Definition splittable {A} {JA: Join A}{PA: Perm_alg A}{agA: ageable A}{AgeA: Age_alg A} (Q: Share.t -> pred A) := 
  forall (sh1 sh2 sh3: Share.t) (rsh1: readable_share sh1) (rsh2: readable_share sh2),
    join sh1 sh2 sh3 ->
    Q sh1 * Q sh2 = Q sh3.

Lemma slice_resource_resource_share: forall r sh sh', resource_share r = Some sh -> join_sub sh' sh -> resource_share (slice_resource sh' r) = Some sh'.