panic("tlog: bad math in treeProofIndex")
	}

	if n == hi {
		if lo == 0 {
			return need
		}
		return subTreeIndex(lo, hi, need)
	}

	if k, _ := maxpow2(hi - lo); n <= lo+k {
		need = treeProofIndex(lo, lo+k, n, need)
		need = subTreeIndex(lo+k, hi, need)
	} else {
		need = subTreeIndex(lo, lo+k, need)
		need = treeProofIndex(lo+k, hi, n, need)
	}
	return need
}

	tileOrder := make(map[Tile]int) // tileOrder[tileKey(tiles[i])] = i
	var tiles []Tile

	// Plan to fetch tiles necessary to recompute tree hash.
	// If it matches, those tiles are authenticated.
	stx := subTreeIndex(0, r.tree.N, nil)
	stxTileOrder := make([]int, len(stx))
	for i, x := range stx {
		tile, _, _ := tileForIndex(h, x)
		tile = tileParent(tile, 0, r.tree.N)
		if j, ok := tileOrder[tile]; ok {