proposition: Lemma Lim_seq_mult (u v : nat -> R) : ex_lim_seq u -> ex_lim_seq v -> ex_Rbar_mult (Lim_seq u) (Lim_seq v) -> Lim_seq (fun n => u n * v n) = Rbar_mult (Lim_seq u) (Lim_seq v).
proof: Proof. move => H1 H2 Hl. apply is_lim_seq_unique. eapply is_lim_seq_mult ; try apply Lim_seq_correct ; try eassumption. by apply Rbar_mult_correct. Qed.
imports: Coq(Reals Psatz ssreflect) Rcomplements Rbar Lub Markov Hierarchy