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Proof step 104 from proof refine-write-data (previous step)

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, n3 < n, abs(pebs, apebs), abs-peb(mkpeb(buf1, 2 * EB_PAGE_SIZE + m2, false), mkpeb(aehdr, avhdr, buf0, m2, false)), is-aligned(n3, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), is-aligned(m1, EB_PAGE_SIZE), mtd-cons(pebs), ubi-io-inv(apebs), 0 + m1 ≤ # apebs[m3].data, m2 ≤ m1, (m1 + 2 * EB_PAGE_SIZE) + n3 ≤ PEB_SIZE, n0 + n ≤ # buf, m1 + n ≤ LEB_SIZE, n0 + n3 ≤ # buf, LEB_SIZE - m1 ≥ n3, LEB_SIZE ≥ m1, ⌊err1⌋ ⊦ n3 = 0, abs (pebs[m3, (pebs[m3].data:= copy(buf, n0, pebs[m3].data, m1 + 2 * EB_PAGE_SIZE, n3)).fill:= ((m1 + 2 * EB_PAGE_SIZE) + n3)], apebs [m3, mkpeb (apebs[m3].echdr, apebs[m3].vidhdr, subarray(apebs[m3].data, 0, m1) + subarray(buf, n0, n3) + mkempbuf(LEB_SIZE - m1 - n3), m1 + n3, apebs[m3].bad) ])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 105:
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, n3 < n, abs(pebs, apebs), abs-peb(mkpeb(buf1, 2 * EB_PAGE_SIZE + m2, false), mkpeb(aehdr, avhdr, buf0, m2, false)), is-aligned(n3, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), is-aligned(m1, EB_PAGE_SIZE), mtd-cons(pebs), ubi-io-inv(apebs), m2 ≤ m1, (m1 + 2 * EB_PAGE_SIZE) + n3 ≤ PEB_SIZE, n0 + n ≤ # buf, m1 + n ≤ LEB_SIZE, n0 + n3 ≤ # buf, n3 + m1 ≤ LEB_SIZE, m2 ≤ LEB_SIZE, m1 ≤ LEB_SIZE, ⌊err1⌋ ⊦ n3 = 0, abs-peb (mkpeb(copy(buf, n0, buf1, m1 + 2 * EB_PAGE_SIZE, n3), (m1 + 2 * EB_PAGE_SIZE) + n3, false), mkpeb(aehdr, avhdr, subarray(buf0, 0, m1) + subarray(buf, n0, n3) + mkempbuf(LEB_SIZE - m1 - n3), m1 + n3, false))

Rule argument

Additional information

Used simplifier rules: ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).bad ↔ boolvar; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).echdr = aehdr; (s)% ⊦ mkpeb(buf, m, boolvar).fill:= m0 = mkpeb(buf, m0, boolvar); (s)% ⊦ mkpeb(buf, m, boolvar).data:= buf0 = mkpeb(buf0, m, boolvar); (s)% ⊦ mkpeb(buf, m, boolvar).data = buf; (s)%n < # apebs ⊦ apebs[n] = mkpeb(aehdr, avhdr, buf, m, boolvar) ∧ ubi-io-inv(apebs) → # buf = LEB_SIZE; (s)% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).data = buf; (s)%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat%⊦ n < # apebs ∧ abs(pebs, apebs) ∧ ubi-io-inv(apebs) → ( abs(pebs[n, peb], apebs[n, apeb]) ↔ abs-peb(pebs[n], apebs[n]) → abs-peb(peb, apeb)); (ss)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)%n0 ≤ n ⊦ m ≤ n - n0 ↔ m + n0 ≤ n; (s)% ⊦ m ≤ n → (n < m ↔ false); (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ n ≥ m ↔ m ≤ n; (s)