(* * Copyright (c) 2009-2010, Andrew Appel, Robert Dockins and Aquinas Hobor. * *)
Definition constructive_join_sub {A} {JOIN: Join A} (w1 w3: A) := {w2 | join w1 w2 w3}.

Lemma cjoin_sub_trans {A} `{Perm_alg A}: forall a b c,
constructive_join_sub a b -> constructive_join_sub b c -> constructive_join_sub a c.