reserve x,x0, r, s, h for Real,

  n for Element of NAT,
  rr, y for set,
  Z for open Subset of REAL,

  f, f1, f2 for PartFunc of REAL,REAL;

theorem Th24:
  [.-1,1.] c= dom arccot
proof
A1: [.PI/4,3/4*PI.] c= ].0,PI.[ by Lm9,Lm10,XXREAL_2:def 12;
  rng (cot | [.PI/4,3/4*PI.]) c= rng (cot | ].0,PI.[)
  proof
    let y be object;
    assume y in rng (cot | [.PI/4,3/4*PI.]);
    then y in cot.:[.PI/4,3/4*PI.] by RELAT_1:115;
    then
    ex x be object st x in dom cot & x in [.PI/4,3/4*PI.] & y = cot.x by
FUNCT_1:def 6;
    then y in cot.:].0,PI.[ by A1,FUNCT_1:def 6;
    hence thesis by RELAT_1:115;
  end;
  hence thesis by Th22,FUNCT_1:33;
end;
