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Proof step 148 from proof abs-nodes-crash-h (previous step)

# buf2 = NODE_HEADER_SIZE, # buf = nd.alignedsize, abs-nodes(buf0, 2 * NODE_HEADER_SIZE + m + nd.alignedsize, x1, lax1, true), is-aligned(n, NODE_HEADER_SIZE), is-encoded(nd, subarray(buf, 0, node-size-headerless(nd))), is-encoded(nodeheader(node-size-headerless(nd), false), buf2), n ≤ 2 * NODE_HEADER_SIZE + nd.alignedsize + # buf0, #(buf2 + buf + validtrailer) ≤ n, n ≤ #(buf2 + buf + validtrailer) + # 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)) ⊦ ∃ x, lax. x ⊑ nd ' + x1 ∧ lax ⊑ @(m, 2 * NODE_HEADER_SIZE + nd.alignedsize) ' + lax1 ∧ abs-nodes((buf2 + buf + validtrailer) + subarray(buf0, 0, n - #(buf2 + buf + validtrailer)), m, x, lax, true)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 149:
# buf = nd.alignedsize, # buf2 = NODE_HEADER_SIZE, 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))), 2 * NODE_HEADER_SIZE + nd.alignedsize ≤ n, n ≤ 2 * 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)) ⊦ ∃ x, lax. x ⊑ nd ' + x1 ∧ lax ⊑ @(m, 2 * NODE_HEADER_SIZE + nd.alignedsize) ' + lax1 ∧ abs-nodes(buf2 + buf + validtrailer + subarray(buf0, 0, n - 2 * NODE_HEADER_SIZE + nd.alignedsize), m, x, lax, true)

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ m + n; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m + m = 2 * m; (s)%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ # validtrailer = NODE_HEADER_SIZE; (s)% ⊦ #(buf + buf0) = # buf + # buf0; (s)