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 Th26:
  arccot | [.-1,1.] = (cot | [.PI/4,3/4*PI.])"
proof
  set h = cot | ].0,PI.[;
A1: [.PI/4,3/4*PI.] c= ].0,PI.[ by Lm9,Lm10,XXREAL_2:def 12;
  then (cot | [.PI/4,3/4*PI.])" = (h | [.PI/4,3/4*PI.])" by RELAT_1:74
    .= h" | (h.:[.PI/4,3/4*PI.]) by RFUNCT_2:17
    .= h" | rng (h | [.PI/4,3/4*PI.]) by RELAT_1:115
    .= h" | ([.-1,1.]) by A1,Th22,RELAT_1:74;
  hence thesis;
end;
