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Proof step 9 from proof ls-subarray-datasize (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ n0 + n1 ≤ # buf ∧ m0 + m1 ≤ n1 → subarray(subarray(buf, n0, n1), m0, m1) = subarray(buf, n0 + m0, m1)
Proof step 11:
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 + 0, align↑(datasize(buf, n), EB_PAGE_SIZE)) + subarray(subarray(buf, 0, n), align↑(datasize(buf, n), EB_PAGE_SIZE), n2), is-aligned(n, EB_PAGE_SIZE), align↑(datasize(buf, n), EB_PAGE_SIZE) ≤ n, n ≤ # buf, align↑(datasize(buf, n), EB_PAGE_SIZE) ≤ # buf, 0 + n ≤ # buf, 0 + align↑(datasize(buf, n), EB_PAGE_SIZE) ≤ n ⊦ subarray(buf, 0, align↑(datasize(buf, n), EB_PAGE_SIZE)) + mkempbuf(n0) = subarray(buf, 0, n) + mkempbuf(n1)

Rule argument

spec: array-copy, inst: buffer name: subarray-subarray-elim seq: ⊦ n0 + n1 ≤ # buf ∧ m0 + m1 ≤ n1 → subarray(subarray(buf, n0, n1), m0, m1) = subarray(buf, n0 + m0, m1) subst: [m1, m0, n1, n0, buf] → [align↑(datasize(buf, n), EB_PAGE_SIZE), 0, n, 0, buf] flags: <all paths>

Additional information

Used simplifier rules: ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: align↑(datasize(buf, n), EB_PAGE_SIZE), 0, n, 0, buf