reserve a,b,c,d,m,x,n,j,k,l for Nat,
  t,u,v,z for Integer,
  f,F for FinSequence of NAT;
reserve p,q,r,s for real number;
reserve a,b,c,d,m,x,n,k,l for Nat,
  t,z for Integer,
  f,F,G for FinSequence of REAL;
reserve q,r,s for real number;
reserve D for set;

theorem Th1:
  for f be FinSequence holds
    f is D-valued iff f is FinSequence of D
  proof
    let f be FinSequence;
    f is D-valued implies f is FinSequence of D
    proof
      assume f is D-valued; then
      rng f c= D by RELAT_1:def 19;
      hence thesis by FINSEQ_1:def 4;
    end;
    hence thesis;
  end;
