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Proof step 39 from proof abs-nodes-notrailer-h (previous step)

# buf2 = NODE_HEADER_SIZE, # buf = nd.alignedsize, abs-nodes(buf0, 2 * NODE_HEADER_SIZE + n + nd.alignedsize, x0, lax0, weak), is-encoded(nd, subarray(buf, 0, node-size-headerless(nd))), is-encoded(nodeheader(node-size-headerless(nd), false), buf2), align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) ≤ nd.alignedsize + # buf0, (NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE)) + NODE_HEADER_SIZE ≤ #(buf2 + buf + validtrailer) ⊦ subarray(buf2 + buf + validtrailer, NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE), NODE_HEADER_SIZE) = validtrailer

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 40:
# buf = nd.alignedsize, # buf2 = NODE_HEADER_SIZE, abs-nodes(buf0, 2 * NODE_HEADER_SIZE + n + nd.alignedsize, x0, lax0, weak), is-encoded(nodeheader(node-size-headerless(nd), false), buf2), is-encoded(nd, subarray(buf, 0, node-size-headerless(nd))), align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) ≤ nd.alignedsize, align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) ≤ nd.alignedsize + # buf0 ⊦ subarray(buf + validtrailer, align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE), NODE_HEADER_SIZE) = validtrailer

Rule argument

Additional information

Used simplifier rules: ⊦ m + n - m = n; (s)%# buf ≤ n0, n0 + m ≤ # buf + # buf0 ⊦ subarray(buf + buf0, n0, m) = subarray(buf0, n0 - # buf, m); (s)% ⊦ m ≤ n → (n < m ↔ false); (s)% ⊦ m < n → n ≠ 0; (s)%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ m ≤ m + 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)%m2 ≠ 0 ⊦ (* m2) * m + n ≤ m + n0 ↔ (m2 - 1) * m + n ≤ n0; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ # validtrailer = NODE_HEADER_SIZE; (s)% ⊦ #(buf + buf0) = # buf + # buf0; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + m = 2 * m; (s)