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Proof step 146 from proof abs-nodes-crash-h (previous step)

# buf = align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE), # buf2 = NODE_HEADER_SIZE, # buf < n0, n0 < NODE_HEADER_SIZE + # buf, abs-nodes(buf0, 2 * NODE_HEADER_SIZE + m + # buf, 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 + # buf + # 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)) ⊦ NODE_HEADER_SIZE = 1, is-aligned(# buf, NODE_HEADER_SIZE) ∧ # buf < n0 ∧ n0 < # buf + NODE_HEADER_SIZE

User applied rule case distinction

And obtained the following new goals

Proof step 147:
# buf2 = NODE_HEADER_SIZE, # buf = align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE), n0 < NODE_HEADER_SIZE + # buf, # buf < n0, abs-nodes(buf0, 2 * NODE_HEADER_SIZE + m + # buf, 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 + # buf + # 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)) ⊦ NODE_HEADER_SIZE = 1, is-aligned(# buf, NODE_HEADER_SIZE)

Rule argument

pos: right 2

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic