intros [H H'].
rewrite Share.lub_commute in H'.
rewrite Share.lub_bot in H'.
auto.
Qed.
(*Got this ltac from permission.v maybe should factor*)
Ltac if_simpl:=
repeat match goal with
| [ H: ?X = true |- context[if ?X then _ else _] ] => rewrite H; simpl
| [ H: ?X = false |- context[if ?X then _ else _] ] => rewrite H; simpl
| [ H: ?X = left _ |- context[match ?X with left _ => _ | right _ => _ end] ]=>
rewrite H; simpl
| [ H: ?X = right _ |- context[match ?X with left _ => _ | right _ => _ end] ]=>
rewrite H; simpl
end.

Lemma top_aint_bot:
eq_dec Share.top Share.bot = right Share.nontrivial.