reserve a,b,c for positive Real,
  m,x,y,z for Real,
  n for Nat,
  s,s1,s2,s3,s4,s5 for Real_Sequence;

theorem
  (x+y+z)^2>=3*(x*y+y*z+x*z)
proof
  x^2+y^2+z^2>=x*y+y*z+x*z by Th10;
  then x^2+y^2+z^2+(2*x*y+2*y*z+2*z*x)>=x*y+y*z+x*z+(2*x*y+2*y*z+2*z*x) by
XREAL_1:6;
  hence thesis;
end;
