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

  rr for set,

  rseq for Real_Sequence;

theorem
  (1 <= r & r <= sqrt 2 & arccosec2 r = PI/4 implies r = sqrt 2) & (1 <=
  r & r <= sqrt 2 & arccosec2 r = PI/2 implies r = 1) by Th32,Th92;
