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Proof step 7 from proof abs-node-abs-node (previous step)

# buf = NODE_HEADER_SIZE, # buf5 = NODE_HEADER_SIZE, # buf6 = nd0.alignedsize, # buf4 = nd1.alignedsize, buf5 + (buf6 + validtrailer) + buf2 = buf + (buf4 + validtrailer) + buf3, is-encoded(nd0, subarray(buf6, 0, node-size-headerless(nd0))), is-encoded(nodeheader(node-size-headerless(nd0), false), buf5), is-encoded(nd1, subarray(buf4, 0, node-size-headerless(nd1))), is-encoded(nodeheader(node-size-headerless(nd1), false), buf) ⊦ buf5 + buf6 = buf + buf4 ∧ nd0 = nd1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ # buf = # buf0 → (buf + buf1 = buf0 + buf2 ↔ buf = buf0 ∧ buf1 = buf2)
Proof step 9:
# buf4 = nd1.alignedsize, # buf6 = nd0.alignedsize, # buf5 = NODE_HEADER_SIZE, # buf = NODE_HEADER_SIZE, # buf5 = # buf, (buf6 + validtrailer) + buf2 = (buf4 + validtrailer) + buf3, buf5 = buf, is-encoded(nodeheader(node-size-headerless(nd1), false), buf), is-encoded(nd1, subarray(buf4, 0, node-size-headerless(nd1))), is-encoded(nodeheader(node-size-headerless(nd0), false), buf5), is-encoded(nd0, subarray(buf6, 0, node-size-headerless(nd0))) ⊦ buf5 + buf6 = buf + buf4 ∧ 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] → [(buf4 + validtrailer) + buf3, buf, (buf6 + validtrailer) + buf2, buf5] flags: <all paths>

Additional information

Used terms: (buf4 + validtrailer) + buf3, buf, (buf6 + validtrailer) + buf2, buf5