Is “Li Mu defeated the Xiongnu, killing over a hundred thousand cavalry; later, while resisting Wang Jian, he was wrongfully executed due to Guo Kai's conspiracy.” true?

In the Records of the Grand Historian, the biography of Lian Po and Lin Xiangru, appended with Li Mu's biography, records that he 'greatly defeated and killed over a hundred thousand Xiongnu cavalry.' Later, Wang Jian 'heavily bribed Zhao's favored minister Guo Kai,' and King Qian of Zhao, believing slander, executed Li Mu, destroying his own Great Wall. The novel accurately reflects this.