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Proof step 80 from proof encode-node (previous step)

# buf = n0 + n + 2 * NODE_HEADER_SIZE + n2 + node-size-headerless(nd), # buf0 = # buf, # buf2 = # buf, align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) = n2 + node-size-headerless(nd), subarray(buf0, n + NODE_HEADER_SIZE, node-size-headerless(nd) + NODE_HEADER_SIZE + n0 + n2) = subarray(buf, n + NODE_HEADER_SIZE, node-size-headerless(nd) + NODE_HEADER_SIZE + n0 + n2), subarray(buf0, 0, n) = subarray(buf, 0, n), subarray(buf2, 0, n + NODE_HEADER_SIZE) = subarray(buf0, 0, n + NODE_HEADER_SIZE), n1 < n0, is-encoded(nd, subarray(buf2, n + NODE_HEADER_SIZE, node-size-headerless(nd))), is-encoded(nodeheader(node-size-headerless(nd), false), subarray(buf0, n, NODE_HEADER_SIZE)), 2 * NODE_HEADER_SIZE + n + n2 + node-size-headerless(nd) ≤ # buf, (n2 + node-size-headerless(nd)) + n + NODE_HEADER_SIZE ≤ # buf, n + 2 * NODE_HEADER_SIZE + n2 + node-size-headerless(nd) ≤ # buf, n + NODE_HEADER_SIZE ≤ # buf, (n + NODE_HEADER_SIZE) + node-size-headerless(nd) ≤ # buf, (n + NODE_HEADER_SIZE + node-size-headerless(nd)) + n2 ≤ # buf, n + NODE_HEADER_SIZE + node-size-headerless(nd) ≤ # buf, NODE_HEADER_SIZE + n1 + n2 < NODE_HEADER_SIZE + n0 + n2 → buf2[((n + NODE_HEADER_SIZE) + node-size-headerless(nd)) + NODE_HEADER_SIZE + n1 + n2] = buf0[((n + NODE_HEADER_SIZE) + node-size-headerless(nd)) + NODE_HEADER_SIZE + n1 + n2] ⊦ buf2[(2 * NODE_HEADER_SIZE + n + node-size-headerless(nd) + n2) + n1] = buf[(n + 2 * NODE_HEADER_SIZE + n2 + node-size-headerless(nd)) + n1]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 81:
# buf2 = # buf, # buf0 = # buf, # buf = n0 + n + 2 * NODE_HEADER_SIZE + n2 + node-size-headerless(nd), buf2[2 * NODE_HEADER_SIZE + n + node-size-headerless(nd) + n1 + n2] = buf0[2 * NODE_HEADER_SIZE + n + node-size-headerless(nd) + n1 + n2], align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) = n2 + node-size-headerless(nd), subarray(buf2, 0, n + NODE_HEADER_SIZE) = subarray(buf0, 0, n + NODE_HEADER_SIZE), subarray(buf0, 0, n) = subarray(buf, 0, n), subarray(buf0, n + NODE_HEADER_SIZE, node-size-headerless(nd) + NODE_HEADER_SIZE + n0 + n2) = subarray(buf, n + NODE_HEADER_SIZE, node-size-headerless(nd) + NODE_HEADER_SIZE + n0 + n2), n1 < n0, is-encoded(nodeheader(node-size-headerless(nd), false), subarray(buf0, n, NODE_HEADER_SIZE)), is-encoded(nd, subarray(buf2, n + NODE_HEADER_SIZE, node-size-headerless(nd))), n + NODE_HEADER_SIZE + node-size-headerless(nd) ≤ # buf, (n + NODE_HEADER_SIZE + node-size-headerless(nd)) + n2 ≤ # buf, (n + NODE_HEADER_SIZE) + node-size-headerless(nd) ≤ # buf, n + NODE_HEADER_SIZE ≤ # buf, n + 2 * NODE_HEADER_SIZE + n2 + node-size-headerless(nd) ≤ # buf, (n2 + node-size-headerless(nd)) + n + NODE_HEADER_SIZE ≤ # buf, 2 * NODE_HEADER_SIZE + n + n2 + node-size-headerless(nd) ≤ # buf ⊦ buf0[2 * NODE_HEADER_SIZE + n + node-size-headerless(nd) + n1 + n2] = buf[(n + 2 * NODE_HEADER_SIZE + n2 + node-size-headerless(nd)) + n1]

Rule argument

Additional information

Used simplifier rules: ⊦ m + m = 2 * m; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n < m + n0 ↔ n < n0; (s)