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Proof step 57 from proof refine-write-data-wl (previous step)

2 * EB_PAGE_SIZE = (avhdr = empty ⊃ EB_PAGE_SIZE;2 * EB_PAGE_SIZE), LEB_SIZE = n0 + n, pebs[m1] = mkpeb(buf1, 2 * EB_PAGE_SIZE, false), apebs[m1] = mkpeb(aehdr, avhdr, emptyleb, 0, false), n = align↑(datasize(buf, n), EB_PAGE_SIZE), subarray(buf1, 2 * EB_PAGE_SIZE, LEB_SIZE) = emptyleb, avhdr.valid?, aehdr.valid?, n1 < LEB_SIZE, m1 < # apebs, m1 < # 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(n, EB_PAGE_SIZE), mtd-cons(pebs), ubi-io-inv(apebs), n ≤ # buf, 2 * EB_PAGE_SIZE + n ≤ PEB_SIZE, n ≤ LEB_SIZE, 2 * EB_PAGE_SIZE ≤ PEB_SIZE ⊦ copy(buf, 0, emptyleb, 0, n)[n1] = (subarray(buf, 0, n) + mkempbuf(n0))[n1], aehdr = empty, datasize(buf, n) = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: array-copy, inst: buffer name: at-copy seq: ⊦ m0 < # buf → copy(buf0, n, buf, n0, m)[m0] = (m0 < n0 ∨ n0 + m ≤ m0 ⊃ buf[m0];buf0[m0 + n - n0]) subst: [m0, m, n0, buf, n, buf0] → [n1, n, 0, emptyleb, 0, buf] flags: <all paths>

Additional information

Used simplifier rules: ⊦ EB_PAGE_SIZE ≠ 0; (s)% ⊦ # emptyleb = LEB_SIZE; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s)%n ≠ 0, m % n = 0 ⊦ align↑(m, n) = m; (s)% ⊦ m ≠ n → (m ≤ n ↔ m < n); (s)%# buf = m, # buf0 = m ⊦ copy(buf, 0, buf0, 0, m) = buf; (s)%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)%n < # pebs ⊦ pebs[n] = mkpeb(buf, m, boolvar) ∧ mtd-cons(pebs) → # buf = PEB_SIZE; (s) Used terms: n1, n, 0, emptyleb, 0, buf