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Proof step 119 from proof refine-write-data (previous step)

2 * EB_PAGE_SIZE + m2 = (avhdr = empty ⊃ EB_PAGE_SIZE;m2 + 2 * EB_PAGE_SIZE), LEB_SIZE = (n1 + n3) + m1, pebs[m3] = mkpeb(buf1, 2 * EB_PAGE_SIZE + m2, false), apebs[m3] = mkpeb(aehdr, avhdr, subarray(buf1, 2 * EB_PAGE_SIZE, LEB_SIZE), m2, false), aehdr.valid?, avhdr.valid?, m3 < # pebs, m3 < # apebs, n3 < n, abs(pebs, apebs), abs-echdr(subarray(buf1, 0, EB_PAGE_SIZE), aehdr), abs-vidhdr(subarray(buf1, EB_PAGE_SIZE, EB_PAGE_SIZE), avhdr), 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, m2 ≤ LEB_SIZE, m1 ≤ LEB_SIZE, n3 + m1 ≤ LEB_SIZE, ⌊err1⌋ ⊦ aehdr = empty, n3 = 0, subarray(copy(buf, n0, buf1, m1 + 2 * EB_PAGE_SIZE, n3), 2 * EB_PAGE_SIZE, LEB_SIZE) = subarray(subarray(buf1, 2 * EB_PAGE_SIZE, LEB_SIZE), 0, m1) + subarray(buf, n0, n3) + mkempbuf(n1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 120:
n1 ≥ m0, m0 + m1 ≤ # buf ⊦ subarray(copy(buf0, n0, buf, n1, n2), m0, m1) = copy(buf0, n0, subarray(buf, m0, m1), n1 - m0, n2)
Proof step 121:
2 * EB_PAGE_SIZE + m2 = (avhdr = empty ⊃ EB_PAGE_SIZE;m2 + 2 * EB_PAGE_SIZE), LEB_SIZE = (n1 + n3) + m1, apebs[m3] = mkpeb(aehdr, avhdr, subarray(buf1, 2 * EB_PAGE_SIZE, LEB_SIZE), m2, false), pebs[m3] = mkpeb(buf1, 2 * EB_PAGE_SIZE + m2, false), avhdr.valid?, aehdr.valid?, n3 < n, m3 < # apebs, m3 < # pebs, abs(pebs, apebs), abs-echdr(subarray(buf1, 0, EB_PAGE_SIZE), aehdr), abs-vidhdr(subarray(buf1, EB_PAGE_SIZE, EB_PAGE_SIZE), avhdr), is-aligned(m1, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), is-aligned(n3, EB_PAGE_SIZE), mtd-cons(pebs), ubi-io-inv(apebs), n3 + m1 ≤ LEB_SIZE, m1 ≤ LEB_SIZE, m2 ≤ LEB_SIZE, n0 + n3 ≤ # buf, m1 + n ≤ LEB_SIZE, n0 + n ≤ # buf, (m1 + 2 * EB_PAGE_SIZE) + n3 ≤ PEB_SIZE, m2 ≤ m1, 2 * EB_PAGE_SIZE + LEB_SIZE ≤ # buf1, m1 + 2 * EB_PAGE_SIZE ≥ 2 * EB_PAGE_SIZE, ⌊err1⌋ ⊦ aehdr = empty, copy(buf, n0, subarray(buf1, 2 * EB_PAGE_SIZE, LEB_SIZE), m1 + 2 * EB_PAGE_SIZE - 2 * EB_PAGE_SIZE, n3) = subarray(subarray(buf1, 2 * EB_PAGE_SIZE, LEB_SIZE), 0, m1) + subarray(buf, n0, n3) + mkempbuf(n1), n3 = 0

Rule argument

spec: array-copy, inst: buffer name: subarray-copy seq: n1 ≥ m0, m0 + m1 ≤ # buf ⊦ subarray(copy(buf0, n0, buf, n1, n2), m0, m1) = copy(buf0, n0, subarray(buf, m0, m1), n1 - m0, n2) subst: [m1, m0, n2, n1, buf, n0, buf0] → [LEB_SIZE, 2 * EB_PAGE_SIZE, n3, m1 + 2 * EB_PAGE_SIZE, buf1, n0, buf] flags: <all paths>

Additional information

Used simplifier rules: ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ m ≤ m + n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ LEB_SIZE + 2 * EB_PAGE_SIZE = PEB_SIZE; (s)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s)%n < # pebs ⊦ pebs[n] = mkpeb(buf, m, boolvar) ∧ mtd-cons(pebs) → # buf = PEB_SIZE; (s)% ⊦ m ≤ m; (s) Used terms: LEB_SIZE, 2 * EB_PAGE_SIZE, n3, m1 + 2 * EB_PAGE_SIZE, buf1, n0, buf