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Proof step 17 from proof range-eq-validtrailer (previous step)

subarray(mkempbuf(n), n0, NODE_HEADER_SIZE) = validtrailer, is-aligned(n0, NODE_HEADER_SIZE), is-aligned(# buf, NODE_HEADER_SIZE), n0 + NODE_HEADER_SIZE ≤ n ⊦ n = 0, isempty(validtrailer, 0, NODE_HEADER_SIZE)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ n0 + n1 ≤ # buf → (isempty(buf, n0, n1) ↔ (∀ n. n0 ≤ n ∧ n < n0 + n1 → buf[n] = empty))
Proof step 19:
subarray(mkempbuf(n), n0, NODE_HEADER_SIZE) = validtrailer, is-aligned(# buf, NODE_HEADER_SIZE), is-aligned(n0, NODE_HEADER_SIZE), n0 + NODE_HEADER_SIZE ≤ n, 0 + NODE_HEADER_SIZE ≤ # validtrailer ⊦ n = 0, ∀ n. 0 ≤ n ∧ n < 0 + NODE_HEADER_SIZE → (validtrailer)[n] = 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] → [NODE_HEADER_SIZE, 0, validtrailer] flags: <all paths>

Additional information

Used simplifier rules: ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ # validtrailer = NODE_HEADER_SIZE; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ ¬ n < n; (s) Used terms: NODE_HEADER_SIZE, 0, validtrailer