(*  a -->  b -->* c    d - by prior lemma |      |      |    e - by induction. v      v      v *      *      * a2 --> d -->* e  *)

(* a   b   c \ / \ / ab  bc \ / d *)
Lemma join_transitive : forall S D a b, Good S D -> joins S D a b -> forall c, joins S D b c -> joins S D a c.