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 Th48:
  arccot|[.-1,1.] is decreasing
proof
A1: [.-1,1.] = cot.:[.PI/4,3/4*PI.] by Th22,RELAT_1:115;
  [.PI/4,3/4*PI.] c= ].0,PI.[ by Lm9,Lm10,XXREAL_2:def 12;
  hence thesis by A1,Th46,RELAT_1:123,RFUNCT_2:29;
end;
