reserve i,j,k,n for Nat,
  X,Y,a,b,c,x for set,
  r,s for Real;

theorem Th3:
  for f be FinSequence of TOP-REAL n for i st 1 <= i & i + 1 <= len
  f holds f/.i in rng f & f/.(i+1) in rng f
proof
  let f be FinSequence of TOP-REAL n;
  let i;
  assume
A1: 1 <= i & i + 1 <= len f;
  then
A2: i in dom f by SEQ_4:134;
  then f.i in rng f by FUNCT_1:3;
  hence f/.i in rng f by A2,PARTFUN1:def 6;
A3: i + 1 in dom f by A1,SEQ_4:134;
  then f.(i+1) in rng f by FUNCT_1:3;
  hence thesis by A3,PARTFUN1:def 6;
end;
