Corollary prev_taken_In : forall h, prev_taken h = vint 1 \/ In (AE (prev_taken h) Empty) h.

Lemma make_shares_ext : forall i d l l' lgood shs (Hlen : Zlength l = Zlength l') (Hi : forall j, 0 <= j < Zlength l -> Znth j l d = i <-> Znth j l' d = i), make_shares shs (combine lgood l) i = make_shares shs (combine lgood l') i.