  We consider an exclusion process representing a reactive dynamics of a pulled
front on the integer lattice, describing the dynamics of first class $X$
particles moving as a simple symmetric exclusion process, and static second
class $Y$ particles. When an $X$ particle jumps to a site with a $Y$ particle,
their position is intechanged and the $Y$ particle becomes an $X$ one.
Initially, there is an arbitrary configuration of $X$ particles at sites $...,
-1,0$, and $Y$ particles only at sites $1,2,...$, with a product Bernoulli law
of parameter $\rho,0<\rho<1$. We prove a law of large numbers and a central
limit theorem for the front defined by the right-most visited site of the $X$
particles at time $t$. These results corroborate Monte-Carlo simulations
performed in a similar context. We also prove that the law of the $X$ particles
as seen from the front converges to a unique invariant measure. The proofs use
regeneration times: we present a direct way to define them within this context.
