theorem Th14:
  for A be non empty set holds chi(A,A)|A is constant
proof
  let A be non empty set;
   reconsider jj=1 as Element of REAL by XREAL_0:def 1;
  for x being Element of A st x in A /\ dom chi(A,A) holds chi(A,A)/.x=jj
  proof
    let x be Element of A;
    assume x in A /\ dom chi(A,A); then
A1: x in dom chi(A,A) by XBOOLE_0:def 4;
    chi(A,A).x=1 by FUNCT_3:def 3;
    hence thesis by A1,PARTFUN1:def 6;
  end;
  hence thesis by PARTFUN2:35;
end;
