equal
deleted
inserted
replaced
689 using not_zero by (simp add: pos_less_divide_eq pos_divide_less_eq) |
689 using not_zero by (simp add: pos_less_divide_eq pos_divide_less_eq) |
690 show "(of_rat (Fract a b) :: 'a::ordered_field) < of_rat (Fract c d) |
690 show "(of_rat (Fract a b) :: 'a::ordered_field) < of_rat (Fract c d) |
691 \<longleftrightarrow> Fract a b < Fract c d" |
691 \<longleftrightarrow> Fract a b < Fract c d" |
692 using not_zero `b * d > 0` |
692 using not_zero `b * d > 0` |
693 by (simp add: of_rat_rat of_int_divide_less_eq of_int_mult [symmetric] del: of_int_mult) |
693 by (simp add: of_rat_rat of_int_divide_less_eq of_int_mult [symmetric] del: of_int_mult) |
694 (auto intro: mult_strict_right_mono mult_right_less_imp_less) |
|
695 qed |
694 qed |
696 |
695 |
697 lemma of_rat_less_eq: |
696 lemma of_rat_less_eq: |
698 "(of_rat r :: 'a::ordered_field) \<le> of_rat s \<longleftrightarrow> r \<le> s" |
697 "(of_rat r :: 'a::ordered_field) \<le> of_rat s \<longleftrightarrow> r \<le> s" |
699 unfolding le_less by (auto simp add: of_rat_less) |
698 unfolding le_less by (auto simp add: of_rat_less) |