reserve x,y,t for Real;

theorem
  x>1 implies ((sqrt(x^2-1))/x)^2<1
proof
A1: -1+x^2<0+x^2 by XREAL_1:6;
  assume x>1;
  then x^2>1^2+0 by SQUARE_1:16;
  then
A2: x^2-1>0 by XREAL_1:20;
  ((sqrt(x^2-1))/x)^2=(sqrt(x^2-1))^2/x^2 by XCMPLX_1:76
    .=(x^2-1)/x^2 by A2,SQUARE_1:def 2;
  hence thesis by A2,A1,XREAL_1:189;
end;
