reserve a,b,c,x,y,z for Real;

theorem Th16:
  0 <= x & x < y implies x^2 < y^2
proof
  assume that
A1: 0 <= x and
A2: x < y;
A3: x*y < y*y by A1,A2,XREAL_1:68;
  x*x <= x*y by A1,A2,XREAL_1:64;
  hence thesis by A3,XXREAL_0:2;
end;
