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Proof step 3 from proof subbarray-alignup-datasize-empty (previous step)

n0 = n1 + align↑(datasize(buf, n0), EB_PAGE_SIZE), n0 ≤ # buf ⊦ subarray(buf, align↑(datasize(buf, n0), EB_PAGE_SIZE), n1) = mkempbuf(n1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n])
Proof step 5:
n0 = n1 + align↑(datasize(buf, n0), EB_PAGE_SIZE), n0 ≤ # buf ⊦ # subarray(buf, align↑(datasize(buf, n0), EB_PAGE_SIZE), n1) = # mkempbuf(n1) ∧ (∀ n. n < # subarray(buf, align↑(datasize(buf, n0), EB_PAGE_SIZE), n1) → subarray(buf, align↑(datasize(buf, n0), EB_PAGE_SIZE), n1)[n] = mkempbuf(n1)[n])

Rule argument

spec: array, inst: buffer name: Extension seq: ⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n]) subst: [buf0, buf] → [mkempbuf(n1), subarray(buf, align↑(datasize(buf, n0), EB_PAGE_SIZE), n1)] flags: <all paths>

Additional information

Used terms: mkempbuf(n1), subarray(buf, align↑(datasize(buf, n0), EB_PAGE_SIZE), n1)