reserve s for set,
  i,j for natural Number,
  k for Nat,
  x,x1,x2,x3 for Real,
  r,r1,r2,r3,r4 for Real,
  F,F1,F2,F3 for real-valued FinSequence,
  R,R1,R2 for Element of i-tuples_on REAL;
reserve z,z1,z2 for Element of COMPLEX;
reserve n for Nat,
  x, y, a for Real,
  p, p1, p2, p3, q, q1, q2 for Element of n-tuples_on REAL;

theorem Th130:
  |(p1 + p2, p3)| = |(p1, p3)| + |(p2, p3)|
proof
  reconsider f1=p1, f2=p2, f3=p3 as real-valued FinSequence;
  len f2=n by CARD_1:def 7;
  then len f1=len f2 & len f2=len f3 by CARD_1:def 7;
  hence thesis by Th120;
end;
