reserve a,b,c for set;

theorem Th22:
  for X,x0,x being set st x in X & x <> x0 holds {x} is open
  Subset of DiscrWithInfin(X,x0)
proof
  let X,x0,x be set;
  set T = DiscrWithInfin(X,x0);
  assume that
A1: x in X and
A2: x <> x0;
A3: the carrier of T = X by Def5;
  not x0 in {x} by A2,TARSKI:def 1;
  hence thesis by A3,A1,Th19,ZFMISC_1:31;
end;
