reserve a,b,s,t,u,lambda for Real,
  n for Nat;
reserve x,x1,x2,x3,y1,y2 for Element of REAL n;

theorem :: EUCLID_2:16
  for x being Element of REAL n holds |(x,x)| = 0 iff |.x.| = 0
proof
  let x be Element of REAL n;
  thus |(x,x)|=0 implies |.x.| = 0;
  |.x.| = 0 implies |(x,x)| = 0^2 by EUCLID_2:4;
  hence thesis;
end;
