-interpretation "Ordered field le" 'leq a b =
- (cic:/matita/ordered_fields_ch0/of_le.con _ a b).
-
-definition lt \def λF:ordered_field_ch0.λa,b:F.a ≤ b ∧ a ≠ b.
-
-interpretation "Ordered field lt" 'lt a b =
- (cic:/matita/ordered_fields_ch0/lt.con _ a b).
-
-lemma le_zero_x_to_le_opp_x_zero: ∀F:ordered_field_ch0.∀x:F. 0 ≤ x → -x ≤ 0.
-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.
-qed.
-
-lemma le_x_zero_to_le_zero_opp_x: ∀F:ordered_field_ch0.∀x:F. x ≤ 0 → 0 ≤ -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.
-qed.
-