The following state diagram depicts a DFA that recognizes the following language: {w | w contains at least three 1s} the alphabet is {0, 1}. Formally prove that the state diagram above is correct. That is, prove that the computation on the automaton for all strings w epsilon {0, 1}* that contain at least 3 '1's ends in an accept state, while computation on all other strings ends in one of the non-accept states. You can use induction or other proof techniques that you find suitable