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Proof step 6 from proof ls-subarray-datasize (previous step)

LEB_SIZE = n + n1, LEB_SIZE = align↑(datasize(buf, n), EB_PAGE_SIZE) + n0, is-aligned(n, EB_PAGE_SIZE), n ≤ # buf, align↑(datasize(buf, n), EB_PAGE_SIZE) < n → subarray(buf, 0, n) = subarray(subarray(buf, 0, n), 0, align↑(datasize(buf, n), EB_PAGE_SIZE)) + subarray(subarray(buf, 0, n), align↑(datasize(buf, n), EB_PAGE_SIZE), n - align↑(datasize(buf, n), EB_PAGE_SIZE)) ⊦ subarray(buf, 0, align↑(datasize(buf, n), EB_PAGE_SIZE)) + mkempbuf(n0) = subarray(buf, 0, n) + mkempbuf(n1)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 7:
LEB_SIZE = align↑(datasize(buf, n), EB_PAGE_SIZE) + n0, LEB_SIZE = n + n1, n = n2 + align↑(datasize(buf, n), EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), n ≤ # buf, align↑(datasize(buf, n), EB_PAGE_SIZE) ≤ n, align↑(datasize(buf, n), EB_PAGE_SIZE) < n → subarray(buf, 0, n) = subarray(subarray(buf, 0, n), 0, align↑(datasize(buf, n), EB_PAGE_SIZE)) + subarray(subarray(buf, 0, n), align↑(datasize(buf, n), EB_PAGE_SIZE), n2) ⊦ subarray(buf, 0, align↑(datasize(buf, n), EB_PAGE_SIZE)) + mkempbuf(n0) = subarray(buf, 0, n) + mkempbuf(n1)

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [n, align↑(datasize(buf, n), EB_PAGE_SIZE), n2]

Additional information

Used simplifier rules: ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ EB_PAGE_SIZE ≠ 0; (s)%n ≠ 0, is-aligned(m, n) ⊦ m < align↑(m0, n) ↔ m < m0; (s)% ⊦ ¬ n < datasize(buf, n); (s)%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: n, align↑(datasize(buf, n), EB_PAGE_SIZE), n2