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

  rr for set,

  rseq for Real_Sequence;

theorem
  (sec | [.0,PI/4.]) qua Function * (arcsec1 | [.1,sqrt 2.]) = id [.1,
  sqrt 2.] by Th41,Th49,FUNCT_1:39;
