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Proof step 20 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?, is-aligned(m, EB_PAGE_SIZE), m + n ≤ LEB_SIZE, m4 ≤ datasize(buf), m4 ≤ LEB_SIZE, m ≤ LEB_SIZE ⊦ 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), # subarray(buf, m, n) = # mkempbuf(n) ∧ (∀ n0. n0 < # subarray(buf, m, n) → subarray(buf, m, n)[n0] = mkempbuf(n)[n0])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
# 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)

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m < n → mkempbuf(n)[m] = empty; (s)% ⊦ n0 < n → subarray(buf, m, n)[n0] = buf[m + n0]; (s)% ⊦ # mkempbuf(n) = n; (s)% ⊦ # subarray(buf, m, n) = n; (s)