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 Th20: :: EUCLID_2:19
  for x1,x2,x3 being Element of REAL n holds |((x1+x2),x3)| = |(x1
  ,x3)| + |(x2,x3)|
proof
  let x1,x2,x3 be Element of REAL n;
A1: len (x3) = n by CARD_1:def 7;
  len x1 = n & len x2 = n by CARD_1:def 7;
  hence thesis by A1,RVSUM_1:120;
end;
