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Proof step 38 from proof refine-write-data (previous step)

LEB_SIZE = (n0 + n) + m1, pebs[m3] = mkpeb(buf1, 2 * EB_PAGE_SIZE + m2, false), apebs[m3] = mkpeb(aehdr, avhdr, buf0, m2, false), aehdr.valid?, avhdr.valid?, m3 < # pebs, m3 < # apebs, abs(pebs, apebs), abs-peb(mkpeb(buf1, 2 * EB_PAGE_SIZE + m2, false), mkpeb(aehdr, avhdr, buf0, m2, false)), is-aligned(n, EB_PAGE_SIZE), is-aligned(m1, EB_PAGE_SIZE), mtd-cons(pebs), ubi-io-inv(apebs), n + m1 ≤ LEB_SIZE, m1 ≤ LEB_SIZE, m2 ≤ LEB_SIZE, m2 ≤ m1, (m1 + 2 * EB_PAGE_SIZE) + n ≤ PEB_SIZE, n2 + n ≤ # buf, m1 + n ≤ LEB_SIZE ⊦ ( mkpeb(copy(buf, n2, buf1, m1 + 2 * EB_PAGE_SIZE, n), (m1 + 2 * EB_PAGE_SIZE) + n, false).bad ↔ mkpeb(aehdr, avhdr, subarray(buf0, 0, m1) + subarray(buf, n2, n) + mkempbuf(n0), m1 + n, false).bad) ∧ ( ¬ mkpeb(copy(buf, n2, buf1, m1 + 2 * EB_PAGE_SIZE, n), (m1 + 2 * EB_PAGE_SIZE) + n, false).bad → mkpeb(copy(buf, n2, buf1, m1 + 2 * EB_PAGE_SIZE, n), (m1 + 2 * EB_PAGE_SIZE) + n, false).fill = (mkpeb(aehdr, avhdr, subarray(buf0, 0, m1) + subarray(buf, n2, n) + mkempbuf(n0), m1 + n, false).echdr = empty ⊃ 0 ;(mkpeb(aehdr, avhdr, subarray(buf0, 0, m1) + subarray(buf, n2, n) + mkempbuf(n0), m1 + n, false).vidhdr = empty ⊃ EB_PAGE_SIZE ;mkpeb(aehdr, avhdr, subarray(buf0, 0, m1) + subarray(buf, n2, n) + mkempbuf(n0), m1 + n, false).fill + 2 * EB_PAGE_SIZE ) ) ∧ abs-echdr (subarray(mkpeb(copy(buf, n2, buf1, m1 + 2 * EB_PAGE_SIZE, n), (m1 + 2 * EB_PAGE_SIZE) + n, false).data, 0, EB_PAGE_SIZE), mkpeb(aehdr, avhdr, subarray(buf0, 0, m1) + subarray(buf, n2, n) + mkempbuf(n0), m1 + n, false).echdr) ∧ abs-vidhdr (subarray(mkpeb(copy(buf, n2, buf1, m1 + 2 * EB_PAGE_SIZE, n), (m1 + 2 * EB_PAGE_SIZE) + n, false).data, EB_PAGE_SIZE, EB_PAGE_SIZE), mkpeb(aehdr, avhdr, subarray(buf0, 0, m1) + subarray(buf, n2, n) + mkempbuf(n0), m1 + n, false).vidhdr) ∧ subarray(mkpeb(copy(buf, n2, buf1, m1 + 2 * EB_PAGE_SIZE, n), (m1 + 2 * EB_PAGE_SIZE) + n, false).data, 2 * EB_PAGE_SIZE, LEB_SIZE) = mkpeb(aehdr, avhdr, subarray(buf0, 0, m1) + subarray(buf, n2, n) + mkempbuf(n0), m1 + n, false).data)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 39:
LEB_SIZE = (n0 + n) + m1, apebs[m3] = mkpeb(aehdr, avhdr, buf0, m2, false), pebs[m3] = mkpeb(buf1, 2 * EB_PAGE_SIZE + m2, false), avhdr.valid?, aehdr.valid?, m3 < # apebs, m3 < # pebs, abs(pebs, apebs), abs-peb(mkpeb(buf1, 2 * EB_PAGE_SIZE + m2, false), mkpeb(aehdr, avhdr, buf0, m2, false)), is-aligned(m1, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), mtd-cons(pebs), ubi-io-inv(apebs), m1 + n ≤ LEB_SIZE, n2 + n ≤ # buf, (m1 + 2 * EB_PAGE_SIZE) + n ≤ PEB_SIZE, m2 ≤ m1, m2 ≤ LEB_SIZE, m1 ≤ LEB_SIZE, n + m1 ≤ LEB_SIZE ⊦ (m1 + 2 * EB_PAGE_SIZE) + n = (aehdr = empty ⊃ 0;(avhdr = empty ⊃ EB_PAGE_SIZE;(m1 + n) + 2 * EB_PAGE_SIZE)) ∧ abs-echdr(subarray(buf1, 0, EB_PAGE_SIZE), aehdr) ∧ abs-vidhdr(subarray(buf1, EB_PAGE_SIZE, EB_PAGE_SIZE), avhdr) ∧ subarray(copy(buf, n2, buf1, m1 + 2 * EB_PAGE_SIZE, n), 2 * EB_PAGE_SIZE, LEB_SIZE) = subarray(buf0, 0, m1) + subarray(buf, n2, n) + mkempbuf(n0)

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ PEB_SIZE < 2 * EB_PAGE_SIZE; (s)% ⊦ m ≤ m + n; (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%m1 ≠ 0 ⊦ m ≤ (* m1) * m + n0; (s)%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ n + 0 = n; (s)% ⊦ mkpeb(buf, m, boolvar).data = buf; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ 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)