reserve a, b for Real;
reserve RNS for RealNormSpace;
reserve x, y, z, g, g1, g2 for Point of RNS;
reserve S, S1, S2 for sequence of RNS;
reserve k, n, m, m1, m2 for Nat;
reserve r for Real;
reserve f for Function;
reserve d, s, t for set;

theorem
  for RNS being non empty 1-sorted, x being Element of RNS ex S being
  sequence of RNS st rng S = {x}
proof
  let RNS be non empty 1-sorted;
  let x be Element of RNS;
  consider f such that
A1: dom f = NAT and
A2: rng f = {x} by FUNCT_1:5;
  reconsider f as sequence of RNS by A1,A2,FUNCT_2:def 1,RELSET_1:4;
  take f;
  thus thesis by A2;
end;
