proposition: Lemma is_terminal_object__is_terminal_category `(IsTerminalCategory one) (HT : P one) : IsTerminalObject (sub_pre_cat P HF) (one; HT).
proof: Proof. typeclasses eauto. Defined.
imports: Category.Objects InitialTerminalCategory.Core InitialTerminalCategory.Functors Functor.Core Category.Strict Functor.Paths Functor.Identity Functor.Composition.Core Functor.Composition.Laws