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 Th131:
  for x being Real holds |(x*p1, p2)| = x*|(p1, p2)|
proof
  let x be Real;
  reconsider f1=p1,f2=p2 as real-valued FinSequence;
  len f1=n & len f2=n by CARD_1:def 7;
  hence thesis by Th121;
end;
