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Proof step 134 from proof encode-node (previous step)

# buf = n1 + (n + NODE_HEADER_SIZE) + node-size-headerless(nd), # buf = n0 + n + 2 * NODE_HEADER_SIZE + nd.alignedsize, # buf0 = # buf, # buf2 = # buf, NODE_HEADER_SIZE + n0 + nd.alignedsize = node-size-headerless(nd) + n1, subarray(buf0, n + NODE_HEADER_SIZE, node-size-headerless(nd) + n1) = subarray(buf, n + NODE_HEADER_SIZE, node-size-headerless(nd) + n1), subarray(buf0, 0, n) = subarray(buf, 0, n), subarray(buf2, (n + NODE_HEADER_SIZE) + node-size-headerless(nd), n1) = subarray(buf0, (n + NODE_HEADER_SIZE) + node-size-headerless(nd), n1), subarray(buf2, 0, n + NODE_HEADER_SIZE) = subarray(buf0, 0, n + NODE_HEADER_SIZE), n1 + node-size-headerless(nd) < NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE), nd.alignedsize < NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE), nd.alignedsize < node-size-headerless(nd), node-size-headerless(nd) < NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE), # buf < 2 * NODE_HEADER_SIZE + n + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE), nd.alignedsize + 1 < NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE), n0 + nd.alignedsize < align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE), is-encoded(nodeheader(node-size-headerless(nd), false), subarray(buf0, n, NODE_HEADER_SIZE)), is-encoded(nd, subarray(buf2, n + NODE_HEADER_SIZE, node-size-headerless(nd))), n + 2 * NODE_HEADER_SIZE + nd.alignedsize ≤ # buf, n + NODE_HEADER_SIZE ≤ # buf, (n + NODE_HEADER_SIZE) + node-size-headerless(nd) ≤ # buf, align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) + n + NODE_HEADER_SIZE ≤ # buf ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: encoding-node-base name: alignedsize seq: ⊦ nd.alignedsize = align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) subst: [nd] → [nd] flags: <all paths>

Additional information

Used simplifier rules: a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m < n → (n ≤ m ↔ false); (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%n ≠ 0, m % n = 0 ⊦ align↑(m, n) = m; (s)% ⊦ m + n = m + n0 ↔ n = n0; (s)% ⊦ m < m + n ↔ n ≠ 0; (s)% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ 1 < m ↔ ¬(m = 0 ∨ m = 1); (s)% ⊦ ¬ m + n < m; (s)% ⊦ ¬ n < n; (s) Used terms: nd