reserve a,b,e,r,x,y for Real,
  i,j,k,n,m for Element of NAT,
  x1 for set,
  p,q for FinSequence of REAL,
  A for non empty closed_interval Subset of REAL,
  D,D1,D2 for Division of A,
  f,g for Function of A,REAL,
  T for DivSequence of A;

theorem Th16:
  x in rng D implies D.1 <= x & x <= D.(len D)
proof
  assume x in rng D;
  then consider i such that
A1: i in dom D and
A2: x=D.i by PARTFUN1:3;
A3: i <= len D by A1,FINSEQ_3:25;
A4: 1 <= i by A1,FINSEQ_3:25;
  then
A5: 1 <= len D by A3,XXREAL_0:2;
  then
A6: len D in dom D by FINSEQ_3:25;
  1 in dom D by A5,FINSEQ_3:25;
  hence thesis by A1,A2,A4,A3,A6,SEQ_4:137;
end;
