Definition Forall_tl (A : Type) (P : A -> Prop) (a : A) (l : list A)
           (H : Forall P (a :: l)): Forall P l.

Lemma minus_lt_compat_r: forall n m p : nat, (n < m)%nat -> (p <= n)%nat -> (n - p < m - p)%nat.