proposition: Lemma NTinv_nt_law : NT_law h.
proof: Proof. unfold NT_law in |- *; intros a b f. apply Trans with ((h a o T a o FMor G f) o h b). apply Comp_r. apply Trans with ((h a o T a) o FMor G f). apply Trans with (Id (G a) o FMor G f). apply Idl1. apply Comp_r; apply Sym; apply (Idl_inv (H a)). apply Ass1. apply Trans with ((h a o FMor F f o T b) o h b). apply Comp_r; apply Comp_l; apply NatCond1. apply Trans with (h a o (FMor F f o T b) o h b). apply Ass1. apply Comp_l. apply Trans with (FMor F f o T b o h b). apply Ass1. apply Trans with (FMor F f o Id _). apply Comp_l; apply (Idr_inv (H b)). apply Idr1. Qed.
imports: CatProperty CatFunct