reserve X1,X2,X3,X4 for set;
reserve n for non zero Nat;
reserve X for non-empty n-element FinSequence;

theorem Thm18:
  for f being Function, X be n-element FinSequence st f in product X holds
  f is n-element FinSequence
  proof
    let f be Function, X be n-element FinSequence;
    assume
A1: f in product X;
A2: dom X = Seg n by FINSEQ_1:89;
    then dom f = Seg n by A1,CARD_3:9;
    then reconsider f as FinSequence by FINSEQ_1:def 2;
    dom f is n-element by A1,A2,CARD_3:9;
    then card dom f = n by CARD_1:def 7;
    then card f = n by CARD_1:62;
    hence thesis by CARD_1:def 7;
  end;
