theorem Th12:
  V is non empty & A is_without_nonatomicND_wrt V &
  (for T holds loc/.1 is_a_value_on T & loc/.3 is_a_value_on T)
  implies
  <* PP_and(Equality(A,loc/.1,loc/.3),factorial_inv(A,loc,n0)),
     SC_assignment(denaming(V,A,loc/.4),z),
     valid_factorial_output(A,z,n0) *> is SFHT of ND(V,A)
  proof
    set s = loc/.4;
    <*SC_Psuperpos(valid_factorial_output(A,z,n0),denaming(V,A,s),z),
      SC_assignment(denaming(V,A,s),z),
      valid_factorial_output(A,z,n0)*> is SFHT of ND(V,A) by NOMIN_3:29;
    hence thesis by Th11,NOMIN_3:15;
  end;
