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Proof step 4 from proof align-down-elim (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 5:
# buf = n0 + align↓(# buf, EB_PAGE_SIZE), align↓(# buf, EB_PAGE_SIZE) ≤ # buf ⊦ buf = subarray(buf, 0, align↓(# buf, EB_PAGE_SIZE)) + subarray(buf, align↓(# buf, EB_PAGE_SIZE), n0) ∧ # buf < EB_PAGE_SIZE + align↓(# buf, EB_PAGE_SIZE)

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [# buf, align↓(# buf, EB_PAGE_SIZE), n]

Additional information

Used simplifier rules: ⊦ EB_PAGE_SIZE ≠ 0; (s)%m ≠ 0 ⊦ align↓(n0, m) ≤ n0; (s)%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: # buf, align↓(# buf, EB_PAGE_SIZE), n