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Proof step 132 from proof refine-write-data (previous step)

2 * EB_PAGE_SIZE + m2 = (avhdr = empty ⊃ EB_PAGE_SIZE;m2 + 2 * EB_PAGE_SIZE), LEB_SIZE = (n2 + 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?, n1 < n2, 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), n0 + n3 ≤ # buf, m2 ≤ m1, (m1 + 2 * EB_PAGE_SIZE) + n3 ≤ PEB_SIZE, n0 + n ≤ # buf, m1 + n ≤ LEB_SIZE, m2 ≤ LEB_SIZE, m1 ≤ LEB_SIZE, m1 + n3 ≤ LEB_SIZE, n3 + m1 ≤ LEB_SIZE, ⌊err1⌋ ⊦ subarray(buf1, 2 * EB_PAGE_SIZE, LEB_SIZE)[(m1 + n3) + n1] = empty, aehdr = empty, n3 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 133:
⊦ n0 < n → subarray(buf, m, n)[n0] = buf[m + n0]
Proof step 134:
2 * EB_PAGE_SIZE + m2 = (avhdr = empty ⊃ EB_PAGE_SIZE;m2 + 2 * EB_PAGE_SIZE), LEB_SIZE = (n2 + 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, n1 < n2, (m1 + n3) + n1 < LEB_SIZE, 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 + n3 ≤ LEB_SIZE, m1 ≤ LEB_SIZE, m2 ≤ LEB_SIZE, m1 + n ≤ LEB_SIZE, n0 + n ≤ # buf, (m1 + 2 * EB_PAGE_SIZE) + n3 ≤ PEB_SIZE, m2 ≤ m1, n0 + n3 ≤ # buf, ⌊err1⌋ ⊦ buf1[2 * EB_PAGE_SIZE + (m1 + n3) + n1] = empty, aehdr = empty, n3 = 0

Rule argument

spec: array-copy, inst: buffer name: subarray-at seq: ⊦ n0 < n → subarray(buf, m, n)[n0] = buf[m + n0] subst: [n0, n, m, buf] → [(m1 + n3) + n1, LEB_SIZE, 2 * EB_PAGE_SIZE, buf1] flags: <all paths>

Additional information

Used simplifier rules: ⊦ 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)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m = m0 + n0 ∧ n < n0 → m0 + n < m; (s)%# buf = n ⊦ subarray(buf, 0, n) = buf; (s) Used terms: (m1 + n3) + n1, LEB_SIZE, 2 * EB_PAGE_SIZE, buf1