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Proof step 115 from proof refine-write-data (previous step)

2 * EB_PAGE_SIZE + m2 = (aehdr = empty ⊃ 0;(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, ⌊err1⌋ ⊦ n3 = 0, (m1 + 2 * EB_PAGE_SIZE) + n3 = (aehdr = empty ⊃ 0;(avhdr = empty ⊃ EB_PAGE_SIZE;(m1 + n3) + 2 * EB_PAGE_SIZE)) ∧ 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 case distinction

And obtained the following new goals

Proof step 116:
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, (m1 + 2 * EB_PAGE_SIZE) + n3 = (aehdr = empty ⊃ 0;(avhdr = empty ⊃ EB_PAGE_SIZE;(m1 + n3) + 2 * EB_PAGE_SIZE)) ∧ 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)

Rule argument

pos: left 1

Additional information

Used simplifier rules: ⊦ m + n = 0 ↔ m = 0 ∧ n = 0; (ws)% ⊦ 2 * m = 0 ↔ m = 0; (s)% ⊦ EB_PAGE_SIZE ≠ 0; (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