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Proof step 21 from proof valid-peb0-write-append (previous step)

# buf = LEB_SIZE, LEB_SIZE = (n + # buf0) + m, subarray(buf, m, n + # buf0) = mkempbuf(n + # buf0), aehdr.valid?, n0 < n, is-aligned(m, EB_PAGE_SIZE), m + n ≤ LEB_SIZE, m4 ≤ datasize(buf), m4 ≤ LEB_SIZE, m ≤ LEB_SIZE ⊦ buf[m + n0] = empty, aehdr = empty, m4 = 0, m4 ≤ (datasize(buf0) = 0 ⊃ datasize(buf, m + n);(m + n) + datasize(buf0)) ∧ checksum(buf, m4) = checksum(subarray(buf, 0, m + n) + buf0, m4)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 22:
⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n])
Proof step 23:
# subarray(buf, m, n + # buf0) = # mkempbuf(n + # buf0), # buf = LEB_SIZE, LEB_SIZE = (n + # buf0) + m, aehdr.valid?, n0 < n, is-aligned(m, EB_PAGE_SIZE), m ≤ LEB_SIZE, m4 ≤ LEB_SIZE, m4 ≤ datasize(buf), m + n ≤ LEB_SIZE, ∀ n0. n0 < # subarray(buf, m, n + # buf0) → subarray(buf, m, n + # buf0)[n0] = mkempbuf(n + # buf0)[n0] ⊦ buf[m + n0] = empty, aehdr = empty, m4 = 0, m4 ≤ (datasize(buf0) = 0 ⊃ datasize(buf, m + n);(m + n) + datasize(buf0)) ∧ checksum(buf, m4) = checksum(subarray(buf, 0, m + n) + buf0, m4)

Rule argument

spec: array, inst: buffer name: Extension seq: ⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n]) subst: [buf0, buf] → [mkempbuf(n + # buf0), subarray(buf, m, n + # buf0)] flags: <all paths>

Additional information

Used terms: mkempbuf(n + # buf0), subarray(buf, m, n + # buf0)