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Proof step 4 from proof align-down-app-same (previous step)

⊦ # subarray(buf0 + buf1, 0, align↓(# buf0 + # buf1, EB_PAGE_SIZE)) = # subarray(buf0, 0, align↓(# buf0, EB_PAGE_SIZE)) ∧ (∀ n. n < # subarray(buf0 + buf1, 0, align↓(# buf0 + # buf1, EB_PAGE_SIZE)) → subarray(buf0 + buf1, 0, align↓(# buf0 + # buf1, EB_PAGE_SIZE))[n] = subarray(buf0, 0, align↓(# buf0, EB_PAGE_SIZE))[n]) ↔ # buf0 % EB_PAGE_SIZE + # buf1 < EB_PAGE_SIZE

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
# buf0 % EB_PAGE_SIZE < # buf0, n < # buf0 + # buf1, # buf0 % EB_PAGE_SIZE + # buf1 < EB_PAGE_SIZE, n < align↓(# buf0 + # buf1, EB_PAGE_SIZE), EB_PAGE_SIZE ≤ # buf0 + # buf1 ⊦ (buf0 + buf1)[n] = subarray(buf0, 0, align↓(# buf0, EB_PAGE_SIZE))[n]

Rule argument

Additional information

Used simplifier rules: ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ m < n → n ≠ 0; (s)%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat% ⊦ m < n ↔ ¬ n ≤ m; (ss)%n ≠ 0 ⊦ align↓(m, n) = 0 ↔ m < n; (s)%aligndown-is-smaller: m ≠ 0 ⊦ n0 < align↓(n, m) → n0 < n; (forward) from specification align%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ n + 0 = n; (s)% ⊦ n0 < n → subarray(buf, m, n)[n0] = buf[m + n0]; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%m ≠ 0 ⊦ align↓(n0 + n1, m) = align↓(n0, m) ↔ n0 % m + n1 < m; (s)% ⊦ EB_PAGE_SIZE ≠ 0; (s)% ⊦ # subarray(buf, m, n) = n; (s)