 reserve j for set;
 reserve p,r for Real;
 reserve S,T,F for RealNormSpace;
 reserve x0 for Point of S;
 reserve g for PartFunc of S,T;
 reserve c for constant sequence of S;
 reserve R for RestFunc of S,T;
 reserve G for RealNormSpace-Sequence;
 reserve i for Element of dom G;
 reserve f for PartFunc of product G,F;
 reserve x for Element of product G;

theorem Th9:
for X be non-empty FinSequence,
    x be set st x in product X holds x is FinSequence
proof
   let X be non-empty FinSequence, x be set;
   assume x in product X; then
   consider g be Function such that
A1: x = g & dom g = dom X
  & for i be object st i in dom X holds g.i in X.i by CARD_3:def 5;
   dom g = Seg len X by A1,FINSEQ_1:def 3;
   hence x is FinSequence by A1,FINSEQ_1:def 2;
end;
