Lemma clos_refl_trans_ind_right : forall (A : Set) (R : relation A) (M : A) (P : A -> Prop), P M -> (forall P0 N : A, R N P0 -> clos_refl_trans A R P0 M -> P P0 -> P N) -> forall a : A, clos_refl_trans A R a M -> P a.