proposition: Lemma pr_mem_map f mu (r : seq U) : uniq r -> \P_[mu] [pred x | f x \in r] = \sum_(y <- r) \P_[mu] [pred x | f x == y].
proof: Proof. elim: r => [_|y r ih]; first by rewrite big_nil pr_pred0_eq //. case/andP=> yNr /ih {ih}h; rewrite big_cons -h -pr_or_indep. by move=> x; rewrite !inE => /eqP->. by apply/eq_pr. Qed.
imports: mathcomp(all_ssreflect all_algebra) mathcomp.classical(boolp classical_sets mathcomp_extra) xfinmap ereal reals discrete topology realseq realsum