theorem Th36:
 for x being object holds chi(A,X).x = 1 implies x in A
proof let x be object;
  assume
A1: chi(A,X).x = 1;
A2: 1 = succ 0 .= {0};
  per cases;
  suppose
    x in X;
    hence thesis by A1,Def3;
  end;
  suppose
    not x in X;
    then not x in dom chi(A,X) by Def3;
    hence thesis by A1,FUNCT_1:def 2,A2;
  end;
end;
