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Proof step 17 from proof decode-contract (previous step)

subarray(buf, n, ENCODED_ELEM_SIZE) = mkempbuf(ENCODED_ELEM_SIZE), n < # buf, n0 < n + ENCODED_ELEM_SIZE, n0 < # buf, is-encoded(a, subarray(buf, n, ENCODED_ELEM_SIZE)), n ≤ n0, n + ENCODED_ELEM_SIZE ≤ # buf ⊦ buf[n0] = empty

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n])
Proof step 19:
# subarray(buf, n, ENCODED_ELEM_SIZE) = # mkempbuf(ENCODED_ELEM_SIZE), n0 < # buf, n0 < n + ENCODED_ELEM_SIZE, n < # buf, is-encoded(a, subarray(buf, n, ENCODED_ELEM_SIZE)), n + ENCODED_ELEM_SIZE ≤ # buf, n ≤ n0, ∀ n0. n0 < # subarray(buf, n, ENCODED_ELEM_SIZE) → subarray(buf, n, ENCODED_ELEM_SIZE)[n0] = mkempbuf(ENCODED_ELEM_SIZE)[n0] ⊦ buf[n0] = empty

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, n, ENCODED_ELEM_SIZE)] flags: <all paths>

Additional information

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