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 Th30: :: EUCLID_2:29
  for x1,x2,y1,y2 being Element of REAL n holds |(x1+x2, y1+y2)| =
  |(x1, y1)| + |(x1, y2)| + |(x2, y1)| + |(x2, y2)|
proof
  let x1,x2,y1,y2 being Element of REAL n;
  thus |(x1+x2, y1+y2)| = |(x1,y1+y2)|+|(x2,y1+y2)| by Th20
    .= |(x1, y1)| + |(x1, y2)| + |(x2, y1+y2)| by Th20
    .= |(x1, y1)| + |(x1, y2)| + (|(x2, y1)| + |(x2, y2)|) by Th20
    .= |(x1, y1)| + |(x1, y2)| + |(x2, y1)| + |(x2, y2)|;
end;
