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Proof step 12 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(buf, 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, align↑(datasize(buf, n), EB_PAGE_SIZE) ≤ n, n ≤ # buf ⊦ 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 13:
⊦ n0 + n1 ≤ # buf ∧ m0 + m1 ≤ n1 → subarray(subarray(buf, n0, n1), m0, m1) = subarray(buf, n0 + m0, m1)
Proof step 14:
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)

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] → [n2, align↑(datasize(buf, n), EB_PAGE_SIZE), n, 0, buf] flags: <all paths>

Additional information

Used simplifier rules: ls-array-append-length0: # buf0 = 0 ⊦ buf + buf0 = buf;% ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m ≠ n → (m ≤ n ↔ m < n); (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ m < n → n ≠ 0; (s)% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ ¬ n < n; (s)%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)% ⊦ EB_PAGE_SIZE ≠ 0; (s)%n ≠ 0, m % n = 0 ⊦ align↑(m, n) = m; (s)% ⊦ # subarray(buf, m, n) = n; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ # mkempbuf(n) = n; (s) Used terms: n2, align↑(datasize(buf, n), EB_PAGE_SIZE), n, 0, buf