
theorem
  for C being Category, I being Indexing of C for T1 being TargetCat of
  I, J being Indexing of T1 for T2 being TargetCat of J for D being Categorial
  Category, F being Functor of T2,D holds (F*J)*I = F*(J*I)
proof
  let C be Category, I be Indexing of C;
  let T1 be TargetCat of I;
  let J be Indexing of T1;
  let T2 be TargetCat of J;
  let D be Categorial Category, F be Functor of T2,D;
  thus (F*J)*I = (F*J)*(I-functor(C,T1)) by Th32
    .= F*(J*(I-functor(C,T1))) by Th34
    .= F*(J*I) by Th32;
end;
