reserve n,m for Element of NAT;
reserve r,s for Real;
reserve z for Complex;
reserve CNS,CNS1,CNS2 for ComplexNormSpace;
reserve RNS for RealNormSpace;

theorem Th4:
  for n being Nat
  for seq be sequence of CNS1, h be PartFunc of CNS1,CNS2 st rng
  seq c= dom h
   holds seq.n in dom h
proof
  let n be Nat;
  let seq be sequence of CNS1;
  let h be PartFunc of CNS1,CNS2;
  n in NAT by ORDINAL1:def 12;
  then
A1: n in dom seq by FUNCT_2:def 1;
  assume rng seq c= dom h;
  then n in dom ((h qua Function)*seq) by A1,RELAT_1:27;
  hence thesis by FUNCT_1:11;
end;
