Inductive alternate (w : word) : Prop :=
alter : forall b : bool, alt b w -> alternate w.
(* (alternate w) iff Exists b  (alt b w)  *)
(*********************************************)
(* Subwords of alternate words are alternate *)
(*********************************************)

Lemma alt_conc_r :
forall u v w : word,
conc u v w ->
forall b : bool, alt b w -> odd u /\ alt (negb b) v \/ even u /\ alt b v.