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_l : forall u v w : word, conc u v w -> forall b : bool, alt b w -> alt b u.