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 Th13:
  for x be Real st x in ].-PI/2,PI/2.[ holds tan.x = tan x
proof
  let x be Real;
  assume x in ].-PI/2,PI/2.[;
  then tan.x = (sin x)/(cos x) by Th1,RFUNCT_1:def 1
    .= tan x by SIN_COS4:def 1;
  hence thesis;
end;
