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Proof step 119 from proof abs-nodes-crash-h (previous step)

# buf = nd.alignedsize, # buf2 = NODE_HEADER_SIZE, abs-nodes(buf0, 2 * NODE_HEADER_SIZE + m + nd.alignedsize, x1, lax1, true), is-aligned(n, NODE_HEADER_SIZE), is-encoded(nodeheader(node-size-headerless(nd), false), buf2), is-encoded(nd, subarray(buf, 0, node-size-headerless(nd))), n ≤ 2 * 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)) ⊦ ∃ x, lax. x ⊑ nd ' + x1 ∧ lax ⊑ @(m, 2 * NODE_HEADER_SIZE + nd.alignedsize) ' + lax1 ∧ abs-nodes(subarray((buf2 + buf + validtrailer) + buf0, 0, n), m, x, lax, true)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: array-splice, inst: buffer name: subarray-append-shift-right seq: ⊦ # buf ≤ m ∧ m ≤ # buf + # buf0 → subarray(buf + buf0, 0, m) = buf + subarray(buf0, 0, m - # buf) subst: [m, buf0, buf] → [n, buf0, buf2 + buf + validtrailer] flags: <all paths>

Additional information

Used terms: n, buf0, buf2 + buf + validtrailer