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Proof step 73 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), 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, m1 + n + n0 - m2 < n3 → buf1[(2 * EB_PAGE_SIZE + m2) + (m1 + n + n0 - m2)] = empty ⊦ buf1[(2 * EB_PAGE_SIZE + m1 + n) + n0] = empty, aehdr = empty

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 74:
# 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, n3 ≤ (m1 - m2) + n + n0 ⊦ buf1[(2 * EB_PAGE_SIZE + m1 + n) + n0] = empty, aehdr = empty

Rule argument

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ n ≤ n0 → (m + (n0 - n)) + n = m + n0; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n ≤ m → m + n0 - n = (m - n) + n0; (s)