Module M.
Check internal_qed@{_ _}.
End M.
Include M.
(* be careful to remove const_private_univs in Include! will be coqchk'd *)
Unset Strict Universe Declaration.
Definition private_transitivity'@{i j|i < j} := private_transitivity@{i j}.
Fail Definition dummy@{i j|j <= i +} := private_transitivity@{i j}.
Unset Private Polymorphic Universes.

Lemma internal_noprivate_qed@{i j|i<=j} (A:Type@{i}) : Type@{j}.