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Algorithmic decision making driven by neural networks has become very prominent in applications that directly affect people's quality of life. In this paper, we study the problem of verifying, training, and guaranteeing individual fairness of neural network models. A popular approach for enforcing fairness is to translate a fairness notion into constraints over the parameters of the model. However, such a translation does not always guarantee fair predictions of the trained neural network model. To address this challenge, we develop a counterexample-guided post-processing technique to provably enforce fairness constraints at prediction time. Contrary to prior work that enforces fairness only on points around test or train data, we are able to enforce and guarantee fairness on all points in the input domain. Additionally, we propose an in-processing technique to use fairness as an inductive bias by iteratively incorporating fairness counterexamples in the learning process. We have implemented these techniques in a tool called FETA. Empirical evaluation on real-world datasets indicates that FETA is not only able to guarantee fairness on-the-fly at prediction time but also is able to train accurate models exhibiting a much higher degree of individual fairness.