Section Univalence.
Context `{Univalence}.
Definition path_universe_uncurried {A B : Type} (f : A <~> B) : A = B
:= (equiv_path A B)^-1 f.
Definition path_universe {A B : Type} (f : A -> B) {feq : IsEquiv f} : (A = B)
:= path_universe_uncurried (BuildEquiv _ _ f feq).
End Univalence.
Definition e : Equiv@{i j} Bool Bool.
admit.
Defined.
Definition p `{Univalence} : @paths Type Bool Bool := path_universe e.

Theorem thm `{Univalence} : (forall A, ((A -> False) -> False) -> A) -> False.