equal
deleted
inserted
replaced
173 "(op >) = (\<lambda>x y :: nat. y < x)" |
173 "(op >) = (\<lambda>x y :: nat. y < x)" |
174 by simp |
174 by simp |
175 |
175 |
176 lemma DEF_MAX[import_const "MAX"]: |
176 lemma DEF_MAX[import_const "MAX"]: |
177 "max = (\<lambda>x y :: nat. if x \<le> y then y else x)" |
177 "max = (\<lambda>x y :: nat. if x \<le> y then y else x)" |
178 by (auto simp add: min_max.le_iff_sup fun_eq_iff) |
178 by (auto simp add: max.absorb_iff2 fun_eq_iff) |
179 |
179 |
180 lemma DEF_MIN[import_const "MIN"]: |
180 lemma DEF_MIN[import_const "MIN"]: |
181 "min = (\<lambda>x y :: nat. if x \<le> y then x else y)" |
181 "min = (\<lambda>x y :: nat. if x \<le> y then x else y)" |
182 by (auto simp add: min_max.le_iff_inf fun_eq_iff) |
182 by (auto simp add: min.absorb_iff1 fun_eq_iff) |
183 |
183 |
184 lemma EVEN[import_const "EVEN" : "Parity.even_odd_class.even"]: |
184 lemma EVEN[import_const "EVEN" : "Parity.even_odd_class.even"]: |
185 "even (id 0\<Colon>nat) = True \<and> (\<forall>n. even (Suc n) = (\<not> even n))" |
185 "even (id 0\<Colon>nat) = True \<and> (\<forall>n. even (Suc n) = (\<not> even n))" |
186 by simp |
186 by simp |
187 |
187 |