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Proof step 58 from proof valid-peb-write-valid-peb (previous step)

# buf = LEB_SIZE, LEB_SIZE = n1 + m0, LEB_SIZE = n0 + m, apebs[n] = mkpeb(aehdr, avidhdr(v, m2, m4, m3, checksum(buf, m3)), buf, m, false), aehdr.valid?, m0 < LEB_SIZE, n < # apebs, m < LEB_SIZE, n2 < LEB_SIZE, is-aligned(m, EB_PAGE_SIZE), m ≤ n2, m0 ≤ n2, m ≤ m0, m3 ≤ datasize(buf), m3 ≤ LEB_SIZE, ∀ n3. n3 < n0 → buf[m + n3] = empty ⊦ buf[n2] = mkempbuf(n1)[n2 - m0], aehdr = empty, m3 = 0, n0 = 0, n1 = 0, m3 ≤ datasize(subarray(buf, 0, m0) + buf1) ∧ checksum(buf, m3) = checksum(subarray(buf, 0, m0) + buf1, m3)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 59:
# buf = LEB_SIZE, LEB_SIZE = n0 + m, LEB_SIZE = n1 + m0, apebs[n] = mkpeb(aehdr, avidhdr(v, m2, m4, m3, checksum(buf, m3)), buf, m, false), n2 = n4 + m0, aehdr.valid?, n2 < LEB_SIZE, m < LEB_SIZE, n < # apebs, m0 < LEB_SIZE, is-aligned(m, EB_PAGE_SIZE), m3 ≤ LEB_SIZE, m3 ≤ datasize(buf), m ≤ m0, m0 ≤ n2, m ≤ n2, ∀ n3. n3 < n0 → buf[m + n3] = empty ⊦ buf[n2] = mkempbuf(n1)[n4], aehdr = empty, m3 = 0, n0 = 0, n1 = 0, m3 ≤ datasize(subarray(buf, 0, m0) + buf1) ∧ checksum(buf, m3) = checksum(subarray(buf, 0, m0) + buf1, m3)

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [n2, m0, n4]

Additional information

Used simplifier rules: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: n2, m0, n4