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Proof step 115 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, 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?, n2 < datasize(buf, n), n2 < # buf, n2 < LEB_SIZE, n2 < n, m1 < # pebs, 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), ubi-io-inv(apebs), n ≤ # buf, n ≤ LEB_SIZE, 2 * EB_PAGE_SIZE + n2 ≤ PEB_SIZE, n2 ≤ # buf, 0 + n2 ≤ # subarray(buf0, 2 * EB_PAGE_SIZE, LEB_SIZE), ⌊err1⌋ ⊦ subarray(subarray(buf0, 2 * EB_PAGE_SIZE, LEB_SIZE), 0, 0) + subarray(buf, 0, n2) + subarray(subarray(buf0, 2 * EB_PAGE_SIZE, LEB_SIZE), 0 + n2, # subarray(buf0, 2 * EB_PAGE_SIZE, LEB_SIZE) - 0 - n2) = subarray(buf, 0, n2) + mkempbuf(n0), aehdr = empty, n0 = 0, n2 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 116:
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⌋ ⊦ aehdr = empty, n0 = 0, n2 = 0, subarray(subarray(buf0, 2 * EB_PAGE_SIZE, LEB_SIZE), n2, LEB_SIZE - n2) = mkempbuf(n0)

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → m ≤ n; (s)% ⊦ buf + buf0 = buf + buf1 ↔ buf0 = buf1; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ mkbuf(0) + buf = buf; (s)% ⊦ m - 0 = m; (s)% ⊦ # subarray(buf, m, n) = n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)% ⊦ subarray(buf, n, 0) = mkbuf(0); (s)