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

  rr for set,

  rseq for Real_Sequence;

theorem Th95:
  arccosec1|[.-sqrt 2,-1.] is continuous
proof
  set f = cosec | [.-PI/2,-PI/4.];
  -PI/2 <= -PI/4 by Lm7,XXREAL_1:3;
  then f|[.-PI/2,-PI/4.] = f & (f|[.-PI/2,-PI/4.])"|(f.:[.-PI/2,-PI/4.]) is
  continuous by Lm31,Lm39,FCONT_1:47,RELAT_1:72;
  then arccosec1|[.-sqrt 2,-1.]|[.-sqrt 2,-1.] is continuous by Th43,Th51,
RELAT_1:115;
  hence thesis by FCONT_1:15;
end;
