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Proof step 140 from proof abs-nodes-crash-h (previous step)

# buf2 = NODE_HEADER_SIZE, # buf = nd.alignedsize, align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) + 1 < NODE_HEADER_SIZE + nd.alignedsize, n0 < NODE_HEADER_SIZE + nd.alignedsize, align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) < n0, align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) < NODE_HEADER_SIZE + nd.alignedsize, align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) < NODE_HEADER_SIZE + nd.alignedsize + # buf0, abs-nodes(buf0, 2 * NODE_HEADER_SIZE + m + nd.alignedsize, x1, lax1, true), is-aligned(n0, NODE_HEADER_SIZE), is-encoded(nd, subarray(buf, 0, node-size-headerless(nd))), is-encoded(nodeheader(node-size-headerless(nd), false), buf2), n0 ≤ NODE_HEADER_SIZE + nd.alignedsize + # buf0, ∀ buf3, m, x, lax, n. # buf3 < #(buf2 + (buf + validtrailer) + buf0) → abs-nodes(buf3, m, x, lax, true) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ n ≤ # buf3 → (∃ x0, lax0. x0 ⊑ x ∧ lax0 ⊑ lax ∧ abs-nodes(subarray(buf3, 0, n), m, x0, lax0, true)) ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 141:
⊦ nd.alignedsize = align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE)
Proof step 142:
# buf = align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE), # buf2 = NODE_HEADER_SIZE, align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) < NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) + # buf0, align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) < NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE), align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) < n0, n0 < NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE), align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) + 1 < NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE), abs-nodes(buf0, 2 * NODE_HEADER_SIZE + m + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE), x1, lax1, true), is-aligned(n0, NODE_HEADER_SIZE), is-encoded(nodeheader(node-size-headerless(nd), false), buf2), is-encoded(nd, subarray(buf, 0, node-size-headerless(nd))), n0 ≤ NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) + # buf0, ∀ buf3, m, x, lax, n. # buf3 < #(buf2 + (buf + validtrailer) + buf0) → abs-nodes(buf3, m, x, lax, true) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ n ≤ # buf3 → (∃ x0, lax0. x0 ⊑ x ∧ lax0 ⊑ lax ∧ abs-nodes(subarray(buf3, 0, n), m, x0, lax0, true)) ⊦

Rule argument

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

Additional information

Used terms: nd