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Proof step 168 from proof encode-node (previous step)

# buf2 = # buf, # buf0 = # buf, # buf = n0 + n + 2 * NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE), # buf = n1 + (n + NODE_HEADER_SIZE) + node-size-headerless(nd), NODE_HEADER_SIZE + n0 + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) = node-size-headerless(nd) + n1, subarray(buf2, 0, n + NODE_HEADER_SIZE) = subarray(buf0, 0, n + NODE_HEADER_SIZE), subarray(buf0, 0, n) = subarray(buf, 0, n), subarray(buf0, n + NODE_HEADER_SIZE, node-size-headerless(nd) + n1) = subarray(buf, n + NODE_HEADER_SIZE, node-size-headerless(nd) + n1), n2 < n0, is-encoded(nodeheader(node-size-headerless(nd), false), subarray(buf0, n, NODE_HEADER_SIZE)), (n + NODE_HEADER_SIZE) + node-size-headerless(nd) ≤ # buf, n + NODE_HEADER_SIZE ≤ # buf, n + 2 * NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) ≤ # buf, ⌊err⌋ , NODE_HEADER_SIZE + n2 + (align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) - node-size-headerless(nd)) < n1 → buf2 [2 * NODE_HEADER_SIZE + n + node-size-headerless(nd) + n2 + (align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) - node-size-headerless(nd)) ] = buf0 [2 * NODE_HEADER_SIZE + n + node-size-headerless(nd) + n2 + (align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) - node-size-headerless(nd)) ] ⊦ buf2[(n + 2 * NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE)) + n2] = buf[(n + 2 * NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE)) + n2]

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 169:
# buf = n1 + (n + NODE_HEADER_SIZE) + node-size-headerless(nd), # buf = n0 + n + 2 * NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE), # buf0 = # buf, # buf2 = # buf, NODE_HEADER_SIZE + n0 + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) = node-size-headerless(nd) + n1, align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) = n3 + node-size-headerless(nd), 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, 0, n + NODE_HEADER_SIZE) = subarray(buf0, 0, n + NODE_HEADER_SIZE), n2 < n0, is-encoded(nodeheader(node-size-headerless(nd), false), subarray(buf0, n, NODE_HEADER_SIZE)), n + 2 * NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) ≤ # buf, n + NODE_HEADER_SIZE ≤ # buf, (n + NODE_HEADER_SIZE) + node-size-headerless(nd) ≤ # buf, node-size-headerless(nd) ≤ align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE), ⌊err⌋ , NODE_HEADER_SIZE + n2 + n3 < n1 → buf2[2 * NODE_HEADER_SIZE + n + node-size-headerless(nd) + n2 + n3] = buf0[2 * NODE_HEADER_SIZE + n + node-size-headerless(nd) + n2 + n3] ⊦ buf2[(n + 2 * NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE)) + n2] = buf[(n + 2 * NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE)) + n2]

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE), node-size-headerless(nd), n3]

Additional information

Used simplifier rules: ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ 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 ≠ 0 ⊦ align↑(n, m) < n ↔ false; (s)%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE), node-size-headerless(nd), n3