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Proof step 8 from proof valid-peb0-write-append (previous step)

# buf = LEB_SIZE, m0 + # buf0 = LEB_SIZE, subarray(buf, m, LEB_SIZE - m) = mkempbuf(LEB_SIZE - m), aehdr.valid?, is-aligned(m, EB_PAGE_SIZE), m4 ≤ datasize(buf), m ≤ m0, m4 ≤ LEB_SIZE, m ≤ LEB_SIZE ⊦ aehdr = empty, m4 = 0, m4 ≤ datasize(subarray(buf, 0, m0) + buf0) ∧ checksum(buf, m4) = checksum(subarray(buf, 0, m0) + buf0, m4)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 9:
# buf = LEB_SIZE, m0 + # buf0 = LEB_SIZE, LEB_SIZE = n0 + m, subarray(buf, m, n0) = mkempbuf(n0), aehdr.valid?, is-aligned(m, EB_PAGE_SIZE), m ≤ LEB_SIZE, m4 ≤ LEB_SIZE, m ≤ m0, m4 ≤ datasize(buf) ⊦ aehdr = empty, m4 = 0, m4 ≤ datasize(subarray(buf, 0, m0) + buf0) ∧ checksum(buf, m4) = checksum(subarray(buf, 0, m0) + buf0, m4)

Rule argument

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

Additional information

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