(* IIi Fi *)

Definition Thl_k_Fi (i : J) := F i.Definition Thl_l_Fi := H1 Thl_k_Fi.Definition Thl_PI_Fi := Pi1 Thl_l_Fi.(* ||u F(codomu) *)

Definition Thl_k_Fu (u : Arrs J) := F (Codom u).Definition Thl_l_Fu := H2 Thl_k_Fu.Definition Thl_PI_Fu := Pi1 Thl_l_Fu.(* qq u. fu : IIi Fi -> ku (= F(codomu)) *)

Definition Thl_fu (u : Arrs J) := Proj1 Thl_l_Fi (Codom u).

(* Specifications: *)
Lemma Thl_diag1 : forall u : Arrs J, Thl_fu u =_S Thl_f o Proj1 Thl_l_Fu u.