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

  rr for set,

  rseq for Real_Sequence;

theorem Th96:
  arccosec2|[.1,sqrt 2.] is continuous
proof
  set f = cosec | [.PI/4,PI/2.];
  PI/4 <= PI/2 by Lm8,XXREAL_1:2;
  then f|[.PI/4,PI/2.] = f & (f|[.PI/4,PI/2.])"|(f.:[.PI/4,PI/2.]) is
  continuous by Lm32,Lm40,FCONT_1:47,RELAT_1:72;
  then arccosec2|[.1,sqrt 2.]|[.1,sqrt 2.] is continuous by Th44,Th52,
RELAT_1:115;
  hence thesis by FCONT_1:15;
end;
