proposition: Lemma summable_fst (mu : {distr (T * U) / R}) x : summable (fun y => mu (x, y)).
proof: Proof. have /summable_seqP /= := summable_mu mu => -[M ge0_M h]. apply/summable_seqP; exists M => // J uqJ; pose X := [seq (x, y) | y <- J]. apply/(le_trans _ (h X _)); last by rewrite map_inj_uniq // => y1 y2 []. by rewrite le_eqVlt big_map eqxx. Qed.
imports: mathcomp(all_ssreflect all_algebra) mathcomp.classical(boolp classical_sets mathcomp_extra) xfinmap ereal reals discrete topology realseq realsum