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Proof step 19 from proof decode-contract (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n])
Proof step 21:
subarray(buf, 0, EB_PAGE_SIZE) = emptypage, is-encoded(a, subarray(buf, 0, ENCODED_ELEM_SIZE)), EB_PAGE_SIZE ≤ # buf, ENCODED_ELEM_SIZE ≤ EB_PAGE_SIZE, ENCODED_ELEM_SIZE ≤ # buf ⊦ # subarray(buf, 0, ENCODED_ELEM_SIZE) = # mkempbuf(ENCODED_ELEM_SIZE) ∧ (∀ n. n < # subarray(buf, 0, ENCODED_ELEM_SIZE) → subarray(buf, 0, ENCODED_ELEM_SIZE)[n] = mkempbuf(ENCODED_ELEM_SIZE)[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(ENCODED_ELEM_SIZE), subarray(buf, 0, ENCODED_ELEM_SIZE)] flags: <all paths>

Additional information

Used terms: mkempbuf(ENCODED_ELEM_SIZE), subarray(buf, 0, ENCODED_ELEM_SIZE)