Remark nu_left_inv_on (y:A) (u:x = y) : nu_inv (nu u) = u.

Theorem eq_dep_eq_dec : forall A:Type, (forall x y:A, {x = y} + {x <> y}) -> forall (P:A->Type) (p:A) (x y:P p), eq_dep A P p x p y -> x = y.