proposition: Lemma expand_φ_ψ {a b} (g : a ~> G b) : φ E (ψ E ((a, b); g)) ≈ φ E ((fst `1 ((lawvere_iso E)⁻¹ ((a, b); g)), snd `1 ((lawvere_iso E)⁻¹ ((a, b); g))); `2 ((lawvere_iso E)⁻¹ ((a, b); g))).
proof: Proof. now rewrite surjective_tripleF. Qed.
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