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Proof step 109 from proof refine-write-data-wl (previous step)

2 * EB_PAGE_SIZE = (avhdr = empty ⊃ EB_PAGE_SIZE;2 * EB_PAGE_SIZE), LEB_SIZE = n0 + 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, m1 < # pebs, n2 < n, n2 < LEB_SIZE, n2 < # buf, n2 < datasize(buf, n), 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, ⌊err1⌋ ⊦ 2 * EB_PAGE_SIZE + n2 = (avhdr = empty ⊃ EB_PAGE_SIZE;n2 + 2 * EB_PAGE_SIZE), aehdr = empty, n0 = 0, n2 = 0

User applied rule case distinction

And closed the goal!

Rule argument

pos: right 1

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic% ⊦ EB_PAGE_SIZE ≠ 0; (s)% ⊦ 1 < n → (m = m * n ↔ m = 0); (s)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult%n ≠ 0, m % n = 0 ⊦ align↑(m, n) = m; (s)