Is “Angrily beheading the envoy and fighting to the death at Mianzhu” true?

Records of the Three Kingdoms, Book of Shu, Biography of Zhuge Zhan records his refusal of Deng Ai's offer of a kingship, beheading the envoy, and dying with his son Zhuge Shang at Mianzhu; the novel Romance of the Three Kingdoms follows the official history exactly.