reserve S for 1-sorted,
  i for Element of NAT,
  p for FinSequence,
  X for set;

theorem
  (for i being Nat st i in dom p holds p.i in S) implies p is FinSequence of S
proof
  assume
A1: for i being Nat st i in dom p holds p.i in S;
  for i being Nat st i in dom p holds p.i in the carrier of S
  by A1,STRUCT_0:def 5;
  hence thesis by FINSEQ_2:12;
end;
