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 Th46:
  arccot|(cot.:].0,PI.[) is decreasing
proof
  set f = cot | ].0,PI.[;
A1: f.:].0,PI.[ = rng(f|].0,PI.[) by RELAT_1:115
    .= rng(cot|].0,PI.[) by RELAT_1:73
    .= cot.:].0,PI.[ by RELAT_1:115;
  f|].0,PI.[ = f by RELAT_1:73;
  hence thesis by A1,Th8,FCONT_3:10;
end;
