reserve Al for QC-alphabet;
reserve i,j,k for Nat,
  A,D for non empty set;

theorem Th1:
  for x being set st x is Element of Valuations_in(Al,A) holds x is
  Function of bound_QC-variables(Al) ,A
proof
  let x be set;
  assume x is Element of Valuations_in(Al,A);
  then ex f being Function st x = f & dom f = bound_QC-variables(Al)
   & rng f c= A by FUNCT_2:def 2;
  hence thesis by FUNCT_2:def 1,RELSET_1:4;
end;
