(* * 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}.
Hint Resolve @constructive_join_sub_refl : core.
Definition constructive_joins {A}  {JOIN: Join A} (w1 w2 : A) := {w3 | join w1 w2 w3}.

Lemma constructive_joins_sym {A} `{Perm_alg A}: forall a b,
constructive_joins a b = constructive_joins b a.