reserve n for Nat;

theorem Th6:
  for f be FinSequence of REAL st dom f = Seg n holds f is Element of REAL n
proof
A1: n in NAT by ORDINAL1:def 12;
  let f be FinSequence of REAL;
  assume dom f= Seg n;
  then len f = n by A1,FINSEQ_1:def 3;
  then f is Element of n-tuples_on REAL by FINSEQ_2:92;
  hence thesis by EUCLID:def 1;
end;
