reserve x,x0, r,r1,r2 for Real,
      th for Real,

  rr for set,

  rseq for Real_Sequence;

theorem Th110:
  -sqrt 2 < r & r < -1 implies 3/4*PI < arcsec2 r & arcsec2 r < PI
proof
  assume
A1: -sqrt 2 < r & r < -1;
  then 3/4*PI <= arcsec2 r & arcsec2 r <= PI by Th106;
  then
  3/4*PI < arcsec2 r & arcsec2 r < PI or 3/4*PI = arcsec2 r or arcsec2 r =
  PI by XXREAL_0:1;
  hence thesis by A1,Th31,Th90;
end;
