src/HOL/SPARK/Examples/Liseq/Longest_Increasing_Subsequence.thy
changeset 41588 9546828c0eb3
parent 41561 d1318f3c86ba
child 44890 22f665a2e91c
equal deleted inserted replaced
41587:e13df75fee79 41588:9546828c0eb3
   159   with assms have "Max js \<in> js"
   159   with assms have "Max js \<in> js"
   160     by auto
   160     by auto
   161   with assms have "Max js < i"
   161   with assms have "Max js < i"
   162     by (auto simp add: iseq_def)
   162     by (auto simp add: iseq_def)
   163   with fin assms have "\<forall>j\<in>js. j < i"
   163   with fin assms have "\<forall>j\<in>js. j < i"
   164     by (simp add: Max_less_iff)
   164     by simp
   165   with assms show ?thesis
   165   with assms show ?thesis
   166     by (simp add: iseq_def)
   166     by (simp add: iseq_def)
   167 qed
   167 qed
   168 
   168 
   169 lemma iseq_mono: "is \<in> iseq xs i \<Longrightarrow> i \<le> j \<Longrightarrow> is \<in> iseq xs j"
   169 lemma iseq_mono: "is \<in> iseq xs i \<Longrightarrow> i \<le> j \<Longrightarrow> is \<in> iseq xs j"