src/HOL/Rational.thy
changeset 30649 57753e0ec1d4
parent 30273 ecd6f0ca62ea
child 30960 fec1a04b7220
equal deleted inserted replaced
30617:620db300c038 30649:57753e0ec1d4
   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)