Lemma concat_prop_per_element : forall P : Predicate A, (forall (i : Nat) (Hi : i < n) (Hi' : i < n + m), Pred_fun P ((v ++ w) (Build_finiteT Hi'))) -> (forall (j : Nat) (Hj : j < m) (Hj' : n + j < n + m), Pred_fun P ((v ++ w) (Build_finiteT Hj'))) -> forall (k : Nat) (Hk : k < n + m), Pred_fun P ((v ++ w) (Build_finiteT Hk)).