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Proof step 49 from proof valid-peb-write-valid-peb (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 50:
⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n])
Proof step 51:
# subarray(buf, m, n0) = # mkempbuf(n0), # 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, ∀ n. n < # subarray(buf, m, n0) → subarray(buf, m, n0)[n] = mkempbuf(n0)[n] ⊦ buf[n2] = (subarray(buf, 0, m0) + mkempbuf(n1))[n2], aehdr = empty, m3 = 0, m3 ≤ datasize(subarray(buf, 0, m0) + buf1) ∧ checksum(buf, m3) = checksum(subarray(buf, 0, m0) + buf1, m3)

Rule argument

spec: array, inst: buffer name: Extension seq: ⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n]) subst: [buf0, buf] → [mkempbuf(n0), subarray(buf, m, n0)] flags: <all paths>

Additional information

Used terms: mkempbuf(n0), subarray(buf, m, n0)