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Proof step 105 from proof refine-write-data (previous step)

pebs[m3] = mkpeb(buf1, 2 * EB_PAGE_SIZE + m2, false), apebs[m3] = mkpeb(aehdr, avhdr, buf0, m2, false), aehdr.valid?, avhdr.valid?, m3 < # pebs, m3 < # apebs, n3 < n, abs(pebs, apebs), abs-peb(mkpeb(buf1, 2 * EB_PAGE_SIZE + m2, false), mkpeb(aehdr, avhdr, buf0, m2, false)), 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, n3 + m1 ≤ LEB_SIZE, m2 ≤ LEB_SIZE, m1 ≤ LEB_SIZE, ⌊err1⌋ ⊦ n3 = 0, abs-peb (mkpeb(copy(buf, n0, buf1, m1 + 2 * EB_PAGE_SIZE, n3), (m1 + 2 * EB_PAGE_SIZE) + n3, false), mkpeb(aehdr, avhdr, subarray(buf0, 0, m1) + subarray(buf, n0, n3) + mkempbuf(LEB_SIZE - m1 - n3), m1 + n3, false))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 106:
LEB_SIZE - m1 = n1 + n3, apebs[m3] = mkpeb(aehdr, avhdr, buf0, 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-peb(mkpeb(buf1, 2 * EB_PAGE_SIZE + m2, false), mkpeb(aehdr, avhdr, buf0, m2, false)), 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), m1 ≤ LEB_SIZE, m2 ≤ LEB_SIZE, n3 + m1 ≤ LEB_SIZE, n0 + n3 ≤ # buf, m1 + n ≤ LEB_SIZE, n0 + n ≤ # buf, (m1 + 2 * EB_PAGE_SIZE) + n3 ≤ PEB_SIZE, m2 ≤ m1, n3 ≤ LEB_SIZE - m1, ⌊err1⌋ ⊦ n3 = 0, abs-peb (mkpeb(copy(buf, n0, buf1, m1 + 2 * EB_PAGE_SIZE, n3), (m1 + 2 * EB_PAGE_SIZE) + n3, false), mkpeb(aehdr, avhdr, subarray(buf0, 0, m1) + subarray(buf, n0, n3) + mkempbuf(n1), m1 + n3, false))

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [LEB_SIZE - m1, n3, n1]

Additional information

Used simplifier rules: ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m ≤ n → (n < m ↔ false); (s)%n0 ≤ n ⊦ m ≤ n - n0 ↔ m + n0 ≤ n; (s)%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: LEB_SIZE - m1, n3, n1