SPOILER I don't see the Tremaine goof

Continuity: In the final battle, Captain Tremaine is struck by Tyreen and falls from his horse into the river, but in the very next shot he is back in the saddle.

I watched Major Dundee again today with the intention of looking for this continuity goof, and I didn't see it. Here is what I saw.

Captain Tremaine stabs Aesop and takes the flag. Tyreen sees this, charges in, and slices at Tremaine, getting the U.S. flag back. But Tremaine never falls from the horse. I think the confusion is caused by how the battle is edited. Right after Tyreen's move, the camera shifts to Dundee shooting a French lancer who falls into the water, not Tremaine.

Then in the next shot when Dundee and Tyreen are holding the flag, a wounded Tremaine straightens back up and shoots Tyreen in the back. Sgt. Chillum then shoots Tremaine, who falls into the river.

Can anyone dispute this, am I just looking at this scene incorrectly?

"Congratulations, Major. It appears that at last you have found yourself a real war." Ben Tyreen