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

  rr for set,

  rseq for Real_Sequence;

theorem Th27:
  rng arccosec1 = [.-PI/2,0.[
proof
  dom (cosec|[.-PI/2,0.[) = [.-PI/2,0.[ by Th3,RELAT_1:62;
  hence thesis by FUNCT_1:33;
end;
