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Proof step 25 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), is-encoded(a, subarray(buf1, 0, ENCODED_ELEM_SIZE)), ENCODED_ELEM_SIZE ≤ EB_PAGE_SIZE, EB_PAGE_SIZE ≤ n0 + ENCODED_ELEM_SIZE, ∀ n. n < EB_PAGE_SIZE → buf1[n] = empty ⊦ subarray(buf1, 0, ENCODED_ELEM_SIZE) = mkempbuf(ENCODED_ELEM_SIZE)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 26:
⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n])
Proof step 27:
# 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 < EB_PAGE_SIZE → buf1[n] = empty ⊦ # subarray(buf1, 0, ENCODED_ELEM_SIZE) = # mkempbuf(ENCODED_ELEM_SIZE) ∧ (∀ n. n < # subarray(buf1, 0, ENCODED_ELEM_SIZE) → subarray(buf1, 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(buf1, 0, ENCODED_ELEM_SIZE)] flags: <all paths>

Additional information

Used terms: mkempbuf(ENCODED_ELEM_SIZE), subarray(buf1, 0, ENCODED_ELEM_SIZE)