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 Th136:
  |(p1+p2, q1+q2)| = |(p1, q1)| + |(p1, q2)| + |(p2, q1)| + |(p2, q2)|
proof
A1: |(p1+p2, q1)| = |(p1, q1)| + |(p2, q1)| & |(p1+p2, q2)| = |(p1, q2)| +
  |(p2, q2)| by Th130;
  |(p1+p2, q1+q2)| = |(p1+p2, q1)| + |(p1+p2, q2)| by Th130
    .= |(p1, q1)|+|(p1, q2)|+|(p2, q1)|+|(p2, q2)| by A1;
  hence thesis;
end;
