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(* Title: functions on lists for Scripts
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Author: Walther Neuper 0108
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(c) due to copyright terms
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*)
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theory ListC imports Complex_Main
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uses ("../library.sml")("../calcelems.sml")
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("termC.sml")("calculate.sml")
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("rewrite.sml")
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begin
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use "../library.sml" (*indent,...*)
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use "../calcelems.sml" (*str_of_type, Thm,...*)
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use "termC.sml" (*num_str,...*)
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use "calculate.sml" (*???*)
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use "rewrite.sml" (*?*** At command "end" (line 205../ListC.thy*)
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text {* 'nat' in List.thy replaced by 'real' *}
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primrec LENGTH :: "'a list => real"
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where
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LENGTH_NIL: "LENGTH [] = 0" (*length: 'a list => nat*)
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| LENGTH_CONS: "LENGTH (x#xs) = 1 + LENGTH xs"
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primrec del :: "['a list, 'a] => 'a list"
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where
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del_base: "del [] x = []"
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| del_rec: "del (y#ys) x = (if x = y then ys else y#(del ys x))"
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definition
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list_diff :: "['a list, 'a list] => 'a list" (* as -- bs *)
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("(_ --/ _)" [66, 66] 65)
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where "a -- b == foldl del a b"
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consts NTH :: "[real, 'a list] => 'a"
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axioms
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(*** more than one non-variable in pattern in "nth_ 1 [x] = x"--*)
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NTH_NIL: "NTH 1 (x#xs) = x"
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(* NTH_CONS: "NTH n (x#xs) = NTH (n+ -1) xs" *)
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(*rewriter does not reach base case ...... ;
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the condition involves another rule set (erls, eval_binop in Atools):*)
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NTH_CONS: "1 < n ==> NTH n (x#xs) = NTH (n+ - 1) xs"
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(*-.-.-.-.-.-isolate response.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.
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(*primrec from Isabelle/src/HOL/List.thy -- def.twice not allowed*)
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(*primrec*)
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hd_thm: "hd(x#xs) = x"
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(*primrec*)
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tl_Nil: "tl([]) = []"
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tl_Cons: "tl(x#xs) = xs"
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(*primrec*)
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null_Nil: "null([]) = True"
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null_Cons: "null(x#xs) = False"
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(*primrec*)
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LAST: "last(x#xs) = (if xs=[] then x else last xs)"
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(*primrec*)
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butlast_Nil: "butlast [] = []"
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butlast_Cons: "butlast(x#xs) = (if xs=[] then [] else x#butlast xs)"
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(*primrec
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mem_Nil: "x mem [] = False"
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mem_Cons: "x mem (y#ys) = (if y=x then True else x mem ys)"
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*)
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mem_Nil: "x : set [] = False"
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mem_Cons: "x : set (y#ys) = (if y=x then True else x : set ys)"
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(*primrec-------already named---
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"set [] = {}"
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"set (x#xs) = insert x (set xs)"
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primrec
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list_all_Nil "list_all P [] = True"
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list_all_Cons "list_all P (x#xs) = (P(x) & list_all P xs)"
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----------------*)
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(*primrec*)
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map_Nil: "map f [] = []"
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map_Cons: "map f (x#xs) = f(x)#map f xs"
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(*primrec*)
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append_Nil: "[] @ys = ys"
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append_Cons: "(x#xs)@ys = x#(xs@ys)"
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(*primrec*)
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rev_Nil: "rev([]) = []"
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rev_Cons: "rev(x#xs) = rev(xs) @ [x]"
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(*primrec*)
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filter_Nil: "filter P [] = []"
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filter_Cons: "filter P (x#xs) =(if P x then x#filter P xs else filter P xs)"
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(*primrec-------already named---
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foldl_Nil "foldl f a [] = a"
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foldl_Cons "foldl f a (x#xs) = foldl f (f a x) xs"
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----------------*)
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(*primrec*)
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foldr_Nil: "foldr f [] a = a"
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foldr_Cons: "foldr f (x#xs) a = f x (foldr f xs a)"
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(*primrec*)
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concat_Nil: "concat([]) = []"
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concat_Cons: "concat(x#xs) = x @ concat(xs)"
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(*primrec-------already named---
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drop_Nil "drop n [] = []"
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drop_Cons "drop n (x#xs) = (case n of 0 => x#xs | Suc(m) => drop m xs)"
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(* Warning: simpset does not contain this definition but separate theorems
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for n=0 / n=Suc k*)
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(*primrec*)
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take_Nil "take n [] = []"
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take_Cons "take n (x#xs) = (case n of 0 => [] | Suc(m) => x # take m xs)"
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(* Warning: simpset does not contain this definition but separate theorems
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for n=0 / n=Suc k*)
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(*primrec*)
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nth_Cons "(x#xs)!n = (case n of 0 => x | (Suc k) => xs!k)"
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(* Warning: simpset does not contain this definition but separate theorems
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for n=0 / n=Suc k*)
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(*primrec*)
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" [][i:=v] = []"
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"(x#xs)[i:=v] = (case i of 0 => v # xs
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| Suc j => x # xs[j:=v])"
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----------------*)
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(*primrec*)
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takeWhile_Nil: "takeWhile P [] = []"
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takeWhile_Cons:
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"takeWhile P (x#xs) = (if P x then x#takeWhile P xs else [])"
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(*primrec*)
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dropWhile_Nil: "dropWhile P [] = []"
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dropWhile_Cons:
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"dropWhile P (x#xs) = (if P x then dropWhile P xs else x#xs)"
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(*primrec*)
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zip_Nil: "zip xs [] = []"
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zip_Cons: "zip xs (y#ys) =(case xs of [] => [] | z#zs =>(z,y)#zip zs ys)"
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(* Warning: simpset does not contain this definition but separate theorems
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for xs=[] / xs=z#zs *)
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(*primrec
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upt_0 "[i..0(] = []"
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upt_Suc "[i..(Suc j)(] = (if i <= j then [i..j(] @ [j] else [])"
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*)
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(*primrec*)
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distinct_Nil: "distinct [] = True"
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distinct_Cons: "distinct (x#xs) = (x ~: set xs & distinct xs)"
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(*primrec*)
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remdups_Nil: "remdups [] = []"
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remdups_Cons: "remdups (x#xs) =
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(if x : set xs then remdups xs else x # remdups xs)"
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(*primrec-------already named---
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replicate_0 "replicate 0 x = []"
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replicate_Suc "replicate (Suc n) x = x # replicate n x"
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----------------*)
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(** Lexicographic orderings on lists ...!!!**)
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ML{* (*the former ListC.ML*)
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(** rule set for evaluating listexpr in scripts **)
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val list_rls =
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Rls{id="list_rls",preconds = [], rew_ord = ("dummy_ord",dummy_ord),
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erls = e_rls, srls = Erls, calc = [], (*asm_thm=[],*)
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rules = (*8.01: copied from*)
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[Thm ("refl", num_str @{thm refl}), (*'a<>b -> FALSE' by fun eval_equal*)
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Thm ("o_apply", num_str @{thm o_apply}),
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Thm ("NTH_CONS",num_str @{thm NTH_CONS}),(*erls for cond. in Atools.ML*)
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Thm ("NTH_NIL",num_str @{thm NTH_NIL}),
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Thm ("append_Cons",num_str @{thm append_Cons}),
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Thm ("append_Nil",num_str @{thm append_Nil}),
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Thm ("butlast_Cons",num_str @{thm butlast_Cons}),
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Thm ("butlast_Nil",num_str @{thm butlast_Nil}),
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Thm ("concat_Cons",num_str @{thm concat_Cons}),
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Thm ("concat_Nil",num_str @{thm concat_Nil}),
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Thm ("del_base",num_str @{thm del_base}),
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Thm ("del_rec",num_str @{thm del_rec}),
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Thm ("distinct_Cons",num_str @{thm distinct_Cons}),
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Thm ("distinct_Nil",num_str @{thm distinct_Nil}),
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Thm ("dropWhile_Cons",num_str @{thm dropWhile_Cons}),
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Thm ("dropWhile_Nil",num_str @{thm dropWhile_Nil}),
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Thm ("filter_Cons",num_str @{thm filter_Cons}),
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Thm ("filter_Nil",num_str @{thm filter_Nil}),
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Thm ("foldr_Cons",num_str @{thm foldr_Cons}),
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Thm ("foldr_Nil",num_str @{thm foldr_Nil}),
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Thm ("hd_thm",num_str @{thm hd_thm}),
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Thm ("LAST",num_str @{thm LAST}),
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Thm ("LENGTH_CONS",num_str @{thm LENGTH_CONS}),
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Thm ("LENGTH_NIL",num_str @{thm LENGTH_NIL}),
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Thm ("list_diff_def",num_str @{thm list_diff_def}),
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Thm ("map_Cons",num_str @{thm map_Cons}),
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Thm ("map_Nil",num_str @{thm map_Cons}),
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Thm ("mem_Cons",num_str @{thm mem_Cons}),
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Thm ("mem_Nil",num_str @{thm mem_Nil}),
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Thm ("null_Cons",num_str @{thm null_Cons}),
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Thm ("null_Nil",num_str @{thm null_Nil}),
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Thm ("remdups_Cons",num_str @{thm remdups_Cons}),
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Thm ("remdups_Nil",num_str @{thm remdups_Nil}),
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Thm ("rev_Cons",num_str @{thm rev_Cons}),
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Thm ("rev_Nil",num_str @{thm rev_Nil}),
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Thm ("take_Nil",num_str @{thm take_Nil}),
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Thm ("take_Cons",num_str @{thm take_Cons}),
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Thm ("tl_Cons",num_str @{thm tl_Cons}),
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Thm ("tl_Nil",num_str @{thm tl_Nil}),
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Thm ("zip_Cons",num_str @{thm zip_Cons}),
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Thm ("zip_Nil",num_str @{thm zip_Nil})
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], scr = EmptyScr}:rls;
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*}
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ML{*
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ruleset' := overwritelthy @{theory} (!ruleset',
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[("list_rls",list_rls)
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]);
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*}
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-.-.-.-.-.-.-isolate response.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.*)
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end
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