reserve x,y,t for Real;

theorem
  0<x & x<1 implies ((1+x^2)/(1-x^2))>1
proof
  assume that
A1: 0<x and
A2: x<1;
  x^2<x by A1,A2,SQUARE_1:13;
  then x^2<1 by A2,XXREAL_0:2;
  then
A3: x^2+(-x^2)<1+(-x^2) by XREAL_1:8;
  0*x<x*x by A1;
  then -x^2+1<x^2+1 by XREAL_1:8;
  hence thesis by A3,XREAL_1:187;
end;
