(** Unfortunately, we do not have [n < m + p -> n - p < m]. For instance [1<0+2] but not [1-2<0]. *)

(** Unfortunately, we do not have [n <= m - p -> n + p <= m]. For instance [0<=1-2] but not [2+0<=1]. *)
Theorem le_add_le_sub_l : forall n m p, n + p <= m -> p <= m - n.