(** * Equivalence between inequalities *)

Notation Zle_plus_swap := Z.le_add_le_sub_r (only parsing).Notation Zlt_plus_swap := Z.lt_add_lt_sub_r (only parsing).Notation Zlt_minus_simpl_swap := Z.lt_sub_pos (only parsing).

Lemma Zle_0_minus_le n m : 0 <= n - m -> m <= n.