  In this paper we explain how 4-dimensional general relativity and in
particular, the Einstein equation, emerge from the spinfoam amplitude in loop
quantum gravity. We propose a new limit which couples both the semiclassical
limit and continuum limit of spinfoam amplitudes. The continuum Einstein
equation emerges in this limit. Solutions of Einstein equation can be
approached by dominant configurations in spinfoam amplitudes. A running scale
is naturally associated to the sequence of refined triangulations. The
continuum limit corresponds to the infrared limit of the running scale. An
important ingredient in the derivation is a regularization for the sum over
spins, which is necessary for the semiclassical continuum limit. We also
explain in this paper the role played by the so-called flatness in spinfoam
formulation, and how to take advantage of it.
