reserve x,y,t for Real;

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