(** * 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 Zeq_plus_swap n m p : n + p = m <-> n = m - p.