author  wenzelm 
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permissions  rwrr 
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(* Title: Provers/clasimp.ML 
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Author: David von Oheimb, TU Muenchen 
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Combination of classical reasoner and simplifier (depends on 
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splitter.ML, classical.ML, blast.ML). 
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*) 
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signature CLASIMP_DATA = 
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sig 

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structure Splitter: SPLITTER 
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structure Classical: CLASSICAL 
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structure Blast: BLAST 

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val notE: thm 
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val iffD1: thm 

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val iffD2: thm 

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end; 
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signature CLASIMP = 
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sig 
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val addSss: Proof.context > Proof.context 
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val addss: Proof.context > Proof.context 

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val clarsimp_tac: Proof.context > int > tactic 

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val mk_auto_tac: Proof.context > int > int > tactic 

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val auto_tac: Proof.context > tactic 

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val force_tac: Proof.context > int > tactic 

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val fast_force_tac: Proof.context > int > tactic 
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val slow_simp_tac: Proof.context > int > tactic 
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val best_simp_tac: Proof.context > int > tactic 

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val iff_add: attribute 
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val iff_add': attribute 

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val iff_del: attribute 

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val iff_modifiers: Method.modifier parser list 
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val clasimp_modifiers: Method.modifier parser list 

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val clasimp_setup: theory > theory 
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end; 
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functor Clasimp(Data: CLASIMP_DATA): CLASIMP = 
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struct 
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structure Splitter = Data.Splitter; 
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structure Classical = Data.Classical; 

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structure Blast = Data.Blast; 

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(* simp as classical wrapper *) 
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(* FIXME !? *) 
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fun clasimp f name tac ctxt = f (ctxt, (name, fn _ => CHANGED o tac ctxt)); 
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(*Add a simpset to the claset!*) 
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(*Caution: only one simpset added can be added by each of addSss and addss*) 

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val addSss = clasimp Classical.addSafter "safe_asm_full_simp_tac" Simplifier.safe_asm_full_simp_tac; 
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val addss = clasimp Classical.addbefore "asm_full_simp_tac" Simplifier.asm_full_simp_tac; 
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(* iffs: addition of rules to simpsets and clasets simultaneously *) 
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local 
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(*Takes (possibly conditional) theorems of the form A<>B to 
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the Safe Intr rule B==>A and 
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the Safe Destruct rule A==>B. 

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Also ~A goes to the Safe Elim rule A ==> ?R 

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Failing other cases, A is added as a Safe Intr rule*) 
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fun add_iff safe unsafe = 
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Thm.declaration_attribute (fn th => 
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let 
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val n = nprems_of th; 
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val (elim, intro) = if n = 0 then safe else unsafe; 
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val zero_rotate = zero_var_indexes o rotate_prems n; 
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in 
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Thm.attribute_declaration intro (zero_rotate (th RS Data.iffD2)) #> 
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Thm.attribute_declaration elim (Tactic.make_elim (zero_rotate (th RS Data.iffD1))) 
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handle THM _ => 
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(Thm.attribute_declaration elim (zero_rotate (th RS Data.notE)) 
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handle THM _ => Thm.attribute_declaration intro th) 
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end); 
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fun del_iff del = Thm.declaration_attribute (fn th => 
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let val zero_rotate = zero_var_indexes o rotate_prems (nprems_of th) in 
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Thm.attribute_declaration del (zero_rotate (th RS Data.iffD2)) #> 
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Thm.attribute_declaration del (Tactic.make_elim (zero_rotate (th RS Data.iffD1))) 
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handle THM _ => 
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(Thm.attribute_declaration del (zero_rotate (th RS Data.notE)) 
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handle THM _ => Thm.attribute_declaration del th) 
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end); 
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in 
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val iff_add = 
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Thm.declaration_attribute (fn th => 
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Thm.attribute_declaration (add_iff 
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(Classical.safe_elim NONE, Classical.safe_intro NONE) 
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(Classical.haz_elim NONE, Classical.haz_intro NONE)) th 
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#> Thm.attribute_declaration Simplifier.simp_add th); 
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val iff_add' = 
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add_iff 
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(Context_Rules.elim_query NONE, Context_Rules.intro_query NONE) 
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(Context_Rules.elim_query NONE, Context_Rules.intro_query NONE); 
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val iff_del = 
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Thm.declaration_attribute (fn th => 
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Thm.attribute_declaration (del_iff Classical.rule_del) th #> 
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Thm.attribute_declaration (del_iff Context_Rules.rule_del) th #> 
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Thm.attribute_declaration Simplifier.simp_del th); 
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end; 
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(* tactics *) 
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fun clarsimp_tac ctxt = 
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Simplifier.safe_asm_full_simp_tac ctxt THEN_ALL_NEW 
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Classical.clarify_tac (addSss ctxt); 
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(* auto_tac *) 
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(* a variant of depth_tac that avoids interference of the simplifier 
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with dup_step_tac when they are combined by auto_tac *) 
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local 
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fun slow_step_tac' ctxt = 
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Classical.appWrappers ctxt 

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(Classical.instp_step_tac ctxt APPEND' Classical.haz_step_tac ctxt); 

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in 

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fun nodup_depth_tac ctxt m i st = 
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SELECT_GOAL 
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(Classical.safe_steps_tac ctxt 1 THEN_ELSE 
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(DEPTH_SOLVE (nodup_depth_tac ctxt m 1), 

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Classical.inst0_step_tac ctxt 1 APPEND COND (K (m = 0)) no_tac 

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(slow_step_tac' ctxt 1 THEN DEPTH_SOLVE (nodup_depth_tac ctxt (m  1) 1)))) i st; 

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end; 
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(*Designed to be idempotent, except if Blast.depth_tac instantiates variables 
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in some of the subgoals*) 
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fun mk_auto_tac ctxt m n = 
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let 
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val main_tac = 

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Blast.depth_tac ctxt m (* fast but can't use wrappers *) 
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ORELSE' 
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(CHANGED o nodup_depth_tac (addss ctxt) n); (* slower but more general *) 
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PARALLEL_GOALS (ALLGOALS (Simplifier.asm_full_simp_tac ctxt)) THEN 
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TRY (Classical.safe_tac ctxt) THEN 
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REPEAT_DETERM (FIRSTGOAL main_tac) THEN 
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TRY (Classical.safe_tac (addSss ctxt)) THEN 
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prune_params_tac 
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end; 
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fun auto_tac ctxt = mk_auto_tac ctxt 4 2; 
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(* force_tac *) 
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(* aimed to solve the given subgoal totally, using whatever tools possible *) 
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fun force_tac ctxt = 
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let val ctxt' = addss ctxt in 

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SELECT_GOAL 
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(Classical.clarify_tac ctxt' 1 THEN 
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IF_UNSOLVED (Simplifier.asm_full_simp_tac ctxt 1) THEN 
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ALLGOALS (Classical.first_best_tac ctxt')) 
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end; 
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(* basic combinations *) 
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val fast_force_tac = Classical.fast_tac o addss; 
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val slow_simp_tac = Classical.slow_tac o addss; 
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val best_simp_tac = Classical.best_tac o addss; 

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(** concrete syntax **) 
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(* attributes *) 

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fun iff_att x = (Scan.lift 
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(Args.del >> K iff_del  
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Scan.option Args.add  Args.query >> K iff_add'  

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Scan.option Args.add >> K iff_add)) x; 
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(* method modifiers *) 

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val iffN = "iff"; 

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val iff_modifiers = 

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[Args.$$$ iffN  Scan.option Args.add  Args.colon >> K ((I, iff_add): Method.modifier), 
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Args.$$$ iffN  Scan.option Args.add  Args.query_colon >> K (I, iff_add'), 

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Args.$$$ iffN  Args.del  Args.colon >> K (I, iff_del)]; 

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val clasimp_modifiers = 
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Simplifier.simp_modifiers @ Splitter.split_modifiers @ 
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Classical.cla_modifiers @ iff_modifiers; 

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(* methods *) 

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fun clasimp_method' tac = 
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Method.sections clasimp_modifiers >> K (SIMPLE_METHOD' o tac); 
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val auto_method = 
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Scan.lift (Scan.option (Parse.nat  Parse.nat))  
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Method.sections clasimp_modifiers >> 
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(fn NONE => SIMPLE_METHOD o CHANGED_PROP o auto_tac 
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 SOME (m, n) => (fn ctxt => SIMPLE_METHOD (CHANGED_PROP (mk_auto_tac ctxt m n)))); 

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214 

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(* theory setup *) 

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val clasimp_setup = 
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Attrib.setup @{binding iff} iff_att "declaration of Simplifier / Classical rules" #> 
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Method.setup @{binding fastforce} (clasimp_method' fast_force_tac) "combined fast and simp" #> 
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Method.setup @{binding slowsimp} (clasimp_method' slow_simp_tac) "combined slow and simp" #> 
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Method.setup @{binding bestsimp} (clasimp_method' best_simp_tac) "combined best and simp" #> 

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Method.setup @{binding force} (clasimp_method' force_tac) "force" #> 

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Method.setup @{binding auto} auto_method "auto" #> 

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Method.setup @{binding clarsimp} (clasimp_method' (CHANGED_PROP oo clarsimp_tac)) 

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"clarify simplified goal"; 

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end; 