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Proof step 102 from proof refine-write-data-wl (previous step)

LEB_SIZE = n0 + n2, 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?, n2 < datasize(buf, n), n2 < # buf, n2 < LEB_SIZE, n2 < n, 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), 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, ⌊err1⌋ ⊦ n0 = 0, n2 = 0, ( mkpeb(copy(buf, 0, buf0, 2 * EB_PAGE_SIZE, n2), 2 * EB_PAGE_SIZE + n2, false).bad ↔ mkpeb(aehdr, avhdr, subarray(buf, 0, n2) + mkempbuf(n0), n2, false).bad) ∧ ( ¬ mkpeb(copy(buf, 0, buf0, 2 * EB_PAGE_SIZE, n2), 2 * EB_PAGE_SIZE + n2, false).bad → mkpeb(copy(buf, 0, buf0, 2 * EB_PAGE_SIZE, n2), 2 * EB_PAGE_SIZE + n2, false).fill = (mkpeb(aehdr, avhdr, subarray(buf, 0, n2) + mkempbuf(n0), n2, false).echdr = empty ⊃ 0 ;(mkpeb(aehdr, avhdr, subarray(buf, 0, n2) + mkempbuf(n0), n2, false).vidhdr = empty ⊃ EB_PAGE_SIZE ;mkpeb(aehdr, avhdr, subarray(buf, 0, n2) + mkempbuf(n0), n2, false).fill + 2 * EB_PAGE_SIZE ) ) ∧ abs-echdr (subarray(mkpeb(copy(buf, 0, buf0, 2 * EB_PAGE_SIZE, n2), 2 * EB_PAGE_SIZE + n2, false).data, 0, EB_PAGE_SIZE), mkpeb(aehdr, avhdr, subarray(buf, 0, n2) + mkempbuf(n0), n2, false).echdr) ∧ abs-vidhdr (subarray(mkpeb(copy(buf, 0, buf0, 2 * EB_PAGE_SIZE, n2), 2 * EB_PAGE_SIZE + n2, false).data, EB_PAGE_SIZE, EB_PAGE_SIZE), mkpeb(aehdr, avhdr, subarray(buf, 0, n2) + mkempbuf(n0), n2, false).vidhdr) ∧ subarray(mkpeb(copy(buf, 0, buf0, 2 * EB_PAGE_SIZE, n2), 2 * EB_PAGE_SIZE + n2, false).data, 2 * EB_PAGE_SIZE, LEB_SIZE) = mkpeb(aehdr, avhdr, subarray(buf, 0, n2) + mkempbuf(n0), n2, false).data)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 103:
LEB_SIZE = n0 + n2, 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), avhdr.valid?, aehdr.valid?, m1 < # apebs, m1 < # pebs, n2 < n, n2 < LEB_SIZE, n2 < # buf, n2 < datasize(buf, n), abs(pebs, apebs), abs-peb(mkpeb(buf0, 2 * EB_PAGE_SIZE, false), mkpeb(aehdr, avhdr, buf2, 0, false)), 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⌋ ⊦ n0 = 0, n2 = 0, 2 * EB_PAGE_SIZE + n2 = (aehdr = empty ⊃ 0;(avhdr = empty ⊃ EB_PAGE_SIZE;n2 + 2 * EB_PAGE_SIZE)) ∧ abs-echdr(subarray(buf0, 0, EB_PAGE_SIZE), aehdr) ∧ abs-vidhdr(subarray(buf0, EB_PAGE_SIZE, EB_PAGE_SIZE), avhdr) ∧ subarray(copy(buf, 0, buf0, 2 * EB_PAGE_SIZE, n2), 2 * EB_PAGE_SIZE, LEB_SIZE) = subarray(buf, 0, n2) + mkempbuf(n0)

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ PEB_SIZE < 2 * EB_PAGE_SIZE; (s)% ⊦ m ≤ m; (s)%0 ≠ m ⊦ (* m) * n ≤ m * n0 ↔ n ≤ n0; (s)% ⊦ m + m = 2 * m; (s)%m0 + m1 ≤ n1, m0 + m1 ≤ # buf ⊦ subarray(copy(buf0, n0, buf, n1, n2), m0, m1) = subarray(buf, m0, m1); (s)% ⊦ ¬ PEB_SIZE < EB_PAGE_SIZE; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).data = buf; (s)%n < # pebs ⊦ pebs[n] = mkpeb(buf, m, boolvar) ∧ mtd-cons(pebs) → # buf = PEB_SIZE; (s)% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult% ⊦ m ≤ 2 * m; (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)% ⊦ mkpeb(buf, m, boolvar).data = buf; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).fill = m; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).echdr = aehdr; (s)% ⊦ mkpeb(buf, m, boolvar).fill = m; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).bad ↔ boolvar; (s)% ⊦ mkpeb(buf, m, boolvar).bad ↔ boolvar; (s)