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Proof step 2 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)) ↔ # buf0 % EB_PAGE_SIZE + # buf1 < EB_PAGE_SIZE

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n])
Proof step 4:
⊦ # 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

Rule argument

spec: array, inst: buffer name: Extension seq: ⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n]) subst: [buf0, buf] → [subarray(buf0, 0, align↓(# buf0, EB_PAGE_SIZE)), subarray (buf0 + buf1, 0, align↓(# buf0 + # buf1, EB_PAGE_SIZE))] flags: <all paths>

Additional information

Used terms: subarray(buf0, 0, align↓(# buf0, EB_PAGE_SIZE)), subarray(buf0 + buf1, 0, align↓(# buf0 + # buf1, EB_PAGE_SIZE))