  "All misfortune of man comes from the fact that he does not stay peacefully
in his room", has once asserted Blaise Pascal. In the present paper we evoke
this statement as the "Pascal principle" in regard to the problem of survival
of an "A" particle, which performs a lattice random walk in presence of a
concentration of randomly moving traps "B", and gets annihilated upon
encounters with any of them. We prove here that at sufficiently large times for
both perfect and imperfect trapping reactions, for arbitrary spatial dimension
"d" and for a rather general class of random walks, the "A" particle survival
probability is less than or equal to the survival probability of an immobile
target in the presence of randomly moving traps.
