proposition: Lemma octet_leq_inf : forall a b c d e f g h : Z, {(e <= a)%Z /\ (f <= b)%Z /\ (g <= c)%Z /\ (h <= d)%Z} + {~ ((e <= a)%Z /\ (f <= b)%Z /\ (g <= c)%Z /\ (h <= d)%Z)}.
proof: Proof. intros. case (Z_le_dec e a); intros; [ case (Z_le_dec f b); intros; [ case (Z_le_dec g c); intros; [ case (Z_le_dec h d); [ intros; left; repeat (split; try assumption) | intros; right ] | intros; right ] | intros; right ] | intros; right ]; (intros (H0, (H1, (H2, H3))); Falsum). Defined.
imports: QArithSternBrocot(Merge_Order)