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;
