reserve i for Nat,
  j for Element of NAT,
  X,Y,x,y,z for set;
reserve C for initialized ConstructorSignature,
  s for SortSymbol of C,
  o for OperSymbol of C,
  c for constructor OperSymbol of C;
reserve a,b for expression of C, an_Adj C;
reserve t, t1,t2 for expression of C, a_Type C;
reserve p for FinSequence of QuasiTerms C;
reserve e for expression of C;
reserve a,a9 for expression of C, an_Adj C;
reserve q for pure expression of C, a_Type C,
  A for finite Subset of QuasiAdjs C;
reserve T for quasi-type of C;
reserve f for valuation of C;
reserve x for variable;

theorem
  for T being quasi-type of C for a being quasi-adjective of C
  holds (a ast T) at f = (a at f) ast (T at f)
proof
  let T be quasi-type of C;
  let a be quasi-adjective of C;
  a in QuasiAdjs C;
  then reconsider A = {a} as Subset of QuasiAdjs C by ZFMISC_1:31;
  thus (a ast T) at f
  = [(adjs (a ast T)) at f,((the_base_of T) at f)]
    .= [(A\/(adjs T)) at f,((the_base_of T) at f)]
    .= [(A at f)\/((adjs T) at f),(the_base_of T) at f] by Th145
    .= [{a at f}\/((adjs T) at f),(the_base_of T) at f] by Th144
    .= [{a at f}\/(adjs (T at f)),(the_base_of T) at f]
    .= (a at f) ast (T at f);
end;
