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Proof step 155 from proof abs-nodes-crash-h (previous step)

# buf = nd.alignedsize, # buf2 = NODE_HEADER_SIZE, abs-nodes(subarray(buf0, 0, n0), 2 * NODE_HEADER_SIZE + m + nd.alignedsize, x, lax, true), abs-nodes(buf0, 2 * NODE_HEADER_SIZE + m + nd.alignedsize, 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 ≤ # buf0, x ⊑ x1, lax ⊑ lax1, ∀ 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)) ⊦ abs-nodes(buf2 + buf + validtrailer + subarray(buf0, 0, n0), m, nd ' + x, @(m, nd.alignedsize + 2 * NODE_HEADER_SIZE) ' + lax, true)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 156:
⊦ abs-nodes(buf, m, a ' + x, lax, weak) ↔ (∃ buf0, buf1. buf = buf0 + buf1 ∧ ( abs-padding(buf0) ∧ abs-nodes(buf1, m + # buf0, a ' + x, lax, weak) ∨ lax ≠ [] ∧ lax.head.off = m ∧ lax.head.size = # buf0 ∧ abs-node(buf0, a) ∧ abs-nodes(buf1, m + # buf0, x, lax.tail, weak)))
Proof step 157:
# buf2 = NODE_HEADER_SIZE, # buf = nd.alignedsize, abs-nodes(buf0, 2 * NODE_HEADER_SIZE + m + nd.alignedsize, x1, lax1, true), abs-nodes(subarray(buf0, 0, n0), 2 * NODE_HEADER_SIZE + m + nd.alignedsize, x, lax, 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 ≤ # buf0, lax ⊑ lax1, x ⊑ x1, ∀ 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)) ⊦ ∃ buf3, buf1. buf2 + buf + validtrailer + subarray(buf0, 0, n0) = buf3 + buf1 ∧ ( abs-padding(buf3) ∧ abs-nodes(buf1, m + # buf3, nd ' + x, @(m, nd.alignedsize + 2 * NODE_HEADER_SIZE) ' + lax, true) ∨ @(m, nd.alignedsize + 2 * NODE_HEADER_SIZE) ' + lax ≠ [] ∧ (@(m, nd.alignedsize + 2 * NODE_HEADER_SIZE) ' + lax).head.off = m ∧ (@(m, nd.alignedsize + 2 * NODE_HEADER_SIZE) ' + lax).head.size = # buf3 ∧ abs-node(buf3, nd) ∧ abs-nodes(buf1, m + # buf3, x, (@(m, nd.alignedsize + 2 * NODE_HEADER_SIZE) ' + lax).tail, true))

Rule argument

spec: <toplevel> name: abs-nodes-rec seq: ⊦ abs-nodes(buf, m, a ' + x, lax, weak) ↔ (∃ buf0, buf1. buf = buf0 + buf1 ∧ ( abs-padding(buf0) ∧ abs-nodes(buf1, m + # buf0, a ' + x, lax, weak) ∨ lax ≠ [] ∧ lax.head.off = m ∧ lax.head.size = # buf0 ∧ abs-node(buf0, a) ∧ abs-nodes(buf1, m + # buf0, x, lax.tail, weak))) subst: [weak, lax, x, a, m, buf] → [true, @(m, nd.alignedsize + 2 * NODE_HEADER_SIZE) ' + lax, x, nd, m, buf2 + buf + validtrailer + subarray(buf0, 0, n0)] flags: <all paths>

Additional information

Used terms: true, @(m, nd.alignedsize + 2 * NODE_HEADER_SIZE) ' + lax, x, nd, m, buf2 + buf + validtrailer + subarray(buf0, 0, n0)