intros. destruct sh.
unfold Rsh. simpl.
rewrite rel_top2.
icase x;simpl.
icase b;simpl.
compute. f_equal. apply proof_irr.
compute. f_equal. apply proof_irr.
Qed.

Lemma lub_rel_recompose: forall sh1 sh2,
lub (rel Lsh sh1) (rel Rsh sh2) = recompose (sh1,sh2).