Prove that nw finbspcap wiisinnnbsp pmiddot w is also an

Question

Let (N, Y, (F_i)_i∈N, s, P) be an Aumann model of incomplete information with beliefs, and let W ⊆ Y be an event. Prove that (N,W, (F_i ∩ W)_i∈N , P(· | W)) is also an Aumann model of incomplete information with beliefs, where for each player i ∈ N

Fi ∩ W = {F ∩ W : F ∈ Fi}

is the partition Fi restricted to W, and P(· | W) is the conditional distribution of P over W.