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

  rr for set,

  rseq for Real_Sequence;

theorem
  (cosec | [.-PI/2,-PI/4.]) qua Function * (arccosec1 | [.-sqrt 2,-1.])
  = id [.-sqrt 2,-1.] by Th43,Th51,FUNCT_1:39;
