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Proof step 44 from proof refine-write-vidhdr (previous step)

# buf2 = EB_PAGE_SIZE, pebs[m2] = mkpeb(buf1, EB_PAGE_SIZE, false), apebs[m2] = mkpeb(aehdr, empty, buf0, m1, false), aehdr.valid?, m2 < # apebs, m2 < # pebs, abs(pebs, apebs), abs-peb(mkpeb(buf1, EB_PAGE_SIZE, false), mkpeb(aehdr, empty, buf0, m1, false)), is-encoded(vidhdr(v, m6, m5, m3, m4), buf2), mtd-cons(pebs), ubi-io-inv(apebs), 2 * EB_PAGE_SIZE ≤ PEB_SIZE ⊦ ( mkpeb(copy(buf2, 0, buf1, EB_PAGE_SIZE, EB_PAGE_SIZE), 2 * EB_PAGE_SIZE, false).bad ↔ mkpeb(aehdr, avidhdr(v, m6, m5, m3, m4), buf0, m1, false).bad) ∧ ( ¬ mkpeb(copy(buf2, 0, buf1, EB_PAGE_SIZE, EB_PAGE_SIZE), 2 * EB_PAGE_SIZE, false).bad → mkpeb(copy(buf2, 0, buf1, EB_PAGE_SIZE, EB_PAGE_SIZE), 2 * EB_PAGE_SIZE, false).fill = (mkpeb(aehdr, avidhdr(v, m6, m5, m3, m4), buf0, m1, false).echdr = empty ⊃ 0 ;(mkpeb(aehdr, avidhdr(v, m6, m5, m3, m4), buf0, m1, false).vidhdr = empty ⊃ EB_PAGE_SIZE ;mkpeb(aehdr, avidhdr(v, m6, m5, m3, m4), buf0, m1, false).fill + 2 * EB_PAGE_SIZE ) ) ∧ abs-echdr (subarray(mkpeb(copy(buf2, 0, buf1, EB_PAGE_SIZE, EB_PAGE_SIZE), 2 * EB_PAGE_SIZE, false).data, 0, EB_PAGE_SIZE), mkpeb(aehdr, avidhdr(v, m6, m5, m3, m4), buf0, m1, false).echdr) ∧ abs-vidhdr (subarray(mkpeb(copy(buf2, 0, buf1, EB_PAGE_SIZE, EB_PAGE_SIZE), 2 * EB_PAGE_SIZE, false).data, EB_PAGE_SIZE, EB_PAGE_SIZE), mkpeb(aehdr, avidhdr(v, m6, m5, m3, m4), buf0, m1, false).vidhdr) ∧ subarray(mkpeb(copy(buf2, 0, buf1, EB_PAGE_SIZE, EB_PAGE_SIZE), 2 * EB_PAGE_SIZE, false).data, 2 * EB_PAGE_SIZE, LEB_SIZE) = mkpeb(aehdr, avidhdr(v, m6, m5, m3, m4), buf0, m1, false).data)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 45:
# buf2 = EB_PAGE_SIZE, apebs[m2] = mkpeb(aehdr, empty, buf0, m1, false), pebs[m2] = mkpeb(buf1, EB_PAGE_SIZE, false), aehdr.valid?, m2 < # pebs, m2 < # apebs, abs(pebs, apebs), abs-peb(mkpeb(buf1, EB_PAGE_SIZE, false), mkpeb(aehdr, empty, buf0, m1, false)), is-encoded(vidhdr(v, m6, m5, m3, m4), buf2), mtd-cons(pebs), ubi-io-inv(apebs), 2 * EB_PAGE_SIZE ≤ PEB_SIZE ⊦ 2 * EB_PAGE_SIZE = (aehdr = empty ⊃ 0;m1 + 2 * EB_PAGE_SIZE) ∧ abs-echdr(subarray(buf1, 0, EB_PAGE_SIZE), aehdr) ∧ abs-vidhdr(buf2, avidhdr(v, m6, m5, m3, m4)) ∧ subarray(buf1, 2 * EB_PAGE_SIZE, LEB_SIZE) = buf0

Rule argument

Additional information

Used simplifier rules: n1 + n2 ≤ m0, m0 + m1 ≤ # buf ⊦ subarray(copy(buf0, n0, buf, n1, n2), m0, m1) = subarray(buf, m0, m1); (s)% ⊦ LEB_SIZE + 2 * EB_PAGE_SIZE = PEB_SIZE; (s)%0 ≠ m ⊦ (* m) * n ≤ m * n0 ↔ n ≤ n0; (s)%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)%m1 + n ≤ # buf ⊦ subarray(copy(buf0, m0, buf, m1, n), m1, n) = subarray(buf0, m0, n); (s)%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult% ⊦ ¬ PEB_SIZE < 2 * EB_PAGE_SIZE; (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)% ⊦ m ≤ 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)% ⊦ empty ≠ avidhdr(v, m, m0, m1, m2); (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)