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
  cot is_differentiable_on ].0,PI.[ & for x st x in ].0,PI.[ holds diff(
  cot,x) = -1/(sin.x)^2 by Lm2,Lm4;
