Definition Z_le_gt_dec : {x <= y} + {x > y}.Definition Z_gt_le_dec : {x > y} + {x <= y}.Definition Z_ge_lt_dec : {x >= y} + {x < y}.Definition Z_le_lt_eq_dec : x <= y -> {x < y} + {x = y}.

Lemma Zlt_cotrans_pos : forall n m:Z, 0 < n + m -> {0 < n} + {0 < m}.