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Proof step 111 from proof decode-node (previous step)

# buf1 = align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE), # buf = NODE_HEADER_SIZE, subarray(buf2, 0, NODE_HEADER_SIZE) = validtrailer, is-encoded(nodeheader(node-size-headerless(nd), false), buf), is-encoded(nd, subarray(buf1 + buf2, 0, node-size-headerless(nd))), NODE_HEADER_SIZE ≤ # buf2, node-size-headerless(nd) ≤ # buf1 + # buf2 ⊦ ∃ buf0, buf3. buf + buf1 = buf0 + buf3 ∧ is-encoded(nodeheader(node-size-headerless(nd), false), buf0) ∧ is-encoded(nd, subarray(buf3, 0, node-size-headerless(nd))) ∧ # buf3 = # buf1

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: array-splice, inst: buffer name: subarray-elim seq: ⊦ n + m ≤ # buf → ( buf0 = subarray(buf, n, m) ↔ (∃ buf1, buf2. buf = buf1 + buf0 + buf2 ∧ # buf1 = n ∧ # buf0 = m)) subst: [buf0, m, n, buf] → [validtrailer, NODE_HEADER_SIZE, 0, buf2] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m ≠ n → (m ≤ n ↔ m < n); (s)% ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m < n → m ≤ n; (s)%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)% ⊦ 2 * m = 0 ↔ m = 0; (s)% ⊦ NODE_HEADER_SIZE ≠ 0; (s)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m ≤ n → (n < m ↔ false); (s)%n ≠ 0, m % n = 0 ⊦ align↑(m, n) = m; (s)%n = # buf ⊦ subarray(buf + buf0, 0, n) = buf; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer] Used terms: validtrailer, NODE_HEADER_SIZE, 0, buf2