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Proof step 23 from proof valid-peb0-write-append (previous step)

# 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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 24:
# buf = LEB_SIZE, LEB_SIZE = (n + # buf0) + m, aehdr.valid?, n0 < n, is-aligned(m, EB_PAGE_SIZE), m + n ≤ LEB_SIZE, m4 ≤ datasize(buf), m4 ≤ LEB_SIZE, m ≤ LEB_SIZE, ∀ n1. n1 < n + # buf0 → buf[m + n1] = empty ⊦ 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 → mkempbuf(n)[m] = empty; (s)% ⊦ n0 < n → subarray(buf, m, n)[n0] = buf[m + n0]; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n = m + n0 ↔ n = n0; (s)% ⊦ # mkempbuf(n) = n; (s)% ⊦ # subarray(buf, m, n) = n; (s)