proposition: Lemma ex_lim_seq_subseq (u : nat -> R) (phi : nat -> nat) : filterlim phi eventually eventually -> ex_lim_seq u -> ex_lim_seq (fun n => u (phi n)).
proof: Proof. move => Hphi [l Hu]. exists l. by apply is_lim_seq_subseq. Qed.
imports: Coq(Reals Psatz ssreflect) Rcomplements Rbar Lub Markov Hierarchy