  The phenomenon of fully coherent energy loss (FCEL) in the collisions of
protons on light ions affects the physics of cosmic ray air showers. As an
illustration, we address two closely related observables: hadron production in
forthcoming proton-oxygen collisions at the LHC, and the atmospheric neutrino
fluxes induced by the semileptonic decays of hadrons produced in proton-air
collisions. In both cases, a significant nuclear suppression due to FCEL is
predicted. The conventional and prompt neutrino fluxes are suppressed by $\sim
10...25\%$ in their relevant neutrino energy ranges. Previous estimates of
atmospheric neutrino fluxes should be scaled down accordingly to account for
FCEL.
