I am writing a proof for a problem, and in that proof, I am simulating a TM M that has k states and terminates after being started on a blank input. I want to show that to simulate M on a TM M', M' would have f(k) number of states, where f is a computable function.
Is it simply sufficient to state that simulating M with k states would require more than k states, and that since M eventually terminates, this number of states is finite and can be written as a function f(k)?
This seems self evident, but I am not sure if I need to be more formal than that.