Indians did not view war as we do. They believed in their visions, as part of their religion, as well as their daily life. He may have traded this gun to someone before this final battle, for a different gun, or used only a hawk in the fight, or some other weapon. He may have had another gun that he took into the battle. He believed that he was going to die in that battle, and would have chosen how he would want to be presented in the hereafter, being absolutely confident in his vision of his own death that day.
See also, Allan Eckert, "Gateway to Empire", p. 689.
I "googled" Tecvumseh, and one of the more interesting pieces of folklore I found was a comment on Wikipedia that the Vice President with Van Buren was elected largely on his claim that it was he, personally, who killed Tecumseh.
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"...Harrison crossed into Upper Canada and on October 5, 1813, won a victory over the British and Native Americans at the Battle of the Thames near Moraviantown. Tecumseh was killed, and shortly after the battle, the tribes of his confederacy surrendered to Harrison at Detroit.[15] In 1836 and 1837, in part because of reports that it was he who had killed Tecumseh, Richard Mentor Johnson was elected vice-president of the United States, to serve with Martin Van Buren...."
http://en.wikipedia.org/wiki/Tecumseh
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As boring as American History was taught in both Grammar School, and HS, I had not been told this piece of "history". And its not in my College History text either. But, then, Vice Presidents don't get much attention in American History unless they go on to he elected President.