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 x1,x2 being complex-valued FinSequence st len x1 <= len x2 holds
  len (x1-x2) = len x1
proof
  let x1,x2 be complex-valued FinSequence;
  assume len x1<=len x2; 
  then
A2: dom x1 c= dom x2 by FINSEQ_3:30;
  dom(x1-x2) = dom x1 /\ dom x2 by VALUED_1:12;
  hence thesis by A2,XBOOLE_1:28,FINSEQ_3:29;
end;
