  Leggett-Garg Inequality~(LGI) is a time analogue of Bell's inequality that
concerns measurements performed on a system at different times. Violation to
LGI indicates quantum coherence. We present a Leggett-Garg-type inequality
compatible with more general neutrino oscillation frameworks, allowing the
effects of decoherence to be taken into consideration. The inequality is
applied to test coherence for data from Daya Bay, MINOS, and KamLAND
experiments, and their results are compared to theoretical predictions to
investigate decoherence. Both Daya Bay and MINOS data exhibit clear violations
of over $10\sigma$, and of over 90$\%$ of theoretical predictions, while the
KamLAND data exhibit violation of $1.9\sigma$, being of 58$\%$ of the
theoretical prediction. The present work is the first to have considered the
energy uncertainties in neutrino coherence tests.

Quantum Physics;High Energy Physics - Phenomenology