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Proof step 100 from proof decode-node (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: array-splice, inst: buffer name: subarray-append-shift-right seq: ⊦ # buf ≤ m ∧ m ≤ # buf + # buf0 → subarray(buf + buf0, 0, m) = buf + subarray(buf0, 0, m - # buf) subst: [m, buf0, buf] → [ 2 * NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE), buf0, buf] flags: <all paths>

Additional information

Used simplifier rules: m1 ≠ 0 ⊦ m ≤ (* m1) * m + n0; (s)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%m2 ≠ 0 ⊦ (* m2) * m + n ≤ m + n0 ↔ (m2 - 1) * m + n ≤ n0; (s)% ⊦ m0 * 1 = m0; (s) Used terms: 2 * NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE), buf0, buf