How to prove that regular language is decidable

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I understand that i am trying to show that: | D is a DFA that accepts w

TM=with input

Stimulate D on w:

1) TM accepts if stimulation ends with accept state of the DFA D

2) TM rejects if stimulation ends with reject state (w was consumed and its not final state)

Is that enough? i am always having trouble writing down the actual proof although i understand the logic.