-(*CSC: qua c'era uno zero*)
-lemma le_x_zero_to_le_zero_opp_x: ∀F:ordered_field_ch0.∀x:F. x ≤ 0 → (zero F) ≤ -x.
- intros;
- generalize in match (of_plus_compat ? ? F ? ? (-x) H); intro;
- rewrite > zero_neutral in H1;
- rewrite > plus_comm in H1;
- rewrite > opp_inverse in H1;
- (*assumption.*) apply H1.
-qed.
+coercion cic:/matita/ordered_fields_ch0/of_cotransitively_ordered_set.con.
+
+record is_ordered_field_ch0 (F:pre_ordered_field_ch0) : Type \def
+ { of_mult_compat: ∀a,b:F. 0≤a → 0≤b → 0≤a*b;
+ of_weak_tricotomy : ∀a,b:F. a≠b → a≤b ∨ b≤a;
+ (* 0 characteristics *)
+ of_char0: ∀n. n > O → sum ? (plus F) 0 1 n ≠ 0
+ }.
+
+record ordered_field_ch0 : Type \def
+ { of_pre_ordered_field_ch0:> pre_ordered_field_ch0;
+ of_ordered_field_properties:> is_ordered_field_ch0 of_pre_ordered_field_ch0
+ }.