theorem Th67:
  for a,b,c,d being Real holds a^2 + b^2 + c^2 + d^2 >= 0
proof
  let a,b,c,d be Real;
A1: a^2 >= 0 by XREAL_1:63;
A2: b^2>= 0 by XREAL_1:63;
A3: c^2 >= 0 by XREAL_1:63;
  d^2 >= 0 by XREAL_1:63;
  hence thesis by A1,A2,A3;
end;
