TRACON Controller conducting training reported the trainee descended an aircraft to an altitude 100 feet below the minimum vectoring altitude.

Narrative

I was training on radar combined (Normal operation). Aircraft X was northbound at 8000 ft. on course; still in the prior sectors airspace. They made several requests trying to avoid clouds even though they were IFR; causing us to have to coordinate with the previous sector multiple times for climb/descent and turns. During this time there was above average frequency congestion; quite a lot of coordination with multiple sectors occurring due to weather; with another aircraft NORDO that we were trying to get a hold of. Aircraft X was eventually at 3000 ft. as requested by the pilot; on course; and had just finished resolving a conflict between them and another aircraft. The traffic had died down and I had started discussing the session with my trainee when I realized that Aircraft X had just crossed over a 3;100 MVA at 3;000 feet. I think this was an example of the laxity that can set in at the end of a busy/complex scenario when you falsely assume that everything has been taken care of and can lead to carelessness/inattentiveness to the operation you are still working.