reserve x,y,t for Real;

theorem
  x^2>1 implies coth"(x)=tanh"(1/x)
proof
  assume x^2>1;
  then
A1: x<>0;
  then tanh"(1/x) =(1/2)*log(number_e,((1+x*1)/x)/(1-(1/x))) by XCMPLX_1:113
    .=(1/2)*log(number_e,((1+x*1)/x)/((1*x-1)/x)) by A1,XCMPLX_1:127
    .=(1/2)*log(number_e,(1+x)/(x-1)) by A1,XCMPLX_1:55;
  hence thesis;
end;
