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Proof step 41 from proof valid-peb-write-valid-peb (previous step)

LEB_SIZE = n0 + m, LEB_SIZE = n1 + m0, apebs[n] = mkpeb(aehdr, avidhdr(v, m2, m4, m3, checksum(subarray(buf, 0, m0), m3)), subarray(buf, 0, m0) + mkempbuf(n1), m, false), datasize(buf1) = 0, subarray(subarray(buf, 0, m0) + mkempbuf(n1), m, n0) = mkempbuf(n0), aehdr.valid?, datasize(subarray(buf, 0, m0), m0) < datasize(subarray(buf, 0, m0)), n < # apebs, datasize(subarray(buf, 0, m0), m0) < m3, datasize(subarray(buf, 0, m0), m0) < LEB_SIZE, datasize(subarray(buf, 0, m0), m0) < m0, is-aligned(m, EB_PAGE_SIZE), m3 ≤ LEB_SIZE, m3 ≤ m0, m ≤ m0, m0 ≤ LEB_SIZE, m ≤ LEB_SIZE, m3 ≤ datasize(subarray(buf, 0, m0)) ⊦ aehdr = empty

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: datasize name: datasize seq: ⊦ datasize(buf) = datasize(buf, # buf) subst: [buf] → [subarray(buf, 0, m0)] flags: <all paths>

Additional information

Used simplifier rules: ls-array-append-length0: # buf0 = 0 ⊦ buf + buf0 = buf;% ⊦ # subarray(buf, m, n) = n; (s)% ⊦ m < n → (n ≤ m ↔ false); (s)%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)% ⊦ # mkempbuf(n) = n; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ ¬ n < n; (s) Used terms: subarray(buf, 0, m0)