theorem
  for t be FinSequence of INT holds t is FinSequence of REAL
proof
  let t be FinSequence of INT;
  now
    let i be Nat;
    assume i in dom t;
    then
A1: t.i in rng t by FUNCT_1:def 3;
    t.i in INT by A1;
    hence t.i in REAL by NUMBERS:15;
  end;
  hence thesis by FINSEQ_2:12;
end;
