  In a large-momentum nucleon state, the matrix element of a gauge-invariant
Euclidean Wilson line operator accessible from lattice QCD can be related to
the standard light-cone parton distribution function through the large-momentum
effective theory (LaMET) expansion. This relation is given by a factorization
theorem with a non-trivial matching coefficient. Using the operator product
expansion we prove the large-momentum factorization of the quasi-parton
distribution function in LaMET, and show that the more recently discussed
Ioffe-time distribution approach also obeys an equivalent factorization
theorem. Explicit results for the coefficients are obtained and compared at
one-loop. Our proof clearly demonstrates that the matching coefficients in the
$\overline{\rm MS}$ scheme depend on the large partonic momentum rather than
the nucleon momentum.
