reserve h,r,r1,r2,x0,x1,x2,x3,x4,x5,x,a,b,c,k for Real,
  f,f1,f2 for Function of REAL,REAL;

theorem
  x0 in dom tan & x1 in dom tan implies [!tan,x0,x1!]=sin(x0-x1)/(cos(x0
  )*cos(x1)*(x0-x1))
proof
  assume that
A1: x0 in dom tan and
A2: x1 in dom tan;
A3: tan.x0 = sin.x0*(cos.x0)" by A1,RFUNCT_1:def 1
    .= sin.x0*(1/(cos.x0)) by XCMPLX_1:215
    .= tan(x0) by XCMPLX_1:99;
A4: tan.x1 = sin.x1*(cos.x1)" by A2,RFUNCT_1:def 1
    .= sin.x1*(1/(cos.x1)) by XCMPLX_1:215
    .= tan(x1) by XCMPLX_1:99;
  cos(x0)<>0 & cos(x1)<>0 by A1,A2,FDIFF_8:1;
  then [!tan,x0,x1!] = sin(x0-x1)/(cos(x0)*cos(x1)) /(x0-x1) by A3,A4,
SIN_COS4:20
    .= sin(x0-x1)/(cos(x0)*cos(x1)*(x0-x1)) by XCMPLX_1:78;
  hence thesis;
end;
