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 Th2:
  for x0 be Point of CNS for g be Real st 0 < g holds {y where y is
  Point of CNS: ||.y-x0 .|| < g} is Neighbourhood of x0
proof
  let x0 be Point of CNS;
  let g be Real such that
A1: g >0;
  set N= {y where y is Point of CNS : ||.y-x0 .|| < g};
  N c= the carrier of CNS
  proof
    let x be object;
    assume x in {y where y is Point of CNS : ||.y-x0 .|| < g};
    then ex y be Point of CNS st x=y & ||.y-x0 .|| < g;
    hence thesis;
  end;
  hence thesis by A1,Def1;
end;
