reserve f,f1,f2,g for PartFunc of REAL,REAL;
reserve A for non empty closed_interval Subset of REAL;
reserve p,r,x,x0 for Real;
reserve n for Element of NAT;
reserve Z for open Subset of REAL;

theorem
  -sin is_differentiable_on REAL
proof
  dom (-sin) = [#]REAL by FUNCT_2:def 1;
  hence thesis by Th23,SIN_COS:68;
end;
