Suppose The Great Wall of China is the collective name of a series of fortification systems generally built across the historical northern borders of China to protect and consolidate territories of Chinese states and empires against various nomadic groups of the steppe and their polities. The nomads do not include the Xiongnu, who dominated the Mongolian Plateau from the 3rd century BC to late 1st century AD.
Can we infer that "The Great Wall of China was mainly built to keep out the Xiongnu nomads"? Yes, no, or maybe?