reserve s for set,
  i,j for Nat,
  c,c1,c2,c3 for Complex,
  F,F1,F2 for complex-valued FinSequence,
  R,R1,R2 for i-element complex-valued FinSequence;

theorem
  for a being Complex, x being complex-valued FinSequence
  holds len (a*x) = len x
proof
  let a be Complex, x be complex-valued FinSequence;
  dom(a*x) = dom x by VALUED_1:def 5;
  hence thesis by FINSEQ_3:29;
end;
