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Proof step 91 from proof abs-nodes-crash-h (previous step)

# buf2 = NODE_HEADER_SIZE, n < 2 * NODE_HEADER_SIZE + # buf, abs-nodes(buf0, 2 * NODE_HEADER_SIZE + m + # buf, nd ' + x1, @(m0, m1) ' + lax0, true), is-aligned(n, NODE_HEADER_SIZE), is-aligned(# buf, 2 * NODE_HEADER_SIZE), is-encoded(nodeheader(# buf, true), buf2), NODE_HEADER_SIZE ≤ # buf0, n ≤ 2 * 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)) ⊦ n = 0, abs-failed(buf2 + subarray(buf + validtrailer, 0, n - NODE_HEADER_SIZE))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 92:
# buf2 = NODE_HEADER_SIZE, n = n0 + NODE_HEADER_SIZE, n < 2 * NODE_HEADER_SIZE + # buf, abs-nodes(buf0, 2 * NODE_HEADER_SIZE + m + # buf, nd ' + x1, @(m0, m1) ' + lax0, true), is-aligned(# buf, 2 * NODE_HEADER_SIZE), is-aligned(n, NODE_HEADER_SIZE), is-encoded(nodeheader(# buf, true), buf2), n ≤ 2 * NODE_HEADER_SIZE + # buf + # buf0, NODE_HEADER_SIZE ≤ # 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, 0, n0))

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [n, NODE_HEADER_SIZE, n0]

Additional information

Used simplifier rules: ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ NODE_HEADER_SIZE ≠ 0; (s)%m ≠ 0 ⊦ is-aligned(n, m) → (n < m ↔ n = 0); (s)%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: n, NODE_HEADER_SIZE, n0