theorem Th62:
  Rseq is P-convergent implies {P-lim Rseq} =
  lim_filter( #Rseq,<. Frechet_Filter(NAT),Frechet_Filter(NAT).))
  proof
    assume Rseq is P-convergent; then
A1: P-lim Rseq in
    lim_filter( #Rseq,<. Frechet_Filter(NAT),Frechet_Filter(NAT).)) by Th60;
    then ex x be Real st
      lim_filter( #Rseq,<. Frechet_Filter(NAT),Frechet_Filter(NAT).)) = {x}
      by Th59;
    hence {P-lim Rseq} =
      lim_filter( #Rseq,<. Frechet_Filter(NAT),Frechet_Filter(NAT).))
      by A1,TARSKI:def 1;
  end;
