(** * Decidability of order on binary integers *)

  Definition Z_lt_dec : {x < y} + {~ x < y}.Definition Z_le_dec : {x <= y} + {~ x <= y}.Definition Z_gt_dec : {x > y} + {~ x > y}.Definition Z_ge_dec : {x >= y} + {~ x >= y}.Definition Z_lt_ge_dec : {x < y} + {x >= y}.

Lemma Z_lt_le_dec : {x < y} + {y <= x}.