reserve X for MetrSpace,
  x,y,z for Element of X,
  A for non empty set,
  G for Function of [:A,A:],REAL,
  f for Function,
  k,n,m,m1,m2 for Nat,
  q,r for Real;
reserve X for non empty MetrSpace,
  x,y for Element of X,
  V for Subset of X,
  S,S1,T for sequence of X,
  Nseq for increasing sequence of NAT;

theorem Th7:
  for x ex S st rng S = {x}
proof
  let x;
  consider f such that
A1: dom f = NAT and
A2: rng f = {x} by FUNCT_1:5;
  reconsider f as sequence of X by A1,A2,FUNCT_2:2;
  take f;
  thus thesis by A2;
end;
