reserve i,j,k,l for natural Number;
reserve A for set, a,b,x,x1,x2,x3 for object;
reserve D,D9,E for non empty set;
reserve d,d1,d2,d3 for Element of D;
reserve d9,d19,d29,d39 for Element of D9;
reserve p,q,r for FinSequence;

theorem Th54:
  for k being natural Number holds (Seg k) --> a is FinSequence
proof
  let k be natural Number;
  reconsider k as Element of NAT by ORDINAL1:def 12;
  dom(Seg k --> a) = Seg k;
  hence thesis by FINSEQ_1:def 2;
end;
