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Proof step 47 from proof refine-write-data-wl (previous step)

2 * EB_PAGE_SIZE = (aehdr = empty ⊃ 0;(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?, 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 ⊦ datasize(buf, n) = 0, 2 * EB_PAGE_SIZE + n = (aehdr = empty ⊃ 0;(avhdr = empty ⊃ EB_PAGE_SIZE;n + 2 * EB_PAGE_SIZE)) ∧ subarray(copy(buf, 0, buf1, 2 * EB_PAGE_SIZE, n), 2 * EB_PAGE_SIZE, LEB_SIZE) = subarray(buf, 0, n) + mkempbuf(n0)

User applied rule case distinction

And obtained the following new goals

Proof step 48:
2 * EB_PAGE_SIZE = (avhdr = empty ⊃ EB_PAGE_SIZE;2 * EB_PAGE_SIZE), LEB_SIZE = n0 + n, apebs[m1] = mkpeb(aehdr, avhdr, emptyleb, 0, false), pebs[m1] = mkpeb(buf1, 2 * EB_PAGE_SIZE, false), n = align↑(datasize(buf, n), EB_PAGE_SIZE), subarray(buf1, 2 * EB_PAGE_SIZE, LEB_SIZE) = emptyleb, aehdr.valid?, avhdr.valid?, m1 < # pebs, m1 < # apebs, 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), 2 * EB_PAGE_SIZE ≤ PEB_SIZE, n ≤ LEB_SIZE, 2 * EB_PAGE_SIZE + n ≤ PEB_SIZE, n ≤ # buf ⊦ aehdr = empty, datasize(buf, n) = 0, 2 * EB_PAGE_SIZE + n = (aehdr = empty ⊃ 0;(avhdr = empty ⊃ EB_PAGE_SIZE;n + 2 * EB_PAGE_SIZE)) ∧ subarray(copy(buf, 0, buf1, 2 * EB_PAGE_SIZE, n), 2 * EB_PAGE_SIZE, LEB_SIZE) = subarray(buf, 0, n) + mkempbuf(n0)

Rule argument

pos: left 1

Additional information

Used simplifier rules: ⊦ EB_PAGE_SIZE ≠ 0; (s)% ⊦ 2 * m = 0 ↔ m = 0; (s)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult%n ≠ 0, m % n = 0 ⊦ align↑(m, n) = m; (s)