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Proof step 36 from proof refine-write-data-wl (previous step)

LEB_SIZE = n0 + n, pebs[m1] = mkpeb(buf1, 2 * EB_PAGE_SIZE, false), apebs[m1] = mkpeb(aehdr, avhdr, buf2, 0, false), n = align↑(datasize(buf, n), EB_PAGE_SIZE), avhdr.valid?, aehdr.valid?, m1 < # apebs, m1 < # pebs, abs(pebs, apebs), abs-peb(mkpeb(buf1, 2 * EB_PAGE_SIZE, false), mkpeb(aehdr, avhdr, buf2, 0, false)), is-aligned(n, EB_PAGE_SIZE), mtd-cons(pebs), range=(buf1, 2 * EB_PAGE_SIZE, emptypeb, 2 * EB_PAGE_SIZE, PEB_SIZE - 2 * EB_PAGE_SIZE), 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, abs-peb (mkpeb(copy(buf, 0, buf1, 2 * EB_PAGE_SIZE, n), 2 * EB_PAGE_SIZE + n, false), mkpeb(aehdr, avhdr, subarray(buf, 0, n) + mkempbuf(n0), n, false))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 37:
LEB_SIZE = n0 + n, PEB_SIZE = n1 + 2 * EB_PAGE_SIZE, apebs[m1] = mkpeb(aehdr, avhdr, buf2, 0, false), pebs[m1] = mkpeb(buf1, 2 * EB_PAGE_SIZE, false), n = align↑(datasize(buf, n), EB_PAGE_SIZE), aehdr.valid?, avhdr.valid?, m1 < # pebs, m1 < # apebs, abs(pebs, apebs), abs-peb(mkpeb(buf1, 2 * EB_PAGE_SIZE, false), mkpeb(aehdr, avhdr, buf2, 0, false)), is-aligned(n, EB_PAGE_SIZE), mtd-cons(pebs), range=(buf1, 2 * EB_PAGE_SIZE, emptypeb, 2 * EB_PAGE_SIZE, n1), ubi-io-inv(apebs), 2 * EB_PAGE_SIZE ≤ PEB_SIZE, n ≤ LEB_SIZE, 2 * EB_PAGE_SIZE + n ≤ PEB_SIZE, n ≤ # buf ⊦ datasize(buf, n) = 0, abs-peb (mkpeb(copy(buf, 0, buf1, 2 * EB_PAGE_SIZE, n), 2 * EB_PAGE_SIZE + n, false), mkpeb(aehdr, avhdr, subarray(buf, 0, n) + mkempbuf(n0), n, false))

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [PEB_SIZE, 2 * EB_PAGE_SIZE, n1]

Additional information

Used simplifier rules: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: PEB_SIZE, 2 * EB_PAGE_SIZE, n1