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Proof step 14 from proof decode-contract (previous step)

subarray(buf, n, ENCODED_ELEM_SIZE) = mkempbuf(ENCODED_ELEM_SIZE), is-encoded(a, subarray(buf, n, ENCODED_ELEM_SIZE)), n + ENCODED_ELEM_SIZE ≤ # buf ⊦ isempty(buf, n, ENCODED_ELEM_SIZE)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ n0 + n1 ≤ # buf → (isempty(buf, n0, n1) ↔ (∀ n. n0 ≤ n ∧ n < n0 + n1 → buf[n] = empty))
Proof step 16:
subarray(buf, n, ENCODED_ELEM_SIZE) = mkempbuf(ENCODED_ELEM_SIZE), is-encoded(a, subarray(buf, n, ENCODED_ELEM_SIZE)), n + ENCODED_ELEM_SIZE ≤ # buf ⊦ ∀ n2. n ≤ n2 ∧ n2 < n + ENCODED_ELEM_SIZE → buf[n2] = empty

Rule argument

spec: eraseblock name: isempty-ext seq: ⊦ n0 + n1 ≤ # buf → ( isempty(buf, n0, n1) ↔ (∀ n. n0 ≤ n ∧ n < n0 + n1 → buf[n] = empty)) subst: [n1, n0, buf] → [ENCODED_ELEM_SIZE, n, buf] flags: <all paths>

Additional information

Used terms: ENCODED_ELEM_SIZE, n, buf