  We derive a new inequality for entanglement for a mixed four-partite state.
Employing this inequality, we present a one-shot lower bound for entanglement
cost and prove that entanglement cost is strictly larger than zero for any
entangled state. We demonstrate that irreversibility occurs in the process of
formation for all non-distillable entangled states. In this way we solve a long
standing problem, of how "real" is entanglement of bound entangled states.
Using the new inequality we also prove impossibility of local-cloning of a
known entangled state.
