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theory Defs
imports Main "HOL-Data_Structures.Tree23" "HOL-Data_Structures.RBT_Set"
begin
fun bhs :: "'a rbt \<Rightarrow> nat set" where
"bhs Tree.Leaf = {0}" |
"bhs (Tree.Node l (_,c) r) = (let H = bhs l \<union> bhs r in if c=Black then Suc ` H else H)"
end
theory Template
imports Defs
begin
fun mk_rbt :: "'a tree23 \<Rightarrow> 'a rbt" where
"mk_rbt _ = undefined"
lemma mk_rbt_inorder_btree: "Tree2.inorder (mk_rbt t) = Tree23.inorder t"
sorry
lemma mk_rbt_color_btree: "color (mk_rbt t) = Black"
sorry
lemma mk_rbt_invh_btree: "Tree23.complete t \<Longrightarrow> invh (mk_rbt t)"
sorry
lemma mk_rbt_invc_btree: "invc (mk_rbt t)"
sorry
corollary invh_iff_bhs: "invh t \<longleftrightarrow> bhs t = {bheight t}"
sorry
end
theory Check
imports Template
begin
lemma mk_rbt_inorder_btree: "Tree2.inorder (mk_rbt t) = Tree23.inorder t"
by(rule mk_rbt_inorder_btree)
lemma mk_rbt_color_btree: "color (mk_rbt t) = Black"
by(rule mk_rbt_color_btree)
lemma mk_rbt_invh_btree: "Tree23.complete t \<Longrightarrow> invh (mk_rbt t)"
by(rule mk_rbt_invh_btree)
lemma mk_rbt_invc_btree: "invc (mk_rbt t)"
by(rule mk_rbt_invc_btree)
corollary invh_iff_bhs: "invh t \<longleftrightarrow> bhs t = {bheight t}"
by(rule invh_iff_bhs)
end