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Proof step 76 from proof synced-write-buf (previous step)

# lpt = # avol, # buf0 + n0 = align↓(# buf0 + n, EB_PAGE_SIZE), avol[m1] = mapped(buf0), m1 < # avol, awbuf-inv(avol, buffered(m1)), is-aligned(# buf0 + n0, EB_PAGE_SIZE), avol0 ↓ avol[m1, mapped(buf0 + subarray(buf, 0, n))], n ≤ # buf, # buf0 + n ≤ LEB_SIZE, EB_PAGE_SIZE ≤ # buf0 % EB_PAGE_SIZE + n, n0 ≤ # buf ⊦ subarray(subarray(buf, 0, n), 0, n0) = subarray(buf, 0, n0), is-aligned(# buf0 + n, EB_PAGE_SIZE)

User applied rule insert rewrite lemma

And obtained the following new goals

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] → [n0, 0, n, 0, buf] flags: <all paths>

Additional information

Used simplifier rules: ⊦ EB_PAGE_SIZE ≠ 0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ subarray(buf, n0, n1) = subarray(buf, n0, n2) ↔ n1 = n2; (ss)%n ≠ 0, m % n = 0 ⊦ align↓(m, n) = m; (s)% ⊦ m + n = m + n0 ↔ n = n0; (s)% ⊦ n + 0 = n; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)%m ≠ 0 ⊦ align↓(n0 + n1, m) = n2 + n1 → ¬ n0 < n2; (s) Used terms: n0, 0, n, 0, buf