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

theorem Th15:
  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_1:64;
  x*x <= x*y by A1,A2,XREAL_1:64;
  hence thesis by A3,XXREAL_0:2;
end;
