"What are my rights as far as what is on paper if they try to change the trade-in amount?"
You don't have to go through with the deal. It is a mutual mistake, the old contract can be renegotiated or canceled completely. Don't let them put you over a barrel about the trade in value. If the car dealer gets nasty with you and starts making threats that shows the weakness of their negotiating position.
You should consult with an attorney in your area to confirm all this.
I do agree with my colleague. But this is really your mistake, however, let's be clear in that you told them something that was not true that presumably inured to your benefit. You know, you can't lie to them and then say "well, you guys should have looked."
But as noted, you are not locked in if this changes the terms. You are also human and allowed to make a mistake. If they try to bully you into a less than favorable contract, you should simply pull out all together and look elsewhere. I am always very skeptical about how these dealerships operate and I know for a fact that they try any and every way to chisel you down in these situations because the margins are just so tight. Be awake and aware when you deal with them.
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