proposition: Lemma pr_eq_comp (f : A -> B) a : injective f -> `Pr[ X = a ] = `Pr[ (f `o X) = f a ].
proof: Proof. move=> inj_f. by rewrite -!pr_eq_set1 !pr_inE' (Pr_fdistmap inj_f) fdistmap_comp imset_set1. Qed.
imports: mathcomp(all_ssreflect ssralg ssrnum matrix) mathcomp(Rstruct reals) Reals Lra ssrR Reals_ext realType_ext logb ssr_ext ssralg_ext bigop_ext fdist