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Proof step 14 from proof ls-subarray-datasize (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
LEB_SIZE = n + n1, LEB_SIZE = align↑(datasize(buf, n), EB_PAGE_SIZE) + n0, n = n2 + align↑(datasize(buf, n), EB_PAGE_SIZE), subarray(buf, 0, n) = subarray(buf, 0, align↑(datasize(buf, n), EB_PAGE_SIZE)) + mkempbuf(n2), is-aligned(n, EB_PAGE_SIZE), n ≤ # buf, align↑(datasize(buf, n), EB_PAGE_SIZE) ≤ n, align↑(datasize(buf, n), EB_PAGE_SIZE) ≤ # buf ⊦ subarray(buf, 0, align↑(datasize(buf, n), EB_PAGE_SIZE)) + mkempbuf(n0) = subarray(buf, 0, n) + mkempbuf(n1)

Rule argument

Additional information

Used simplifier rules: subbarray-alignup-datasize-empty: ⊦ n0 ≤ # buf ∧ n0 = n1 + align↑(datasize(buf, n0), EB_PAGE_SIZE) → subarray(buf, align↑(datasize(buf, n0), EB_PAGE_SIZE), n1) = mkempbuf(n1);% ⊦ m ≤ m; (s)%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)