reserve x,a,b,c for Real,
  n for Nat,
  Z for open Subset of REAL,
  f, f1,f2 for PartFunc of REAL,REAL;

theorem Th1:
  x in dom tan implies cos.x<>0
proof
  assume x in dom tan;
  then x in dom sin /\ (dom cos \ cos"{0}) by RFUNCT_1:def 1;
  then x in dom cos \ cos"{0} by XBOOLE_0:def 4;
  then x in dom (cos^) by RFUNCT_1:def 2;
  hence thesis by RFUNCT_1:3;
end;
