Inductive alternate (w : word) : Prop :=
    alter : forall b : bool, alt b w -> alternate w.Inductive alternate (w : word) : Prop :=
    alter : forall b : bool, alt b w -> alternate w.

(* Specifications: *)
Lemma alt_conc_l : forall u v w : word, conc u v w -> forall b : bool, alt b w -> alt b u.
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.
Lemma alt_conc : forall u v w : word, conc u v w -> alternate w -> alternate u /\ alternate v.