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Proof step 22 from proof encode-contract (previous step)

# buf1 = n0 + ENCODED_ELEM_SIZE, # buf = n0 + ENCODED_ELEM_SIZE, subarray(buf1, ENCODED_ELEM_SIZE, n0) = subarray(buf, ENCODED_ELEM_SIZE, n0), subarray(buf1, 0, EB_PAGE_SIZE) = emptypage, is-encoded(a, subarray(buf1, 0, ENCODED_ELEM_SIZE)), ENCODED_ELEM_SIZE ≤ EB_PAGE_SIZE, EB_PAGE_SIZE ≤ n0 + ENCODED_ELEM_SIZE ⊦ subarray(buf1, 0, ENCODED_ELEM_SIZE) = mkempbuf(ENCODED_ELEM_SIZE)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 23:
⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n])
Proof step 24:
# subarray(buf1, 0, EB_PAGE_SIZE) = # emptypage, # buf = n0 + ENCODED_ELEM_SIZE, # buf1 = n0 + ENCODED_ELEM_SIZE, subarray(buf1, ENCODED_ELEM_SIZE, n0) = subarray(buf, ENCODED_ELEM_SIZE, n0), is-encoded(a, subarray(buf1, 0, ENCODED_ELEM_SIZE)), EB_PAGE_SIZE ≤ n0 + ENCODED_ELEM_SIZE, ENCODED_ELEM_SIZE ≤ EB_PAGE_SIZE, ∀ n. n < # subarray(buf1, 0, EB_PAGE_SIZE) → subarray(buf1, 0, EB_PAGE_SIZE)[n] = (emptypage)[n] ⊦ subarray(buf1, 0, ENCODED_ELEM_SIZE) = mkempbuf(ENCODED_ELEM_SIZE)

Rule argument

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

Additional information

Used terms: emptypage, subarray(buf1, 0, EB_PAGE_SIZE)