reserve n,m for Nat;
reserve x,X,X1 for set;
reserve s,g,r,p for Real;
reserve S,T for RealNormSpace;
reserve f,f1,f2 for PartFunc of S,T;
reserve s1,s2 for sequence of S;
reserve x0,x1,x2 for Point of S;
reserve Y for Subset of S;

theorem Th5:
  for seq be sequence of S, h be PartFunc of S,T st rng seq c= dom h holds
  seq.n in dom h
proof
  let seq be sequence of S;
A1: n in NAT by ORDINAL1:def 12;
  dom seq = NAT by FUNCT_2:def 1;
  then seq.n in rng seq by FUNCT_1:def 3,A1;
  hence thesis;
end;
