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Proof step 9 from proof valid-peb0-write-append (previous step)

# 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)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ m ≤ n ↔ (∃ n0. m + n0 = n)
Proof step 11:
# 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), m4 ≤ datasize(buf), m4 ≤ LEB_SIZE, m ≤ LEB_SIZE, ∃ n0. m + n0 = m0 ⊦ 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: le-addex seq: ⊦ m ≤ n ↔ (∃ n0. m + n0 = n) subst: [n, m] → [m0, m] flags: <all paths>

Additional information

Used terms: m0, m