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Proof step 125 from proof refine-write-data (previous step)

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), 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, n3 + m1 ≤ LEB_SIZE, m1 + n3 ≤ LEB_SIZE, ⌊err1⌋ ⊦ aehdr = empty, n3 = 0, subarray(subarray(buf1, 2 * EB_PAGE_SIZE, LEB_SIZE), m1 + n3, LEB_SIZE - m1 - n3) = mkempbuf(n1)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 126:
2 * EB_PAGE_SIZE + m2 = (avhdr = empty ⊃ EB_PAGE_SIZE;m2 + 2 * EB_PAGE_SIZE), LEB_SIZE - m1 = n2 + n3, 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), m1 + n3 ≤ LEB_SIZE, n3 + m1 ≤ 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, n3 ≤ LEB_SIZE - m1, ⌊err1⌋ ⊦ aehdr = empty, n3 = 0, subarray(subarray(buf1, 2 * EB_PAGE_SIZE, LEB_SIZE), m1 + n3, n2) = mkempbuf(n1)

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [LEB_SIZE - m1, n3, n2]

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)%n0 ≤ n ⊦ m ≤ n - n0 ↔ m + n0 ≤ n; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m ≤ n → (n < m ↔ false); (s)%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)%c: ⊦ m + n = n + m; from specification nat-basic%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: LEB_SIZE - m1, n3, n2