That's tough. If you were incorporated then there would be a record with the Secratary of State and it would show a dissolution date.
I'm thinking the only way to do this is to write a long detailed letter of explanation saying you ran the business because you were renting the property and with the supporting docs you will no longer be doing this. Is there enough time to get your taxes filed immediately? You could dfile your 2012 returns with no Schedule C to show the business is no longer.