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theory Defs
imports "HOL-Data_Structures.Cmp" "HOL-Data_Structures.Set_Specs"
begin
type_synonym bv = "bool list"
definition set_bv :: "bv \<Rightarrow> nat set"
where "set_bv bs = { i. i<length bs \<and> bs!i }"
datatype 'a itree = iLeaf | iNode "'a itree" "'a \<times> 'a" "'a itree"
fun set_itree2:: "'a::ord itree \<Rightarrow> 'a set" where
"set_itree2 iLeaf = {}"
| "set_itree2 (iNode l (low, high) r) = {low .. high} \<union> ((set_itree2 l) \<union> (set_itree2 r))"
fun set_itree3:: "'a itree \<Rightarrow> ('a \<times> 'a) set" where
"set_itree3 iLeaf = {}"
| "set_itree3 (iNode l (low, high) r) = {(low, high)} \<union> ((set_itree3 l) \<union> (set_itree3 r))"
consts ibst :: "'a::linorder itree \<Rightarrow> bool"
consts delete :: "int \<Rightarrow> int itree \<Rightarrow> int itree"
end
theory Submission
imports Defs
begin
interpretation bv_set: Set \<comment> \<open>Your parameters here\<close>
oops
fun ibst :: "'a::linorder itree \<Rightarrow> bool" where
"ibst _ = False"
fun delete :: "int \<Rightarrow> int itree \<Rightarrow> int itree" where
"delete _ _ = iLeaf"
lemma delete_set_minus: "ibst t \<Longrightarrow> set_itree2 (delete x t) = (set_itree2 t) - {x}"
sorry
lemma ibst_delete: "ibst t \<Longrightarrow> ibst (delete x t)"
sorry
end
theory Check
imports Submission
begin
lemma delete_set_minus: "ibst t \<Longrightarrow> set_itree2 (delete x t) = (set_itree2 t) - {x}"
by (rule Submission.delete_set_minus)
lemma ibst_delete: "ibst t \<Longrightarrow> ibst (delete x t)"
by (rule Submission.ibst_delete)
end