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

Theorem eq_rect_eq_dec : forall A:Type, (forall x y:A, {x = y} + {x <> y}) -> forall (p:A) (Q:A -> Type) (x:Q p) (h:p = p), x = eq_rect p Q x p h.