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Proof step 54 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?, n < # apebs, n2 < LEB_SIZE, is-aligned(m, EB_PAGE_SIZE), m ≤ LEB_SIZE, m0 ≤ LEB_SIZE, m ≤ m0, m3 ≤ datasize(buf), m3 ≤ LEB_SIZE, ∀ n3. n3 < n0 → buf[m + n3] = empty ⊦ buf[n2] = (subarray(buf, 0, m0) + mkempbuf(n1))[n2], aehdr = empty, m3 = 0, n2 < # subarray(buf, 0, m0), m3 ≤ datasize(subarray(buf, 0, m0) + buf1) ∧ checksum(buf, m3) = checksum(subarray(buf, 0, m0) + buf1, m3)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 55:
# 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, n2 < LEB_SIZE, m < 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] = (subarray(buf, 0, m0) + mkempbuf(n1))[n2], 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

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m < m + n ↔ n ≠ 0; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ m < n → m ≤ n; (s)%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ # subarray(buf, m, n) = n; (s)