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Proof step 139 from proof abs-nodes-crash-h (previous step)

# buf = nd.alignedsize, # buf2 = NODE_HEADER_SIZE, n0 < NODE_HEADER_SIZE + nd.alignedsize, 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 ≤ 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)) ⊦ buf2 + subarray((buf + validtrailer) + buf0, 0, n0) = buf2 + subarray((buf + validtrailer) + buf0, 0, n0) ∧ # buf2 = NODE_HEADER_SIZE ∧ ( is-garbage-header(buf2) ∨ (∃ ndhd. is-encoded(ndhd, buf2) ∧ # subarray((buf + validtrailer) + buf0, 0, n0) ≤ align↑(ndhd.size, 2 * NODE_HEADER_SIZE)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 140:
# 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)) ⊦

Rule argument

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ NODE_HEADER_SIZE + n ≠ 0; (s)% ⊦ m +1 = m + 1; (s)% ⊦ m < n → n ≠ 0; (s)%trans: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification nat-basic%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ nodeheader(m, boolvar).size = m; (s)% ⊦ # subarray(buf, m, n) = n; (s)% ⊦ is-encoded(ndhd, buf) → (is-encoded(ndhd0, buf) ↔ ndhd = ndhd0); (s)% ⊦ is-encoded(ndhd, buf) → ¬ is-garbage-header(buf); (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]