Lemma comm_loc_share_join : forall good lsh1 lsh2 lsh comm g g0 g1 g2 bufs sh gsh h1 h2 h (Hsh : sepalg.join lsh1 lsh2 lsh) (Hh : Permutation.Permutation (h1 ++ h2) h) (Hsh1 : lsh1 <> Share.bot) (Hsh2 : lsh2 <> Share.bot) (Hdisj : disjoint h1 h2), comm_loc good lsh1 comm g g0 g1 g2 bufs sh gsh h1 * comm_loc good lsh2 comm g g0 g1 g2 bufs sh gsh h2 = comm_loc good lsh comm g g0 g1 g2 bufs sh gsh h.