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

  rr for set,

  rseq for Real_Sequence;

theorem
  (1 <= r & r <= sqrt 2 & arcsec1 r = 0 implies r = 1) & (1 <= r & r <=
  sqrt 2 & arcsec1 r = PI/4 implies r = sqrt 2) by Th31,Th89;
