Section RtRft.
Variable A:Type.
Variable R:relation A.
Let Rt := clos_trans A R.
Let Rft := clos_refl_trans A R.
End RtRft.
Hint Resolve rt_refl : core.
Definition laterR {A} `{ageable A} : relation A := clos_trans A age.
Definition necR   {A} `{ageable A} : relation A := clos_refl_trans A age.
Require Coq.Wellfounded.Wellfounded.
Definition laterR_induction {A} `{ageable A} :=
@well_founded_induction A (transp A laterR) laterR_wf.

Lemma age_later_nec {A} `{HA: ageable A} : forall x y z,
age x y ->
laterR x z ->
necR y z.