New Zealand Law
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Was your choice of resignation before the termination letter? Was the termination based on your resignation, or on the morning and being caught sleeping?
That may be grounds for dismissal, but they should have had a meeting with you to discuss this before they gave you the letter. So you could possibly claim a personal grievance based on bad procedure, although the dismissal might be justified
It is a well established requirement to have a meeting for the termination. They may have been entitled to fire you, but procedure requires a meeting at which you could give an explanation, and have an opportunity to be heard. So you could claim a personal grievance based on bad procedure, although if they were entitled to fire you, you won't get much in the way of damages