reserve a,a1,b,b1,x,y for Real,
  F,G,H for FinSequence of REAL,
  i,j,k,n,m for Element of NAT,
  I for Subset of REAL,
  X for non empty set,
  x1,R,s for set;
reserve A for non empty closed_interval Subset of REAL;
reserve A, B for non empty closed_interval Subset of REAL;
reserve r for Real;
reserve D, D1, D2 for Division of A;
reserve f, g for Function of A,REAL;

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;
