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

Theorem K_dec_set : forall A:Set, (forall x y:A, {x = y} + {x <> y}) -> forall (x:A) (P:x = x -> Prop), P (eq_refl x) -> forall p:x = x, P p.