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

Theorem K_dec_type (A:Type) (eq_dec:forall x y:A, {x = y} + {x <> y}) (x:A) (P:x = x -> Prop) (H:P (eq_refl x)) (p:x = x) : P p.