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Proof step 3 from proof abs-node-subarray-failed (previous step)

# buf0 = NODE_HEADER_SIZE, # buf1 = nd.alignedsize, n < 2 * NODE_HEADER_SIZE + nd.alignedsize, is-aligned(n, NODE_HEADER_SIZE), is-encoded(nd, subarray(buf1, 0, node-size-headerless(nd))), is-encoded(nodeheader(node-size-headerless(nd), false), buf0) ⊦ n = 0, abs-failed(subarray(buf0 + buf1 + validtrailer, 0, n))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ abs-failed(buf) ↔ # buf ≥ NODE_HEADER_SIZE ∧ is-aligned(# buf, NODE_HEADER_SIZE) ∧ (∃ buf0, buf1. buf = buf0 + buf1 ∧ # buf0 = NODE_HEADER_SIZE ∧ (is-garbage-header(buf0) ∨ (∃ ndhd. is-encoded(ndhd, buf0) ∧ # buf1 ≤ align↑(ndhd.size, 2 * NODE_HEADER_SIZE))))
Proof step 5:
# buf1 = nd.alignedsize, # buf0 = NODE_HEADER_SIZE, n < 2 * NODE_HEADER_SIZE + nd.alignedsize, is-aligned(n, NODE_HEADER_SIZE), is-encoded(nodeheader(node-size-headerless(nd), false), buf0), is-encoded(nd, subarray(buf1, 0, node-size-headerless(nd))) ⊦ n = 0, # subarray(buf0 + buf1 + validtrailer, 0, n) ≥ NODE_HEADER_SIZE ∧ is-aligned(# subarray(buf0 + buf1 + validtrailer, 0, n), NODE_HEADER_SIZE) ∧ (∃ buf2, buf3. subarray(buf0 + buf1 + validtrailer, 0, n) = buf2 + buf3 ∧ # buf2 = NODE_HEADER_SIZE ∧ (is-garbage-header(buf2) ∨ (∃ ndhd. is-encoded(ndhd, buf2) ∧ # buf3 ≤ align↑(ndhd.size, 2 * NODE_HEADER_SIZE))))

Rule argument

spec: <toplevel> name: abs-failed seq: ⊦ abs-failed(buf) ↔ # buf ≥ NODE_HEADER_SIZE ∧ is-aligned(# buf, NODE_HEADER_SIZE) ∧ (∃ buf0, buf1. buf = buf0 + buf1 ∧ # buf0 = NODE_HEADER_SIZE ∧ ( is-garbage-header(buf0) ∨ (∃ ndhd. is-encoded(ndhd, buf0) ∧ # buf1 ≤ align↑(ndhd.size, 2 * NODE_HEADER_SIZE)))) subst: [buf] → [subarray(buf0 + buf1 + validtrailer, 0, n)] flags: <all paths>

Additional information

Used terms: subarray(buf0 + buf1 + validtrailer, 0, n)