fact: Definition lawvere_to_from_iso {a b} (g : a ~> G b) : ((a, b); φ' E (ψ' E g)) ≅[Id[D] ↓ G] ((a, b); g) := iso_compose (`1 (iso_to_from (lawvere_iso E)) ((a, b); g)) (iso_sym (@lawvere_iso_to_from _ _ g)).
imports: Category.Lib Category.Theory.Category Category.Theory.Isomorphism Category.Theory.Functor Category.Theory.Natural.Transformation Category.Theory.Adjunction Category.Adjunction.Natural.Transformation Category.Adjunction.Natural.Transformation.Universal Category.Construction.Comma Category.Construction.Product Category.Instance.Cat Category.Instance.Fun Category.Instance.Sets