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Proof step 15 from proof abs-node-abs-node-append-subarray (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ (buf + buf0) + buf1 = buf + buf0 + buf1
Proof step 17:
# 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

Rule argument

spec: array-splice, inst: buffer name: append-a seq: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1 subst: [buf1, buf0, buf] → [buf0, validtrailer, buf2] flags: <all paths>

Additional information

Used terms: buf0, validtrailer, buf2