ PEB_SIZE, 0 + PEB_SIZE ≤ # buf1, 0 + PEB_SIZE ≤ # emptypeb ⊦ avhdr = empty ∧ abs-echdr(buf2, aechdr(m3))

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] → [PEB_SIZE, 0, emptypeb, 0, buf1] flags: <all paths>

Additional information

Used terms: PEB_SIZE, 0, emptypeb, 0, buf1