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Proof step 42 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, align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) ≤ nd.alignedsize ⊦ subarray(buf + validtrailer, align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE), NODE_HEADER_SIZE) = validtrailer, # buf ≤ align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) ∧ align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) + NODE_HEADER_SIZE ≤ # buf + # validtrailer

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 43:
# buf = nd.alignedsize, # buf2 = NODE_HEADER_SIZE, align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) < nd.alignedsize, 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 + # buf0 ⊦ nd.alignedsize = align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE), 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 → n ≠ 0; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m ≠ n → (m ≤ n ↔ m < n); (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m ≤ n → (n ≤ m ↔ m = n); (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ # validtrailer = NODE_HEADER_SIZE; (s)