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Proof step 6 from proof align-down-elim (previous step)

⊦ buf = subarray(buf, 0, align↓(# buf, EB_PAGE_SIZE)) + subarray(buf, align↓(# buf, EB_PAGE_SIZE), # buf % EB_PAGE_SIZE) ∧ # buf < EB_PAGE_SIZE + align↓(# buf, EB_PAGE_SIZE)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ n0 + n1 ≤ # buf → subarray(buf, 0, n0) + subarray(buf, n0, n1) = subarray(buf, 0, n0 + n1)

Rule argument

spec: array-splice, inst: buffer name: subarray-append-consec0 seq: ⊦ n0 + n1 ≤ # buf → subarray(buf, 0, n0) + subarray(buf, n0, n1) = subarray(buf, 0, n0 + n1) subst: [n1, n0, buf] → [# buf % EB_PAGE_SIZE, align↓(# buf, EB_PAGE_SIZE), buf] flags: <all paths>

Additional information

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