reserve a,b,c,d,e for Real;
reserve X,Y for set,
          Z for non empty set,
          r for Real,
          s for ExtReal,
          A for Subset of REAL,
          f for real-valued Function;
reserve I for non empty closed_interval Subset of REAL,
       TD for tagged_division of I,
        D for Division of I,
        T for Element of set_of_tagged_Division(D),
        f for PartFunc of I,REAL;

theorem Th24:
  Y c= X implies chi(X,Y) = chi(Y,Y)
  proof
    assume
A1: Y c= X;
    now
      thus dom chi(X,Y) = Y by FUNCT_3:def 3
                       .= dom chi(Y,Y) by FUNCT_3:def 3;
      hereby
        let x be object;
        assume
A2:     x in dom chi(X,Y);
        then x in Y & x in X by A1;
        hence (chi(X,Y)).x = 1 by FUNCT_3:def 3
                           .= (chi(Y,Y)).x by A2,FUNCT_3:def 3;
      end;
    end;
    hence thesis;
  end;
