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Proof step 158 from proof abs-nodes-crash-h (previous step)

# buf = nd.alignedsize, # buf2 = NODE_HEADER_SIZE, abs-nodes(subarray(buf0, 0, n0), 2 * NODE_HEADER_SIZE + m + nd.alignedsize, x, lax, true), 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 ≤ # buf0, x ⊑ x1, lax ⊑ lax1, ∀ 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)) ⊦ ∃ buf1, buf3. buf2 + buf + validtrailer + subarray(buf0, 0, n0) = buf1 + buf3 ∧ ( abs-padding(buf1) ∧ abs-nodes(buf3, m + # buf1, nd ' + x, @(m, nd.alignedsize + 2 * NODE_HEADER_SIZE) ' + lax, true) ∨ nd.alignedsize + 2 * NODE_HEADER_SIZE = # buf1 ∧ abs-node(buf1, nd) ∧ abs-nodes(buf3, m + # buf1, x, lax, true))

Heuristic quantifier closing applied rule exists right

And closed the goal!

Rule argument

pos: right 1 terms: buf2 + buf + validtrailer, subarray(buf0, 0, n0)

Additional information

Used simplifier rules: abs-nodes-unique-weak-h: ⊦ abs-nodes(buf, m, x0, lax0, true) → (abs-nodes(buf, m, x1, lax1, true) ↔ x0 = x1 ∧ lax0 = lax1);%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ #(buf + buf0) = # buf + # buf0; (s)% ⊦ # validtrailer = NODE_HEADER_SIZE; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%m2 ≠ 0 ⊦ (* m2) * m + n = m + n0 ↔ (m2 - 1) * m + n = n0; (s)% ⊦ m0 * 1 = m0; (s)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult%c: ⊦ m + n = n + m; from specification nat-basic%⊦ # buf1 = nd.alignedsize ∧ is-encoded(nodeheader(node-size-headerless(nd), false), buf0) ∧ is-encoded(nd, subarray(buf1, 0, node-size-headerless(nd))) → abs-node(buf0 + buf1 + validtrailer, nd); (ss)% ⊦ m + m = 2 * m; (s) Used terms: buf2 + buf + validtrailer, subarray(buf0, 0, n0)