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Proof step 134 from proof abs-nodes-crash-h (previous step)

# buf = nd.alignedsize, # buf2 = NODE_HEADER_SIZE, n = n0 + NODE_HEADER_SIZE, n < 2 * NODE_HEADER_SIZE + nd.alignedsize, 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, NODE_HEADER_SIZE ≤ n, ∀ 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)) ⊦ n = 0, abs-failed(buf2 + subarray((buf + validtrailer) + buf0, 0, n0))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 135:
# 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)) ⊦ abs-failed(buf2 + subarray((buf + validtrailer) + buf0, 0, n0))

Rule argument

Additional information

Used simplifier rules: f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%m1 ≠ 0 ⊦ m + n < (* m1) * m + n0 ↔ n < (m1 - 1) * m + n0; (s)%m ≠ 0, is-aligned(n1, m) ⊦ is-aligned(n0 + n1, m) ↔ is-aligned(n0, m); (s)%n ≠ 0 ⊦ is-aligned(n, n); (s)%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult% ⊦ m0 * 1 = m0; (s)%m1 ≠ 0 ⊦ m + n ≤ (* m1) * m + n0 ↔ n ≤ (m1 - 1) * m + n0; (s)%m ≠ 0 ⊦ is-aligned(n, m) → (m ≤ n ↔ n ≠ 0); (s)% ⊦ NODE_HEADER_SIZE ≠ 0; (s)%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)