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.

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.