Definition weqtopathsStatement := ∏ ( T1 T2 : UU ), T1 ≃ T2 -> T1 = T2.
Definition funcontrFromUnivalence: univalenceStatement -> funcontrStatement Definition funextsecweqFromUnivalence: univalenceStatement -> isweqtoforallpathsStatement Definition funextemptyFromUnivalence: univalenceStatement -> funextemptyStatement Definition propositionalUnivalenceFromUnivalence: univalenceStatement -> propositionalUnivalenceStatement Definition funextcontrStatementFromUnivalence: univalenceStatement ->  funextcontrStatement