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Proof step 165 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, 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 + nd.alignedsize ≤ # buf, n + NODE_HEADER_SIZE ≤ # buf, (n + NODE_HEADER_SIZE) + node-size-headerless(nd) ≤ # buf, ⌊err⌋ , NODE_HEADER_SIZE + n2 + (nd.alignedsize - node-size-headerless(nd)) < n1 → buf2[2 * NODE_HEADER_SIZE + n + node-size-headerless(nd) + n2 + (nd.alignedsize - node-size-headerless(nd))] = buf0[2 * NODE_HEADER_SIZE + n + node-size-headerless(nd) + n2 + (nd.alignedsize - node-size-headerless(nd))] ⊦ buf2[(n + 2 * NODE_HEADER_SIZE + nd.alignedsize) + n2] = buf[(n + 2 * NODE_HEADER_SIZE + nd.alignedsize) + n2]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 166:
⊦ nd.alignedsize = align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE)
Proof step 167:
# 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]

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 terms: nd