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Proof step 50 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 - m1 = n1 + n, LEB_SIZE = (n0 + n) + 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, 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), is-aligned(m1, EB_PAGE_SIZE), mtd-cons(pebs), ubi-io-inv(apebs), n2 + n ≤ # buf, m1 ≤ LEB_SIZE, m2 ≤ LEB_SIZE, m2 ≤ m1, (m1 + 2 * EB_PAGE_SIZE) + n ≤ PEB_SIZE, m1 + n ≤ LEB_SIZE, n + m1 ≤ LEB_SIZE ⊦ (m1 + 2 * EB_PAGE_SIZE) + n = (aehdr = empty ⊃ 0;(avhdr = empty ⊃ EB_PAGE_SIZE;(m1 + n) + 2 * EB_PAGE_SIZE)) ∧ subarray(subarray(buf1, 2 * EB_PAGE_SIZE, LEB_SIZE), m1 + n, n1) = mkempbuf(n0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 51:
2 * EB_PAGE_SIZE + m2 = (aehdr = empty ⊃ 0;(avhdr = empty ⊃ EB_PAGE_SIZE;m2 + 2 * EB_PAGE_SIZE)), LEB_SIZE = (n0 + n) + m1, LEB_SIZE = 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), n3 = n1 + n, avhdr.valid?, aehdr.valid?, 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), mtd-cons(pebs), ubi-io-inv(apebs), n + m1 ≤ LEB_SIZE, m1 + n ≤ LEB_SIZE, (m1 + 2 * EB_PAGE_SIZE) + n ≤ PEB_SIZE, m2 ≤ m1, m2 ≤ LEB_SIZE, m1 ≤ LEB_SIZE, n2 + n ≤ # buf ⊦ (m1 + 2 * EB_PAGE_SIZE) + n = (aehdr = empty ⊃ 0;(avhdr = empty ⊃ EB_PAGE_SIZE;(m1 + n) + 2 * EB_PAGE_SIZE)) ∧ subarray(subarray(buf1, 2 * EB_PAGE_SIZE, LEB_SIZE), m1 + n, n1) = mkempbuf(n0)

Rule argument

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

Additional information

Used simplifier rules: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: LEB_SIZE, m1, n3