src/HOL/simpdata.ML
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* HOL: removed obsolete expand_if = split_if; theorems if_splits = split_if split_if_asm;
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(*  Title:      HOL/simpdata.ML
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    ID:         $Id$
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    Author:     Tobias Nipkow
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    Copyright   1991  University of Cambridge
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Instantiation of the generic simplifier for HOL.
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*)
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section "Simplifier";
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(*** Addition of rules to simpsets and clasets simultaneously ***)	(* FIXME move to Provers/clasimp.ML? *)
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infix 4 addIffs delIffs;
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(*Takes UNCONDITIONAL 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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local
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  val iff_const = HOLogic.eq_const HOLogic.boolT;
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  fun addIff ((cla, simp), th) = 
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      (case HOLogic.dest_Trueprop (#prop (rep_thm th)) of
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                (Const("Not", _) $ A) =>
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                    cla addSEs [zero_var_indexes (th RS notE)]
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              | (con $ _ $ _) =>
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                    if con = iff_const
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                    then cla addSIs [zero_var_indexes (th RS iffD2)]  
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                              addSDs [zero_var_indexes (th RS iffD1)]
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                    else  cla addSIs [th]
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              | _ => cla addSIs [th],
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       simp addsimps [th])
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      handle TERM _ => error ("AddIffs: theorem must be unconditional\n" ^ 
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                         string_of_thm th);
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  fun delIff ((cla, simp), th) = 
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      (case HOLogic.dest_Trueprop (#prop (rep_thm th)) of
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	   (Const ("Not", _) $ A) =>
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	       cla delrules [zero_var_indexes (th RS notE)]
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	 | (con $ _ $ _) =>
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	       if con = iff_const
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	       then cla delrules 
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		        [zero_var_indexes (th RS iffD2),
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			 cla_make_elim (zero_var_indexes (th RS iffD1))]
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	       else cla delrules [th]
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	 | _ => cla delrules [th],
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       simp delsimps [th])
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      handle TERM _ => (warning("DelIffs: ignoring conditional theorem\n" ^ 
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				string_of_thm th); (cla, simp));
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  fun store_clasimp (cla, simp) = (claset_ref () := cla; simpset_ref () := simp)
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in
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val op addIffs = foldl addIff;
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val op delIffs = foldl delIff;
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fun AddIffs thms = store_clasimp ((claset (), simpset ()) addIffs thms);
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fun DelIffs thms = store_clasimp ((claset (), simpset ()) delIffs thms);
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end;
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val [prem] = goal (the_context ()) "x==y ==> x=y";
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by (rewtac prem);
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by (rtac refl 1);
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qed "meta_eq_to_obj_eq";
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Goal "(%s. f s) = f";
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br refl 1;
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qed "eta_contract_eq";
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local
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  fun prover s = prove_goal (the_context ()) s (fn _ => [(Blast_tac 1)]);
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(*Make meta-equalities.  The operator below is Trueprop*)
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fun mk_meta_eq r = r RS eq_reflection;
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val Eq_TrueI  = mk_meta_eq(prover  "P --> (P = True)"  RS mp);
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val Eq_FalseI = mk_meta_eq(prover "~P --> (P = False)" RS mp);
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fun mk_eq th = case concl_of th of
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        Const("==",_)$_$_       => th
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    |   _$(Const("op =",_)$_$_) => mk_meta_eq th
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    |   _$(Const("Not",_)$_)    => th RS Eq_FalseI
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    |   _                       => th RS Eq_TrueI;
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(* last 2 lines requires all formulae to be of the from Trueprop(.) *)
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fun mk_eq_True r = Some(r RS meta_eq_to_obj_eq RS Eq_TrueI);
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fun mk_meta_cong rl =
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  standard(mk_meta_eq(replicate (nprems_of rl) meta_eq_to_obj_eq MRS rl))
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  handle THM _ =>
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  error("Premises and conclusion of congruence rules must be =-equalities");
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val not_not = prover "(~ ~ P) = P";
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val simp_thms = [not_not] @ map prover
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 [ "(x=x) = True",
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   "(~True) = False", "(~False) = True",
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   "(~P) ~= P", "P ~= (~P)", "(P ~= Q) = (P = (~Q))",
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   "(True=P) = P", "(P=True) = P", "(False=P) = (~P)", "(P=False) = (~P)",
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   "(True --> P) = P", "(False --> P) = True", 
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   "(P --> True) = True", "(P --> P) = True",
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   "(P --> False) = (~P)", "(P --> ~P) = (~P)",
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   "(P & True) = P", "(True & P) = P", 
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   "(P & False) = False", "(False & P) = False",
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   "(P & P) = P", "(P & (P & Q)) = (P & Q)",
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   "(P & ~P) = False",    "(~P & P) = False",
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   "(P | True) = True", "(True | P) = True", 
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   "(P | False) = P", "(False | P) = P",
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   "(P | P) = P", "(P | (P | Q)) = (P | Q)",
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   "(P | ~P) = True",    "(~P | P) = True",
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   "((~P) = (~Q)) = (P=Q)",
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   "(!x. P) = P", "(? x. P) = P", "? x. x=t", "? x. t=x", 
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(*two needed for the one-point-rule quantifier simplification procs*)
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   "(? x. x=t & P(x)) = P(t)",		(*essential for termination!!*)
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   "(! x. t=x --> P(x)) = P(t)" ];      (*covers a stray case*)
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(* Add congruence rules for = (instead of ==) *)
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(* ###FIXME: Move to simplifier, 
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   taking mk_meta_cong as input, eliminating addeqcongs and deleqcongs *)
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infix 4 addcongs delcongs;
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fun ss addcongs congs = ss addeqcongs (map mk_meta_cong congs);
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fun ss delcongs congs = ss deleqcongs (map mk_meta_cong congs);
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fun Addcongs congs = (simpset_ref() := simpset() addcongs congs);
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fun Delcongs congs = (simpset_ref() := simpset() delcongs congs);
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val cong_add_global = Simplifier.change_global_ss (op addcongs);
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val cong_del_global = Simplifier.change_global_ss (op delcongs);
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val cong_add_local = Simplifier.change_local_ss (op addcongs);
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val cong_del_local = Simplifier.change_local_ss (op delcongs);
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val cong_attrib_setup =
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 [Attrib.add_attributes [("cong",
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   (Attrib.add_del_args cong_add_global cong_del_global,
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    Attrib.add_del_args cong_add_local cong_del_local),
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    "declare Simplifier congruence rules")]];
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val imp_cong = impI RSN
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    (2, prove_goal (the_context ()) "(P=P')--> (P'--> (Q=Q'))--> ((P-->Q) = (P'-->Q'))"
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        (fn _=> [(Blast_tac 1)]) RS mp RS mp);
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(*Miniscoping: pushing in existential quantifiers*)
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val ex_simps = map prover
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                ["(EX x. P x & Q)   = ((EX x. P x) & Q)",
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                 "(EX x. P & Q x)   = (P & (EX x. Q x))",
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                 "(EX x. P x | Q)   = ((EX x. P x) | Q)",
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                 "(EX x. P | Q x)   = (P | (EX x. Q x))",
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                 "(EX x. P x --> Q) = ((ALL x. P x) --> Q)",
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                 "(EX x. P --> Q x) = (P --> (EX x. Q x))"];
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78e5bfcbc1e9 Added miniscoping to the simplifier: quantifiers are now pushed in
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(*Miniscoping: pushing in universal quantifiers*)
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val all_simps = map prover
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                ["(ALL x. P x & Q)   = ((ALL x. P x) & Q)",
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                 "(ALL x. P & Q x)   = (P & (ALL x. Q x))",
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                 "(ALL x. P x | Q)   = ((ALL x. P x) | Q)",
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                 "(ALL x. P | Q x)   = (P | (ALL x. Q x))",
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                 "(ALL x. P x --> Q) = ((EX x. P x) --> Q)",
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                 "(ALL x. P --> Q x) = (P --> (ALL x. Q x))"];
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(* elimination of existential quantifiers in assumptions *)
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val ex_all_equiv =
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  let val lemma1 = prove_goal (the_context ())
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        "(? x. P(x) ==> PROP Q) ==> (!!x. P(x) ==> PROP Q)"
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        (fn prems => [resolve_tac prems 1, etac exI 1]);
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      val lemma2 = prove_goalw (the_context ()) [Ex_def]
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        "(!!x. P(x) ==> PROP Q) ==> (? x. P(x) ==> PROP Q)"
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        (fn prems => [(REPEAT(resolve_tac prems 1))])
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  in equal_intr lemma1 lemma2 end;
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end;
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bind_thms ("ex_simps", ex_simps);
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bind_thms ("all_simps", all_simps);
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bind_thm ("not_not", not_not);
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(* Elimination of True from asumptions: *)
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val True_implies_equals = prove_goal (the_context ())
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 "(True ==> PROP P) == PROP P"
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(fn _ => [rtac equal_intr_rule 1, atac 2,
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          METAHYPS (fn prems => resolve_tac prems 1) 1,
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          rtac TrueI 1]);
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fun prove nm thm  = qed_goal nm (the_context ()) thm (fn _ => [(Blast_tac 1)]);
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prove "eq_commute" "(a=b)=(b=a)";
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prove "eq_left_commute" "(P=(Q=R)) = (Q=(P=R))";
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prove "eq_assoc" "((P=Q)=R) = (P=(Q=R))";
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val eq_ac = [eq_commute, eq_left_commute, eq_assoc];
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prove "conj_commute" "(P&Q) = (Q&P)";
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prove "conj_left_commute" "(P&(Q&R)) = (Q&(P&R))";
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val conj_comms = [conj_commute, conj_left_commute];
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prove "conj_assoc" "((P&Q)&R) = (P&(Q&R))";
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1922
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prove "disj_commute" "(P|Q) = (Q|P)";
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prove "disj_left_commute" "(P|(Q|R)) = (Q|(P|R))";
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val disj_comms = [disj_commute, disj_left_commute];
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prove "disj_assoc" "((P|Q)|R) = (P|(Q|R))";
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prove "conj_disj_distribL" "(P&(Q|R)) = (P&Q | P&R)";
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prove "conj_disj_distribR" "((P|Q)&R) = (P&R | Q&R)";
1485
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1892
23765bc3e8e2 Added two new distributive laws
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prove "disj_conj_distribL" "(P|(Q&R)) = ((P|Q) & (P|R))";
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prove "disj_conj_distribR" "((P&Q)|R) = ((P|R) & (Q|R))";
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prove "imp_conjR" "(P --> (Q&R)) = ((P-->Q) & (P-->R))";
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prove "imp_conjL" "((P&Q) -->R)  = (P --> (Q --> R))";
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prove "imp_disjL" "((P|Q) --> R) = ((P-->R)&(Q-->R))";
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(*These two are specialized, but imp_disj_not1 is useful in Auth/Yahalom.ML*)
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prove "imp_disj_not1" "(P --> Q | R) = (~Q --> P --> R)";
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prove "imp_disj_not2" "(P --> Q | R) = (~R --> P --> Q)";
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prove "imp_disj1" "((P-->Q)|R) = (P--> Q|R)";
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prove "imp_disj2" "(Q|(P-->R)) = (P--> Q|R)";
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prove "de_Morgan_disj" "(~(P | Q)) = (~P & ~Q)";
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prove "de_Morgan_conj" "(~(P & Q)) = (~P | ~Q)";
3446
a14e5451f613 Addition of not_imp (which pushes negation into implication) as a default
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prove "not_imp" "(~(P --> Q)) = (P & ~Q)";
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prove "not_iff" "(P~=Q) = (P = (~Q))";
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   229
prove "disj_not1" "(~P | Q) = (P --> Q)";
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prove "disj_not2" "(P | ~Q) = (Q --> P)"; (* changes orientation :-( *)
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cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
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prove "imp_conv_disj" "(P --> Q) = ((~P) | Q)";
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
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cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
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prove "iff_conv_conj_imp" "(P = Q) = ((P --> Q) & (Q --> P))";
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   234
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(*Avoids duplication of subgoals after split_if, when the true and false 
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  cases boil down to the same thing.*) 
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prove "cases_simp" "((P --> Q) & (~P --> Q)) = Q";
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prove "not_all" "(~ (! x. P(x))) = (? x.~P(x))";
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prove "imp_all" "((! x. P x) --> Q) = (? x. P x --> Q)";
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prove "not_ex"  "(~ (? x. P(x))) = (! x.~P(x))";
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prove "imp_ex" "((? x. P x) --> Q) = (! x. P x --> Q)";
1660
8cb42cd97579 *** empty log message ***
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1655
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prove "ex_disj_distrib" "(? x. P(x) | Q(x)) = ((? x. P(x)) | (? x. Q(x)))";
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prove "all_conj_distrib" "(!x. P(x) & Q(x)) = ((! x. P(x)) & (! x. Q(x)))";
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(* '&' congruence rule: not included by default!
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   May slow rewrite proofs down by as much as 50% *)
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let val th = prove_goal (the_context ()) 
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                "(P=P')--> (P'--> (Q=Q'))--> ((P&Q) = (P'&Q'))"
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                (fn _=> [(Blast_tac 1)])
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in  bind_thm("conj_cong",standard (impI RSN (2, th RS mp RS mp)))  end;
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let val th = prove_goal (the_context ()) 
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                "(Q=Q')--> (Q'--> (P=P'))--> ((P&Q) = (P'&Q'))"
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                (fn _=> [(Blast_tac 1)])
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in  bind_thm("rev_conj_cong",standard (impI RSN (2, th RS mp RS mp)))  end;
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(* '|' congruence rule: not included by default! *)
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let val th = prove_goal (the_context ()) 
2134
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                "(P=P')--> (~P'--> (Q=Q'))--> ((P|Q) = (P'|Q'))"
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                (fn _=> [(Blast_tac 1)])
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in  bind_thm("disj_cong",standard (impI RSN (2, th RS mp RS mp)))  end;
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04a71407089d Renamed and shuffled a few thms.
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prove "eq_sym_conv" "(x=y) = (y=x)";
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5278
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(** if-then-else rules **)
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Goalw [if_def] "(if True then x else y) = x";
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by (Blast_tac 1);
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qed "if_True";
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Goalw [if_def] "(if False then x else y) = y";
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by (Blast_tac 1);
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qed "if_False";
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Goalw [if_def] "P ==> (if P then x else y) = x";
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by (Blast_tac 1);
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qed "if_P";
5304
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7127
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Goalw [if_def] "~P ==> (if P then x else y) = y";
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by (Blast_tac 1);
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qed "if_not_P";
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Goal "P(if Q then x else y) = ((Q --> P(x)) & (~Q --> P(y)))";
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by (res_inst_tac [("Q","Q")] (excluded_middle RS disjE) 1);
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by (stac if_P 2);
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by (stac if_not_P 1);
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by (ALLGOALS (Blast_tac));
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qed "split_if";
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Goal "P(if Q then x else y) = (~((Q & ~P x) | (~Q & ~P y)))";
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by (stac split_if 1);
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by (Blast_tac 1);
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qed "split_if_asm";
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bind_thms ("if_splits", [split_if, split_if_asm]);
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Goal "(if c then x else x) = x";
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by (stac split_if 1);
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by (Blast_tac 1);
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qed "if_cancel";
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Goal "(if x = y then y else x) = x";
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by (stac split_if 1);
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by (Blast_tac 1);
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qed "if_eq_cancel";
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(*This form is useful for expanding IFs on the RIGHT of the ==> symbol*)
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Goal "(if P then Q else R) = ((P-->Q) & (~P-->R))";
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by (rtac split_if 1);
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qed "if_bool_eq_conj";
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(*And this form is useful for expanding IFs on the LEFT*)
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Goal "(if P then Q else R) = ((P&Q) | (~P&R))";
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by (stac split_if 1);
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by (Blast_tac 1);
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qed "if_bool_eq_disj";
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(*** make simplification procedures for quantifier elimination ***)
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structure Quantifier1 = Quantifier1Fun(
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struct
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  (*abstract syntax*)
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  fun dest_eq((c as Const("op =",_)) $ s $ t) = Some(c,s,t)
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    | dest_eq _ = None;
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  fun dest_conj((c as Const("op &",_)) $ s $ t) = Some(c,s,t)
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    | dest_conj _ = None;
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  val conj = HOLogic.conj
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  val imp  = HOLogic.imp
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  (*rules*)
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  val iff_reflection = eq_reflection
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  val iffI = iffI
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  val sym  = sym
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  val conjI= conjI
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  val conjE= conjE
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  val impI = impI
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  val impE = impE
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  val mp   = mp
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  val exI  = exI
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  val exE  = exE
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  val allI = allI
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  val allE = allE
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end);
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local
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val ex_pattern =
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  Thm.read_cterm (Theory.sign_of (the_context ())) ("EX x. P(x) & Q(x)",HOLogic.boolT)
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val all_pattern =
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  Thm.read_cterm (Theory.sign_of (the_context ())) ("ALL x. P(x) & P'(x) --> Q(x)",HOLogic.boolT)
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24d9e6639cd4 Moved the quantifier elimination simp procs into Provers.
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   358
in
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val defEX_regroup =
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  mk_simproc "defined EX" [ex_pattern] Quantifier1.rearrange_ex;
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val defALL_regroup =
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  mk_simproc "defined ALL" [all_pattern] Quantifier1.rearrange_all;
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end;
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(*** Case splitting ***)
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structure SplitterData =
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  struct
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  structure Simplifier = Simplifier
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  val mk_eq          = mk_eq
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  val meta_eq_to_iff = meta_eq_to_obj_eq
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  val iffD           = iffD2
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  val disjE          = disjE
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  val conjE          = conjE
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  val exE            = exE
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  val contrapos      = contrapos
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  val contrapos2     = contrapos2
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  val notnotD        = notnotD
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  end;
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structure Splitter = SplitterFun(SplitterData);
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   383
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   384
val split_tac        = Splitter.split_tac;
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   385
val split_inside_tac = Splitter.split_inside_tac;
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   386
val split_asm_tac    = Splitter.split_asm_tac;
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   387
val op addsplits     = Splitter.addsplits;
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   388
val op delsplits     = Splitter.delsplits;
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   389
val Addsplits        = Splitter.Addsplits;
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   390
val Delsplits        = Splitter.Delsplits;
4718
fc2ba9fb2135 new rewrite rules not1_or, not2_or, and if_eq_cancel
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   391
2134
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   392
(*In general it seems wrong to add distributive laws by default: they
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   393
  might cause exponential blow-up.  But imp_disjL has been in for a while
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   394
  and cannot be removed without affecting existing proofs.  Moreover, 
04a71407089d Renamed and shuffled a few thms.
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   395
  rewriting by "(P|Q --> R) = ((P-->R)&(Q-->R))" might be justified on the
04a71407089d Renamed and shuffled a few thms.
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   396
  grounds that it allows simplification of R in the two cases.*)
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   397
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   398
fun gen_all th = forall_elim_vars (#maxidx(rep_thm th)+1) th;
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   399
2134
04a71407089d Renamed and shuffled a few thms.
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   400
val mksimps_pairs =
04a71407089d Renamed and shuffled a few thms.
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   401
  [("op -->", [mp]), ("op &", [conjunct1,conjunct2]),
04a71407089d Renamed and shuffled a few thms.
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   402
   ("All", [spec]), ("True", []), ("False", []),
4769
bb60149fe21b changed if_bool_eq to if_bool_eq_conj and added if_bool_eq_disj
paulson
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diff changeset
   403
   ("If", [if_bool_eq_conj RS iffD1])];
1758
60613b065e9b Added ex_imp
nipkow
parents: 1722
diff changeset
   404
5552
dcd3e7711cac simplified CLASIMP_DATA
oheimb
parents: 5447
diff changeset
   405
(* ###FIXME: move to Provers/simplifier.ML
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   406
val mk_atomize:      (string * thm list) list -> thm -> thm list
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   407
*)
5552
dcd3e7711cac simplified CLASIMP_DATA
oheimb
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diff changeset
   408
(* ###FIXME: move to Provers/simplifier.ML *)
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c133f16febc7 the splitter is now defined as a functor
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   409
fun mk_atomize pairs =
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diff changeset
   410
  let fun atoms th =
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   411
        (case concl_of th of
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   412
           Const("Trueprop",_) $ p =>
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diff changeset
   413
             (case head_of p of
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diff changeset
   414
                Const(a,_) =>
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diff changeset
   415
                  (case assoc(pairs,a) of
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diff changeset
   416
                     Some(rls) => flat (map atoms ([th] RL rls))
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diff changeset
   417
                   | None => [th])
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   418
              | _ => [th])
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diff changeset
   419
         | _ => [th])
c133f16febc7 the splitter is now defined as a functor
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   420
  in atoms end;
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diff changeset
   421
5552
dcd3e7711cac simplified CLASIMP_DATA
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diff changeset
   422
fun mksimps pairs = (map mk_eq o mk_atomize pairs o gen_all);
5304
c133f16febc7 the splitter is now defined as a functor
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   423
7570
a9391550eea1 Mod because of new solver interface.
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diff changeset
   424
fun unsafe_solver_tac prems =
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diff changeset
   425
  FIRST'[resolve_tac(reflexive_thm::TrueI::refl::prems), atac, etac FalseE];
a9391550eea1 Mod because of new solver interface.
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diff changeset
   426
val unsafe_solver = mk_solver "HOL unsafe" unsafe_solver_tac;
a9391550eea1 Mod because of new solver interface.
nipkow
parents: 7369
diff changeset
   427
2636
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   428
(*No premature instantiation of variables during simplification*)
7570
a9391550eea1 Mod because of new solver interface.
nipkow
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diff changeset
   429
fun safe_solver_tac prems =
a9391550eea1 Mod because of new solver interface.
nipkow
parents: 7369
diff changeset
   430
  FIRST'[match_tac(reflexive_thm::TrueI::refl::prems),
a9391550eea1 Mod because of new solver interface.
nipkow
parents: 7369
diff changeset
   431
         eq_assume_tac, ematch_tac [FalseE]];
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nipkow
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diff changeset
   432
val safe_solver = mk_solver "HOL safe" safe_solver_tac;
2443
a81d4c219c3c factored out HOL_base_ss and val HOL_min_ss, added HOL_safe_min_ss
oheimb
parents: 2263
diff changeset
   433
2636
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   434
val HOL_basic_ss = empty_ss setsubgoaler asm_simp_tac
7570
a9391550eea1 Mod because of new solver interface.
nipkow
parents: 7369
diff changeset
   435
			    setSSolver safe_solver
2636
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   436
			    setSolver  unsafe_solver
4677
c4b07b8579fd Reorganized simplifier. May now reorient rules.
nipkow
parents: 4669
diff changeset
   437
			    setmksimps (mksimps mksimps_pairs)
5552
dcd3e7711cac simplified CLASIMP_DATA
oheimb
parents: 5447
diff changeset
   438
			    setmkeqTrue mk_eq_True;
2443
a81d4c219c3c factored out HOL_base_ss and val HOL_min_ss, added HOL_safe_min_ss
oheimb
parents: 2263
diff changeset
   439
3446
a14e5451f613 Addition of not_imp (which pushes negation into implication) as a default
paulson
parents: 3282
diff changeset
   440
val HOL_ss = 
a14e5451f613 Addition of not_imp (which pushes negation into implication) as a default
paulson
parents: 3282
diff changeset
   441
    HOL_basic_ss addsimps 
a14e5451f613 Addition of not_imp (which pushes negation into implication) as a default
paulson
parents: 3282
diff changeset
   442
     ([triv_forall_equality, (* prunes params *)
3654
ebad042c0bba Added True_implies_equals
nipkow
parents: 3615
diff changeset
   443
       True_implies_equals, (* prune asms `True' *)
9023
09d02e7365c1 added eta_contract_eq, also to simpset
oheimb
parents: 8955
diff changeset
   444
       eta_contract_eq, (* prunes eta-expansions *)
4718
fc2ba9fb2135 new rewrite rules not1_or, not2_or, and if_eq_cancel
oheimb
parents: 4681
diff changeset
   445
       if_True, if_False, if_cancel, if_eq_cancel,
5304
c133f16febc7 the splitter is now defined as a functor
oheimb
parents: 5278
diff changeset
   446
       imp_disjL, conj_assoc, disj_assoc,
3904
c0d56e4c823e New simprules imp_disj1, imp_disj2
paulson
parents: 3896
diff changeset
   447
       de_Morgan_conj, de_Morgan_disj, imp_disj1, imp_disj2, not_imp,
8955
714497ad2348 installing the plus_ac0 simprules
paulson
parents: 8644
diff changeset
   448
       disj_not1, not_all, not_ex, cases_simp, Eps_eq, Eps_sym_eq,
714497ad2348 installing the plus_ac0 simprules
paulson
parents: 8644
diff changeset
   449
       thm"plus_ac0.zero", thm"plus_ac0_zero_right"]
3446
a14e5451f613 Addition of not_imp (which pushes negation into implication) as a default
paulson
parents: 3282
diff changeset
   450
     @ ex_simps @ all_simps @ simp_thms)
4032
4b1c69d8b767 For each datatype `t' there is now a theorem `split_t_case' of the form
nipkow
parents: 3919
diff changeset
   451
     addsimprocs [defALL_regroup,defEX_regroup]
4744
4469d498cd48 moved addsplits [expand_if] from HOL_basic_ss to HOL_ss;
wenzelm
parents: 4743
diff changeset
   452
     addcongs [imp_cong]
4830
bd73675adbed Added a few lemmas.
nipkow
parents: 4794
diff changeset
   453
     addsplits [split_if];
2082
8659e3063a30 Addition of de Morgan laws
paulson
parents: 2054
diff changeset
   454
6293
2a4357301973 simpler proofs of congruence rules
paulson
parents: 6128
diff changeset
   455
(*Simplifies x assuming c and y assuming ~c*)
2a4357301973 simpler proofs of congruence rules
paulson
parents: 6128
diff changeset
   456
val prems = Goalw [if_def]
2a4357301973 simpler proofs of congruence rules
paulson
parents: 6128
diff changeset
   457
  "[| b=c; c ==> x=u; ~c ==> y=v |] ==> \
2a4357301973 simpler proofs of congruence rules
paulson
parents: 6128
diff changeset
   458
\  (if b then x else y) = (if c then u else v)";
2a4357301973 simpler proofs of congruence rules
paulson
parents: 6128
diff changeset
   459
by (asm_simp_tac (HOL_ss addsimps prems) 1);
2a4357301973 simpler proofs of congruence rules
paulson
parents: 6128
diff changeset
   460
qed "if_cong";
2a4357301973 simpler proofs of congruence rules
paulson
parents: 6128
diff changeset
   461
7127
48e235179ffb added parentheses to cope with a possible reduction of the precedence of unary
paulson
parents: 7031
diff changeset
   462
(*Prevents simplification of x and y: faster and allows the execution
48e235179ffb added parentheses to cope with a possible reduction of the precedence of unary
paulson
parents: 7031
diff changeset
   463
  of functional programs. NOW THE DEFAULT.*)
7031
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   464
Goal "b=c ==> (if b then x else y) = (if c then x else y)";
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   465
by (etac arg_cong 1);
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   466
qed "if_weak_cong";
6293
2a4357301973 simpler proofs of congruence rules
paulson
parents: 6128
diff changeset
   467
2a4357301973 simpler proofs of congruence rules
paulson
parents: 6128
diff changeset
   468
(*Prevents simplification of t: much faster*)
7031
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   469
Goal "a = b ==> (let x=a in t(x)) = (let x=b in t(x))";
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   470
by (etac arg_cong 1);
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   471
qed "let_weak_cong";
6293
2a4357301973 simpler proofs of congruence rules
paulson
parents: 6128
diff changeset
   472
7031
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   473
Goal "f(if c then x else y) = (if c then f x else f y)";
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   474
by (simp_tac (HOL_ss setloop (split_tac [split_if])) 1);
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   475
qed "if_distrib";
1655
5be64540f275 Added a number of lemmas
nipkow
parents: 1548
diff changeset
   476
4327
2335f6584a1b Added comments
paulson
parents: 4321
diff changeset
   477
(*For expand_case_tac*)
7584
5be4bb8e4e3f tidied; added lemma restrict_to_left
paulson
parents: 7570
diff changeset
   478
val prems = Goal "[| P ==> Q(True); ~P ==> Q(False) |] ==> Q(P)";
2948
f18035b1d531 Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents: 2935
diff changeset
   479
by (case_tac "P" 1);
f18035b1d531 Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents: 2935
diff changeset
   480
by (ALLGOALS (asm_simp_tac (HOL_ss addsimps prems)));
7584
5be4bb8e4e3f tidied; added lemma restrict_to_left
paulson
parents: 7570
diff changeset
   481
qed "expand_case";
2948
f18035b1d531 Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents: 2935
diff changeset
   482
4327
2335f6584a1b Added comments
paulson
parents: 4321
diff changeset
   483
(*Used in Auth proofs.  Typically P contains Vars that become instantiated
2335f6584a1b Added comments
paulson
parents: 4321
diff changeset
   484
  during unification.*)
2948
f18035b1d531 Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents: 2935
diff changeset
   485
fun expand_case_tac P i =
f18035b1d531 Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents: 2935
diff changeset
   486
    res_inst_tac [("P",P)] expand_case i THEN
f18035b1d531 Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents: 2935
diff changeset
   487
    Simp_tac (i+1) THEN 
f18035b1d531 Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents: 2935
diff changeset
   488
    Simp_tac i;
f18035b1d531 Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents: 2935
diff changeset
   489
7584
5be4bb8e4e3f tidied; added lemma restrict_to_left
paulson
parents: 7570
diff changeset
   490
(*This lemma restricts the effect of the rewrite rule u=v to the left-hand
5be4bb8e4e3f tidied; added lemma restrict_to_left
paulson
parents: 7570
diff changeset
   491
  side of an equality.  Used in {Integ,Real}/simproc.ML*)
5be4bb8e4e3f tidied; added lemma restrict_to_left
paulson
parents: 7570
diff changeset
   492
Goal "x=y ==> (x=z) = (y=z)";
5be4bb8e4e3f tidied; added lemma restrict_to_left
paulson
parents: 7570
diff changeset
   493
by (asm_simp_tac HOL_ss 1);
5be4bb8e4e3f tidied; added lemma restrict_to_left
paulson
parents: 7570
diff changeset
   494
qed "restrict_to_left";
2948
f18035b1d531 Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents: 2935
diff changeset
   495
7357
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents: 7213
diff changeset
   496
(* default simpset *)
7584
5be4bb8e4e3f tidied; added lemma restrict_to_left
paulson
parents: 7570
diff changeset
   497
val simpsetup = 
5be4bb8e4e3f tidied; added lemma restrict_to_left
paulson
parents: 7570
diff changeset
   498
    [fn thy => (simpset_ref_of thy := HOL_ss addcongs [if_weak_cong]; 
5be4bb8e4e3f tidied; added lemma restrict_to_left
paulson
parents: 7570
diff changeset
   499
		thy)];
3615
e5322197cfea Moved some functions which used to be part of thy_data.ML
berghofe
parents: 3577
diff changeset
   500
4652
d24cca140eeb factored out common code of HOL/simpdata.ML and FOL/simpdata.ML concerning
oheimb
parents: 4651
diff changeset
   501
5219
924359415f09 functorized Clasimp module;
wenzelm
parents: 5190
diff changeset
   502
(*** integration of simplifier with classical reasoner ***)
2636
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   503
5219
924359415f09 functorized Clasimp module;
wenzelm
parents: 5190
diff changeset
   504
structure Clasimp = ClasimpFun
8473
2798d2f71ec2 splitter setup;
wenzelm
parents: 8114
diff changeset
   505
 (structure Simplifier = Simplifier and Splitter = Splitter
2798d2f71ec2 splitter setup;
wenzelm
parents: 8114
diff changeset
   506
   and Classical  = Classical and Blast = Blast);
4652
d24cca140eeb factored out common code of HOL/simpdata.ML and FOL/simpdata.ML concerning
oheimb
parents: 4651
diff changeset
   507
open Clasimp;
2636
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   508
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   509
val HOL_css = (HOL_cs, HOL_ss);
5975
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   510
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   511
8641
978db2870862 change_global/local_css move to Provers/clasimp.ML;
wenzelm
parents: 8473
diff changeset
   512
(* "iff" attribute *)
978db2870862 change_global/local_css move to Provers/clasimp.ML;
wenzelm
parents: 8473
diff changeset
   513
978db2870862 change_global/local_css move to Provers/clasimp.ML;
wenzelm
parents: 8473
diff changeset
   514
val iff_add_global = Clasimp.change_global_css (op addIffs);
978db2870862 change_global/local_css move to Provers/clasimp.ML;
wenzelm
parents: 8473
diff changeset
   515
val iff_add_local = Clasimp.change_local_css (op addIffs);
978db2870862 change_global/local_css move to Provers/clasimp.ML;
wenzelm
parents: 8473
diff changeset
   516
978db2870862 change_global/local_css move to Provers/clasimp.ML;
wenzelm
parents: 8473
diff changeset
   517
val iff_attrib_setup =
978db2870862 change_global/local_css move to Provers/clasimp.ML;
wenzelm
parents: 8473
diff changeset
   518
  [Attrib.add_attributes [("iff", (Attrib.no_args iff_add_global, Attrib.no_args iff_add_local),
978db2870862 change_global/local_css move to Provers/clasimp.ML;
wenzelm
parents: 8473
diff changeset
   519
    "add rules to simpset and claset simultaneously")]];
978db2870862 change_global/local_css move to Provers/clasimp.ML;
wenzelm
parents: 8473
diff changeset
   520
978db2870862 change_global/local_css move to Provers/clasimp.ML;
wenzelm
parents: 8473
diff changeset
   521
978db2870862 change_global/local_css move to Provers/clasimp.ML;
wenzelm
parents: 8473
diff changeset
   522
5975
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   523
(*** A general refutation procedure ***)
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   524
 
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   525
(* Parameters:
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   526
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   527
   test: term -> bool
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   528
   tests if a term is at all relevant to the refutation proof;
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   529
   if not, then it can be discarded. Can improve performance,
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   530
   esp. if disjunctions can be discarded (no case distinction needed!).
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   531
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   532
   prep_tac: int -> tactic
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   533
   A preparation tactic to be applied to the goal once all relevant premises
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   534
   have been moved to the conclusion.
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   535
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   536
   ref_tac: int -> tactic
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   537
   the actual refutation tactic. Should be able to deal with goals
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   538
   [| A1; ...; An |] ==> False
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   539
   where the Ai are atomic, i.e. no top-level &, | or ?
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   540
*)
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   541
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   542
fun refute_tac test prep_tac ref_tac =
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   543
  let val nnf_simps =
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   544
        [imp_conv_disj,iff_conv_conj_imp,de_Morgan_disj,de_Morgan_conj,
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   545
         not_all,not_ex,not_not];
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   546
      val nnf_simpset =
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   547
        empty_ss setmkeqTrue mk_eq_True
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   548
                 setmksimps (mksimps mksimps_pairs)
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   549
                 addsimps nnf_simps;
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   550
      val prem_nnf_tac = full_simp_tac nnf_simpset;
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   551
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   552
      val refute_prems_tac =
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   553
        REPEAT(eresolve_tac [conjE, exE] 1 ORELSE
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   554
               filter_prems_tac test 1 ORELSE
6301
08245f5a436d expandshort
paulson
parents: 6293
diff changeset
   555
               etac disjE 1) THEN
5975
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   556
        ref_tac 1;
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   557
  in EVERY'[TRY o filter_prems_tac test,
6128
2acc5d36610c More arith refinements.
nipkow
parents: 5975
diff changeset
   558
            DETERM o REPEAT o etac rev_mp, prep_tac, rtac ccontr, prem_nnf_tac,
5975
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   559
            SELECT_GOAL (DEPTH_SOLVE refute_prems_tac)]
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   560
  end;