A Completely Not Important Poker Question

The other night, at my regular game, we were playing seven-card high-low. I had a very good hand -- ace, two, three, four, five, seven, plus a stray jack. I decided to declare both high and low (when the hands are complete, each remaining player declares whether he's going to play his high cards or his low cards -- the perfect low being an ace, 2,3,4 and six.) I had a great low, plus a straight, so I declared both high and low. There were two others still in the game; one declared high, the other low. So I was competing against both. The prize was the entire pot (which by then was in the tens of dollars), but if either the low or the high beat my hand, I would lose everything. I would win the entire pot, of course, and not split it, if I won.

When we showed our cards, my low beat the other player's low, but my high hand -- a straight -- matched exactly the hand of the player who went high. We had never seen this before, and we were flummoxed. We turned to the Intertubes, but couldn't find an answer there. Eventually, the table decided that in order for me to have won the hand, I would have had to beat, and not merely, tie, both remaining players. The question out there is: What is the actual rule? Is there such a thing as a tie? Please send me your responses to [e-mail]. Please, no e-mails telling us to stick to Texas Hold 'em.