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
  tan is_differentiable_on ].-PI/2,PI/2.[ & for x st x in ].-PI/2,PI/2.[
  holds diff(tan,x) = 1/(cos.x)^2 by Lm1,Lm3;
