src/HOL/Import/HOL_Light_Maps.thy
changeset 54863 82acc20ded73
parent 47364 637074507956
child 55393 ce5cebfaedda
equal deleted inserted replaced
54862:c65e5cbdbc97 54863:82acc20ded73
   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