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Proof step 12 from proof abs-node-abs-node-append-subarray (previous step)

# buf3 = NODE_HEADER_SIZE, # buf1 = NODE_HEADER_SIZE, # buf2 = nd0.alignedsize, # buf = nd1.alignedsize, buf1 + subarray((buf2 + validtrailer) + buf0, 0, NODE_HEADER_SIZE + nd1.alignedsize) = buf3 + buf + validtrailer, is-encoded(nd0, subarray(buf2, 0, node-size-headerless(nd0))), is-encoded(nodeheader(node-size-headerless(nd0), false), buf1), is-encoded(nd1, subarray(buf, 0, node-size-headerless(nd1))), is-encoded(nodeheader(node-size-headerless(nd1), false), buf3), nd1.alignedsize ≤ nd0.alignedsize + # buf0 ⊦ nd0 = nd1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ # buf = # buf0 → (buf + buf1 = buf0 + buf2 ↔ buf = buf0 ∧ buf1 = buf2)
Proof step 14:
# buf = nd1.alignedsize, # buf2 = nd0.alignedsize, # buf1 = NODE_HEADER_SIZE, # buf3 = NODE_HEADER_SIZE, # buf1 = # buf3, buf1 = buf3, subarray((buf2 + validtrailer) + buf0, 0, NODE_HEADER_SIZE + nd1.alignedsize) = buf + validtrailer, is-encoded(nodeheader(node-size-headerless(nd1), false), buf3), is-encoded(nd1, subarray(buf, 0, node-size-headerless(nd1))), is-encoded(nodeheader(node-size-headerless(nd0), false), buf1), is-encoded(nd0, subarray(buf2, 0, node-size-headerless(nd0))), nd1.alignedsize ≤ nd0.alignedsize + # buf0 ⊦ nd0 = nd1

Rule argument

spec: array-splice, inst: buffer name: append-inj seq: ⊦ # buf = # buf0 → (buf + buf1 = buf0 + buf2 ↔ buf = buf0 ∧ buf1 = buf2) subst: [buf2, buf0, buf1, buf] → [buf + validtrailer, buf3, subarray ((buf2 + validtrailer) + buf0, 0, NODE_HEADER_SIZE + nd1.alignedsize), buf1] flags: <all paths>

Additional information

Used terms: buf + validtrailer, buf3, subarray ((buf2 + validtrailer) + buf0, 0, NODE_HEADER_SIZE + nd1.alignedsize), buf1