proposition: Lemma Prf_E1_law3 : Equalizer_law3 E1_mor E1_diese.
proof: Proof. unfold Equalizer_law3, E1_mor, Equalizer_eq in |- *. intros r h p q H. unfold E1_diese in |- *; apply (Prf_limit2 l). unfold Limit_eq in |- *; simpl in |- *. intro x; elim x; simpl in |- *. apply Sym; apply H. apply Trans with ((q o E1_mor) o k (Witness l)). apply Trans with (q o E1_mor o k (Witness l)). apply Comp_l. apply (EqC (Limiting_cone l) (PA_f (Witness l))). apply Ass. apply Comp_r; apply Sym; apply H. Qed.
imports: Equalizers PA Limit