reserve x,y,t for Real;

theorem Th31:
  (t^2-1)/(t^2+1)<1
proof
A1: 0<t^2+1 by Lm6;
  -1+t^2<1+t^2 by XREAL_1:8;
  then (-1+t^2)/((1+t^2))<(1+t^2)/((1+t^2)) by A1,XREAL_1:74;
  hence thesis by A1,XCMPLX_1:60;
end;
