reserve x,y,t for Real;

theorem Th18:
  0<x & x<1 implies (2*x)/(1-x^2)>0
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*2<x*2 by A1;
  hence thesis by A3;
end;
