src/HOL/Library/Tree.thy
changeset 68109 cebf36c14226
parent 67399 eab6ce8368fa
child 68998 818898556504
equal deleted inserted replaced
68097:5f3cffe16311 68109:cebf36c14226
   444 using bst_wrt_mono less_imp_le by blast
   444 using bst_wrt_mono less_imp_le by blast
   445 
   445 
   446 lemma bst_wrt_le_iff_sorted: "bst_wrt (\<le>) t \<longleftrightarrow> sorted (inorder t)"
   446 lemma bst_wrt_le_iff_sorted: "bst_wrt (\<le>) t \<longleftrightarrow> sorted (inorder t)"
   447 apply (induction t)
   447 apply (induction t)
   448  apply(simp)
   448  apply(simp)
   449 by (fastforce simp: sorted_append sorted_Cons intro: less_imp_le less_trans)
   449 by (fastforce simp: sorted_append intro: less_imp_le less_trans)
   450 
   450 
   451 lemma bst_iff_sorted_wrt_less: "bst t \<longleftrightarrow> sorted_wrt (<) (inorder t)"
   451 lemma bst_iff_sorted_wrt_less: "bst t \<longleftrightarrow> sorted_wrt (<) (inorder t)"
   452 apply (induction t)
   452 apply (induction t)
   453  apply simp
   453  apply simp
   454 apply (fastforce simp: sorted_wrt_Cons sorted_wrt_append)
   454 apply (fastforce simp: sorted_wrt_append)
   455 done
   455 done
   456 
   456 
   457 
   457 
   458 subsection \<open>@{const heap}\<close>
   458 subsection \<open>@{const heap}\<close>
   459 
   459