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Proof step 118 from proof refine-write-data-wl (previous step)

2 * EB_PAGE_SIZE = (avhdr = empty ⊃ EB_PAGE_SIZE;2 * EB_PAGE_SIZE), LEB_SIZE = n1 + n2, apebs[m1] = mkpeb(aehdr, avhdr, subarray(buf0, 2 * EB_PAGE_SIZE, LEB_SIZE), 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-echdr(subarray(buf0, 0, EB_PAGE_SIZE), aehdr), abs-vidhdr(subarray(buf0, EB_PAGE_SIZE, EB_PAGE_SIZE), avhdr), 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⌋ ⊦ aehdr = empty, n1 = 0, n2 = 0, subarray(subarray(buf0, 2 * EB_PAGE_SIZE, LEB_SIZE), n2, n1) = mkempbuf(n1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 119:
⊦ n0 + n1 ≤ # buf ∧ m0 + m1 ≤ n1 → subarray(subarray(buf, n0, n1), m0, m1) = subarray(buf, n0 + m0, m1)
Proof step 120:
2 * EB_PAGE_SIZE = (avhdr = empty ⊃ EB_PAGE_SIZE;2 * EB_PAGE_SIZE), LEB_SIZE = n1 + n2, pebs[m1] = mkpeb(buf0, 2 * EB_PAGE_SIZE, false), apebs[m1] = mkpeb(aehdr, avhdr, subarray(buf0, 2 * EB_PAGE_SIZE, LEB_SIZE), 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-echdr(subarray(buf0, 0, EB_PAGE_SIZE), aehdr), abs-vidhdr(subarray(buf0, EB_PAGE_SIZE, EB_PAGE_SIZE), avhdr), 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, 2 * EB_PAGE_SIZE + LEB_SIZE ≤ # buf0, n2 + n1 ≤ LEB_SIZE, ⌊err1⌋ ⊦ aehdr = empty, n1 = 0, n2 = 0, subarray(buf0, 2 * EB_PAGE_SIZE + n2, n1) = mkempbuf(n1)

Rule argument

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

Additional information

Used simplifier rules: ⊦ 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%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ 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)% ⊦ EB_PAGE_SIZE ≠ 0; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ m < n → n ≠ 0; (s)% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ ¬ n < n; (s)%n ≠ 0, m % n = 0 ⊦ align↑(m, n) = m; (s)%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)% ⊦ m < n → ¬ n < m; (s) Used terms: n1, n2, LEB_SIZE, 2 * EB_PAGE_SIZE, buf0