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Proof step 48 from proof valid-peb-write-valid-peb (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 49:
# 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)

Rule argument

Additional information

Used simplifier rules: ⊦ LEB_SIZE ≠ 0; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ # mkempbuf(n) = n; (s)% ⊦ # subarray(buf, m, n) = n; (s)% ⊦ #(buf + buf0) = # buf + # buf0; (s)