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Proof step 17 from proof abs-node-abs-node-append-subarray (previous step)

# buf = nd1.alignedsize, # buf2 = nd0.alignedsize, # buf3 = NODE_HEADER_SIZE, node-size-headerless(nd1) = node-size-headerless(nd0), subarray(buf2 + validtrailer + buf0, 0, NODE_HEADER_SIZE + nd1.alignedsize) = buf + validtrailer, is-encoded(nd0, subarray(buf2, 0, node-size-headerless(nd0))), is-encoded(nodeheader(node-size-headerless(nd0), false), buf3), is-encoded(nd1, subarray(buf, 0, node-size-headerless(nd0))), nd1.alignedsize ≤ nd0.alignedsize + # buf0 ⊦ nd0 = nd1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ nd.alignedsize = align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE)
Proof step 19:
# buf3 = NODE_HEADER_SIZE, # buf2 = nd0.alignedsize, # buf = align↑(node-size-headerless(nd1), 2 * NODE_HEADER_SIZE), node-size-headerless(nd1) = node-size-headerless(nd0), subarray(buf2 + validtrailer + buf0, 0, NODE_HEADER_SIZE + align↑(node-size-headerless(nd1), 2 * NODE_HEADER_SIZE)) = buf + validtrailer, is-encoded(nd1, subarray(buf, 0, node-size-headerless(nd0))), is-encoded(nodeheader(node-size-headerless(nd0), false), buf3), is-encoded(nd0, subarray(buf2, 0, node-size-headerless(nd0))), align↑(node-size-headerless(nd1), 2 * NODE_HEADER_SIZE) ≤ nd0.alignedsize + # buf0 ⊦ nd0 = nd1

Rule argument

spec: encoding-node-base name: alignedsize seq: ⊦ nd.alignedsize = align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) subst: [nd] → [nd1] flags: <all paths>

Additional information

Used terms: nd1