Definition sectohfiber { X : UU } (P:X -> UU): (∏ x:X, P x) -> (hfiber (λ f, λ x, pr1 (f x)) (λ x:X, x)) := (fun a : ∏ x:X, P x => tpair _ (λ x, tpair _ x (a x)) (idpath (λ x:X, x))).
Definition funcontrFromUnivalence: univalenceStatement -> funcontrStatement Definition funextsecweqFromUnivalence: univalenceStatement -> isweqtoforallpathsStatement Definition funextemptyFromUnivalence: univalenceStatement -> funextemptyStatement Definition propositionalUnivalenceFromUnivalence: univalenceStatement -> propositionalUnivalenceStatement Definition funextcontrStatementFromUnivalence: univalenceStatement ->  funextcontrStatement