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

subarray(buf, 0, EB_PAGE_SIZE) = emptypage, n < ENCODED_ELEM_SIZE, n < # buf, n < EB_PAGE_SIZE, is-encoded(a, subarray(buf, 0, ENCODED_ELEM_SIZE)), ENCODED_ELEM_SIZE ≤ # buf, ENCODED_ELEM_SIZE ≤ EB_PAGE_SIZE, EB_PAGE_SIZE ≤ # buf ⊦ buf[n] = empty

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(buf, 0, EB_PAGE_SIZE) = # emptypage, n < EB_PAGE_SIZE, n < # buf, n < ENCODED_ELEM_SIZE, is-encoded(a, subarray(buf, 0, ENCODED_ELEM_SIZE)), EB_PAGE_SIZE ≤ # buf, ENCODED_ELEM_SIZE ≤ EB_PAGE_SIZE, ENCODED_ELEM_SIZE ≤ # buf, ∀ n. n < # subarray(buf, 0, EB_PAGE_SIZE) → subarray(buf, 0, EB_PAGE_SIZE)[n] = (emptypage)[n] ⊦ buf[n] = empty

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(buf, 0, EB_PAGE_SIZE)] flags: <all paths>

Additional information

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