
theorem
  for C being Category, I being Indexing of C for D being TargetCat of I
, J being Indexing of D for E being TargetCat of J, K being Indexing of E holds
  (K*J)*I = K*(J*I)
proof
  let C be Category, I be Indexing of C;
  let D be TargetCat of I, J be Indexing of D;
  let E be TargetCat of J, K be Indexing of E;
  thus (K*J)*I = (K*J)*(I-functor(C,D)) by Th32
    .= K*(J*(I-functor(C,D))) by Th37
    .= K*(J*I) by Th32;
end;
