reserve n,m for Nat,
  r,r1,r2,s,t for Real,
  x,y for set;

theorem Th30:
  for D be non empty set, f be FinSequence, d be Element of D
  holds d is_common_for_dom CHI(f,D)
proof
  let D be non empty set, f be FinSequence, d be Element of D;
  let n;
  assume n in dom CHI(f,D);
  then CHI(f,D).n = chi(f.n,D) by Def6;
  then dom (CHI(f,D).n) = D by RFUNCT_1:61;
  hence thesis;
end;
