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

  rr for set,

  rseq for Real_Sequence;

theorem Th78:
  arcsec2|(sec.:].PI/2,PI.]) is increasing
proof
  set f = sec | ].PI/2,PI.];
A1: f.:].PI/2,PI.] = rng(f|].PI/2,PI.]) by RELAT_1:115
    .= rng(sec|].PI/2,PI.]) by RELAT_1:73
    .= sec.:].PI/2,PI.] by RELAT_1:115;
  f|].PI/2,PI.] = f by RELAT_1:73;
  hence thesis by A1,Th18,FCONT_3:9;
end;
